CSE_E---1.7.THM-CRf.s

%------------------------------------------------------------------------------
% File     : CSE_E---1.7
% Problem  : SWW318+1 : TPTP v9.2.1. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d

% Computer : n014.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue May  5 05:31:29 PM UTC 2026

% Result   : Theorem 36.09s 22.32s
% Output   : CNFRefutation 36.88s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_6062)

% Comments : 
%------------------------------------------------------------------------------
fof(fact_of__int__num,axiom,
    ! [X87,X5] :
      ( class_Rings_Oring__1(X5)
     => ( ( X87 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hAPP(c_Int_Oring__1__class_Oof__int(X5),X87) = c_Groups_Ozero__class_Ozero(X5) )
        & ( X87 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X87),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
             => hAPP(c_Int_Oring__1__class_Oof__int(X5),X87) = hAPP(c_Groups_Ouminus__class_Ouminus(X5),hAPP(c_Int_Oring__1__class_Oof__int(X5),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X87))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X87),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
             => hAPP(c_Int_Oring__1__class_Oof__int(X5),X87) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,X5),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(X5,X5)),tc_fun(tc_Int_Oint,X5)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,X5),X5),tc_fun(tc_fun(tc_Int_Oint,tc_fun(X5,X5)),tc_fun(tc_Int_Oint,X5)),tc_Int_Oint),c_COMBB(tc_fun(X5,X5),X5,tc_Int_Oint)),hAPP(hAPP(c_COMBB(X5,tc_fun(tc_fun(X5,X5),X5),tc_Int_Oint),c_HOL_OLet(X5,X5)),c_Int_Oring__1__class_Oof__int(X5)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X5,X5),tc_fun(X5,X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X5,X5)),tc_fun(tc_fun(X5,X5),tc_fun(X5,X5)),tc_Int_Oint),c_COMBS(X5,X5,X5)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X5,X5),tc_fun(X5,tc_fun(X5,X5))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X5,X5)),tc_fun(tc_fun(X5,X5),tc_fun(X5,tc_fun(X5,X5))),tc_Int_Oint),c_COMBB(X5,tc_fun(X5,X5),X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5,tc_fun(X5,X5)),tc_Int_Oint),c_If(X5)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBS(X5,X5,X5),c_Groups_Oplus__class_Oplus(X5)),c_COMBI(X5))))),hAPP(hAPP(c_COMBC(X5,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X5),c_Groups_Oplus__class_Oplus(X5)),hAPP(hAPP(c_COMBS(X5,X5,X5),c_Groups_Oplus__class_Oplus(X5)),c_COMBI(X5)))),c_Groups_Oone__class_Oone(X5))))),c_Divides_Odivmod__int(X87,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__num) ).

fof(fact_not__sum__power2__lt__zero,axiom,
    ! [X65,X66,X58] :
      ( class_Rings_Olinordered__idom(X58)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X66),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(X58),X65),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X58))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__sum__power2__lt__zero) ).

fof(fact_power2__less__0,axiom,
    ! [X62,X58] :
      ( class_Rings_Olinordered__idom(X58)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X58))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power2__less__0) ).

fof(fact_zmod__number__of__Bit1,axiom,
    ! [X136,X128] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X136)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X128))) = 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),X136),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)))),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),X128)))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X136)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X128))) = 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),X136)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__number__of__Bit1) ).

fof(fact_negDivAlg__eqn__number__of,axiom,
    ! [X128,X136] :
      ( 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),X136)))
     => ( ( 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),X128)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136))))
         => c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)) = 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),X128)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136))) )
        & ( ~ 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),X128)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136))))
         => c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)),c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128),hAPP(hAPP(c_Groups_Otimes__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),X136)))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negDivAlg__eqn__number__of) ).

fof(fact_negDivAlg__eqn__1__number__of,axiom,
    ! [X128] :
      ( 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),X128)))
     => ( ( 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),X128))))
         => c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)) = 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),X128))) )
        & ( ~ 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),X128))))
         => c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)),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),X128)))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negDivAlg__eqn__1__number__of) ).

fof(fact_posDivAlg__eqn__number__of,axiom,
    ! [X128,X136] :
      ( 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),X136)))
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)))
         => c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)) = 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),X128)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)))
         => c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)),c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128),hAPP(hAPP(c_Groups_Otimes__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),X136)))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_posDivAlg__eqn__number__of) ).

fof(fact_posDivAlg__eqn__1__number__of,axiom,
    ! [X128] :
      ( 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),X128)))
     => ( ( 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),X128)))
         => c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)) = 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),X128)))
         => c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)),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),X128)))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_posDivAlg__eqn__1__number__of) ).

fof(fact_negDivAlg__eqn,axiom,
    ! [X62,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)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X62),X90)))
         => c_Divides_OnegDivAlg(X62,X90) = 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),X62),X90)) )
        & ( ~ 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),X62),X90)))
         => c_Divides_OnegDivAlg(X62,X90) = hAPP(c_Divides_Oadjust(X90),c_Divides_OnegDivAlg(X62,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X90))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negDivAlg__eqn) ).

fof(fact_posDivAlg__eqn,axiom,
    ! [X62,X90] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X90))
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X62),X90))
         => c_Divides_OposDivAlg(X62,X90) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X62) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X62),X90))
         => c_Divides_OposDivAlg(X62,X90) = hAPP(c_Divides_Oadjust(X90),c_Divides_OposDivAlg(X62,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X90))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_posDivAlg__eqn) ).

fof(fact_hd__dropWhile,axiom,
    ! [X239,X18,X5] :
      ( c_List_OdropWhile(X5,X18,X239) != c_List_Olist_ONil(X5)
     => ~ hBOOL(hAPP(X18,hAPP(c_List_Ohd(X5),c_List_OdropWhile(X5,X18,X239)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hd__dropWhile) ).

fof(fact_power__number__of__odd__number__of,axiom,
    ! [X123,X121,X5] :
      ( class_Int_Onumber__ring(X5)
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X121)))
         => hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X123)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X121))) = hAPP(hAPP(c_HOL_OLet(X5,X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X123)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X121))),hAPP(hAPP(c_COMBS(X5,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X5),c_Groups_Otimes__class_Otimes(X5)),hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X123)))),c_COMBI(X5))) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X121)))
         => hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X123)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X121))) = c_Groups_Oone__class_Oone(X5) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__number__of__odd__number__of) ).

fof(fact_takeWhile__eq__filter,axiom,
    ! [X239,X18,X5] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),c_List_OdropWhile(X5,X18,X239))))
         => ~ hBOOL(hAPP(X18,X3)) )
     => c_List_OtakeWhile(X5,X18,X239) = hAPP(c_List_Ofilter(X5,X18),X239) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_takeWhile__eq__filter) ).

fof(fact_power__number__of__odd,axiom,
    ! [X120,X121,X5] :
      ( class_Int_Onumber__ring(X5)
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X121)))
         => hAPP(hAPP(c_Power_Opower__class_Opower(X5),X120),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X121))) = hAPP(hAPP(c_HOL_OLet(X5,X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X120),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X121))),hAPP(hAPP(c_COMBS(X5,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X5),c_Groups_Otimes__class_Otimes(X5)),hAPP(c_Groups_Otimes__class_Otimes(X5),X120))),c_COMBI(X5))) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X121)))
         => hAPP(hAPP(c_Power_Opower__class_Opower(X5),X120),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X121))) = c_Groups_Oone__class_Oone(X5) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__number__of__odd) ).

fof(fact_zpower__number__of__odd,axiom,
    ! [X120,X121] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X121)))
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X120),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X121))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X120),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X121))),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),X120))),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),X121)))
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X120),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X121))) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zpower__number__of__odd) ).

fof(fact_irrefl__tranclI,axiom,
    ! [X25,X171,X5] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X5,X5),X171)),c_Transitive__Closure_Ortrancl(X5,X171)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X5),tc_HOL_Obool))
     => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X25)),c_Transitive__Closure_Otrancl(X5,X171))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_irrefl__tranclI) ).

fof(fact_dropWhile__append1,axiom,
    ! [X251,X18,X239,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X239)))
     => ( ~ hBOOL(hAPP(X18,X25))
       => c_List_OdropWhile(X5,X18,hAPP(hAPP(c_List_Oappend(X5),X239),X251)) = hAPP(hAPP(c_List_Oappend(X5),c_List_OdropWhile(X5,X18,X239)),X251) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dropWhile__append1) ).

fof(fact_acyclic__def,axiom,
    ! [X171,X5] :
      ( c_Wellfounded_Oacyclic(X5,X171)
    <=> ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X3)),c_Transitive__Closure_Otrancl(X5,X171))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acyclic__def) ).

fof(fact_zdiv__number__of__Bit1,axiom,
    ! [X136,X128] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X136))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X128))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X136))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X128))) = 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),X136)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__number__of__Bit1) ).

fof(fact_acyclicI,axiom,
    ! [X171,X5] :
      ( ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X3)),c_Transitive__Closure_Otrancl(X5,X171)))
     => c_Wellfounded_Oacyclic(X5,X171) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acyclicI) ).

fof(fact_dropWhile_Osimps_I2_J,axiom,
    ! [X239,X5,X25,X18] :
      ( ( hBOOL(hAPP(X18,X25))
       => c_List_OdropWhile(X5,X18,hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239)) = c_List_OdropWhile(X5,X18,X239) )
      & ( ~ hBOOL(hAPP(X18,X25))
       => c_List_OdropWhile(X5,X18,hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239)) = hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dropWhile_Osimps_I2_J) ).

fof(fact_nat__number__of__Bit1,axiom,
    ! [X121] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X121)))
       => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X121)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X121)))
       => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X121)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X121)),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/sandbox/benchmark/theBenchmark.p',fact_nat__number__of__Bit1) ).

fof(fact_upt__rec__number__of,axiom,
    ! [X57,X72] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X72)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X57)))
       => c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X72),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X57)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X72)),c_List_Oupt(hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X72)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X57))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X72)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X57)))
       => c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X72),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X57)) = c_List_Olist_ONil(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_upt__rec__number__of) ).

fof(fact_iszero__number__of__Bit1,axiom,
    ! [X128,X58] :
      ( ( class_Int_Onumber__ring(X58)
        & class_Int_Oring__char__0(X58) )
     => ~ c_Int_Oiszero(X58,hAPP(c_Int_Onumber__class_Onumber__of(X58),c_Int_OBit1(X128))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_iszero__number__of__Bit1) ).

fof(fact_dropWhile__eq__Cons__conv,axiom,
    ! [X251,X33,X239,X18,X5] :
      ( c_List_OdropWhile(X5,X18,X239) = hAPP(hAPP(c_List_Olist_OCons(X5),X33),X251)
    <=> ( X239 = hAPP(hAPP(c_List_Oappend(X5),c_List_OtakeWhile(X5,X18,X239)),hAPP(hAPP(c_List_Olist_OCons(X5),X33),X251))
        & ~ hBOOL(hAPP(X18,X33)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dropWhile__eq__Cons__conv) ).

fof(fact_not__iszero__Numeral1,axiom,
    ! [X58] :
      ( class_Int_Onumber__ring(X58)
     => ~ c_Int_Oiszero(X58,hAPP(c_Int_Onumber__class_Onumber__of(X58),c_Int_OBit1(c_Int_OPls))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__iszero__Numeral1) ).

fof(fact_removeAll__id,axiom,
    ! [X239,X25,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X239)))
     => hAPP(c_List_OremoveAll(X5,X25),X239) = X239 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_removeAll__id) ).

fof(fact_removeAll__filter__not,axiom,
    ! [X239,X5,X25,X18] :
      ( ~ hBOOL(hAPP(X18,X25))
     => hAPP(c_List_OremoveAll(X5,X25),hAPP(c_List_Ofilter(X5,X18),X239)) = hAPP(c_List_Ofilter(X5,X18),X239) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_removeAll__filter__not) ).

fof(fact_Suc__nat__number__of__add,axiom,
    ! [X57,X136] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)))
       => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)),X57)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X57) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)))
       => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)),X57)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X136))),X57) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__nat__number__of__add) ).

fof(fact_upt__Suc,axiom,
    ! [X97,X98] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X98),X97))
       => c_List_Oupt(X98,hAPP(c_Nat_OSuc,X97)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X98,X97)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X97),c_List_Olist_ONil(tc_Nat_Onat))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X98),X97))
       => c_List_Oupt(X98,hAPP(c_Nat_OSuc,X97)) = c_List_Olist_ONil(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_upt__Suc) ).

fof(fact_upt__rec,axiom,
    ! [X97,X98] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),X97))
       => c_List_Oupt(X98,X97) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X98),c_List_Oupt(hAPP(c_Nat_OSuc,X98),X97)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),X97))
       => c_List_Oupt(X98,X97) = c_List_Olist_ONil(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_upt__rec) ).

fof(fact_nat__number__of__diff__1,axiom,
    ! [X136] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X136),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)),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),X136),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(X136)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__number__of__diff__1) ).

fof(fact_nat__number__of__add__1,axiom,
    ! [X136] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X136),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)),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),X136),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X136)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__number__of__add__1) ).

fof(fact_nat__1__add__number__of,axiom,
    ! [X136] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X136),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),X136)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X136),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),X136)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X136)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__1__add__number__of) ).

fof(fact_Suc__nat__number__of,axiom,
    ! [X136] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)))
       => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)))
       => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X136)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__nat__number__of) ).

fof(fact_member__rec_I2_J,axiom,
    ! [X65,X58] : ~ hBOOL(hAPP(hAPP(c_List_Omember(X58),c_List_Olist_ONil(X58)),X65)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_member__rec_I2_J) ).

fof(fact_adjust__def,axiom,
    ! [X24] : c_Divides_Oadjust(X24) = 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)),X24))))),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)),X24))))),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/sandbox/benchmark/theBenchmark.p',fact_adjust__def) ).

fof(fact_succ__Bit0,axiom,
    ! [X96] : c_Int_Osucc(c_Int_OBit0(X96)) = c_Int_OBit1(X96),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_succ__Bit0) ).

fof(fact_Bit0__def,axiom,
    ! [X96] : c_Int_OBit0(X96) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X96),X96),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bit0__def) ).

fof(fact_diff__bin__simps_I2_J,axiom,
    ! [X96] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X96),c_Int_OMin) = c_Int_Osucc(X96),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__bin__simps_I2_J) ).

fof(fact_prod__fun__imageE,axiom,
    ! [X32,X1,X2,X115,X116,X23,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X20)),X23),hAPP(c_Set_Oimage(tc_prod(X116,X115),tc_prod(X5,X20),c_Product__Type_Omap__pair(X116,X5,X115,X20,X2,X1)),X32)))
     => ~ ! [X3,X177] :
            ( X23 = hAPP(hAPP(c_Product__Type_OPair(X5,X20),hAPP(X2,X3)),hAPP(X1,X177))
           => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X116,X115)),hAPP(hAPP(c_Product__Type_OPair(X116,X115),X3),X177)),X32)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_prod__fun__imageE) ).

fof(fact_divmod__int__pdivmod,axiom,
    ! [X156,X87] :
      ( ( X87 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Divides_Odivmod__int(X87,X156) = 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)) )
      & ( X87 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => ( ( X156 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
           => c_Divides_Odivmod__int(X87,X156) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X87) )
          & ( X156 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
           => c_Divides_Odivmod__int(X87,X156) = 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,X156))),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)),X156)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X87))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X156),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X87),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(X87,X156)),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),X156))))),c_Divides_Opdivmod(X87,X156)))) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__int__pdivmod) ).

fof(fact_apsnd__def,axiom,
    ! [X2,X5,X116,X20] : c_Product__Type_Oapsnd(X20,X116,X5,X2) = c_Product__Type_Omap__pair(X5,X5,X20,X116,c_Fun_Oid(X5),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_apsnd__def) ).

fof(fact_divmod__int__code,axiom,
    ! [X156,X87] :
      ( ( X87 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Divides_Odivmod__int(X87,X156) = 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)) )
      & ( X87 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => ( ( X156 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
           => c_Divides_Odivmod__int(X87,X156) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X87) )
          & ( X156 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
           => c_Divides_Odivmod__int(X87,X156) = 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,X156))),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,X87)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,X156))),c_Divides_Opdivmod(X87,X156)),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),X156))))),c_Divides_Opdivmod(X87,X156)))) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__int__code) ).

fof(fact_Nitpick_Oplus__frac__def,axiom,
    ! [X171,X153,X5] : c_Nitpick_Oplus__frac(X5,X153,X171) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X5),c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(X5),X153),hAPP(c_Nitpick_Odenom(X5),X171))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,X5),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,X5),tc_Int_Oint),c_Nitpick_Ofrac(X5)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(X5),X153))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(X5),X153))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(X5),X171))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(X5),X171)))))),c_COMBI(tc_Int_Oint))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Oplus__frac__def) ).

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

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

fof(fact_reflcl__set__eq,axiom,
    ! [X33,X25,X171,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBC(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_prod(X5,X5)),tc_fun(X5,tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X5),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool),X5),c_member(tc_prod(X5,X5)))),c_Product__Type_OPair(X5,X5)))),X171)),c_fequal),X25),X33))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X33)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X171),c_Relation_OId(X5)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_reflcl__set__eq) ).

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

fof(fact_adjust__eq,axiom,
    ! [X171,X153,X24] : hAPP(c_Divides_Oadjust(X24),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X153),X171)) = 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),X171),X24)),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)))),X153)),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)))),X153)),X171))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_adjust__eq) ).

fof(fact_trancl__insert,axiom,
    ! [X171,X25,X33,X5] : c_Transitive__Closure_Otrancl(X5,hAPP(hAPP(c_Set_Oinsert(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X33),X25)),X171)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X5,X171)),hAPP(c_Set_OCollect(tc_prod(X5,X5)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X5,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X5,X5),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool),X5),c_member(tc_prod(X5,X5))),hAPP(hAPP(c_COMBC(X5,X5,tc_prod(X5,X5)),c_Product__Type_OPair(X5,X5)),X33))),c_Transitive__Closure_Ortrancl(X5,X171))))),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X5,X5),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool),X5),c_member(tc_prod(X5,X5))),hAPP(c_Product__Type_OPair(X5,X5),X25))),c_Transitive__Closure_Ortrancl(X5,X171)))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__insert) ).

fof(fact_trancl__unfold__left,axiom,
    ! [X171,X5] : c_Transitive__Closure_Otrancl(X5,X171) = hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),X171),c_Transitive__Closure_Ortrancl(X5,X171)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__unfold__left) ).

fof(fact_SUP2__E,axiom,
    ! [X23,X24,X113,X21,X116,X20,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X20,tc_fun(X116,tc_HOL_Obool))),X21),X113),X24),X23))
     => ~ ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X21))
           => ~ hBOOL(hAPP(hAPP(hAPP(X113,X3),X24),X23)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUP2__E) ).

fof(fact_sum__power2__le__zero__iff,axiom,
    ! [X33,X25,X5] :
      ( class_Rings_Olinordered__idom(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X25),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X33),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X5)))
      <=> ( X25 = c_Groups_Ozero__class_Ozero(X5)
          & X33 = c_Groups_Ozero__class_Ozero(X5) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__power2__le__zero__iff) ).

fof(fact_transpose_Opsimps_I3_J,axiom,
    ! [X286,X239,X25,X5] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(X5)),c_List_Otranspose__rel(X5)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X5)),hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239)),X286)))
     => c_List_Otranspose(X5,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X5)),hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239)),X286)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X5)),hAPP(hAPP(c_List_Olist_OCons(X5),X25),c_List_Oconcat(X5,hAPP(hAPP(c_List_Omap(tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olist_Olist__case(tc_List_Olist(X5),X5,c_List_Olist_ONil(X5),hAPP(hAPP(c_COMBB(tc_List_Olist(X5),tc_fun(tc_List_Olist(X5),tc_List_Olist(X5)),X5),c_COMBK(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_COMBC(X5,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olist_OCons(X5)),c_List_Olist_ONil(X5))))),X286)))),c_List_Otranspose(X5,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X5)),X239),c_List_Oconcat(tc_List_Olist(X5),hAPP(hAPP(c_List_Omap(tc_List_Olist(X5),tc_List_Olist(tc_List_Olist(X5))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(X5)),X5,c_List_Olist_ONil(tc_List_Olist(X5)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X5),tc_List_Olist(tc_List_Olist(X5))),X5),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_List_Olist(tc_List_Olist(X5)),tc_List_Olist(tc_List_Olist(X5))),c_List_Olist_OCons(tc_List_Olist(X5))),c_List_Olist_ONil(tc_List_Olist(X5)))))),X286))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose_Opsimps_I3_J) ).

fof(fact_concat__conv__foldl,axiom,
    ! [X286,X5] : c_List_Oconcat(X5,X286) = hAPP(c_List_Ofoldl(tc_List_Olist(X5),tc_List_Olist(X5),c_List_Oappend(X5),c_List_Olist_ONil(X5)),X286),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_concat__conv__foldl) ).

fof(fact_transpose_Osimps_I3_J,axiom,
    ! [X286,X239,X25,X5] : c_List_Otranspose(X5,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X5)),hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239)),X286)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X5)),hAPP(hAPP(c_List_Olist_OCons(X5),X25),c_List_Oconcat(X5,hAPP(hAPP(c_List_Omap(tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olist_Olist__case(tc_List_Olist(X5),X5,c_List_Olist_ONil(X5),hAPP(hAPP(c_COMBB(tc_List_Olist(X5),tc_fun(tc_List_Olist(X5),tc_List_Olist(X5)),X5),c_COMBK(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_COMBC(X5,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olist_OCons(X5)),c_List_Olist_ONil(X5))))),X286)))),c_List_Otranspose(X5,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X5)),X239),c_List_Oconcat(tc_List_Olist(X5),hAPP(hAPP(c_List_Omap(tc_List_Olist(X5),tc_List_Olist(tc_List_Olist(X5))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(X5)),X5,c_List_Olist_ONil(tc_List_Olist(X5)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X5),tc_List_Olist(tc_List_Olist(X5))),X5),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_List_Olist(tc_List_Olist(X5)),tc_List_Olist(tc_List_Olist(X5))),c_List_Olist_OCons(tc_List_Olist(X5))),c_List_Olist_ONil(tc_List_Olist(X5)))))),X286))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose_Osimps_I3_J) ).

fof(fact_odd__power__less__zero,axiom,
    ! [X57,X62,X58] :
      ( class_Rings_Olinordered__idom(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X62),c_Groups_Ozero__class_Ozero(X58)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),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)))),X57)))),c_Groups_Ozero__class_Ozero(X58))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_odd__power__less__zero) ).

fof(fact_rel__compE,axiom,
    ! [X76,X171,X116,X298,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X20)),X298),hAPP(hAPP(c_Relation_Orel__comp(X5,X116,X20),X171),X76)))
     => ~ ! [X3,X177,X154] :
            ( X298 = hAPP(hAPP(c_Product__Type_OPair(X5,X20),X3),X154)
           => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X116)),hAPP(hAPP(c_Product__Type_OPair(X5,X116),X3),X177)),X171))
             => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X116,X20)),hAPP(hAPP(c_Product__Type_OPair(X116,X20),X177),X154)),X76)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__compE) ).

fof(fact_odd__0__le__power__imp__0__le,axiom,
    ! [X57,X62,X58] :
      ( class_Rings_Olinordered__idom(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),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)))),X57)))))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),X62)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_odd__0__le__power__imp__0__le) ).

fof(fact_Cons__eq__filter__iff,axiom,
    ! [X251,X18,X239,X25,X5] :
      ( hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239) = hAPP(c_List_Ofilter(X5,X18),X251)
    <=> ? [X252,X260] :
          ( X251 = hAPP(hAPP(c_List_Oappend(X5),X252),hAPP(hAPP(c_List_Olist_OCons(X5),X25),X260))
          & ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X252)))
             => ~ hBOOL(hAPP(X18,X3)) )
          & hBOOL(hAPP(X18,X25))
          & X239 = hAPP(c_List_Ofilter(X5,X18),X260) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Cons__eq__filter__iff) ).

fof(fact_filter__eq__Cons__iff,axiom,
    ! [X239,X25,X251,X18,X5] :
      ( hAPP(c_List_Ofilter(X5,X18),X251) = hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239)
    <=> ? [X252,X260] :
          ( X251 = hAPP(hAPP(c_List_Oappend(X5),X252),hAPP(hAPP(c_List_Olist_OCons(X5),X25),X260))
          & ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X252)))
             => ~ hBOOL(hAPP(X18,X3)) )
          & hBOOL(hAPP(X18,X25))
          & X239 = hAPP(c_List_Ofilter(X5,X18),X260) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter__eq__Cons__iff) ).

fof(fact_power2__diff,axiom,
    ! [X65,X66,X58] :
      ( class_Int_Onumber__ring(X58)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X58),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X58),X66),X65)),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(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X66),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(X58),X65),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(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),hAPP(c_Int_Onumber__class_Onumber__of(X58),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X66)),X65)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power2__diff) ).

fof(fact_power2__sum,axiom,
    ! [X65,X66,X58] :
      ( class_Int_Onumber__ring(X58)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X66),X65)),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(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X66),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(X58),X65),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(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),hAPP(c_Int_Onumber__class_Onumber__of(X58),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X66)),X65)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power2__sum) ).

fof(fact_Nitpick_Osetsum_H__def,axiom,
    ! [X2,X21,X5,X20] :
      ( class_Groups_Ocomm__monoid__add(X20)
     => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
         => c_Nitpick_Osetsum_H(X5,X20,X2,X21) = hAPP(c_List_Omonoid__add__class_Olistsum(X20),hAPP(hAPP(c_List_Omap(X5,X20),X2),c_Hilbert__Choice_OEps(tc_List_Olist(X5),hAPP(hAPP(c_COMBS(tc_List_Olist(X5),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X5)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X5)),c_fequal),c_List_Oset(X5))),X21))),c_List_Odistinct(X5))))) )
        & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
         => c_Nitpick_Osetsum_H(X5,X20,X2,X21) = c_Groups_Ozero__class_Ozero(X20) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Osetsum_H__def) ).

fof(fact_sum__power2__gt__zero__iff,axiom,
    ! [X33,X25,X5] :
      ( class_Rings_Olinordered__idom(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X25),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X33),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(X5)
          | X33 != c_Groups_Ozero__class_Ozero(X5) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__power2__gt__zero__iff) ).

fof(fact_transpose__aux__max,axiom,
    ! [X286,X20,X239,X5] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239))),c_List_Ofoldr(tc_List_Olist(X20),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X20)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X20))),X286,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239)),c_List_Ofoldr(tc_List_Olist(X20),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X20)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(X20),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X20)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X20)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_List_Ofilter(tc_List_Olist(X20),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X20)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X20),tc_List_Olist(X20),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X20)))),X286),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose__aux__max) ).

fof(fact_foldr__foldl,axiom,
    ! [X6,X239,X2,X5,X20] : c_List_Ofoldr(X20,X5,X2,X239,X6) = hAPP(c_List_Ofoldl(X5,X20,hAPP(c_COMBC(X20,X5,X5),X2),X6),hAPP(c_List_Orev(X20),X239)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldr__foldl) ).

fof(fact_sublist__shift__lemma,axiom,
    ! [X82,X239,X21,X5] : hAPP(hAPP(c_List_Omap(tc_prod(X5,tc_Nat_Onat),X5),c_Product__Type_Ofst(X5,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X5,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X5,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(X5,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(X5,tc_Nat_Onat))),X21)),hAPP(hAPP(c_List_Ozip(X5,tc_Nat_Onat),X239),c_List_Oupt(X82,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X82),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239)))))) = hAPP(hAPP(c_List_Omap(tc_prod(X5,tc_Nat_Onat),X5),c_Product__Type_Ofst(X5,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X5,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X5,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(X5,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(X5,tc_Nat_Onat),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_prod(X5,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(X5,tc_Nat_Onat))),X82))),X21)),hAPP(hAPP(c_List_Ozip(X5,tc_Nat_Onat),X239),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sublist__shift__lemma) ).

fof(fact_sorted__list__of__set__range,axiom,
    ! [X50,X95] : c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X95),X50)) = c_List_Oupt(X95,X50),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__list__of__set__range) ).

fof(fact_Random_Osimps,axiom,
    ! [X293,X1,X5,X294] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X294),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))
       => c_Random__Sequence_ORandom(X5,X1,X294,X293) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(X5)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X294),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))
       => c_Random__Sequence_ORandom(X5,X1,X294,X293) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X5,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm)),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(X1,X293)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_prod(X5,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random__Sequence_ORandom(X5,X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X294),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X293))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5))))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_prod(X5,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5))))),c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5))))),tc_prod(X5,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Ounion(X5)),hAPP(hAPP(c_COMBB(X5,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_prod(X5,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Osingle(X5)),c_Product__Type_Ofst(X5,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))))))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Random_Osimps) ).

fof(fact_Suc__div__eq__add3__div__number__of,axiom,
    ! [X136,X72] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X72)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)) = 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)))),X72)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__div__eq__add3__div__number__of) ).

fof(fact_Suc__div__eq__add3__div,axiom,
    ! [X57,X72] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X72)))),X57) = 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)))),X72)),X57),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__div__eq__add3__div) ).

fof(fact_New__DSequence_Opos__not__seq__def,axiom,
    ! [X82,X277] : hAPP(c_New__DSequence_Opos__not__seq(X277),X82) = c_Lazy__Sequence_Ohb__not__seq(hAPP(X277,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)))),X82))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_New__DSequence_Opos__not__seq__def) ).

fof(fact_mem__splitE,axiom,
    ! [X160,X23,X116,X20,X120,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X120),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X20,X116,tc_fun(X5,tc_HOL_Obool)),X23),X160)))
     => ~ ! [X3,X177] :
            ( X160 = hAPP(hAPP(c_Product__Type_OPair(X20,X116),X3),X177)
           => ~ hBOOL(hAPP(hAPP(c_member(X5),X120),hAPP(hAPP(X23,X3),X177))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__splitE) ).

fof(fact_fun__left__comm_Ofold__graph__insertE,axiom,
    ! [X123,X21,X25,X120,X2,X20,X5] :
      ( c_Finite__Set_Ofun__left__comm(X5,X20,X2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X20,X2,X120,hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)),X123))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => ~ ! [X177] :
                ( X123 = hAPP(hAPP(X2,X25),X177)
               => ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X20,X2,X120,X21),X177)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__graph__insertE) ).

fof(fact_int__of__code,axiom,
    ! [X96] :
      ( ( X96 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => hAPP(c_Code__Numeral_Oint__of,X96) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( X96 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => ( ( c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X96,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,X96) = hAPP(hAPP(c_Groups_Otimes__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),X96),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,X96,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,X96) = 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),X96),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/sandbox/benchmark/theBenchmark.p',fact_int__of__code) ).

fof(fact_sum__power2__ge__zero,axiom,
    ! [X65,X66,X58] :
      ( class_Rings_Olinordered__idom(X58)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X66),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(X58),X65),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__power2__ge__zero) ).

fof(fact_pigeonhole__infinite,axiom,
    ! [X2,X20,X21,X5] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X20),hAPP(c_Set_Oimage(X5,X20,X2),X21)))
       => ? [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X21))
            & ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X21))),hAPP(hAPP(c_COMBC(X5,X20,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X20,tc_fun(X20,tc_HOL_Obool),X5),c_fequal),X2)),hAPP(X2,X3)))))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pigeonhole__infinite) ).

fof(fact_concat__injective,axiom,
    ! [X251,X239,X5] :
      ( c_List_Oconcat(X5,X239) = c_List_Oconcat(X5,X251)
     => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5))),X239) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5))),X251)
       => ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),X3),hAPP(c_List_Oset(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(X5),tc_List_Olist(X5)),X239),X251))))
             => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X5),tc_List_Olist(X5),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_fun(tc_List_Olist(X5),tc_Nat_Onat),tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X5),tc_Nat_Onat),tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),tc_List_Olist(X5)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X5))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X5)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X5))))),c_Nat_Osize__class_Osize(tc_List_Olist(X5)))),X3)) )
         => X239 = X251 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_concat__injective) ).

fof(fact_concat__eq__concat__iff,axiom,
    ! [X251,X239,X5] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),X3),hAPP(c_List_Oset(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(X5),tc_List_Olist(X5)),X239),X251))))
         => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X5),tc_List_Olist(X5),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_fun(tc_List_Olist(X5),tc_Nat_Onat),tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X5),tc_Nat_Onat),tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),tc_List_Olist(X5)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X5))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X5)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X5))))),c_Nat_Osize__class_Osize(tc_List_Olist(X5)))),X3)) )
     => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5))),X239) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5))),X251)
       => ( c_List_Oconcat(X5,X239) = c_List_Oconcat(X5,X251)
        <=> X239 = X251 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_concat__eq__concat__iff) ).

fof(fact_nat__rec__add__eq__if,axiom,
    ! [X50,X123,X2,X6,X5] : hAPP(c_Nat_Onat_Onat__rec(X5,X6,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X123)),X50)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X5),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X123))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X5,X5),hAPP(hAPP(c_COMBC(tc_Int_Oint,X5,tc_fun(X5,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5,tc_fun(X5,X5)),tc_Int_Oint),c_If(X5)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(X5,X6,X2),X50))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X5,X5),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X5,X5),tc_Int_Oint),X2),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),X50))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X5,tc_Int_Oint),c_Nat_Onat_Onat__rec(X5,X6,X2)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),X50))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__rec__add__eq__if) ).

fof(fact_add__Min__right,axiom,
    ! [X96] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X96),c_Int_OMin) = c_Int_Opred(X96),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Min__right) ).

fof(fact_neg__zmod__mult__2,axiom,
    ! [X90,X62] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X62),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)))),X90)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X62)) = 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),X90),c_Groups_Oone__class_Oone(tc_Int_Oint)),X62))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__zmod__mult__2) ).

fof(fact_neg__zdiv__mult__2,axiom,
    ! [X90,X62] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X62),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)))),X90))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X62)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X90),c_Groups_Oone__class_Oone(tc_Int_Oint))),X62) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__zdiv__mult__2) ).

fof(fact_pos__zdiv__mult__2,axiom,
    ! [X90,X62] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X62))
     => 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)))),X90))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X62)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X90),X62) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__zdiv__mult__2) ).

fof(fact_eq__number__of__Suc,axiom,
    ! [X50,X123] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X123) = hAPP(c_Nat_OSuc,X50)
    <=> 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(X123))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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)),X50))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__number__of__Suc) ).

fof(fact_Suc__eq__number__of,axiom,
    ! [X123,X50] :
      ( hAPP(c_Nat_OSuc,X50) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X123)
    <=> 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(X123))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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)),X50))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__number__of) ).

fof(fact_Nitpick_Ocard_H__def,axiom,
    ! [X21,X5] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => c_Nitpick_Ocard_H(X5,X21) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_Hilbert__Choice_OEps(tc_List_Olist(X5),hAPP(hAPP(c_COMBS(tc_List_Olist(X5),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X5)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X5)),c_fequal),c_List_Oset(X5))),X21))),c_List_Odistinct(X5)))) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => c_Nitpick_Ocard_H(X5,X21) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Ocard_H__def) ).

fof(fact_card__less__Suc2,axiom,
    ! [X82,X210] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X210))
     => 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)),X210))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X82)))) = 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)),X210))),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,X82))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__less__Suc2) ).

fof(fact_power2__le__imp__le,axiom,
    ! [X65,X66,X58] :
      ( class_Rings_Olinordered__semidom(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X66),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(X58),X65),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(X58),c_Groups_Ozero__class_Ozero(X58)),X65))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X66),X65)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power2__le__imp__le) ).

fof(fact_power2__less__imp__less,axiom,
    ! [X65,X66,X58] :
      ( class_Rings_Olinordered__semidom(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X66),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(X58),X65),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(X58),c_Groups_Ozero__class_Ozero(X58)),X65))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X66),X65)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power2__less__imp__less) ).

fof(fact_vimage__if,axiom,
    ! [X113,X20,X22,X21,X23,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X23),X21))
       => ( ( hBOOL(hAPP(hAPP(c_member(X5),X22),X21))
           => hAPP(c_Set_Ovimage(X20,X5,hAPP(hAPP(c_COMBC(X20,X5,X5),hAPP(hAPP(c_COMBC(X20,X5,tc_fun(X5,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5,tc_fun(X5,X5)),X20),c_If(X5)),hAPP(hAPP(c_COMBC(X20,tc_fun(X20,tc_HOL_Obool),tc_HOL_Obool),c_member(X20)),X113))),X23)),X22)),X21) = c_Orderings_Otop__class_Otop(tc_fun(X20,tc_HOL_Obool)) )
          & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X22),X21))
           => hAPP(c_Set_Ovimage(X20,X5,hAPP(hAPP(c_COMBC(X20,X5,X5),hAPP(hAPP(c_COMBC(X20,X5,tc_fun(X5,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5,tc_fun(X5,X5)),X20),c_If(X5)),hAPP(hAPP(c_COMBC(X20,tc_fun(X20,tc_HOL_Obool),tc_HOL_Obool),c_member(X20)),X113))),X23)),X22)),X21) = X113 ) ) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X23),X21))
       => ( ( hBOOL(hAPP(hAPP(c_member(X5),X22),X21))
           => hAPP(c_Set_Ovimage(X20,X5,hAPP(hAPP(c_COMBC(X20,X5,X5),hAPP(hAPP(c_COMBC(X20,X5,tc_fun(X5,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5,tc_fun(X5,X5)),X20),c_If(X5)),hAPP(hAPP(c_COMBC(X20,tc_fun(X20,tc_HOL_Obool),tc_HOL_Obool),c_member(X20)),X113))),X23)),X22)),X21) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20,tc_HOL_Obool)),X113) )
          & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X22),X21))
           => hAPP(c_Set_Ovimage(X20,X5,hAPP(hAPP(c_COMBC(X20,X5,X5),hAPP(hAPP(c_COMBC(X20,X5,tc_fun(X5,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5,tc_fun(X5,X5)),X20),c_If(X5)),hAPP(hAPP(c_COMBC(X20,tc_fun(X20,tc_HOL_Obool),tc_HOL_Obool),c_member(X20)),X113))),X23)),X22)),X21) = c_Orderings_Obot__class_Obot(tc_fun(X20,tc_HOL_Obool)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__if) ).

fof(fact_pos__zmod__mult__2,axiom,
    ! [X90,X62] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X62))
     => 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)))),X90)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X62)) = 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,X90,X62))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__zmod__mult__2) ).

fof(fact_Suc__mod__eq__add3__mod__number__of,axiom,
    ! [X136,X72] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X72))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)) = 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)))),X72),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mod__eq__add3__mod__number__of) ).

fof(fact_zero__le__even__power_H,axiom,
    ! [X57,X62,X58] :
      ( class_Rings_Olinordered__idom(X58)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),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)))),X57)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__even__power_H) ).

fof(fact_Suc__mod__eq__add3__mod,axiom,
    ! [X57,X72] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X72))),X57) = 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)))),X72),X57),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mod__eq__add3__mod) ).

fof(fact_mod__Suc__eq__mod__add3,axiom,
    ! [X57,X72] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X72,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X57)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X72,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)))),X57)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__Suc__eq__mod__add3) ).

fof(fact_div__Suc__eq__div__add3,axiom,
    ! [X57,X72] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X72),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X57)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X72),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)))),X57)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__Suc__eq__div__add3) ).

fof(fact_trancl__Int__subset,axiom,
    ! [X76,X171,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X171),X76))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X5,X171)),X76)),X171)),X76))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X5,X171)),X76)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__Int__subset) ).

fof(fact_setprod__gen__delta,axiom,
    ! [X23,X24,X6,X192,X5,X20] :
      ( class_Groups_Ocomm__monoid__mult(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X192))
       => ( ( hBOOL(hAPP(hAPP(c_member(X5),X6),X192))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),hAPP(hAPP(c_COMBC(X5,X20,X20),hAPP(hAPP(c_COMBS(X5,X20,tc_fun(X20,X20)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X20,tc_fun(X20,X20)),X5),c_If(X20)),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X6))),X24)),X23)),X192) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20),hAPP(X24,X6)),hAPP(hAPP(c_Power_Opower__class_Opower(X20),X23),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X192)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
          & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X192))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),hAPP(hAPP(c_COMBC(X5,X20,X20),hAPP(hAPP(c_COMBS(X5,X20,tc_fun(X20,X20)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X20,tc_fun(X20,X20)),X5),c_If(X20)),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X6))),X24)),X23)),X192) = hAPP(hAPP(c_Power_Opower__class_Opower(X20),X23),hAPP(c_Finite__Set_Ocard(X5),X192)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__gen__delta) ).

fof(fact_setsum__delta,axiom,
    ! [X24,X6,X192,X5,X20] :
      ( class_Groups_Ocomm__monoid__add(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X192))
       => ( ( hBOOL(hAPP(hAPP(c_member(X5),X6),X192))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),hAPP(hAPP(c_COMBC(X5,X20,X20),hAPP(hAPP(c_COMBS(X5,X20,tc_fun(X20,X20)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X20,tc_fun(X20,X20)),X5),c_If(X20)),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X6))),X24)),c_Groups_Ozero__class_Ozero(X20))),X192) = hAPP(X24,X6) )
          & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X192))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),hAPP(hAPP(c_COMBC(X5,X20,X20),hAPP(hAPP(c_COMBS(X5,X20,tc_fun(X20,X20)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X20,tc_fun(X20,X20)),X5),c_If(X20)),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X6))),X24)),c_Groups_Ozero__class_Ozero(X20))),X192) = c_Groups_Ozero__class_Ozero(X20) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__delta) ).

fof(fact_setprod__delta,axiom,
    ! [X24,X6,X192,X5,X20] :
      ( class_Groups_Ocomm__monoid__mult(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X192))
       => ( ( hBOOL(hAPP(hAPP(c_member(X5),X6),X192))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),hAPP(hAPP(c_COMBC(X5,X20,X20),hAPP(hAPP(c_COMBS(X5,X20,tc_fun(X20,X20)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X20,tc_fun(X20,X20)),X5),c_If(X20)),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X6))),X24)),c_Groups_Oone__class_Oone(X20))),X192) = hAPP(X24,X6) )
          & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X192))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),hAPP(hAPP(c_COMBC(X5,X20,X20),hAPP(hAPP(c_COMBS(X5,X20,tc_fun(X20,X20)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X20,tc_fun(X20,X20)),X5),c_If(X20)),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X6))),X24)),c_Groups_Oone__class_Oone(X20))),X192) = c_Groups_Oone__class_Oone(X20) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__delta) ).

fof(fact_le__Suc__number__of,axiom,
    ! [X123,X50] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X50)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X123)))
    <=> 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(X123))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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),X50)),c_Int_Onat))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__Suc__number__of) ).

fof(fact_less__Suc__number__of,axiom,
    ! [X123,X50] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X50)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X123)))
    <=> 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(X123))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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),X50)),c_Int_Onat))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__number__of) ).

fof(fact_apsnd__apfst__commute,axiom,
    ! [X160,X1,X115,X2,X5,X20,X116] : hAPP(c_Product__Type_Oapsnd(X116,X20,X5,X2),hAPP(c_Product__Type_Oapfst(X115,X5,X116,X1),X160)) = hAPP(c_Product__Type_Oapfst(X115,X5,X20,X1),hAPP(c_Product__Type_Oapsnd(X116,X20,X115,X2),X160)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_apsnd__apfst__commute) ).

fof(fact_apfst__def,axiom,
    ! [X2,X20,X116,X5] : c_Product__Type_Oapfst(X5,X116,X20,X2) = c_Product__Type_Omap__pair(X5,X116,X20,X20,X2,c_Fun_Oid(X20)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_apfst__def) ).

fof(fact_lexord__append__leftD,axiom,
    ! [X171,X123,X159,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(hAPP(c_List_Oappend(X5),X25),X159)),hAPP(hAPP(c_List_Oappend(X5),X25),X123))),c_List_Olexord(X5,X171)))
     => ( ! [X187] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X187),X187)),X171))
       => 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)),X159),X123)),c_List_Olexord(X5,X171))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexord__append__leftD) ).

fof(fact_rel__pow__E2,axiom,
    ! [X32,X50,X120,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X120)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X50),X32)))
     => ( ( X50 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => X25 != X120 )
       => ~ ! [X177,X86] :
              ( X50 = hAPP(c_Nat_OSuc,X86)
             => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X177)),X32))
               => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X177),X120)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X86),X32))) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__pow__E2) ).

fof(fact_power__odd__eq,axiom,
    ! [X57,X62,X58] :
      ( class_Groups_Omonoid__mult(X58)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),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)))),X57))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),hAPP(hAPP(c_Power_Opower__class_Opower(X58),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),X57)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__odd__eq) ).

fof(fact_takeWhile__neq__rev,axiom,
    ! [X25,X239,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),X239))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X239)))
       => c_List_OtakeWhile(X5,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X25)),hAPP(c_List_Orev(X5),X239)) = hAPP(c_List_Orev(X5),hAPP(c_List_Otl(X5),c_List_OdropWhile(X5,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X25)),X239))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_takeWhile__neq__rev) ).

fof(fact_dropWhile__eq__drop,axiom,
    ! [X239,X18,X5] : c_List_OdropWhile(X5,X18,X239) = hAPP(hAPP(c_List_Odrop(X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_OtakeWhile(X5,X18,X239))),X239),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dropWhile__eq__drop) ).

fof(fact_apsnd__compose,axiom,
    ! [X25,X1,X115,X2,X5,X20,X116] : hAPP(c_Product__Type_Oapsnd(X116,X20,X5,X2),hAPP(c_Product__Type_Oapsnd(X115,X116,X5,X1),X25)) = hAPP(c_Product__Type_Oapsnd(X115,X20,X5,hAPP(c_Fun_Ocomp(X116,X20,X115,X2),X1)),X25),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_apsnd__compose) ).

fof(fact_apfst__compose,axiom,
    ! [X25,X1,X115,X2,X20,X5,X116] : hAPP(c_Product__Type_Oapfst(X116,X5,X20,X2),hAPP(c_Product__Type_Oapfst(X115,X116,X20,X1),X25)) = hAPP(c_Product__Type_Oapfst(X115,X5,X20,hAPP(c_Fun_Ocomp(X116,X5,X115,X2),X1)),X25),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_apfst__compose) ).

fof(fact_sum__power2__eq__zero__iff,axiom,
    ! [X33,X25,X5] :
      ( class_Rings_Olinordered__idom(X5)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X25),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X33),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(X5)
      <=> ( X25 = c_Groups_Ozero__class_Ozero(X5)
          & X33 = c_Groups_Ozero__class_Ozero(X5) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__power2__eq__zero__iff) ).

fof(fact_transpose__rectangle,axiom,
    ! [X50,X5,X239] :
      ( ( X239 = c_List_Olist_ONil(tc_List_Olist(X5))
       => X50 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
     => ( ! [X146] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X146),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5))),X239)))
           => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X5)),X239),X146)) = X50 )
       => c_List_Otranspose(X5,X239) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X5)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X5)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X5),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X5)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X5)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X5),hAPP(hAPP(c_COMBB(tc_List_Olist(X5),tc_fun(tc_Nat_Onat,X5),tc_Nat_Onat),c_List_Onth(X5)),hAPP(c_List_Onth(tc_List_Olist(X5)),X239))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5))),X239)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X50)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose__rectangle) ).

fof(fact_negDivAlg_Opinduct,axiom,
    ! [X18,X27,X191] :
      ( 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),X191),X27)))
     => ( ! [X187,X188] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X187),X188)))
           => ( ( ~ ( 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),X187),X188)))
                    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X188),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
               => hBOOL(hAPP(hAPP(X18,X187),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X188))) )
             => hBOOL(hAPP(hAPP(X18,X187),X188)) ) )
       => hBOOL(hAPP(hAPP(X18,X191),X27)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negDivAlg_Opinduct) ).

fof(fact_setsum__delta_H,axiom,
    ! [X24,X6,X192,X5,X20] :
      ( class_Groups_Ocomm__monoid__add(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X192))
       => ( ( hBOOL(hAPP(hAPP(c_member(X5),X6),X192))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),hAPP(hAPP(c_COMBC(X5,X20,X20),hAPP(hAPP(c_COMBS(X5,X20,tc_fun(X20,X20)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X20,tc_fun(X20,X20)),X5),c_If(X20)),hAPP(c_fequal,X6))),X24)),c_Groups_Ozero__class_Ozero(X20))),X192) = hAPP(X24,X6) )
          & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X192))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),hAPP(hAPP(c_COMBC(X5,X20,X20),hAPP(hAPP(c_COMBS(X5,X20,tc_fun(X20,X20)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X20,tc_fun(X20,X20)),X5),c_If(X20)),hAPP(c_fequal,X6))),X24)),c_Groups_Ozero__class_Ozero(X20))),X192) = c_Groups_Ozero__class_Ozero(X20) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__delta_H) ).

fof(fact_setprod__delta_H,axiom,
    ! [X24,X6,X192,X5,X20] :
      ( class_Groups_Ocomm__monoid__mult(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X192))
       => ( ( hBOOL(hAPP(hAPP(c_member(X5),X6),X192))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),hAPP(hAPP(c_COMBC(X5,X20,X20),hAPP(hAPP(c_COMBS(X5,X20,tc_fun(X20,X20)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X20,tc_fun(X20,X20)),X5),c_If(X20)),hAPP(c_fequal,X6))),X24)),c_Groups_Oone__class_Oone(X20))),X192) = hAPP(X24,X6) )
          & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X192))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),hAPP(hAPP(c_COMBC(X5,X20,X20),hAPP(hAPP(c_COMBS(X5,X20,tc_fun(X20,X20)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X20,tc_fun(X20,X20)),X5),c_If(X20)),hAPP(c_fequal,X6))),X24)),c_Groups_Oone__class_Oone(X20))),X192) = c_Groups_Oone__class_Oone(X20) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__delta_H) ).

fof(fact_posDivAlg_Opinduct,axiom,
    ! [X18,X27,X191] :
      ( 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),X191),X27)))
     => ( ! [X187,X188] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X187),X188)))
           => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X187),X188))
                    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X188),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
               => hBOOL(hAPP(hAPP(X18,X187),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X188))) )
             => hBOOL(hAPP(hAPP(X18,X187),X188)) ) )
       => hBOOL(hAPP(hAPP(X18,X191),X27)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_posDivAlg_Opinduct) ).

fof(fact_listrel__Cons2,axiom,
    ! [X171,X251,X33,X239,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X239),hAPP(hAPP(c_List_Olist_OCons(X5),X33),X251))),c_List_Olistrel(X5,X171)))
     => ~ ! [X3,X263] :
            ( X239 = hAPP(hAPP(c_List_Olist_OCons(X5),X3),X263)
           => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X33)),X171))
             => ~ 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)),X263),X251)),c_List_Olistrel(X5,X171))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__Cons2) ).

fof(fact_rel__pow__Suc__E2,axiom,
    ! [X32,X50,X120,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X120)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),hAPP(c_Nat_OSuc,X50)),X32)))
     => ~ ! [X177] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X177)),X32))
           => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X177),X120)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X50),X32))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__pow__Suc__E2) ).

fof(fact_Nitpick_Otimes__frac__def,axiom,
    ! [X134,X140,X58] : c_Nitpick_Otimes__frac(X58,X140,X134) = hAPP(hAPP(c_Nitpick_Ofrac(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(X58),X140)),hAPP(c_Nitpick_Onum(X58),X134))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Odenom(X58),X140)),hAPP(c_Nitpick_Odenom(X58),X134))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Otimes__frac__def) ).

fof(fact_rel__pow__E,axiom,
    ! [X32,X50,X120,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X120)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X50),X32)))
     => ( ( X50 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => X25 != X120 )
       => ~ ! [X177,X86] :
              ( X50 = hAPP(c_Nat_OSuc,X86)
             => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X177)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X86),X32)))
               => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X177),X120)),X32)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__pow__E) ).

fof(fact_rel__pow__Suc__E,axiom,
    ! [X32,X50,X120,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X120)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),hAPP(c_Nat_OSuc,X50)),X32)))
     => ~ ! [X177] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X177)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X50),X32)))
           => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X177),X120)),X32)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__pow__Suc__E) ).

fof(fact_negDivAlg_Opsimps,axiom,
    ! [X24,X6] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X6),X24)))
     => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X6),X24)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
         => c_Divides_OnegDivAlg(X6,X24) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X6),X24)) )
        & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X6),X24)))
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
         => c_Divides_OnegDivAlg(X6,X24) = hAPP(c_Divides_Oadjust(X24),c_Divides_OnegDivAlg(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X24))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negDivAlg_Opsimps) ).

fof(fact_posDivAlg_Opsimps,axiom,
    ! [X24,X6] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X6),X24)))
     => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X6),X24))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
         => c_Divides_OposDivAlg(X6,X24) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6) )
        & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X6),X24))
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
         => c_Divides_OposDivAlg(X6,X24) = hAPP(c_Divides_Oadjust(X24),c_Divides_OposDivAlg(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X24))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_posDivAlg_Opsimps) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J,axiom,
    ! [X57,X66,X58] :
      ( class_Rings_Ocomm__semiring__1(X58)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X58),X66),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)))),X57))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X66),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X66),X57)),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X66),X57))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J) ).

fof(fact_arith__series__int,axiom,
    ! [X50,X22,X6] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X6)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),X22))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X50))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X50)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X6),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X50),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X22)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_arith__series__int) ).

fof(fact_le__number__of__Suc,axiom,
    ! [X50,X123] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X123)),hAPP(c_Nat_OSuc,X50)))
    <=> 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(X123))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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)),X50)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__number__of__Suc) ).

fof(fact_less__number__of__Suc,axiom,
    ! [X50,X123] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X123)),hAPP(c_Nat_OSuc,X50)))
    <=> 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(X123))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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)),X50)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__number__of__Suc) ).

fof(fact_of__nat__double,axiom,
    ! [X66,X58] :
      ( class_Rings_Osemiring__1(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X66))
       => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X58),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)))),X66))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X58),hAPP(c_Int_Onat,X66))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X58),hAPP(c_Int_Onat,X66))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__double) ).

fof(fact_negDivAlg_Osimps,axiom,
    ! [X90,X62] :
      ( ( ( 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),X62),X90)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X90),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
       => c_Divides_OnegDivAlg(X62,X90) = 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),X62),X90)) )
      & ( ~ ( 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),X62),X90)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X90),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
       => c_Divides_OnegDivAlg(X62,X90) = hAPP(c_Divides_Oadjust(X90),c_Divides_OnegDivAlg(X62,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X90))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negDivAlg_Osimps) ).

fof(fact_posDivAlg_Osimps,axiom,
    ! [X90,X62] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X62),X90))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X90),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
       => c_Divides_OposDivAlg(X62,X90) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X62) )
      & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X62),X90))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X90),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
       => c_Divides_OposDivAlg(X62,X90) = hAPP(c_Divides_Oadjust(X90),c_Divides_OposDivAlg(X62,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X90))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_posDivAlg_Osimps) ).

fof(fact_power__minus1__odd,axiom,
    ! [X57,X58] :
      ( class_Rings_Oring__1(X58)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X58),hAPP(c_Groups_Ouminus__class_Ouminus(X58),c_Groups_Oone__class_Oone(X58))),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)))),X57))) = hAPP(c_Groups_Ouminus__class_Ouminus(X58),c_Groups_Oone__class_Oone(X58)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__minus1__odd) ).

fof(fact_power__minus__even,axiom,
    ! [X57,X62,X58] :
      ( class_Rings_Oring__1(X58)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X58),hAPP(c_Groups_Ouminus__class_Ouminus(X58),X62)),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)))),X57)) = hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),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)))),X57)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__minus__even) ).

fof(fact_power__m1__odd,axiom,
    ! [X57,X58] :
      ( class_Int_Onumber__ring(X58)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X58),hAPP(c_Int_Onumber__class_Onumber__of(X58),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)))),X57))) = hAPP(c_Int_Onumber__class_Onumber__of(X58),c_Int_OMin) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__m1__odd) ).

fof(fact_Suc3__eq__add__3,axiom,
    ! [X57] : hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X57))) = 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)))),X57),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc3__eq__add__3) ).

fof(fact_ImageE,axiom,
    ! [X21,X171,X20,X24,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X24),hAPP(c_Relation_OImage(X20,X5,X171),X21)))
     => ~ ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(X20,X5)),hAPP(hAPP(c_Product__Type_OPair(X20,X5),X3),X24)),X171))
           => ~ hBOOL(hAPP(hAPP(c_member(X20),X3),X21)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ImageE) ).

fof(fact_n__lists_Osimps_I2_J,axiom,
    ! [X239,X50,X5] : c_Enum_On__lists(X5,hAPP(c_Nat_OSuc,X50),X239) = c_List_Oconcat(tc_List_Olist(X5),hAPP(hAPP(c_List_Omap(tc_List_Olist(X5),tc_List_Olist(tc_List_Olist(X5))),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_List_Olist(X5),tc_List_Olist(tc_List_Olist(X5))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_List_Olist(X5)),tc_fun(tc_List_Olist(X5),tc_List_Olist(tc_List_Olist(X5))),tc_List_Olist(X5)),c_List_Omap(X5,tc_List_Olist(X5))),hAPP(c_COMBC(X5,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olist_OCons(X5)))),X239)),c_Enum_On__lists(X5,X50,X239))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__lists_Osimps_I2_J) ).

fof(fact_nat__case__add__eq__if,axiom,
    ! [X50,X123,X2,X6,X5] : c_Nat_Onat_Onat__case(X5,X6,X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X123)),X50)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X5),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X123))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X5,X5),hAPP(hAPP(c_COMBC(tc_Int_Oint,X5,tc_fun(X5,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5,tc_fun(X5,X5)),tc_Int_Oint),c_If(X5)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(X5,X6,X2,X50))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X5,tc_Int_Oint),X2),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),X50)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__case__add__eq__if) ).

fof(fact_mod2__gr__0,axiom,
    ! [X95] :
      ( 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,X95,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,X95,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/sandbox/benchmark/theBenchmark.p',fact_mod2__gr__0) ).

fof(fact_apsnd__eq__conv,axiom,
    ! [X1,X25,X2,X5,X20,X116] :
      ( hAPP(c_Product__Type_Oapsnd(X116,X20,X5,X2),X25) = hAPP(c_Product__Type_Oapsnd(X116,X20,X5,X1),X25)
    <=> hAPP(X2,hAPP(c_Product__Type_Osnd(X5,X116),X25)) = hAPP(X1,hAPP(c_Product__Type_Osnd(X5,X116),X25)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_apsnd__eq__conv) ).

fof(fact_apfst__eq__conv,axiom,
    ! [X1,X25,X2,X20,X5,X116] :
      ( hAPP(c_Product__Type_Oapfst(X116,X5,X20,X2),X25) = hAPP(c_Product__Type_Oapfst(X116,X5,X20,X1),X25)
    <=> hAPP(X2,hAPP(c_Product__Type_Ofst(X116,X20),X25)) = hAPP(X1,hAPP(c_Product__Type_Ofst(X116,X20),X25)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_apfst__eq__conv) ).

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

fof(fact_apsnd__apfst,axiom,
    ! [X25,X1,X115,X2,X5,X20,X116] : hAPP(c_Product__Type_Oapsnd(X116,X20,X5,X2),hAPP(c_Product__Type_Oapfst(X115,X5,X116,X1),X25)) = hAPP(hAPP(c_Product__Type_OPair(X5,X20),hAPP(X1,hAPP(c_Product__Type_Ofst(X115,X116),X25))),hAPP(X2,hAPP(c_Product__Type_Osnd(X115,X116),X25))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_apsnd__apfst) ).

fof(fact_apfst__apsnd,axiom,
    ! [X25,X1,X115,X2,X20,X5,X116] : hAPP(c_Product__Type_Oapfst(X116,X5,X20,X2),hAPP(c_Product__Type_Oapsnd(X115,X20,X116,X1),X25)) = hAPP(hAPP(c_Product__Type_OPair(X5,X20),hAPP(X2,hAPP(c_Product__Type_Ofst(X116,X115),X25))),hAPP(X1,hAPP(c_Product__Type_Osnd(X116,X115),X25))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_apfst__apsnd) ).

fof(fact_half__gt__zero__iff,axiom,
    ! [X171,X5] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X5)
        & class_Int_Onumber__ring(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X171),hAPP(c_Int_Onumber__class_Onumber__of(X5),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X171)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_half__gt__zero__iff) ).

fof(fact_max__Suc__number__of,axiom,
    ! [X50,X123] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X123)),hAPP(c_Nat_OSuc,X50)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X123))),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,X50))),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)),X50)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__Suc__number__of) ).

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

fof(fact_min__Suc__number__of,axiom,
    ! [X50,X123] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X123)),hAPP(c_Nat_OSuc,X50)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X123))),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)),X50)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__Suc__number__of) ).

fof(fact_nat__rec__number__of,axiom,
    ! [X123,X2,X6,X5] : hAPP(c_Nat_Onat_Onat__rec(X5,X6,X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X123)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X5),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X123))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X5,X5),hAPP(hAPP(c_COMBC(tc_Int_Oint,X5,tc_fun(X5,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5,tc_fun(X5,X5)),tc_Int_Oint),c_If(X5)),c_Nat__Numeral_Oneg)),X6)),hAPP(hAPP(c_COMBS(tc_Int_Oint,X5,X5),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X5,X5),tc_Int_Oint),X2),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X5,tc_Int_Oint),c_Nat_Onat_Onat__rec(X5,X6,X2)),c_Int_Onat)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__rec__number__of) ).

fof(fact_transpose__aux__filter__head,axiom,
    ! [X286,X5] : c_List_Oconcat(X5,hAPP(hAPP(c_List_Omap(tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olist_Olist__case(tc_List_Olist(X5),X5,c_List_Olist_ONil(X5),hAPP(hAPP(c_COMBB(tc_List_Olist(X5),tc_fun(tc_List_Olist(X5),tc_List_Olist(X5)),X5),c_COMBK(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_COMBC(X5,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olist_OCons(X5)),c_List_Olist_ONil(X5))))),X286)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(X5),X5),c_List_Ohd(X5)),hAPP(c_List_Ofilter(tc_List_Olist(X5),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X5)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_List_Olist(X5),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X5)))),X286)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose__aux__filter__head) ).

fof(fact_transpose__aux__filter__tail,axiom,
    ! [X286,X5] : c_List_Oconcat(tc_List_Olist(X5),hAPP(hAPP(c_List_Omap(tc_List_Olist(X5),tc_List_Olist(tc_List_Olist(X5))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(X5)),X5,c_List_Olist_ONil(tc_List_Olist(X5)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X5),tc_List_Olist(tc_List_Olist(X5))),X5),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_List_Olist(tc_List_Olist(X5)),tc_List_Olist(tc_List_Olist(X5))),c_List_Olist_OCons(tc_List_Olist(X5))),c_List_Olist_ONil(tc_List_Olist(X5)))))),X286)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Otl(X5)),hAPP(c_List_Ofilter(tc_List_Olist(X5),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X5)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_List_Olist(X5),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X5)))),X286)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose__aux__filter__tail) ).

fof(fact_rtrancl__Int__subset,axiom,
    ! [X171,X76,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Relation_OId(X5)),X76))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X5,X171)),X76)),X171)),X76))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X5,X171)),X76)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__Int__subset) ).

fof(fact_listrel__Cons1,axiom,
    ! [X171,X239,X251,X33,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(hAPP(c_List_Olist_OCons(X5),X33),X251)),X239)),c_List_Olistrel(X5,X171)))
     => ~ ! [X177,X262] :
            ( X239 = hAPP(hAPP(c_List_Olist_OCons(X5),X177),X262)
           => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X33),X177)),X171))
             => ~ 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)),X251),X262)),c_List_Olistrel(X5,X171))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__Cons1) ).

fof(fact_power__even__eq,axiom,
    ! [X57,X62,X58] :
      ( class_Groups_Omonoid__mult(X58)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),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)))),X57)) = hAPP(hAPP(c_Power_Opower__class_Opower(X58),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),X57)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__even__eq) ).

fof(fact_sublist__def,axiom,
    ! [X21,X239,X5] : c_List_Osublist(X5,X239,X21) = hAPP(hAPP(c_List_Omap(tc_prod(X5,tc_Nat_Onat),X5),c_Product__Type_Ofst(X5,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X5,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X5,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(X5,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(X5,tc_Nat_Onat))),X21)),hAPP(hAPP(c_List_Ozip(X5,tc_Nat_Onat),X239),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sublist__def) ).

fof(fact_fold1Set_Oequations,axiom,
    ! [X63,X26,X27,X2,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(X5,X2,hAPP(hAPP(c_Set_Oinsert(X5),X27),X26)),X63))
    <=> ? [X187,X226] :
          ( hAPP(hAPP(c_Set_Oinsert(X5),X27),X26) = hAPP(hAPP(c_Set_Oinsert(X5),X187),X226)
          & hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X5,X2,X187,X226),X63))
          & ~ hBOOL(hAPP(hAPP(c_member(X5),X187),X226)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1Set_Oequations) ).

fof(fact_Nitpick_Ouminus__frac__def,axiom,
    ! [X140,X58] : c_Nitpick_Ouminus__frac(X58,X140) = c_Nitpick_OAbs__Frac(X58,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(X58),X140))),hAPP(c_Nitpick_Odenom(X58),X140))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Ouminus__frac__def) ).

fof(fact_snd__apsnd,axiom,
    ! [X25,X2,X116,X5,X20] : hAPP(c_Product__Type_Osnd(X20,X5),hAPP(c_Product__Type_Oapsnd(X116,X5,X20,X2),X25)) = hAPP(X2,hAPP(c_Product__Type_Osnd(X20,X116),X25)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_snd__apsnd) ).

fof(fact_fst__apfst,axiom,
    ! [X25,X2,X116,X20,X5] : hAPP(c_Product__Type_Ofst(X5,X20),hAPP(c_Product__Type_Oapfst(X116,X5,X20,X2),X25)) = hAPP(X2,hAPP(c_Product__Type_Ofst(X116,X20),X25)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fst__apfst) ).

fof(fact_fst__apsnd,axiom,
    ! [X25,X2,X116,X20,X5] : hAPP(c_Product__Type_Ofst(X5,X20),hAPP(c_Product__Type_Oapsnd(X116,X20,X5,X2),X25)) = hAPP(c_Product__Type_Ofst(X5,X116),X25),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fst__apsnd) ).

fof(fact_snd__apfst,axiom,
    ! [X25,X2,X116,X5,X20] : hAPP(c_Product__Type_Osnd(X20,X5),hAPP(c_Product__Type_Oapfst(X116,X20,X5,X2),X25)) = hAPP(c_Product__Type_Osnd(X116,X5),X25),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_snd__apfst) ).

fof(fact_nat__case__number__of,axiom,
    ! [X123,X2,X6,X5] : c_Nat_Onat_Onat__case(X5,X6,X2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X123)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X5),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X123))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X5,X5),hAPP(hAPP(c_COMBC(tc_Int_Oint,X5,tc_fun(X5,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5,tc_fun(X5,X5)),tc_Int_Oint),c_If(X5)),c_Nat__Numeral_Oneg)),X6)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X5,tc_Int_Oint),X2),c_Int_Onat))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__case__number__of) ).

fof(fact_max__number__of__Suc,axiom,
    ! [X123,X50] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X50)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X123)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X123))),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,X50))),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),X50)),c_Int_Onat)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__number__of__Suc) ).

fof(fact_min__number__of__Suc,axiom,
    ! [X123,X50] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X50)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X123)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X123))),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),X50)),c_Int_Onat)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__number__of__Suc) ).

fof(fact_Suc__n__div__2__gt__zero,axiom,
    ! [X57] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X57))
     => 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),X57),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/sandbox/benchmark/theBenchmark.p',fact_Suc__n__div__2__gt__zero) ).

fof(fact_half__gt__zero,axiom,
    ! [X134,X58] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X58)
        & class_Int_Onumber__ring(X58) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),X134))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X134),hAPP(c_Int_Onumber__class_Onumber__of(X58),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_half__gt__zero) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom,
    ! [X57,X66,X58] :
      ( class_Rings_Ocomm__semiring__1(X58)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X58),X66),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)))),X57)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X66),X57)),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X66),X57)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).

fof(fact_div__2__gt__zero,axiom,
    ! [X57] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X57))
     => 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),X57),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__2__gt__zero) ).

fof(fact_power3__eq__cube,axiom,
    ! [X62,X58] :
      ( class_Groups_Omonoid__mult(X58)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),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(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X62)),X62) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power3__eq__cube) ).

fof(fact_zero__le__power2,axiom,
    ! [X62,X58] :
      ( class_Rings_Olinordered__idom(X58)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__power2) ).

fof(fact_power__minus1__even,axiom,
    ! [X57,X58] :
      ( class_Rings_Oring__1(X58)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X58),hAPP(c_Groups_Ouminus__class_Ouminus(X58),c_Groups_Oone__class_Oone(X58))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X57)) = c_Groups_Oone__class_Oone(X58) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__minus1__even) ).

fof(fact_power__m1__even,axiom,
    ! [X57,X58] :
      ( class_Int_Onumber__ring(X58)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X58),hAPP(c_Int_Onumber__class_Onumber__of(X58),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)))),X57)) = c_Groups_Oone__class_Oone(X58) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__m1__even) ).

fof(fact_diff__nat__number__of,axiom,
    ! [X123,X168] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X168),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X123)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X168)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X123) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X168),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X123)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X168)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X123),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X168)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__nat__number__of) ).

fof(fact_dropWhile__map,axiom,
    ! [X239,X2,X20,X18,X5] : c_List_OdropWhile(X5,X18,hAPP(hAPP(c_List_Omap(X20,X5),X2),X239)) = hAPP(hAPP(c_List_Omap(X20,X5),X2),c_List_OdropWhile(X20,hAPP(c_Fun_Ocomp(X5,tc_HOL_Obool,X20,X18),X2),X239)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dropWhile__map) ).

fof(fact_diff__nat__eq__if,axiom,
    ! [X120,X137] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,X137))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X120)),hAPP(c_Int_Onat,X137)) = hAPP(c_Int_Onat,X120) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X137))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X120)),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),X120),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/sandbox/benchmark/theBenchmark.p',fact_diff__nat__eq__if) ).

fof(fact_dropWhile__neq__rev,axiom,
    ! [X25,X239,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),X239))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X239)))
       => c_List_OdropWhile(X5,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X25)),hAPP(c_List_Orev(X5),X239)) = hAPP(hAPP(c_List_Olist_OCons(X5),X25),hAPP(c_List_Orev(X5),c_List_OtakeWhile(X5,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X25)),X239))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dropWhile__neq__rev) ).

fof(fact_fold__graph__permute__diff,axiom,
    ! [X6,X25,X21,X24,X5] :
      ( class_Groups_Oab__semigroup__mult(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X5,c_Groups_Otimes__class_Otimes(X5),X24,X21),X25))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X21))
         => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X24),X21))
           => hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X5,c_Groups_Otimes__class_Otimes(X5),X6,hAPP(hAPP(c_Set_Oinsert(X5),X24),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))),X25)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__graph__permute__diff) ).

fof(fact_concat__map__singleton,axiom,
    ! [X239,X2,X20,X5] : c_List_Oconcat(X5,hAPP(hAPP(c_List_Omap(X20,tc_List_Olist(X5)),hAPP(hAPP(c_COMBC(X20,tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(hAPP(c_COMBB(X5,tc_fun(tc_List_Olist(X5),tc_List_Olist(X5)),X20),c_List_Olist_OCons(X5)),X2)),c_List_Olist_ONil(X5))),X239)) = hAPP(hAPP(c_List_Omap(X20,X5),X2),X239),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_concat__map__singleton) ).

fof(fact_Nitpick_Oless__eq__frac__def,axiom,
    ! [X171,X153,X5] :
      ( c_Nitpick_Oless__eq__frac(X5,X153,X171)
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(X5),c_Nitpick_Oplus__frac(X5,X153,c_Nitpick_Ouminus__frac(X5,X171)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Oless__eq__frac__def) ).

fof(fact_Nitpick_Oless__frac__def,axiom,
    ! [X171,X153,X5] :
      ( c_Nitpick_Oless__frac(X5,X153,X171)
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(X5),c_Nitpick_Oplus__frac(X5,X153,c_Nitpick_Ouminus__frac(X5,X171)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Oless__frac__def) ).

fof(fact_power2__eq__imp__eq,axiom,
    ! [X65,X66,X58] :
      ( class_Rings_Olinordered__semidom(X58)
     => ( hAPP(hAPP(c_Power_Opower__class_Opower(X58),X66),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(X58),X65),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(X58),c_Groups_Ozero__class_Ozero(X58)),X66))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),X65))
           => X66 = X65 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power2__eq__imp__eq) ).

fof(fact_less__2__cases,axiom,
    ! [X57] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X57),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
     => ( X57 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X57 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__2__cases) ).

fof(fact_div2__Suc__Suc,axiom,
    ! [X72] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X72))),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),X72),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div2__Suc__Suc) ).

fof(fact_abs__power2,axiom,
    ! [X62,X58] :
      ( class_Rings_Olinordered__idom(X58)
     => hAPP(c_Groups_Oabs__class_Oabs(X58),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),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(X58),X62),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__power2) ).

fof(fact_Nitpick_Oof__frac__def,axiom,
    ! [X140,X58,X5] :
      ( ( class_Rings_Oinverse(X5)
        & class_Rings_Oring__1(X5) )
     => c_Nitpick_Oof__frac(X58,X5,X140) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),hAPP(c_Int_Oring__1__class_Oof__int(X5),hAPP(c_Nitpick_Onum(X58),X140))),hAPP(c_Int_Oring__1__class_Oof__int(X5),hAPP(c_Nitpick_Odenom(X58),X140))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Oof__frac__def) ).

fof(fact_converseE,axiom,
    ! [X171,X297,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X20)),X297),hAPP(c_Relation_Oconverse(X20,X5),X171)))
     => ~ ! [X3,X177] :
            ( X297 = hAPP(hAPP(c_Product__Type_OPair(X5,X20),X177),X3)
           => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X20,X5)),hAPP(hAPP(c_Product__Type_OPair(X20,X5),X3),X177)),X171)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converseE) ).

fof(fact_setsum__natinterval__difff,axiom,
    ! [X2,X50,X95,X5] :
      ( class_Groups_Oab__group__add(X5)
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X50))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(X5)),X2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X5,tc_Nat_Onat),X2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X95,X50)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),hAPP(X2,X95)),hAPP(X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X50),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X50))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(X5)),X2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X5,tc_Nat_Onat),X2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X95,X50)) = c_Groups_Ozero__class_Ozero(X5) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__natinterval__difff) ).

fof(fact_fold__graph__insert__swap,axiom,
    ! [X120,X33,X21,X24,X5] :
      ( class_Groups_Oab__semigroup__mult(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X5,c_Groups_Otimes__class_Otimes(X5),X24,X21),X33))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X24),X21))
         => hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X5,c_Groups_Otimes__class_Otimes(X5),X120,hAPP(hAPP(c_Set_Oinsert(X5),X24),X21)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X120),X33))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__graph__insert__swap) ).

fof(fact_fold__graph_OinsertI,axiom,
    ! [X33,X120,X2,X20,X21,X25,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X20,X2,X120,X21),X33))
       => hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X20,X2,X120,hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)),hAPP(hAPP(X2,X25),X33))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__graph_OinsertI) ).

fof(fact_tranclD,axiom,
    ! [X32,X33,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X33)),c_Transitive__Closure_Otrancl(X5,X32)))
     => ? [X154] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X154)),X32))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X154),X33)),c_Transitive__Closure_Ortrancl(X5,X32))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tranclD) ).

fof(fact_tranclD2,axiom,
    ! [X32,X33,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X33)),c_Transitive__Closure_Otrancl(X5,X32)))
     => ? [X154] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X154)),c_Transitive__Closure_Ortrancl(X5,X32)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X154),X33)),X32)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tranclD2) ).

fof(fact_apfst__conv,axiom,
    ! [X33,X25,X2,X20,X5,X116] : hAPP(c_Product__Type_Oapfst(X116,X5,X20,X2),hAPP(hAPP(c_Product__Type_OPair(X116,X20),X25),X33)) = hAPP(hAPP(c_Product__Type_OPair(X5,X20),hAPP(X2,X25)),X33),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_apfst__conv) ).

fof(fact_apsnd__conv,axiom,
    ! [X33,X25,X2,X5,X20,X116] : hAPP(c_Product__Type_Oapsnd(X116,X20,X5,X2),hAPP(hAPP(c_Product__Type_OPair(X5,X116),X25),X33)) = hAPP(hAPP(c_Product__Type_OPair(X5,X20),X25),hAPP(X2,X33)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_apsnd__conv) ).

fof(fact_list__ex1__simps_I2_J,axiom,
    ! [X239,X25,X18,X5] :
      ( c_List_Olist__ex1(X5,X18,hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239))
    <=> ( ( hBOOL(hAPP(X18,X25))
         => c_List_Olist__all(X5,hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),X18))),hAPP(c_fequal,X25)),X239) )
        & ( ~ hBOOL(hAPP(X18,X25))
         => c_List_Olist__ex1(X5,X18,X239) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__ex1__simps_I2_J) ).

fof(fact_transpose__max__length,axiom,
    ! [X239,X5] : c_List_Ofoldr(tc_List_Olist(X5),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X5)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X5))),c_List_Otranspose(X5,X239),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5))),hAPP(c_List_Ofilter(tc_List_Olist(X5),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X5)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_List_Olist(X5),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X5)))),X239)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose__max__length) ).

fof(fact_dropWhile__nth,axiom,
    ! [X239,X18,X5,X157] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X157),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_OdropWhile(X5,X18,X239))))
     => hAPP(hAPP(c_List_Onth(X5),c_List_OdropWhile(X5,X18,X239)),X157) = hAPP(hAPP(c_List_Onth(X5),X239),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X157),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_OtakeWhile(X5,X18,X239)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dropWhile__nth) ).

fof(fact_zmod__number__of__Bit0,axiom,
    ! [X128,X136] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X136)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X128))) = hAPP(hAPP(c_Groups_Otimes__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),X136),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__number__of__Bit0) ).

fof(fact_power2__abs,axiom,
    ! [X62,X58] :
      ( class_Rings_Olinordered__idom(X58)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X58),hAPP(c_Groups_Oabs__class_Oabs(X58),X62)),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(X58),X62),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power2__abs) ).

fof(fact_power2__minus,axiom,
    ! [X62,X58] :
      ( class_Rings_Oring__1(X58)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X58),hAPP(c_Groups_Ouminus__class_Ouminus(X58),X62)),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(X58),X62),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power2__minus) ).

fof(fact_mod2__Suc__Suc,axiom,
    ! [X72] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X72)),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,X72,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod2__Suc__Suc) ).

fof(fact_finite__subset__induct,axiom,
    ! [X18,X21,X205,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X205))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X205),X21))
       => ( hBOOL(hAPP(X18,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))
         => ( ! [X187,X230] :
                ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X230))
               => ( hBOOL(hAPP(hAPP(c_member(X5),X187),X21))
                 => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X187),X230))
                   => ( hBOOL(hAPP(X18,X230))
                     => hBOOL(hAPP(X18,hAPP(hAPP(c_Set_Oinsert(X5),X187),X230))) ) ) ) )
           => hBOOL(hAPP(X18,X205)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__subset__induct) ).

fof(fact_mult__2,axiom,
    ! [X94,X58] :
      ( class_Int_Onumber__ring(X58)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),hAPP(c_Int_Onumber__class_Onumber__of(X58),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X94) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X94),X94) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__2) ).

fof(fact_listsum__map__filter,axiom,
    ! [X2,X18,X239,X5,X20] :
      ( class_Groups_Omonoid__add(X20)
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X239)))
           => ( ~ hBOOL(hAPP(X18,X3))
             => hAPP(X2,X3) = c_Groups_Ozero__class_Ozero(X20) ) )
       => hAPP(c_List_Omonoid__add__class_Olistsum(X20),hAPP(hAPP(c_List_Omap(X5,X20),X2),hAPP(c_List_Ofilter(X5,X18),X239))) = hAPP(c_List_Omonoid__add__class_Olistsum(X20),hAPP(hAPP(c_List_Omap(X5,X20),X2),X239)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__map__filter) ).

fof(fact_nat__mult__2,axiom,
    ! [X94] : 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)))),X94) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X94),X94),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__2) ).

fof(fact_add__2__eq__Suc,axiom,
    ! [X57] : 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)))),X57) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X57)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__2__eq__Suc) ).

fof(fact_length__dropWhile__le,axiom,
    ! [X239,X18,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_OdropWhile(X5,X18,X239))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__dropWhile__le) ).

fof(fact_folding__image__simple_Oinsert,axiom,
    ! [X25,X21,X205,X1,X120,X2,X20,X5] :
      ( c_Finite__Set_Ofolding__image__simple(X5,X20,X2,X120,X1,X205)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X20),X21))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X20),X25),X21))
         => hAPP(X205,hAPP(hAPP(c_Set_Oinsert(X20),X25),X21)) = hAPP(hAPP(X2,hAPP(X1,X25)),hAPP(X205,X21)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple_Oinsert) ).

fof(fact_RangeE,axiom,
    ! [X171,X20,X24,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X24),hAPP(c_Relation_ORange(X20,X5),X171)))
     => ~ ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X20,X5)),hAPP(hAPP(c_Product__Type_OPair(X20,X5),X3),X24)),X171)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_RangeE) ).

fof(fact_trancl__trans,axiom,
    ! [X23,X171,X24,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X24)),c_Transitive__Closure_Otrancl(X5,X171)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X24),X23)),c_Transitive__Closure_Otrancl(X5,X171)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X23)),c_Transitive__Closure_Otrancl(X5,X171))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__trans) ).

fof(fact_trancl__converseI,axiom,
    ! [X171,X33,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X33)),hAPP(c_Relation_Oconverse(X5,X5),c_Transitive__Closure_Otrancl(X5,X171))))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X33)),c_Transitive__Closure_Otrancl(X5,hAPP(c_Relation_Oconverse(X5,X5),X171)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__converseI) ).

fof(fact_trancl__converseD,axiom,
    ! [X171,X33,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X33)),c_Transitive__Closure_Otrancl(X5,hAPP(c_Relation_Oconverse(X5,X5),X171))))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X33)),hAPP(c_Relation_Oconverse(X5,X5),c_Transitive__Closure_Otrancl(X5,X171)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__converseD) ).

fof(fact_fold1Set_Ointros,axiom,
    ! [X25,X21,X6,X2,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X5,X2,X6,X21),X25))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X21))
       => hBOOL(hAPP(c_Finite__Set_Ofold1Set(X5,X2,hAPP(hAPP(c_Set_Oinsert(X5),X6),X21)),X25)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1Set_Ointros) ).

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

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

fof(fact_removeAll__append,axiom,
    ! [X241,X242,X66,X58] : hAPP(c_List_OremoveAll(X58,X66),hAPP(hAPP(c_List_Oappend(X58),X242),X241)) = hAPP(hAPP(c_List_Oappend(X58),hAPP(c_List_OremoveAll(X58,X66),X242)),hAPP(c_List_OremoveAll(X58,X66),X241)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_removeAll__append) ).

fof(fact_removeAll__filter__not__eq,axiom,
    ! [X25,X5] : c_List_OremoveAll(X5,X25) = c_List_Ofilter(X5,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),hAPP(c_fequal,X25))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_removeAll__filter__not__eq) ).

fof(fact_rotate__rev,axiom,
    ! [X242,X57,X58] : hAPP(c_List_Orotate(X58,X57),hAPP(c_List_Orev(X58),X242)) = hAPP(c_List_Orev(X58),hAPP(c_List_Orotate(X58,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X57,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242)))),X242)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate__rev) ).

fof(fact_rotate__def,axiom,
    ! [X50,X5] : c_List_Orotate(X5,X50) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X5),tc_List_Olist(X5)),X50),c_List_Orotate1(X5)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate__def) ).

fof(fact_rtrancl__trancl__trancl,axiom,
    ! [X120,X171,X33,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X33)),c_Transitive__Closure_Ortrancl(X5,X171)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X33),X120)),c_Transitive__Closure_Otrancl(X5,X171)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X120)),c_Transitive__Closure_Otrancl(X5,X171))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__trancl__trancl) ).

fof(fact_trancl__rtrancl__trancl,axiom,
    ! [X23,X171,X24,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X24)),c_Transitive__Closure_Otrancl(X5,X171)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X24),X23)),c_Transitive__Closure_Ortrancl(X5,X171)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X23)),c_Transitive__Closure_Otrancl(X5,X171))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__rtrancl__trancl) ).

fof(fact_trancl__into__trancl2,axiom,
    ! [X23,X171,X24,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X24)),X171))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X24),X23)),c_Transitive__Closure_Otrancl(X5,X171)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X23)),c_Transitive__Closure_Otrancl(X5,X171))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__into__trancl2) ).

fof(fact_Transitive__Closure_Otrancl__into__trancl,axiom,
    ! [X23,X171,X24,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X24)),c_Transitive__Closure_Otrancl(X5,X171)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X24),X23)),X171))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X23)),c_Transitive__Closure_Otrancl(X5,X171))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Transitive__Closure_Otrancl__into__trancl) ).

fof(fact_Collect__conv__if,axiom,
    ! [X5,X6,X18] :
      ( ( hBOOL(hAPP(X18,X6))
       => hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X6))),X18)) = hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) )
      & ( ~ hBOOL(hAPP(X18,X6))
       => hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X6))),X18)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__conv__if) ).

fof(fact_foldr__map,axiom,
    ! [X6,X239,X2,X116,X1,X5,X20] : c_List_Ofoldr(X20,X5,X1,hAPP(hAPP(c_List_Omap(X116,X20),X2),X239),X6) = c_List_Ofoldr(X116,X5,hAPP(c_Fun_Ocomp(X20,tc_fun(X5,X5),X116,X1),X2),X239,X6),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldr__map) ).

fof(fact_fun__upd__image,axiom,
    ! [X33,X2,X20,X21,X25,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
       => hAPP(c_Set_Oimage(X5,X20,c_Fun_Ofun__upd(X5,X20,X2,X25,X33)),X21) = hAPP(hAPP(c_Set_Oinsert(X20),X33),hAPP(c_Set_Oimage(X5,X20,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
       => hAPP(c_Set_Oimage(X5,X20,c_Fun_Ofun__upd(X5,X20,X2,X25,X33)),X21) = hAPP(c_Set_Oimage(X5,X20,X2),X21) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__image) ).

fof(fact_trancl__subset__Sigma,axiom,
    ! [X21,X171,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X171),hAPP(hAPP(c_Product__Type_OSigma(X5,X5),X21),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X5),X21))))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X5,X171)),hAPP(hAPP(c_Product__Type_OSigma(X5,X5),X21),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X5),X21)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__subset__Sigma) ).

fof(fact_norm__frac_Opsimps,axiom,
    ! [X24,X6] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X6),X24)))
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => c_Nitpick_Onorm__frac(X6,X24) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X6),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X24)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => ( ( ( X6 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
                | X24 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
             => c_Nitpick_Onorm__frac(X6,X24) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
            & ( ~ ( X6 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
                  | X24 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
             => c_Nitpick_Onorm__frac(X6,X24) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X6),X24)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X6))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X24))) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__frac_Opsimps) ).

fof(fact_foldr__append,axiom,
    ! [X6,X251,X239,X2,X5,X20] : c_List_Ofoldr(X20,X5,X2,hAPP(hAPP(c_List_Oappend(X20),X239),X251),X6) = c_List_Ofoldr(X20,X5,X2,X239,c_List_Ofoldr(X20,X5,X2,X251,X6)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldr__append) ).

fof(fact_psubset__insert__iff,axiom,
    ! [X113,X25,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),X113)))
    <=> ( ( hBOOL(hAPP(hAPP(c_member(X5),X25),X113))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X21),X113)) )
        & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X113))
         => ( ( hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),X113)) )
            & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),X113)) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__insert__iff) ).

fof(fact_lexord__irreflexive,axiom,
    ! [X33,X171,X5] :
      ( ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X3)),X171))
     => ~ 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)),X33),X33)),c_List_Olexord(X5,X171))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexord__irreflexive) ).

fof(fact_diff__bin__simps_I8_J,axiom,
    ! [X99,X96] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(X96)),c_Int_OBit1(X99)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_Opred(X96)),X99)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__bin__simps_I8_J) ).

fof(fact_inj__on__insert,axiom,
    ! [X21,X6,X2,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,X2,hAPP(hAPP(c_Set_Oinsert(X5),X6),X21))
    <=> ( c_Fun_Oinj__on(X5,X20,X2,X21)
        & ~ hBOOL(hAPP(hAPP(c_member(X20),hAPP(X2,X6)),hAPP(c_Set_Oimage(X5,X20,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__insert) ).

fof(fact_apfst__id,axiom,
    ! [X20,X5] : c_Product__Type_Oapfst(X5,X5,X20,c_Fun_Oid(X5)) = c_Fun_Oid(tc_prod(X5,X20)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_apfst__id) ).

fof(fact_apsnd__id,axiom,
    ! [X5,X20] : c_Product__Type_Oapsnd(X20,X20,X5,c_Fun_Oid(X20)) = c_Fun_Oid(tc_prod(X5,X20)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_apsnd__id) ).

fof(fact_trancl__reflcl,axiom,
    ! [X171,X5] : c_Transitive__Closure_Otrancl(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X171),c_Relation_OId(X5))) = c_Transitive__Closure_Ortrancl(X5,X171),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__reflcl) ).

fof(fact_subset__insert__iff,axiom,
    ! [X113,X25,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),X113)))
    <=> ( ( hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),X113)) )
        & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),X113)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__insert__iff) ).

fof(fact_eq__special_I4_J,axiom,
    ! [X25,X5] :
      ( class_Int_Onumber__ring(X5)
     => ( hAPP(c_Int_Onumber__class_Onumber__of(X5),X25) = c_Groups_Oone__class_Oone(X5)
      <=> c_Int_Oiszero(X5,hAPP(c_Int_Onumber__class_Onumber__of(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__special_I4_J) ).

fof(fact_eq__special_I2_J,axiom,
    ! [X33,X5] :
      ( class_Int_Onumber__ring(X5)
     => ( c_Groups_Oone__class_Oone(X5) = hAPP(c_Int_Onumber__class_Onumber__of(X5),X33)
      <=> c_Int_Oiszero(X5,hAPP(c_Int_Onumber__class_Onumber__of(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X33)))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__special_I2_J) ).

fof(fact_norm__frac_Osimps,axiom,
    ! [X6,X24] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => c_Nitpick_Onorm__frac(X6,X24) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X6),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X24)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => ( ( ( X6 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
              | X24 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
           => c_Nitpick_Onorm__frac(X6,X24) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
          & ( ~ ( X6 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
                | X24 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
           => c_Nitpick_Onorm__frac(X6,X24) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X6),X24)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X6))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X24))) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__frac_Osimps) ).

fof(fact_rtrancl__into__trancl2,axiom,
    ! [X23,X171,X24,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X24)),X171))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X24),X23)),c_Transitive__Closure_Ortrancl(X5,X171)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X23)),c_Transitive__Closure_Otrancl(X5,X171))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__into__trancl2) ).

fof(fact_rtrancl__into__trancl1,axiom,
    ! [X23,X171,X24,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X24)),c_Transitive__Closure_Ortrancl(X5,X171)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X24),X23)),X171))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X23)),c_Transitive__Closure_Otrancl(X5,X171))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__into__trancl1) ).

fof(fact_power2__eq__square__number__of,axiom,
    ! [X128,X5] :
      ( ( class_Groups_Omonoid__mult(X5)
        & class_Int_Onumber(X5) )
     => hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X128)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X128)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X128)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power2__eq__square__number__of) ).

fof(fact_r__r__into__trancl,axiom,
    ! [X23,X32,X24,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X24)),X32))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X24),X23)),X32))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X23)),c_Transitive__Closure_Otrancl(X5,X32))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_r__r__into__trancl) ).

fof(fact_DomainE,axiom,
    ! [X171,X20,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(c_Relation_ODomain(X5,X20),X171)))
     => ~ ! [X177] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X20)),hAPP(hAPP(c_Product__Type_OPair(X5,X20),X6),X177)),X171)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DomainE) ).

fof(fact_add__self__div__2,axiom,
    ! [X72] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X72),X72)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = X72,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__self__div__2) ).

fof(fact_mult__2__right,axiom,
    ! [X94,X58] :
      ( class_Int_Onumber__ring(X58)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X94),hAPP(c_Int_Onumber__class_Onumber__of(X58),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X94),X94) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__2__right) ).

fof(fact_power2__eq__square,axiom,
    ! [X62,X58] :
      ( class_Groups_Omonoid__mult(X58)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),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(X58),X62),X62) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power2__eq__square) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
    ! [X66,X58] :
      ( class_Rings_Ocomm__semiring__1(X58)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X66),X66) = hAPP(hAPP(c_Power_Opower__class_Opower(X58),X66),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).

fof(fact_INF2__E,axiom,
    ! [X6,X23,X24,X113,X21,X116,X20,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X20,tc_fun(X116,tc_HOL_Obool))),X21),X113),X24),X23))
     => ( ~ hBOOL(hAPP(hAPP(hAPP(X113,X6),X24),X23))
       => ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X21)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF2__E) ).

fof(fact_nat__mult__2__right,axiom,
    ! [X94] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X94),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),X94),X94),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__2__right) ).

fof(fact_add__2__eq__Suc_H,axiom,
    ! [X57] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X57),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,X57)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__2__eq__Suc_H) ).

fof(fact_one__power2,axiom,
    ! [X58] :
      ( class_Rings_Osemiring__1(X58)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X58),c_Groups_Oone__class_Oone(X58)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(X58) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__power2) ).

fof(fact_zero__power2,axiom,
    ! [X58] :
      ( class_Rings_Osemiring__1(X58)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X58),c_Groups_Ozero__class_Ozero(X58)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(X58) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__power2) ).

fof(fact_map__fun__upd,axiom,
    ! [X123,X2,X20,X239,X33,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X33),hAPP(c_List_Oset(X5),X239)))
     => hAPP(hAPP(c_List_Omap(X5,X20),c_Fun_Ofun__upd(X5,X20,X2,X33,X123)),X239) = hAPP(hAPP(c_List_Omap(X5,X20),X2),X239) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__fun__upd) ).

fof(fact_trancl__mono,axiom,
    ! [X76,X171,X160,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X160),c_Transitive__Closure_Otrancl(X5,X171)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X171),X76))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X160),c_Transitive__Closure_Otrancl(X5,X76))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__mono) ).

fof(fact_not__sum__squares__lt__zero,axiom,
    ! [X65,X66,X58] :
      ( class_Rings_Olinordered__ring(X58)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X66),X66)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X65),X65))),c_Groups_Ozero__class_Ozero(X58))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__sum__squares__lt__zero) ).

fof(fact_trancl__subset__Field2,axiom,
    ! [X171,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X5,X171)),hAPP(hAPP(c_Product__Type_OSigma(X5,X5),hAPP(c_Relation_OField(X5),X171)),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X5),hAPP(c_Relation_OField(X5),X171))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__subset__Field2) ).

fof(fact_sup2E,axiom,
    ! [X33,X25,X113,X21,X20,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_fun(X20,tc_HOL_Obool))),X21),X113),X25),X33))
     => ( ~ hBOOL(hAPP(hAPP(X21,X25),X33))
       => hBOOL(hAPP(hAPP(X113,X25),X33)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup2E) ).

fof(fact_rtrancl__eq__or__trancl,axiom,
    ! [X32,X33,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X33)),c_Transitive__Closure_Ortrancl(X5,X32)))
    <=> ( X25 = X33
        | ( X25 != X33
          & hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X33)),c_Transitive__Closure_Otrancl(X5,X32))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__eq__or__trancl) ).

fof(fact_trancl__into__rtrancl,axiom,
    ! [X171,X24,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X24)),c_Transitive__Closure_Otrancl(X5,X171)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X24)),c_Transitive__Closure_Ortrancl(X5,X171))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__into__rtrancl) ).

fof(fact_inf2E,axiom,
    ! [X33,X25,X113,X21,X20,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_fun(X20,tc_HOL_Obool))),X21),X113),X25),X33))
     => ~ ( hBOOL(hAPP(hAPP(X21,X25),X33))
         => ~ hBOOL(hAPP(hAPP(X113,X25),X33)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf2E) ).

fof(fact_less__eq__int__code_I16_J,axiom,
    ! [X169,X170] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X170)),c_Int_OBit1(X169)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X170),X169)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__int__code_I16_J) ).

fof(fact_rel__simps_I34_J,axiom,
    ! [X156,X87] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X87)),c_Int_OBit1(X156)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X87),X156)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I34_J) ).

fof(fact_less__int__code_I16_J,axiom,
    ! [X169,X170] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X170)),c_Int_OBit1(X169)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X170),X169)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__int__code_I16_J) ).

fof(fact_rel__simps_I17_J,axiom,
    ! [X156,X87] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X87)),c_Int_OBit1(X156)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X87),X156)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I17_J) ).

fof(fact_distinct__removeAll,axiom,
    ! [X66,X242,X58] :
      ( hBOOL(hAPP(c_List_Odistinct(X58),X242))
     => hBOOL(hAPP(c_List_Odistinct(X58),hAPP(c_List_OremoveAll(X58,X66),X242))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__removeAll) ).

fof(fact_map__removeAll__inj__on,axiom,
    ! [X239,X25,X2,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,X2,hAPP(hAPP(c_Set_Oinsert(X5),X25),hAPP(c_List_Oset(X5),X239)))
     => hAPP(hAPP(c_List_Omap(X5,X20),X2),hAPP(c_List_OremoveAll(X5,X25),X239)) = hAPP(c_List_OremoveAll(X20,hAPP(X2,X25)),hAPP(hAPP(c_List_Omap(X5,X20),X2),X239)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__removeAll__inj__on) ).

fof(fact_dropWhile__append2,axiom,
    ! [X251,X18,X239,X5] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X239)))
         => hBOOL(hAPP(X18,X3)) )
     => c_List_OdropWhile(X5,X18,hAPP(hAPP(c_List_Oappend(X5),X239),X251)) = c_List_OdropWhile(X5,X18,X251) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dropWhile__append2) ).

fof(fact_map__removeAll__inj,axiom,
    ! [X239,X25,X2,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => hAPP(hAPP(c_List_Omap(X5,X20),X2),hAPP(c_List_OremoveAll(X5,X25),X239)) = hAPP(c_List_OremoveAll(X20,hAPP(X2,X25)),hAPP(hAPP(c_List_Omap(X5,X20),X2),X239)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__removeAll__inj) ).

fof(fact_nth__length__takeWhile,axiom,
    ! [X239,X18,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_OtakeWhile(X5,X18,X239))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239)))
     => ~ hBOOL(hAPP(X18,hAPP(hAPP(c_List_Onth(X5),X239),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_OtakeWhile(X5,X18,X239))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__length__takeWhile) ).

fof(fact_length__transpose,axiom,
    ! [X239,X5] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5))),c_List_Otranspose(X5,X239)) = c_List_Ofoldr(tc_List_Olist(X5),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X5)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X5))),X239,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__transpose) ).

fof(fact_trancl__power,axiom,
    ! [X32,X160,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X160),c_Transitive__Closure_Otrancl(X5,X32)))
    <=> ? [X69] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X69))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X160),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X69),X32))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__power) ).

fof(fact_concat__append,axiom,
    ! [X241,X242,X58] : c_List_Oconcat(X58,hAPP(hAPP(c_List_Oappend(tc_List_Olist(X58)),X242),X241)) = hAPP(hAPP(c_List_Oappend(X58),c_List_Oconcat(X58,X242)),c_List_Oconcat(X58,X241)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_concat__append) ).

fof(fact_distinct__list__update,axiom,
    ! [X82,X6,X239,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),X239))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),X239)),hAPP(hAPP(c_Set_Oinsert(X5),hAPP(hAPP(c_List_Onth(X5),X239),X82)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))
       => hBOOL(hAPP(c_List_Odistinct(X5),hAPP(hAPP(c_List_Olist__update(X5,X239),X82),X6))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__list__update) ).

fof(fact_pigeonhole,axiom,
    ! [X21,X2,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),hAPP(c_Set_Oimage(X20,X5,X2),X21))),hAPP(c_Finite__Set_Ocard(X20),X21)))
     => ~ c_Fun_Oinj__on(X20,X5,X2,X21) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pigeonhole) ).

fof(fact_rtranclD,axiom,
    ! [X32,X24,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X24)),c_Transitive__Closure_Ortrancl(X5,X32)))
     => ( X6 = X24
        | ( X6 != X24
          & hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X24)),c_Transitive__Closure_Otrancl(X5,X32))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtranclD) ).

fof(fact_takeWhile__eq__take__P__nth,axiom,
    ! [X18,X239,X5,X50] :
      ( ! [X146] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X146),X50))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X146),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239)))
           => hBOOL(hAPP(X18,hAPP(hAPP(c_List_Onth(X5),X239),X146))) ) )
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X50),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239)))
         => ~ hBOOL(hAPP(X18,hAPP(hAPP(c_List_Onth(X5),X239),X50))) )
       => c_List_OtakeWhile(X5,X18,X239) = hAPP(hAPP(c_List_Otake(X5),X50),X239) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_takeWhile__eq__take__P__nth) ).

fof(fact_trancl_Or__into__trancl,axiom,
    ! [X171,X24,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X24)),X171))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X24)),c_Transitive__Closure_Otrancl(X5,X171))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl_Or__into__trancl) ).

fof(fact_divide__le__eq__number__of,axiom,
    ! [X121,X23,X24,X5] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X5)
        & class_Int_Onumber(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X24),X23)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)),X23))) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)),X23)),X24)) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121))) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__le__eq__number__of) ).

fof(fact_divide__less__eq__number__of,axiom,
    ! [X121,X23,X24,X5] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X5)
        & class_Int_Onumber(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X24),X23)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)),X23))) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)),X23)),X24)) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121))) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__less__eq__number__of) ).

fof(fact_le__divide__eq__number__of,axiom,
    ! [X23,X24,X121,X5] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X5)
        & class_Int_Onumber(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X24),X23)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)),X23)),X24)) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)),X23))) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)),c_Groups_Ozero__class_Ozero(X5))) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__divide__eq__number__of) ).

fof(fact_less__divide__eq__number__of,axiom,
    ! [X23,X24,X121,X5] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X5)
        & class_Int_Onumber(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X24),X23)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)),X23)),X24)) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)),X23))) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)),c_Groups_Ozero__class_Ozero(X5))) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__divide__eq__number__of) ).

fof(fact_inj__on__fun__updI,axiom,
    ! [X25,X33,X21,X2,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,X2,X21)
     => ( ~ hBOOL(hAPP(hAPP(c_member(X20),X33),hAPP(c_Set_Oimage(X5,X20,X2),X21)))
       => c_Fun_Oinj__on(X5,X20,c_Fun_Ofun__upd(X5,X20,X2,X25,X33),X21) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__fun__updI) ).

fof(fact_distinct__concat,axiom,
    ! [X239,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X5)),X239))
     => ( ! [X262] :
            ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X262),hAPP(c_List_Oset(tc_List_Olist(X5)),X239)))
           => hBOOL(hAPP(c_List_Odistinct(X5),X262)) )
       => ( ! [X262] :
              ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X262),hAPP(c_List_Oset(tc_List_Olist(X5)),X239)))
             => ! [X289] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X289),hAPP(c_List_Oset(tc_List_Olist(X5)),X239)))
                 => ( X262 != X289
                   => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),X262)),hAPP(c_List_Oset(X5),X289)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ) ) )
         => hBOOL(hAPP(c_List_Odistinct(X5),c_List_Oconcat(X5,X239))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__concat) ).

fof(fact_Collect__conv__if2,axiom,
    ! [X5,X6,X18] :
      ( ( hBOOL(hAPP(X18,X6))
       => hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(c_fequal,X6))),X18)) = hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) )
      & ( ~ hBOOL(hAPP(X18,X6))
       => hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(c_fequal,X6))),X18)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__conv__if2) ).

fof(fact_rotate__drop__take,axiom,
    ! [X242,X57,X58] : hAPP(c_List_Orotate(X58,X57),X242) = hAPP(hAPP(c_List_Oappend(X58),hAPP(hAPP(c_List_Odrop(X58),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X57,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242))),X242)),hAPP(hAPP(c_List_Otake(X58),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X57,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242))),X242)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate__drop__take) ).

fof(fact_in__set__zipE,axiom,
    ! [X251,X239,X33,X25,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X20)),hAPP(hAPP(c_Product__Type_OPair(X5,X20),X25),X33)),hAPP(c_List_Oset(tc_prod(X5,X20)),hAPP(hAPP(c_List_Ozip(X5,X20),X239),X251))))
     => ~ ( hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X239)))
         => ~ hBOOL(hAPP(hAPP(c_member(X20),X33),hAPP(c_List_Oset(X20),X251))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__set__zipE) ).

fof(fact_removeAll_Osimps_I2_J,axiom,
    ! [X242,X58,X65,X66] :
      ( ( X66 = X65
       => hAPP(c_List_OremoveAll(X58,X66),hAPP(hAPP(c_List_Olist_OCons(X58),X65),X242)) = hAPP(c_List_OremoveAll(X58,X66),X242) )
      & ( X66 != X65
       => hAPP(c_List_OremoveAll(X58,X66),hAPP(hAPP(c_List_Olist_OCons(X58),X65),X242)) = hAPP(hAPP(c_List_Olist_OCons(X58),X65),hAPP(c_List_OremoveAll(X58,X66),X242)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_removeAll_Osimps_I2_J) ).

fof(fact_acyclic__insert,axiom,
    ! [X171,X25,X33,X5] :
      ( c_Wellfounded_Oacyclic(X5,hAPP(hAPP(c_Set_Oinsert(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X33),X25)),X171))
    <=> ( c_Wellfounded_Oacyclic(X5,X171)
        & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X33)),c_Transitive__Closure_Ortrancl(X5,X171))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acyclic__insert) ).

fof(fact_wf__insert,axiom,
    ! [X171,X25,X33,X5] :
      ( c_Wellfounded_Owf(X5,hAPP(hAPP(c_Set_Oinsert(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X33),X25)),X171))
    <=> ( c_Wellfounded_Owf(X5,X171)
        & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X33)),c_Transitive__Closure_Ortrancl(X5,X171))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__insert) ).

fof(fact_trancl__unfold,axiom,
    ! [X171,X5] : c_Transitive__Closure_Otrancl(X5,X171) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X171),hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),c_Transitive__Closure_Otrancl(X5,X171)),X171)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__unfold) ).

fof(fact_wf__eq__minimal,axiom,
    ! [X171,X5] :
      ( c_Wellfounded_Owf(X5,X171)
    <=> ! [X296] :
          ( ? [X3] : hBOOL(hAPP(hAPP(c_member(X5),X3),X296))
         => ? [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),X296))
              & ! [X177] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X177),X3)),X171))
                 => ~ hBOOL(hAPP(hAPP(c_member(X5),X177),X296)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__eq__minimal) ).

fof(fact_less__eq__int__code_I15_J,axiom,
    ! [X169,X170] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X170)),c_Int_OBit0(X169)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X170),X169)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__int__code_I15_J) ).

fof(fact_rel__simps_I33_J,axiom,
    ! [X156,X87] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X87)),c_Int_OBit0(X156)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X87),X156)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I33_J) ).

fof(fact_rel__simps_I16_J,axiom,
    ! [X156,X87] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X87)),c_Int_OBit0(X156)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X87),X156)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I16_J) ).

fof(fact_less__int__code_I15_J,axiom,
    ! [X169,X170] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X170)),c_Int_OBit0(X169)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X170),X169)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__int__code_I15_J) ).

fof(fact_Nitpick_Oint__lcm__def,axiom,
    ! [X65,X66] : c_Nitpick_Oint__lcm(X66,X65) = 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),X66)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X65)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Oint__lcm__def) ).

fof(fact_Nitpick_Onat__lcm__def,axiom,
    ! [X65,X66] : c_Nitpick_Onat__lcm(X66,X65) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X66),X65)),c_Nitpick_Onat__gcd(X66,X65)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Onat__lcm__def) ).

fof(fact_foldr_Osimps_I2_J,axiom,
    ! [X6,X239,X25,X2,X5,X20] : c_List_Ofoldr(X20,X5,X2,hAPP(hAPP(c_List_Olist_OCons(X20),X25),X239),X6) = hAPP(hAPP(X2,X25),c_List_Ofoldr(X20,X5,X2,X239,X6)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldr_Osimps_I2_J) ).

fof(fact_wf__not__sym,axiom,
    ! [X25,X6,X171,X5] :
      ( c_Wellfounded_Owf(X5,X171)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X25)),X171))
       => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X6)),X171)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__not__sym) ).

fof(fact_wf__asym,axiom,
    ! [X25,X6,X171,X5] :
      ( c_Wellfounded_Owf(X5,X171)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X25)),X171))
       => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X6)),X171)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__asym) ).

fof(fact_divmod__nat__rel__def,axiom,
    ! [X193,X50,X95] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X95,X50),X193))
    <=> ( X95 = 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),X193)),X50)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X193))
        & ( X50 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X193) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        & ( X50 != 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)),X50))
             => ( 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),X193)))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X193)),X50)) ) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X50))
             => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X50),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X193)))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X193)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__rel__def) ).

fof(fact_divide__le__eq__number__of1,axiom,
    ! [X6,X121,X24,X5] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X5)
        & class_Int_Onumber(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X24),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121))),X6))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)))) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121))),X24)) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),X6)) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__le__eq__number__of1) ).

fof(fact_divide__less__eq__number__of1,axiom,
    ! [X6,X121,X24,X5] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X5)
        & class_Int_Onumber(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X24),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121))),X6))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)))) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121))),X24)) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X6)) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__less__eq__number__of1) ).

fof(fact_minus__Bit1,axiom,
    ! [X96] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(X96)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X96))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__Bit1) ).

fof(fact_evaln_Oequations_I8_J,axiom,
    ! [X77,X60,X26,X63,X27] :
      ( c_Natural_Oevaln(c_Com_Ocom_OWhile(X27,X63),X26,X60,X77)
    <=> ( ( X77 = X26
          & ~ hBOOL(hAPP(X27,X26)) )
        | ( hBOOL(hAPP(X27,X26))
          & ? [X61] :
              ( c_Natural_Oevaln(X63,X26,X60,X61)
              & c_Natural_Oevaln(c_Com_Ocom_OWhile(X27,X63),X61,X60,X77) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_Oequations_I8_J) ).

fof(fact_small__lazy_H_Opinduct,axiom,
    ! [X18,X27,X191] :
      ( 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),X191),X27)))
     => ( ! [X158,X146] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X158),X146)))
           => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X158),X146))
               => hBOOL(hAPP(hAPP(X18,X158),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X146),c_Groups_Oone__class_Oone(tc_Int_Oint)))) )
             => hBOOL(hAPP(hAPP(X18,X158),X146)) ) )
       => hBOOL(hAPP(hAPP(X18,X191),X27)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_small__lazy_H_Opinduct) ).

fof(fact_evaln__elim__cases_I4_J,axiom,
    ! [X54,X57,X48,X64,X52] :
      ( c_Natural_Oevaln(c_Com_Ocom_OSemi(X52,X64),X48,X57,X54)
     => ~ ! [X61] :
            ( c_Natural_Oevaln(X52,X48,X57,X61)
           => ~ c_Natural_Oevaln(X64,X61,X57,X54) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln__elim__cases_I4_J) ).

fof(fact_less__eq,axiom,
    ! [X50,X95] :
      ( 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),X95),X50)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),X50)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq) ).

fof(fact_quotientE,axiom,
    ! [X171,X21,X194,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X194),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X21),X171)))
     => ~ ! [X3] :
            ( X194 = hAPP(c_Relation_OImage(X5,X5,X171),hAPP(hAPP(c_Set_Oinsert(X5),X3),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))
           => ~ hBOOL(hAPP(hAPP(c_member(X5),X3),X21)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotientE) ).

fof(fact_divmod__nat__if,axiom,
    ! [X95,X50] :
      ( ( ( X50 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),X50)) )
       => c_Divides_Odivmod__nat(X95,X50) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X95) )
      & ( ~ ( X50 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),X50)) )
       => c_Divides_Odivmod__nat(X95,X50) = 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),X95),X50),X50)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__if) ).

fof(fact_divmod__nat__def,axiom,
    ! [X50,X95] : c_Divides_Odivmod__nat(X95,X50) = c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X95,X50)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__def) ).

fof(fact_bin__less__0__simps_I4_J,axiom,
    ! [X121] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X121)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X121),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bin__less__0__simps_I4_J) ).

fof(fact_append__eq__append__conv__if,axiom,
    ! [X264,X265,X266,X267,X5] :
      ( hAPP(hAPP(c_List_Oappend(X5),X267),X266) = hAPP(hAPP(c_List_Oappend(X5),X265),X264)
    <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X267)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X265)))
         => ( X267 = hAPP(hAPP(c_List_Otake(X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X267)),X265)
            & X266 = hAPP(hAPP(c_List_Oappend(X5),hAPP(hAPP(c_List_Odrop(X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X267)),X265)),X264) ) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X267)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X265)))
         => ( hAPP(hAPP(c_List_Otake(X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X265)),X267) = X265
            & hAPP(hAPP(c_List_Oappend(X5),hAPP(hAPP(c_List_Odrop(X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X265)),X267)),X266) = X264 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__eq__append__conv__if) ).

fof(fact_rel__simps_I30_J,axiom,
    ! [X87] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X87)),c_Int_OMin))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X87),c_Int_OMin)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I30_J) ).

fof(fact_rel__simps_I29_J,axiom,
    ! [X87] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X87)),c_Int_OPls))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X87),c_Int_OPls)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I29_J) ).

fof(fact_rel__simps_I12_J,axiom,
    ! [X87] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X87)),c_Int_OPls))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X87),c_Int_OPls)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I12_J) ).

fof(fact_rel__simps_I13_J,axiom,
    ! [X87] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X87)),c_Int_OMin))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X87),c_Int_OMin)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I13_J) ).

fof(fact_neg__number__of__Bit1,axiom,
    ! [X121] :
      ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X121))))
    <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X121))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__number__of__Bit1) ).

fof(fact_length__remdups__concat,axiom,
    ! [X286,X5] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_Oremdups(X5,c_List_Oconcat(X5,X286))) = hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(X5),tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(X5)),X286)),c_List_Oset(X5))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__remdups__concat) ).

fof(fact_le__special_I2_J,axiom,
    ! [X33,X5] :
      ( ( class_Int_Onumber__ring(X5)
        & class_Rings_Olinordered__idom(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Oone__class_Oone(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X33)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X33)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__special_I2_J) ).

fof(fact_less__special_I2_J,axiom,
    ! [X33,X5] :
      ( ( class_Int_Onumber__ring(X5)
        & class_Rings_Olinordered__idom(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Oone__class_Oone(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X33)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X33)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__special_I2_J) ).

fof(fact_le__divide__eq__number__of1,axiom,
    ! [X121,X24,X6,X5] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X5)
        & class_Int_Onumber(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X24),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121))))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121))),X24)) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)))) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),c_Groups_Ozero__class_Ozero(X5))) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__divide__eq__number__of1) ).

fof(fact_less__divide__eq__number__of1,axiom,
    ! [X121,X24,X6,X5] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X5)
        & class_Int_Onumber(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X24),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121))))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121))),X24)) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)))) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),c_Groups_Ozero__class_Ozero(X5))) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__divide__eq__number__of1) ).

fof(fact_sup2CI,axiom,
    ! [X20,X5,X21,X33,X25,X113] :
      ( ( ~ hBOOL(hAPP(hAPP(X113,X25),X33))
       => hBOOL(hAPP(hAPP(X21,X25),X33)) )
     => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_fun(X20,tc_HOL_Obool))),X21),X113),X25),X33)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup2CI) ).

fof(fact_not__acc__down,axiom,
    ! [X32,X25,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),c_Wellfounded_Oacc(X5,X32)))
     => ~ ! [X154] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X154),X25)),X32))
           => hBOOL(hAPP(hAPP(c_member(X5),X154),c_Wellfounded_Oacc(X5,X32))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__acc__down) ).

fof(fact_flat__lub__def,axiom,
    ! [X24,X21,X5] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X24),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))
       => c_Partial__Function_Oflat__lub(X5,X24,X21) = X24 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X24),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))
       => c_Partial__Function_Oflat__lub(X5,X24,X21) = c_HOL_OThe(X5,hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X24),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_flat__lub__def) ).

fof(fact_evalc_Oequations_I8_J,axiom,
    ! [X59,X26,X63,X27] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X27,X63)),X26),X59))
    <=> ( ( X59 = X26
          & ~ hBOOL(hAPP(X27,X26)) )
        | ( hBOOL(hAPP(X27,X26))
          & ? [X61] :
              ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X63),X26),X61))
              & hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X27,X63)),X61),X59)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_Oequations_I8_J) ).

fof(fact_not__Nil__listrel1,axiom,
    ! [X171,X239,X5] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olist_ONil(X5)),X239)),c_List_Olistrel1(X5,X171))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__Nil__listrel1) ).

fof(fact_Nil__notin__lex,axiom,
    ! [X171,X251,X5] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olist_ONil(X5)),X251)),c_List_Olex(X5,X171))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nil__notin__lex) ).

fof(fact_not__listrel1__Nil,axiom,
    ! [X171,X239,X5] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X239),c_List_Olist_ONil(X5))),c_List_Olistrel1(X5,X171))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__listrel1__Nil) ).

fof(fact_lexord__Nil__right,axiom,
    ! [X171,X25,X5] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X25),c_List_Olist_ONil(X5))),c_List_Olexord(X5,X171))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexord__Nil__right) ).

fof(fact_Nil2__notin__lex,axiom,
    ! [X171,X239,X5] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X239),c_List_Olist_ONil(X5))),c_List_Olex(X5,X171))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nil2__notin__lex) ).

fof(fact_foldl__foldr1__lemma,axiom,
    ! [X239,X6,X5] :
      ( class_Groups_Omonoid__add(X5)
     => hAPP(c_List_Ofoldl(X5,X5,c_Groups_Oplus__class_Oplus(X5),X6),X239) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),c_List_Ofoldr(X5,X5,c_Groups_Oplus__class_Oplus(X5),X239,c_Groups_Ozero__class_Ozero(X5))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldl__foldr1__lemma) ).

fof(fact_pair__in__Id__conv,axiom,
    ! [X24,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X24)),c_Relation_OId(X5)))
    <=> X6 = X24 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__in__Id__conv) ).

fof(fact_finite__induct,axiom,
    ! [X18,X205,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X205))
     => ( hBOOL(hAPP(X18,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))
       => ( ! [X3,X230] :
              ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X230))
             => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X3),X230))
               => ( hBOOL(hAPP(X18,X230))
                 => hBOOL(hAPP(X18,hAPP(hAPP(c_Set_Oinsert(X5),X3),X230))) ) ) )
         => hBOOL(hAPP(X18,X205)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__induct) ).

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

fof(fact_set__removeAll,axiom,
    ! [X239,X25,X5] : hAPP(c_List_Oset(X5),hAPP(c_List_OremoveAll(X5,X25),X239)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),X239)),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__removeAll) ).

fof(fact_divmod__nat__step,axiom,
    ! [X72,X57] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X57))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X57),X72))
       => c_Divides_Odivmod__nat(X72,X57) = 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),X72),X57)),X57))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X72),X57),X57)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__step) ).

fof(fact_evalc__elim__cases_I4_J,axiom,
    ! [X54,X48,X64,X52] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(X52,X64)),X48),X54))
     => ~ ! [X61] :
            ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X52),X48),X61))
           => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X64),X61),X54)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc__elim__cases_I4_J) ).

fof(fact_foldl__foldr,axiom,
    ! [X239,X6,X2,X20,X5] : hAPP(c_List_Ofoldl(X5,X20,X2,X6),X239) = c_List_Ofoldr(X20,X5,hAPP(c_COMBC(X5,X20,X5),X2),hAPP(c_List_Orev(X20),X239),X6),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldl__foldr) ).

fof(fact_distinct__dropWhile,axiom,
    ! [X18,X239,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),X239))
     => hBOOL(hAPP(c_List_Odistinct(X5),c_List_OdropWhile(X5,X18,X239))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__dropWhile) ).

fof(fact_comm__monoid__big_OF__eq,axiom,
    ! [X1,X21,X205,X120,X2,X20,X5] :
      ( c_Big__Operators_Ocomm__monoid__big(X5,X20,X2,X120,X205)
     => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X20),X21))
         => hAPP(hAPP(X205,X1),X21) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X5,X20,X2),X1),X120),X21) )
        & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20),X21))
         => hAPP(hAPP(X205,X1),X21) = X120 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__monoid__big_OF__eq) ).

fof(fact_in__measure,axiom,
    ! [X2,X33,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X33)),hAPP(c_Wellfounded_Omeasure(X5),X2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X2,X25)),hAPP(X2,X33))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__measure) ).

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

fof(fact_SigmaE2,axiom,
    ! [X113,X21,X24,X6,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X20)),hAPP(hAPP(c_Product__Type_OPair(X5,X20),X6),X24)),hAPP(hAPP(c_Product__Type_OSigma(X5,X20),X21),X113)))
     => ~ ( hBOOL(hAPP(hAPP(c_member(X5),X6),X21))
         => ~ hBOOL(hAPP(hAPP(c_member(X20),X24),hAPP(X113,X6))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SigmaE2) ).

fof(fact_map__concat,axiom,
    ! [X239,X2,X5,X20] : hAPP(hAPP(c_List_Omap(X20,X5),X2),c_List_Oconcat(X20,X239)) = c_List_Oconcat(X5,hAPP(hAPP(c_List_Omap(tc_List_Olist(X20),tc_List_Olist(X5)),hAPP(c_List_Omap(X20,X5),X2)),X239)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__concat) ).

fof(fact_diff__bin__simps_I9_J,axiom,
    ! [X99,X96] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(X96)),c_Int_OBit0(X99)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X96),X99)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__bin__simps_I9_J) ).

fof(fact_add__Bit1__Bit0,axiom,
    ! [X99,X96] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(X96)),c_Int_OBit0(X99)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X96),X99)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Bit1__Bit0) ).

fof(fact_insort__insert__insort__key,axiom,
    ! [X239,X20,X25,X2,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( ~ hBOOL(hAPP(hAPP(c_member(X5),hAPP(X2,X25)),hAPP(c_Set_Oimage(X20,X5,X2),hAPP(c_List_Oset(X20),X239))))
       => c_List_Olinorder__class_Oinsort__insert__key(X20,X5,X2,X25,X239) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X20,X5,X2),X25),X239) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insort__insert__insort__key) ).

fof(fact_total__on__diff__Id,axiom,
    ! [X171,X21,X5] :
      ( c_Relation_Ototal__on(X5,X21,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X171),c_Relation_OId(X5)))
    <=> c_Relation_Ototal__on(X5,X21,X171) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_total__on__diff__Id) ).

fof(fact_Suc__diff__eq__diff__pred,axiom,
    ! [X72,X57] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)),X57))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X72)),X57) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X72),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X57),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__diff__eq__diff__pred) ).

fof(fact_mult__Bit1,axiom,
    ! [X99,X96] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(X96)),X99) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X96),X99))),X99),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__Bit1) ).

fof(fact_number__of1,axiom,
    ! [X57] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X57)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X57))))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__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(X57)))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of1) ).

fof(fact_add__Bit1__Bit1,axiom,
    ! [X99,X96] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(X96)),c_Int_OBit1(X99)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X96),c_Int_Osucc(X99))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Bit1__Bit1) ).

fof(fact_less__eq__int__code_I14_J,axiom,
    ! [X169,X170] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X170)),c_Int_OBit1(X169)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X170),X169)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__int__code_I14_J) ).

fof(fact_rel__simps_I32_J,axiom,
    ! [X156,X87] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X87)),c_Int_OBit1(X156)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X87),X156)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I32_J) ).

fof(fact_less__int__code_I14_J,axiom,
    ! [X169,X170] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X170)),c_Int_OBit1(X169)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X170),X169)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__int__code_I14_J) ).

fof(fact_rel__simps_I15_J,axiom,
    ! [X156,X87] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X87)),c_Int_OBit1(X156)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X87),X156)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I15_J) ).

fof(fact_antisym__reflcl,axiom,
    ! [X171,X5] :
      ( c_Relation_Oantisym(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X171),c_Relation_OId(X5)))
    <=> c_Relation_Oantisym(X5,X171) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_antisym__reflcl) ).

fof(fact_finite__trancl,axiom,
    ! [X171,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X5,X5)),c_Transitive__Closure_Otrancl(X5,X171)))
    <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X5,X5)),X171)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__trancl) ).

fof(fact_card__Diff__insert,axiom,
    ! [X113,X6,X21,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X21))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X113))
         => hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X6),X113))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),X113))),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Diff__insert) ).

fof(fact_rev__concat,axiom,
    ! [X239,X5] : hAPP(c_List_Orev(X5),c_List_Oconcat(X5,X239)) = c_List_Oconcat(X5,hAPP(hAPP(c_List_Omap(tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Orev(X5)),hAPP(c_List_Orev(tc_List_Olist(X5)),X239))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__concat) ).

fof(fact_fold__image__insert,axiom,
    ! [X120,X1,X6,X21,X5,X20] :
      ( class_Groups_Oab__semigroup__mult(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X21))
         => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X20,X5,c_Groups_Otimes__class_Otimes(X20)),X1),X120),hAPP(hAPP(c_Set_Oinsert(X5),X6),X21)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20),hAPP(X1,X6)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X20,X5,c_Groups_Otimes__class_Otimes(X20)),X1),X120),X21)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__image__insert) ).

fof(fact_filter__concat,axiom,
    ! [X239,X160,X5] : hAPP(c_List_Ofilter(X5,X160),c_List_Oconcat(X5,X239)) = c_List_Oconcat(X5,hAPP(hAPP(c_List_Omap(tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Ofilter(X5,X160)),X239)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter__concat) ).

fof(fact_in__measures_I1_J,axiom,
    ! [X33,X25,X5] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X33)),c_List_Omeasures(X5,c_List_Olist_ONil(tc_fun(X5,tc_Nat_Onat))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__measures_I1_J) ).

fof(fact_divide__le__eq,axiom,
    ! [X6,X23,X24,X5] :
      ( class_Fields_Olinordered__field__inverse__zero(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X24),X23)),X6))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X23))) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X23)),X24)) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),X6)) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__le__eq) ).

fof(fact_divide__less__eq,axiom,
    ! [X6,X23,X24,X5] :
      ( class_Fields_Olinordered__field__inverse__zero(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X24),X23)),X6))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X23))) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X23)),X24)) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X6)) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__less__eq) ).

fof(fact_distinct__rotate,axiom,
    ! [X239,X50,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),hAPP(c_List_Orotate(X5,X50),X239)))
    <=> hBOOL(hAPP(c_List_Odistinct(X5),X239)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__rotate) ).

fof(fact_Not__Domain__rtrancl,axiom,
    ! [X33,X32,X25,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_Relation_ODomain(X5,X5),X32)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X33)),c_Transitive__Closure_Ortrancl(X5,X32)))
      <=> X25 = X33 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Not__Domain__rtrancl) ).

fof(fact_add__Bit0__Bit1,axiom,
    ! [X99,X96] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(X96)),c_Int_OBit1(X99)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X96),X99)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Bit0__Bit1) ).

fof(fact_comm__monoid__big_Oinfinite,axiom,
    ! [X1,X21,X205,X120,X2,X20,X5] :
      ( c_Big__Operators_Ocomm__monoid__big(X5,X20,X2,X120,X205)
     => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20),X21))
       => hAPP(hAPP(X205,X1),X21) = X120 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__monoid__big_Oinfinite) ).

fof(fact_diff__special_I2_J,axiom,
    ! [X136,X58] :
      ( class_Int_Onumber__ring(X58)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X58),hAPP(c_Int_Onumber__class_Onumber__of(X58),X136)),c_Groups_Oone__class_Oone(X58)) = hAPP(c_Int_Onumber__class_Onumber__of(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X136),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__special_I2_J) ).

fof(fact_distinct__insort,axiom,
    ! [X239,X25,X2,X5,X20] :
      ( class_Orderings_Olinorder(X20)
     => ( hBOOL(hAPP(c_List_Odistinct(X5),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X20,X2),X25),X239)))
      <=> ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X239)))
          & hBOOL(hAPP(c_List_Odistinct(X5),X239)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__insort) ).

fof(fact_diff__special_I1_J,axiom,
    ! [X128,X58] :
      ( class_Int_Onumber__ring(X58)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X58),c_Groups_Oone__class_Oone(X58)),hAPP(c_Int_Onumber__class_Onumber__of(X58),X128)) = hAPP(c_Int_Onumber__class_Onumber__of(X58),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),X128))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__special_I1_J) ).

fof(fact_r__into__trancl_H,axiom,
    ! [X171,X160,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X160),X171))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X160),c_Transitive__Closure_Otrancl(X5,X171))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_r__into__trancl_H) ).

fof(fact_concat_Osimps_I2_J,axiom,
    ! [X242,X66,X58] : c_List_Oconcat(X58,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X58)),X66),X242)) = hAPP(hAPP(c_List_Oappend(X58),X66),c_List_Oconcat(X58,X242)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_concat_Osimps_I2_J) ).

fof(fact_add__special_I2_J,axiom,
    ! [X128,X58] :
      ( class_Int_Onumber__ring(X58)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),c_Groups_Oone__class_Oone(X58)),hAPP(c_Int_Onumber__class_Onumber__of(X58),X128)) = hAPP(c_Int_Onumber__class_Onumber__of(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X128)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__special_I2_J) ).

fof(fact_atLeastatMost__psubset__iff,axiom,
    ! [X22,X23,X24,X6,X5] :
      ( class_Orderings_Oorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,X24)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X23,X22)))
      <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),X24))
            | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X23),X6))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X24),X22))
              & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),X6))
                | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X24),X22)) ) ) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X23),X22)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastatMost__psubset__iff) ).

fof(fact_insert__partition,axiom,
    ! [X205,X25,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X25),X205))
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(tc_fun(X5,tc_HOL_Obool)),X25),X205)))
           => ! [X204] :
                ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X204),hAPP(hAPP(c_Set_Oinsert(tc_fun(X5,tc_HOL_Obool)),X25),X205)))
               => ( X3 != X204
                 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X3),X204) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ) ) )
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X25),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X205)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__partition) ).

fof(fact_reflcl__trancl,axiom,
    ! [X171,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X5,X171)),c_Relation_OId(X5)) = c_Transitive__Closure_Ortrancl(X5,X171),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_reflcl__trancl) ).

fof(fact_list__update__append,axiom,
    ! [X66,X241,X242,X58,X57] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X57),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242)))
       => hAPP(hAPP(c_List_Olist__update(X58,hAPP(hAPP(c_List_Oappend(X58),X242),X241)),X57),X66) = hAPP(hAPP(c_List_Oappend(X58),hAPP(hAPP(c_List_Olist__update(X58,X242),X57),X66)),X241) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X57),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242)))
       => hAPP(hAPP(c_List_Olist__update(X58,hAPP(hAPP(c_List_Oappend(X58),X242),X241)),X57),X66) = hAPP(hAPP(c_List_Oappend(X58),X242),hAPP(hAPP(c_List_Olist__update(X58,X241),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X57),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242))),X66)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update__append) ).

fof(fact_le__divide__eq,axiom,
    ! [X23,X24,X6,X5] :
      ( class_Fields_Olinordered__field__inverse__zero(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X24),X23)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X23)),X24)) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X23))) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),c_Groups_Ozero__class_Ozero(X5))) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__divide__eq) ).

fof(fact_less__divide__eq,axiom,
    ! [X23,X24,X6,X5] :
      ( class_Fields_Olinordered__field__inverse__zero(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X24),X23)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X23)),X24)) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X23))) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),c_Groups_Ozero__class_Ozero(X5))) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__divide__eq) ).

fof(fact_lazy__sequence_Osimps_I5_J,axiom,
    ! [X307,X6,X89,X19,X20,X5] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X5,X20,X19,X89,c_Lazy__Sequence_Olazy__sequence_OInsert(X20,X6,X307)) = hAPP(hAPP(X89,X6),X307),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lazy__sequence_Osimps_I5_J) ).

fof(fact_seq__case,axiom,
    ! [X277,X1,X2,X20,X5] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X5,X20,X2,X1,X277) = c_Option_Ooption_Ooption__case(X5,tc_prod(X20,tc_Lazy__Sequence_Olazy__sequence(X20)),X2,hAPP(c_Product__Type_Oprod_Oprod__case(X20,tc_Lazy__Sequence_Olazy__sequence(X20),X5),X1),hAPP(c_Lazy__Sequence_Oyield(X20),X277)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_seq__case) ).

fof(fact_mult__numeral__1,axiom,
    ! [X62,X58] :
      ( class_Int_Onumber__ring(X58)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),hAPP(c_Int_Onumber__class_Onumber__of(X58),c_Int_OBit1(c_Int_OPls))),X62) = X62 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__numeral__1) ).

fof(fact_list__ex__iff__not__all__inverval__int,axiom,
    ! [X157,X82,X18] :
      ( c_List_Olist__ex(tc_Int_Oint,X18,c_List_Oupto(X82,X157))
    <=> ~ c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint,c_fNot),X18),X82,X157) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__ex__iff__not__all__inverval__int) ).

fof(fact_rotate__add,axiom,
    ! [X50,X95,X5] : c_List_Orotate(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X95),X50)) = hAPP(c_Fun_Ocomp(tc_List_Olist(X5),tc_List_Olist(X5),tc_List_Olist(X5),c_List_Orotate(X5,X95)),c_List_Orotate(X5,X50)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate__add) ).

fof(fact_atLeastatMost__subset__iff,axiom,
    ! [X22,X23,X24,X6,X5] :
      ( class_Orderings_Oorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,X24)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X23,X22)))
      <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),X24))
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X23),X6))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X24),X22)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastatMost__subset__iff) ).

fof(fact_le__special_I4_J,axiom,
    ! [X25,X5] :
      ( ( class_Int_Onumber__ring(X5)
        & class_Rings_Olinordered__idom(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X25)),c_Groups_Oone__class_Oone(X5)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25),c_Int_OBit1(c_Int_OPls))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__special_I4_J) ).

fof(fact_less__special_I4_J,axiom,
    ! [X25,X5] :
      ( ( class_Int_Onumber__ring(X5)
        & class_Rings_Olinordered__idom(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X25)),c_Groups_Oone__class_Oone(X5)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25),c_Int_OBit1(c_Int_OPls))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__special_I4_J) ).

fof(fact_IdE,axiom,
    ! [X160,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X160),c_Relation_OId(X5)))
     => ~ ! [X3] : X160 != hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_IdE) ).

fof(fact_evalc_Oequations_I5_J,axiom,
    ! [X60,X26,X59,X63,X27] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X27,X63,X59)),X26),X60))
    <=> ( ( hBOOL(hAPP(X27,X26))
          & hBOOL(hAPP(hAPP(c_Natural_Oevalc(X63),X26),X60)) )
        | ( ~ hBOOL(hAPP(X27,X26))
          & hBOOL(hAPP(hAPP(c_Natural_Oevalc(X59),X26),X60)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_Oequations_I5_J) ).

fof(fact_evalc_Oequations_I6_J,axiom,
    ! [X60,X26,X63,X59,X27] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X27,X59,X63)),X26),X60))
    <=> ( ( hBOOL(hAPP(X27,X26))
          & hBOOL(hAPP(hAPP(c_Natural_Oevalc(X59),X26),X60)) )
        | ( ~ hBOOL(hAPP(X27,X26))
          & hBOOL(hAPP(hAPP(c_Natural_Oevalc(X63),X26),X60)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_Oequations_I6_J) ).

fof(fact_evalc__elim__cases_I5_J,axiom,
    ! [X15,X76,X106,X105,X24] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X24,X105,X106)),X76),X15))
     => ( ( hBOOL(hAPP(X24,X76))
         => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X105),X76),X15)) )
       => ~ ( ~ hBOOL(hAPP(X24,X76))
           => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X106),X76),X15)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc__elim__cases_I5_J) ).

fof(fact_diff__bin__simps_I4_J,axiom,
    ! [X99] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X99)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X99)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__bin__simps_I4_J) ).

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

fof(fact_foldl__conv__concat,axiom,
    ! [X286,X239,X5] : hAPP(c_List_Ofoldl(tc_List_Olist(X5),tc_List_Olist(X5),c_List_Oappend(X5),X239),X286) = hAPP(hAPP(c_List_Oappend(X5),X239),c_List_Oconcat(X5,X286)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldl__conv__concat) ).

fof(fact_diff__bin__simps_I10_J,axiom,
    ! [X99,X96] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(X96)),c_Int_OBit1(X99)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X96),X99)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__bin__simps_I10_J) ).

fof(fact_insort__insert__insort,axiom,
    ! [X239,X25,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X239)))
       => c_List_Olinorder__class_Oinsort__insert__key(X5,X5,c_COMBI(X5),X25,X239) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X5,c_COMBI(X5)),X25),X239) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insort__insert__insort) ).

fof(fact_irrefl__def,axiom,
    ! [X171,X5] :
      ( c_Relation_Oirrefl(X5,X171)
    <=> ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X3)),X171)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_irrefl__def) ).

fof(fact_wf__not__refl,axiom,
    ! [X6,X171,X5] :
      ( c_Wellfounded_Owf(X5,X171)
     => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X6)),X171)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__not__refl) ).

fof(fact_wf__irrefl,axiom,
    ! [X6,X171,X5] :
      ( c_Wellfounded_Owf(X5,X171)
     => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X6)),X171)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__irrefl) ).

fof(fact_rtrancl__unfold,axiom,
    ! [X171,X5] : c_Transitive__Closure_Ortrancl(X5,X171) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Relation_OId(X5)),hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),c_Transitive__Closure_Ortrancl(X5,X171)),X171)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__unfold) ).

fof(fact_INT__E,axiom,
    ! [X6,X113,X21,X20,X24,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X24),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X20,tc_fun(X5,tc_HOL_Obool)),X21),X113)))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X24),hAPP(X113,X6)))
       => ~ hBOOL(hAPP(hAPP(c_member(X20),X6),X21)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__E) ).

fof(fact_rel__simps_I22_J,axiom,
    ! [X87] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X87)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I22_J) ).

fof(fact_rel__simps_I5_J,axiom,
    ! [X87] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X87)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I5_J) ).

fof(fact_rel__simps_I26_J,axiom,
    ! [X87] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X87)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I26_J) ).

fof(fact_rel__simps_I9_J,axiom,
    ! [X87] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X87)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I9_J) ).

fof(fact_power__number__of__even__number__of,axiom,
    ! [X121,X123,X5] :
      ( class_Int_Onumber__ring(X5)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X123)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X121))) = hAPP(hAPP(c_HOL_OLet(X5,X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X123)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X121))),hAPP(hAPP(c_COMBS(X5,X5,X5),c_Groups_Otimes__class_Otimes(X5)),c_COMBI(X5))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__number__of__even__number__of) ).

fof(fact_image__minus__const__atLeastLessThan__nat,axiom,
    ! [X25,X33,X23] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23),X33))
       => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X23)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X25),X33)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25),X23)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X33),X23)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23),X33))
       => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),X33))
           => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X23)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X25),X33)) = 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),X25),X33))
           => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X23)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X25),X33)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__minus__const__atLeastLessThan__nat) ).

fof(fact_foldl__foldr1,axiom,
    ! [X239,X5] :
      ( class_Groups_Omonoid__add(X5)
     => hAPP(c_List_Ofoldl(X5,X5,c_Groups_Oplus__class_Oplus(X5),c_Groups_Ozero__class_Ozero(X5)),X239) = c_List_Ofoldr(X5,X5,c_Groups_Oplus__class_Oplus(X5),X239,c_Groups_Ozero__class_Ozero(X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldl__foldr1) ).

fof(fact_nth__map__upt,axiom,
    ! [X2,X5,X95,X50,X82] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X82),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X50),X95)))
     => hAPP(hAPP(c_List_Onth(X5),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X5),X2),c_List_Oupt(X95,X50))),X82) = hAPP(X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X95),X82)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__map__upt) ).

fof(fact_rotate__rotate,axiom,
    ! [X242,X57,X72,X58] : hAPP(c_List_Orotate(X58,X72),hAPP(c_List_Orotate(X58,X57),X242)) = hAPP(c_List_Orotate(X58,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X72),X57)),X242),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate__rotate) ).

fof(fact_foldr__conv__foldl,axiom,
    ! [X6,X239,X5] :
      ( class_Groups_Oab__semigroup__add(X5)
     => c_List_Ofoldr(X5,X5,c_Groups_Oplus__class_Oplus(X5),X239,X6) = hAPP(c_List_Ofoldl(X5,X5,c_Groups_Oplus__class_Oplus(X5),X6),X239) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldr__conv__foldl) ).

fof(fact_lazy__sequence_Osimps_I4_J,axiom,
    ! [X89,X19,X20,X5] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X5,X20,X19,X89,c_Lazy__Sequence_Olazy__sequence_OEmpty(X20)) = X19,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lazy__sequence_Osimps_I4_J) ).

fof(fact_rotate__conv__mod,axiom,
    ! [X242,X57,X58] : hAPP(c_List_Orotate(X58,X57),X242) = hAPP(c_List_Orotate(X58,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X57,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242))),X242),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate__conv__mod) ).

fof(fact_pred__Bit0,axiom,
    ! [X96] : c_Int_Opred(c_Int_OBit0(X96)) = c_Int_OBit1(c_Int_Opred(X96)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__Bit0) ).

fof(fact_setprod__diff1,axiom,
    ! [X6,X2,X21,X5,X20] :
      ( class_Fields_Ofield(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( hAPP(X2,X6) != c_Groups_Ozero__class_Ozero(X20)
         => ( ( hBOOL(hAPP(hAPP(c_member(X5),X6),X21))
             => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X20),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X2),X21)),hAPP(X2,X6)) )
            & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X21))
             => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X2),X21) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__diff1) ).

fof(fact_refl__reflcl,axiom,
    ! [X171,X5] : c_Relation_Orefl__on(X5,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X171),c_Relation_OId(X5))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__reflcl) ).

fof(fact_takeWhile__dropWhile__id,axiom,
    ! [X239,X18,X5] : hAPP(hAPP(c_List_Oappend(X5),c_List_OtakeWhile(X5,X18,X239)),c_List_OdropWhile(X5,X18,X239)) = X239,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_takeWhile__dropWhile__id) ).

fof(fact_setsum__diff1,axiom,
    ! [X2,X6,X21,X5,X20] :
      ( class_Groups_Oab__group__add(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( ( hBOOL(hAPP(hAPP(c_member(X5),X6),X21))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X2),X21)),hAPP(X2,X6)) )
          & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X21))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X2),X21) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__diff1) ).

fof(fact_set__concat,axiom,
    ! [X239,X5] : hAPP(c_List_Oset(X5),c_List_Oconcat(X5,X239)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(X5),tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(X5)),X239)),c_List_Oset(X5)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__concat) ).

fof(fact_length__concat,axiom,
    ! [X286,X5] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_Oconcat(X5,X286)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X5),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X5))),X286)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__concat) ).

fof(fact_INF1__E,axiom,
    ! [X6,X24,X113,X21,X20,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X20,tc_HOL_Obool)),X21),X113),X24))
     => ( ~ hBOOL(hAPP(hAPP(X113,X6),X24))
       => ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X21)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF1__E) ).

fof(fact_trans__diff__Id,axiom,
    ! [X171,X5] :
      ( c_Relation_Otrans(X5,X171)
     => ( c_Relation_Oantisym(X5,X171)
       => c_Relation_Otrans(X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X171),c_Relation_OId(X5))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__diff__Id) ).

fof(fact_foldr__max__sorted,axiom,
    ! [X33,X239,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( c_List_Olinorder__class_Osorted(X5,hAPP(c_List_Orev(X5),X239))
       => ( ( X239 = c_List_Olist_ONil(X5)
           => c_List_Ofoldr(X5,X5,c_Orderings_Oord__class_Omax(X5),X239,X33) = X33 )
          & ( X239 != c_List_Olist_ONil(X5)
           => c_List_Ofoldr(X5,X5,c_Orderings_Oord__class_Omax(X5),X239,X33) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),hAPP(hAPP(c_List_Onth(X5),X239),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X33) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldr__max__sorted) ).

fof(fact_trans__reflclI,axiom,
    ! [X171,X5] :
      ( c_Relation_Otrans(X5,X171)
     => c_Relation_Otrans(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X171),c_Relation_OId(X5))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__reflclI) ).

fof(fact_length__filter__less,axiom,
    ! [X18,X239,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X239)))
     => ( ~ hBOOL(hAPP(X18,X25))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),hAPP(c_List_Ofilter(X5,X18),X239))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__filter__less) ).

fof(fact_rtrancl__reflcl,axiom,
    ! [X32,X5] : c_Transitive__Closure_Ortrancl(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X32),c_Relation_OId(X5))) = c_Transitive__Closure_Ortrancl(X5,X32),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__reflcl) ).

fof(fact_rtrancl__r__diff__Id,axiom,
    ! [X171,X5] : c_Transitive__Closure_Ortrancl(X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X171),c_Relation_OId(X5))) = c_Transitive__Closure_Ortrancl(X5,X171),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__r__diff__Id) ).

fof(fact_irrefl__diff__Id,axiom,
    ! [X171,X5] : c_Relation_Oirrefl(X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X171),c_Relation_OId(X5))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_irrefl__diff__Id) ).

fof(fact_divmod__int__relI,axiom,
    ! [X134,X140,X90,X62] :
      ( X62 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X90),X140)),X134)
     => ( ( ( 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)),X134))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X134),X90)) ) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X90))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X90),X134))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X134),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
       => hBOOL(hAPP(c_Divides_Odivmod__int__rel(X62,X90),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X140),X134))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__int__relI) ).

fof(fact_diff__bin__simps_I5_J,axiom,
    ! [X99] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X99)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X99)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__bin__simps_I5_J) ).

fof(fact_setsum__diff1__nat,axiom,
    ! [X2,X21,X6,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X6),X21))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),X2),X21)),hAPP(X2,X6)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X21))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),X2),X21) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__diff1__nat) ).

fof(fact_wf__converse__trancl,axiom,
    ! [X171,X5] :
      ( c_Wellfounded_Owf(X5,hAPP(c_Relation_Oconverse(X5,X5),X171))
     => c_Wellfounded_Owf(X5,hAPP(c_Relation_Oconverse(X5,X5),c_Transitive__Closure_Otrancl(X5,X171))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__converse__trancl) ).

fof(fact_concat__eq__Nil__conv,axiom,
    ! [X286,X5] :
      ( c_List_Oconcat(X5,X286) = c_List_Olist_ONil(X5)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X3),hAPP(c_List_Oset(tc_List_Olist(X5)),X286)))
         => X3 = c_List_Olist_ONil(X5) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_concat__eq__Nil__conv) ).

fof(fact_Nil__eq__concat__conv,axiom,
    ! [X286,X5] :
      ( c_List_Olist_ONil(X5) = c_List_Oconcat(X5,X286)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X3),hAPP(c_List_Oset(tc_List_Olist(X5)),X286)))
         => X3 = c_List_Olist_ONil(X5) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nil__eq__concat__conv) ).

fof(fact_upt__add__eq__append,axiom,
    ! [X96,X97,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X98),X97))
     => c_List_Oupt(X98,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X97),X96)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X98,X97)),c_List_Oupt(X97,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X97),X96))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_upt__add__eq__append) ).

fof(fact_setsum__cl__ivl__Suc,axiom,
    ! [X2,X95,X50,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X50)),X95))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X95,hAPP(c_Nat_OSuc,X50))) = c_Groups_Ozero__class_Ozero(X5) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X50)),X95))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X95,hAPP(c_Nat_OSuc,X50))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X95,X50))),hAPP(X2,hAPP(c_Nat_OSuc,X50))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__cl__ivl__Suc) ).

fof(fact_UnE,axiom,
    ! [X113,X21,X23,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X23),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113)))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X23),X21))
       => hBOOL(hAPP(hAPP(c_member(X5),X23),X113)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UnE) ).

fof(fact_dropWhile__eq__Nil__conv,axiom,
    ! [X239,X18,X5] :
      ( c_List_OdropWhile(X5,X18,X239) = c_List_Olist_ONil(X5)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X239)))
         => hBOOL(hAPP(X18,X3)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dropWhile__eq__Nil__conv) ).

fof(fact_folding_Oinsert,axiom,
    ! [X25,X21,X205,X2,X20,X5] :
      ( c_Finite__Set_Ofolding(X5,X20,X2,X205)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => hAPP(X205,hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(c_Fun_Ocomp(X20,X20,X20,hAPP(X205,X21)),hAPP(X2,X25)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Oinsert) ).

fof(fact_sorted__dropWhile,axiom,
    ! [X18,X239,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( c_List_Olinorder__class_Osorted(X5,X239)
       => c_List_Olinorder__class_Osorted(X5,c_List_OdropWhile(X5,X18,X239)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__dropWhile) ).

fof(fact_in__set__conv__decomp__last,axiom,
    ! [X239,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X239)))
    <=> ? [X262,X289] :
          ( X239 = hAPP(hAPP(c_List_Oappend(X5),X262),hAPP(hAPP(c_List_Olist_OCons(X5),X25),X289))
          & ~ hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X289))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__set__conv__decomp__last) ).

fof(fact_in__set__conv__decomp__first,axiom,
    ! [X239,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X239)))
    <=> ? [X262] :
          ( ? [X289] : X239 = hAPP(hAPP(c_List_Oappend(X5),X262),hAPP(hAPP(c_List_Olist_OCons(X5),X25),X289))
          & ~ hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X262))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__set__conv__decomp__first) ).

fof(fact_succ__Bit1,axiom,
    ! [X96] : c_Int_Osucc(c_Int_OBit1(X96)) = c_Int_OBit0(c_Int_Osucc(X96)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_succ__Bit1) ).

fof(fact_evaln__elim__cases_I6_J,axiom,
    ! [X45,X57,X48,X49] :
      ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X49),X48,X57,X45)
     => ~ ! [X69] :
            ( X57 = hAPP(c_Nat_OSuc,X69)
           => ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X49)),X48,X69,X45) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln__elim__cases_I6_J) ).

fof(fact_power__number__of__even,axiom,
    ! [X121,X120,X5] :
      ( class_Int_Onumber__ring(X5)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X5),X120),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X121))) = hAPP(hAPP(c_HOL_OLet(X5,X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X120),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X121))),hAPP(hAPP(c_COMBS(X5,X5,X5),c_Groups_Otimes__class_Otimes(X5)),c_COMBI(X5))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__number__of__even) ).

fof(fact_Diff__iff,axiom,
    ! [X113,X21,X23,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X23),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),X113)))
    <=> ( hBOOL(hAPP(hAPP(c_member(X5),X23),X21))
        & ~ hBOOL(hAPP(hAPP(c_member(X5),X23),X113)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__iff) ).

fof(fact_DiffD2,axiom,
    ! [X113,X21,X23,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X23),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),X113)))
     => ~ hBOOL(hAPP(hAPP(c_member(X5),X23),X113)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DiffD2) ).

fof(fact_transfer__nat__int__list__functions_I1_J,axiom,
    ! [X72,X99] : hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),X99),X72) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint),c_List_Oembed__list(X99)),c_List_Oembed__list(X72))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__list__functions_I1_J) ).

fof(fact_return__list__def,axiom,
    ! [X156] : c_List_Oreturn__list(X156) = hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),X156),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_return__list__def) ).

fof(fact_embed__list__def,axiom,
    ! [X156] : c_List_Oembed__list(X156) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X156),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_embed__list__def) ).

fof(fact_card__Suc__eq,axiom,
    ! [X87,X21,X5] :
      ( hAPP(c_Finite__Set_Ocard(X5),X21) = hAPP(c_Nat_OSuc,X87)
    <=> ? [X188,X211] :
          ( X21 = hAPP(hAPP(c_Set_Oinsert(X5),X188),X211)
          & ~ hBOOL(hAPP(hAPP(c_member(X5),X188),X211))
          & hAPP(c_Finite__Set_Ocard(X5),X211) = X87
          & ( X87 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
           => X211 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Suc__eq) ).

fof(fact_distinct__remove1__removeAll,axiom,
    ! [X66,X242,X58] :
      ( hBOOL(hAPP(c_List_Odistinct(X58),X242))
     => c_List_Oremove1(X58,X66,X242) = hAPP(c_List_OremoveAll(X58,X66),X242) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__remove1__removeAll) ).

fof(fact_take__upt,axiom,
    ! [X57,X72,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),X72)),X57))
     => hAPP(hAPP(c_List_Otake(tc_Nat_Onat),X72),c_List_Oupt(X98,X57)) = c_List_Oupt(X98,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),X72)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__upt) ).

fof(fact_rotate__map,axiom,
    ! [X239,X2,X20,X50,X5] : hAPP(c_List_Orotate(X5,X50),hAPP(hAPP(c_List_Omap(X20,X5),X2),X239)) = hAPP(hAPP(c_List_Omap(X20,X5),X2),hAPP(c_List_Orotate(X20,X50),X239)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate__map) ).

fof(fact_trancl__converse,axiom,
    ! [X171,X5] : c_Transitive__Closure_Otrancl(X5,hAPP(c_Relation_Oconverse(X5,X5),X171)) = hAPP(c_Relation_Oconverse(X5,X5),c_Transitive__Closure_Otrancl(X5,X171)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__converse) ).

fof(fact_insort__key_Osimps_I2_J,axiom,
    ! [X251,X20,X33,X25,X2,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(X2,X25)),hAPP(X2,X33)))
         => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X20,X5,X2),X25),hAPP(hAPP(c_List_Olist_OCons(X20),X33),X251)) = hAPP(hAPP(c_List_Olist_OCons(X20),X25),hAPP(hAPP(c_List_Olist_OCons(X20),X33),X251)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(X2,X25)),hAPP(X2,X33)))
         => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X20,X5,X2),X25),hAPP(hAPP(c_List_Olist_OCons(X20),X33),X251)) = hAPP(hAPP(c_List_Olist_OCons(X20),X33),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X20,X5,X2),X25),X251)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insort__key_Osimps_I2_J) ).

fof(fact_upto__rec__number__of,axiom,
    ! [X57,X72] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X72)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X57)))
       => c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X72),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X57)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X72)),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X72)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X57))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X72)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X57)))
       => c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X72),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X57)) = c_List_Olist_ONil(tc_Int_Oint) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_upto__rec__number__of) ).

fof(fact_subset__insert,axiom,
    ! [X113,X21,X25,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),X113)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),X113)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__insert) ).

fof(fact_IntE,axiom,
    ! [X113,X21,X23,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X23),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113)))
     => ~ ( hBOOL(hAPP(hAPP(c_member(X5),X23),X21))
         => ~ hBOOL(hAPP(hAPP(c_member(X5),X23),X113)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_IntE) ).

fof(fact_upto_Opsimps,axiom,
    ! [X157,X82] :
      ( 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),X82),X157)))
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X82),X157))
         => c_List_Oupto(X82,X157) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),X82),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X82),c_Groups_Oone__class_Oone(tc_Int_Oint)),X157)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X82),X157))
         => c_List_Oupto(X82,X157) = c_List_Olist_ONil(tc_Int_Oint) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_upto_Opsimps) ).

fof(fact_fun__left__comm_Ofold__insert,axiom,
    ! [X120,X25,X21,X2,X20,X5] :
      ( c_Finite__Set_Ofun__left__comm(X5,X20,X2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => hAPP(hAPP(c_Finite__Set_Ofold(X5,X20,X2),X120),hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(hAPP(X2,X25),hAPP(hAPP(c_Finite__Set_Ofold(X5,X20,X2),X120),X21)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__insert) ).

fof(fact_evalc_OIfFalse,axiom,
    ! [X103,X104,X105,X76,X24] :
      ( ~ hBOOL(hAPP(X24,X76))
     => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X105),X76),X104))
       => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X24,X103,X105)),X76),X104)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_OIfFalse) ).

fof(fact_small__lazy_H_Opsimps,axiom,
    ! [X82,X22] :
      ( 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),X22),X82)))
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22),X82))
         => c_Lazy__Sequence_Osmall__lazy_H(X22,X82) = c_Lazy__Sequence_Oempty(tc_Int_Oint) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22),X82))
         => c_Lazy__Sequence_Osmall__lazy_H(X22,X82) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),X82),c_Lazy__Sequence_Osmall__lazy_H(X22,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X82),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_small__lazy_H_Opsimps) ).

fof(fact_notin__set__remove1,axiom,
    ! [X33,X239,X25,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X239)))
     => ~ hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),c_List_Oremove1(X5,X33,X239)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_notin__set__remove1) ).

fof(fact_notin__set__sublistI,axiom,
    ! [X221,X239,X25,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X239)))
     => ~ hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),c_List_Osublist(X5,X239,X221)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_notin__set__sublistI) ).

fof(fact_nth__upt,axiom,
    ! [X97,X96,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),X96)),X97))
     => hAPP(hAPP(c_List_Onth(tc_Nat_Onat),c_List_Oupt(X98,X97)),X96) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),X96) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__upt) ).

fof(fact_zpower__number__of__even,axiom,
    ! [X121,X120] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X120),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X121))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X120),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X121))),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/sandbox/benchmark/theBenchmark.p',fact_zpower__number__of__even) ).

fof(fact_less__fun__def,axiom,
    ! [X1,X2,X5,X20] :
      ( class_Orderings_Oord(X20)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,X20)),X2),X1))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X20)),X2),X1))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X20)),X1),X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__fun__def) ).

fof(fact_pick_Osimps,axiom,
    ! [X242,X66,X58,X98] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X98),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X58),X66)))
       => hAPP(c_Random_Opick(X58,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X58)),X66),X242)),X98) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X58),X66) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X98),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X58),X66)))
       => hAPP(c_Random_Opick(X58,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X58)),X66),X242)),X98) = hAPP(c_Random_Opick(X58,X242),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X98),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X58),X66))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pick_Osimps) ).

fof(fact_UnionE,axiom,
    ! [X112,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X21),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X112)))
     => ~ ! [X291] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X21),X291))
           => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X291),X112)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UnionE) ).

fof(fact_rel__simps_I31_J,axiom,
    ! [X156,X87] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X87)),c_Int_OBit0(X156)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X87),X156)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I31_J) ).

fof(fact_less__eq__int__code_I13_J,axiom,
    ! [X169,X170] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X170)),c_Int_OBit0(X169)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X170),X169)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__int__code_I13_J) ).

fof(fact_rel__simps_I14_J,axiom,
    ! [X156,X87] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X87)),c_Int_OBit0(X156)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X87),X156)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I14_J) ).

fof(fact_less__int__code_I13_J,axiom,
    ! [X169,X170] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X170)),c_Int_OBit0(X169)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X170),X169)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__int__code_I13_J) ).

fof(fact_removeAll_Osimps_I1_J,axiom,
    ! [X66,X58] : hAPP(c_List_OremoveAll(X58,X66),c_List_Olist_ONil(X58)) = c_List_Olist_ONil(X58),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_removeAll_Osimps_I1_J) ).

fof(fact_card__Diff__singleton__if,axiom,
    ! [X25,X21,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
     => ( ( hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X21)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
        & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(X5),X21) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Diff__singleton__if) ).

fof(fact_add__special_I3_J,axiom,
    ! [X136,X58] :
      ( class_Int_Onumber__ring(X58)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(c_Int_Onumber__class_Onumber__of(X58),X136)),c_Groups_Oone__class_Oone(X58)) = hAPP(c_Int_Onumber__class_Onumber__of(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X136),c_Int_OBit1(c_Int_OPls))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__special_I3_J) ).

fof(fact_le__number__of__eq__not__less,axiom,
    ! [X121,X123,X5] :
      ( ( class_Int_Onumber(X5)
        & class_Orderings_Olinorder(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X123)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)))
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X123))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__number__of__eq__not__less) ).

fof(fact_bot2E,axiom,
    ! [X33,X25,X20,X5] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_fun(X20,tc_HOL_Obool))),X25),X33)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot2E) ).

fof(fact_evaln_Oequations_I6_J,axiom,
    ! [X59,X60,X26,X63,X77,X27] :
      ( c_Natural_Oevaln(c_Com_Ocom_OCond(X27,X77,X63),X26,X60,X59)
    <=> ( ( hBOOL(hAPP(X27,X26))
          & c_Natural_Oevaln(X77,X26,X60,X59) )
        | ( ~ hBOOL(hAPP(X27,X26))
          & c_Natural_Oevaln(X63,X26,X60,X59) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_Oequations_I6_J) ).

fof(fact_evaln_Oequations_I5_J,axiom,
    ! [X59,X60,X26,X77,X63,X27] :
      ( c_Natural_Oevaln(c_Com_Ocom_OCond(X27,X63,X77),X26,X60,X59)
    <=> ( ( hBOOL(hAPP(X27,X26))
          & c_Natural_Oevaln(X63,X26,X60,X59) )
        | ( ~ hBOOL(hAPP(X27,X26))
          & c_Natural_Oevaln(X77,X26,X60,X59) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_Oequations_I5_J) ).

fof(fact_evaln__elim__cases_I5_J,axiom,
    ! [X15,X50,X76,X106,X105,X24] :
      ( c_Natural_Oevaln(c_Com_Ocom_OCond(X24,X105,X106),X76,X50,X15)
     => ( ( hBOOL(hAPP(X24,X76))
         => ~ c_Natural_Oevaln(X105,X76,X50,X15) )
       => ~ ( ~ hBOOL(hAPP(X24,X76))
           => ~ c_Natural_Oevaln(X106,X76,X50,X15) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln__elim__cases_I5_J) ).

fof(fact_divmod__int__rel__mod__eq,axiom,
    ! [X65,X147,X148,X149] :
      ( X149 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X148),X147)),X65)
     => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X148))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X65))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X65),X148)) ) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X148))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X148),X65))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X65),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
       => ( X148 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => c_Divides_Odiv__class_Omod(tc_Int_Oint,X149,X148) = X65 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__int__rel__mod__eq) ).

fof(fact_foldr_Osimps_I1_J,axiom,
    ! [X6,X2,X5,X20] : c_List_Ofoldr(X20,X5,X2,c_List_Olist_ONil(X20),X6) = X6,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldr_Osimps_I1_J) ).

fof(fact_concat__map__maps,axiom,
    ! [X239,X2,X20,X5] : c_List_Oconcat(X5,hAPP(hAPP(c_List_Omap(X20,tc_List_Olist(X5)),X2),X239)) = c_List_Omaps(X20,X5,X2,X239),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_concat__map__maps) ).

fof(fact_maps__def,axiom,
    ! [X239,X2,X5,X20] : c_List_Omaps(X20,X5,X2,X239) = c_List_Oconcat(X5,hAPP(hAPP(c_List_Omap(X20,tc_List_Olist(X5)),X2),X239)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_maps__def) ).

fof(fact_divmod__int__rel__div__eq,axiom,
    ! [X152,X65,X148,X149] :
      ( X149 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X148),X65)),X152)
     => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X148))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X152))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X152),X148)) ) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X148))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X148),X152))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X152),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
       => ( X148 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X149),X148) = X65 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__int__rel__div__eq) ).

fof(fact_rotate__Suc,axiom,
    ! [X242,X57,X58] : hAPP(c_List_Orotate(X58,hAPP(c_Nat_OSuc,X57)),X242) = hAPP(c_List_Orotate1(X58),hAPP(c_List_Orotate(X58,X57),X242)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate__Suc) ).

fof(fact_fun__left__comm_Ofold__insert2,axiom,
    ! [X120,X25,X21,X2,X20,X5] :
      ( c_Finite__Set_Ofun__left__comm(X5,X20,X2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => hAPP(hAPP(c_Finite__Set_Ofold(X5,X20,X2),X120),hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X20,X2),hAPP(hAPP(X2,X25),X120)),X21) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__insert2) ).

fof(fact_upt__eq__Cons__conv,axiom,
    ! [X239,X25,X157,X82] :
      ( c_List_Oupt(X82,X157) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X25),X239)
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X82),X157))
        & X82 = X25
        & c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X82),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X157) = X239 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_upt__eq__Cons__conv) ).

fof(fact_setsum__op__ivl__Suc,axiom,
    ! [X2,X95,X50,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X50),X95))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X95),hAPP(c_Nat_OSuc,X50))) = c_Groups_Ozero__class_Ozero(X5) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X50),X95))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X95),hAPP(c_Nat_OSuc,X50))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X95),X50))),hAPP(X2,X50)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__op__ivl__Suc) ).

fof(fact_sup1E,axiom,
    ! [X25,X113,X21,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113),X25))
     => ( ~ hBOOL(hAPP(X21,X25))
       => hBOOL(hAPP(X113,X25)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup1E) ).

fof(fact_pred__Bit1,axiom,
    ! [X96] : c_Int_Opred(c_Int_OBit1(X96)) = c_Int_OBit0(X96),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__Bit1) ).

fof(fact_nat__number__of__add__left,axiom,
    ! [X96,X164,X136] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X164)),X96)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X164)),X96) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)))
       => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X164)))
           => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X164)),X96)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)),X96) )
          & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X164)))
           => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X164)),X96)) = 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),X136),X164))),X96) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__number__of__add__left) ).

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

fof(fact_setsum__set__upt__conv__listsum__nat,axiom,
    ! [X50,X95,X2,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X95,X50))) = hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X5),X2),c_List_Oupt(X95,X50))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__set__upt__conv__listsum__nat) ).

fof(fact_interv__listsum__conv__setsum__set__nat,axiom,
    ! [X50,X95,X2,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X5),X2),c_List_Oupt(X95,X50))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X95,X50))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_interv__listsum__conv__setsum__set__nat) ).

fof(fact_inf1E,axiom,
    ! [X25,X113,X21,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113),X25))
     => ~ ( hBOOL(hAPP(X21,X25))
         => ~ hBOOL(hAPP(X113,X25)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf1E) ).

fof(fact_rotate1__rotate__swap,axiom,
    ! [X242,X57,X58] : hAPP(c_List_Orotate1(X58),hAPP(c_List_Orotate(X58,X57),X242)) = hAPP(c_List_Orotate(X58,X57),hAPP(c_List_Orotate1(X58),X242)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate1__rotate__swap) ).

fof(fact_number__of__Bit1,axiom,
    ! [X128,X58] :
      ( class_Int_Onumber__ring(X58)
     => hAPP(c_Int_Onumber__class_Onumber__of(X58),c_Int_OBit1(X128)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),c_Groups_Oone__class_Oone(X58)),hAPP(c_Int_Onumber__class_Onumber__of(X58),X128))),hAPP(c_Int_Onumber__class_Onumber__of(X58),X128)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__Bit1) ).

fof(fact_DiffI,axiom,
    ! [X113,X21,X23,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X23),X21))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X23),X113))
       => hBOOL(hAPP(hAPP(c_member(X5),X23),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),X113))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DiffI) ).

fof(fact_code__numeral_Orecs_I2_J,axiom,
    ! [X174,X89,X19,X5] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X5,X19,X89,c_Code__Numeral_OSuc__code__numeral(X174)) = hAPP(hAPP(X89,X174),c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X5,X19,X89,X174)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_code__numeral_Orecs_I2_J) ).

fof(fact_Suc__code__numeral__def,axiom,
    ! [X96] : c_Code__Numeral_OSuc__code__numeral(X96) = hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X96))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__code__numeral__def) ).

fof(fact_card__def,axiom,
    ! [X21,X5] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => hAPP(c_Finite__Set_Ocard(X5),X21) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,X5,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,X5),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X21) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => hAPP(c_Finite__Set_Ocard(X5),X21) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__def) ).

fof(fact_Id__O__R,axiom,
    ! [X32,X20,X5] : hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X20),c_Relation_OId(X5)),X32) = X32,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Id__O__R) ).

fof(fact_divide__Numeral1,axiom,
    ! [X66,X58] :
      ( ( class_Fields_Ofield(X58)
        & class_Int_Onumber__ring(X58) )
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X66),hAPP(c_Int_Onumber__class_Onumber__of(X58),c_Int_OBit1(c_Int_OPls))) = X66 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__Numeral1) ).

fof(fact_divide__numeral__1,axiom,
    ! [X62,X58] :
      ( ( class_Fields_Ofield(X58)
        & class_Int_Onumber__ring(X58) )
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X62),hAPP(c_Int_Onumber__class_Onumber__of(X58),c_Int_OBit1(c_Int_OPls))) = X62 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__numeral__1) ).

fof(fact_le__supE,axiom,
    ! [X66,X90,X62,X58] :
      ( class_Lattices_Osemilattice__sup(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X62),X90)),X66))
       => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X62),X66))
           => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X90),X66)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__supE) ).

fof(fact_min__max_Ole__supE,axiom,
    ! [X66,X90,X62,X58] :
      ( class_Orderings_Olinorder(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Orderings_Oord__class_Omax(X58),X62),X90)),X66))
       => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X62),X66))
           => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X90),X66)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ole__supE) ).

fof(fact_mult__numeral__1__right,axiom,
    ! [X62,X58] :
      ( class_Int_Onumber__ring(X58)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),hAPP(c_Int_Onumber__class_Onumber__of(X58),c_Int_OBit1(c_Int_OPls))) = X62 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__numeral__1__right) ).

fof(fact_member__rec_I1_J,axiom,
    ! [X33,X239,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_List_Omember(X5),hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239)),X33))
    <=> ( X25 = X33
        | hBOOL(hAPP(hAPP(c_List_Omember(X5),X239),X33)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_member__rec_I1_J) ).

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

fof(fact_hd__rotate__conv__nth,axiom,
    ! [X57,X58,X242] :
      ( X242 != c_List_Olist_ONil(X58)
     => hAPP(c_List_Ohd(X58),hAPP(c_List_Orotate(X58,X57),X242)) = hAPP(hAPP(c_List_Onth(X58),X242),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X57,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hd__rotate__conv__nth) ).

fof(fact_nat__number__of__mult__left,axiom,
    ! [X96,X164,X136] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X136),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X164)),X96)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X136),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X164)),X96)) = 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),X136),X164))),X96) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__number__of__mult__left) ).

fof(fact_rotate__length01,axiom,
    ! [X57,X242,X58] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
     => hAPP(c_List_Orotate(X58,X57),X242) = X242 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate__length01) ).

fof(fact_Int__insert__left,axiom,
    ! [X113,X112,X6,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X6),X112))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X6),X113)),X112) = hAPP(hAPP(c_Set_Oinsert(X5),X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X113),X112)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X112))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X6),X113)),X112) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X113),X112) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__insert__left) ).

fof(fact_UnCI,axiom,
    ! [X21,X113,X23,X5] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X5),X23),X113))
       => hBOOL(hAPP(hAPP(c_member(X5),X23),X21)) )
     => hBOOL(hAPP(hAPP(c_member(X5),X23),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UnCI) ).

fof(fact_not__square__less__zero,axiom,
    ! [X62,X58] :
      ( class_Rings_Olinordered__ring(X58)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X62)),c_Groups_Ozero__class_Ozero(X58))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__square__less__zero) ).

fof(fact_bin__less__0__simps_I3_J,axiom,
    ! [X121] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X121)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X121),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bin__less__0__simps_I3_J) ).

fof(fact_zdiv__number__of__Bit0,axiom,
    ! [X128,X136] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X136))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X128))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__number__of__Bit0) ).

fof(fact_add__leE,axiom,
    ! [X57,X96,X72] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X72),X96)),X57))
     => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X72),X57))
         => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X96),X57)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leE) ).

fof(fact_rel__simps_I27_J,axiom,
    ! [X87] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X87)),c_Int_OPls))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X87),c_Int_OPls)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I27_J) ).

fof(fact_rel__simps_I28_J,axiom,
    ! [X87] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X87)),c_Int_OMin))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X87),c_Int_OMin)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I28_J) ).

fof(fact_rel__simps_I11_J,axiom,
    ! [X87] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X87)),c_Int_OMin))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X87),c_Int_OMin)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I11_J) ).

fof(fact_rel__simps_I10_J,axiom,
    ! [X87] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X87)),c_Int_OPls))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X87),c_Int_OPls)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I10_J) ).

fof(fact_neg__number__of__Bit0,axiom,
    ! [X121] :
      ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X121))))
    <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X121))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__number__of__Bit0) ).

fof(fact_Image__Id,axiom,
    ! [X21,X5] : hAPP(c_Relation_OImage(X5,X5,c_Relation_OId(X5)),X21) = X21,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__Id) ).

fof(fact_insert__Diff__if,axiom,
    ! [X21,X113,X25,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X25),X113))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)),X113) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),X113) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X113))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)),X113) = hAPP(hAPP(c_Set_Oinsert(X5),X25),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),X113)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__Diff__if) ).

fof(fact_le__iff__pred__less,axiom,
    ! [X156,X87] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X87),X156))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(X87)),X156)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__iff__pred__less) ).

fof(fact_diff__bin__simps_I6_J,axiom,
    ! [X99] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X99)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X99)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__bin__simps_I6_J) ).

fof(fact_evaln_OIfFalse,axiom,
    ! [X103,X104,X50,X105,X76,X24] :
      ( ~ hBOOL(hAPP(X24,X76))
     => ( c_Natural_Oevaln(X105,X76,X50,X104)
       => c_Natural_Oevaln(c_Com_Ocom_OCond(X24,X103,X105),X76,X50,X104) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_OIfFalse) ).

fof(fact_div__if,axiom,
    ! [X72,X57] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X57))
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X72),X57))
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X72),X57) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X72),X57))
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X72),X57) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X72),X57)),X57)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__if) ).

fof(fact_div__geq,axiom,
    ! [X72,X57] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X57))
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X72),X57))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X72),X57) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X72),X57)),X57)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__geq) ).

fof(fact_not__zle__0__negative,axiom,
    ! [X57] : ~ 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,X57))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__zle__0__negative) ).

fof(fact_rtrancl__reflcl__absorb,axiom,
    ! [X32,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X5,X32)),c_Relation_OId(X5)) = c_Transitive__Closure_Ortrancl(X5,X32),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__reflcl__absorb) ).

fof(fact_upt__Suc__append,axiom,
    ! [X97,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X98),X97))
     => c_List_Oupt(X98,hAPP(c_Nat_OSuc,X97)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X98,X97)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X97),c_List_Olist_ONil(tc_Nat_Onat))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_upt__Suc__append) ).

fof(fact_Int__insert__right,axiom,
    ! [X113,X21,X6,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X6),X21))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X6),X113)) = hAPP(hAPP(c_Set_Oinsert(X5),X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X21))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X6),X113)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__insert__right) ).

fof(fact_setsum_OF__eq,axiom,
    ! [X1,X21,X5,X20] :
      ( class_Groups_Ocomm__monoid__add(X20)
     => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X1),X21) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X20,X5,c_Groups_Oplus__class_Oplus(X20)),X1),c_Groups_Ozero__class_Ozero(X20)),X21) )
        & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X1),X21) = c_Groups_Ozero__class_Ozero(X20) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum_OF__eq) ).

fof(fact_setprod_OF__eq,axiom,
    ! [X1,X21,X5,X20] :
      ( class_Groups_Ocomm__monoid__mult(X20)
     => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X1),X21) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X20,X5,c_Groups_Otimes__class_Otimes(X20)),X1),c_Groups_Oone__class_Oone(X20)),X21) )
        & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X1),X21) = c_Groups_Oone__class_Oone(X20) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod_OF__eq) ).

fof(fact_nth__append,axiom,
    ! [X241,X242,X58,X57] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X57),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242)))
       => hAPP(hAPP(c_List_Onth(X58),hAPP(hAPP(c_List_Oappend(X58),X242),X241)),X57) = hAPP(hAPP(c_List_Onth(X58),X242),X57) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X57),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242)))
       => hAPP(hAPP(c_List_Onth(X58),hAPP(hAPP(c_List_Oappend(X58),X242),X241)),X57) = hAPP(hAPP(c_List_Onth(X58),X241),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X57),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__append) ).

fof(fact_ComplE,axiom,
    ! [X21,X23,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X23),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X21)))
     => ~ hBOOL(hAPP(hAPP(c_member(X5),X23),X21)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ComplE) ).

fof(fact_ComplD,axiom,
    ! [X21,X23,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X23),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X21)))
     => ~ hBOOL(hAPP(hAPP(c_member(X5),X23),X21)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ComplD) ).

fof(fact_Compl__iff,axiom,
    ! [X21,X23,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X23),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X21)))
    <=> ~ hBOOL(hAPP(hAPP(c_member(X5),X23),X21)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__iff) ).

fof(fact_nat__number__of__Bit0,axiom,
    ! [X121] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X121)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X121)),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/sandbox/benchmark/theBenchmark.p',fact_nat__number__of__Bit0) ).

fof(fact_max__number__of,axiom,
    ! [X136,X55,X5] :
      ( ( class_Int_Onumber(X5)
        & class_Orderings_Oord(X5) )
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X55)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X136)))
         => hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X55)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X136)) = hAPP(c_Int_Onumber__class_Onumber__of(X5),X136) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X55)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X136)))
         => hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X55)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X136)) = hAPP(c_Int_Onumber__class_Onumber__of(X5),X55) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__number__of) ).

fof(fact_min__number__of,axiom,
    ! [X136,X55,X5] :
      ( ( class_Int_Onumber(X5)
        & class_Orderings_Oord(X5) )
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X55)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X136)))
         => hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X55)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X136)) = hAPP(c_Int_Onumber__class_Onumber__of(X5),X55) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X55)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X136)))
         => hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X55)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X136)) = hAPP(c_Int_Onumber__class_Onumber__of(X5),X136) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__number__of) ).

fof(fact_not__add__less1,axiom,
    ! [X97,X98] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),X97)),X98)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__add__less1) ).

fof(fact_not__add__less2,axiom,
    ! [X98,X97] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X97),X98)),X98)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__add__less2) ).

fof(fact_remove1__append,axiom,
    ! [X251,X239,X25,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X239)))
       => c_List_Oremove1(X5,X25,hAPP(hAPP(c_List_Oappend(X5),X239),X251)) = hAPP(hAPP(c_List_Oappend(X5),c_List_Oremove1(X5,X25,X239)),X251) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X239)))
       => c_List_Oremove1(X5,X25,hAPP(hAPP(c_List_Oappend(X5),X239),X251)) = hAPP(hAPP(c_List_Oappend(X5),X239),c_List_Oremove1(X5,X25,X251)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_remove1__append) ).

fof(fact_neg__number__of__pred__iff__0,axiom,
    ! [X123] :
      ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X123))))
    <=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X123) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__number__of__pred__iff__0) ).

fof(fact_empty__fold1SetE,axiom,
    ! [X25,X2,X5] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X5,X2,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),X25)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__fold1SetE) ).

fof(fact_rel__simps_I51_J,axiom,
    ! [X156,X87] :
      ( c_Int_OBit1(X87) = c_Int_OBit1(X156)
    <=> X87 = X156 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I51_J) ).

fof(fact_concat__replicate__trivial,axiom,
    ! [X98,X58] : c_List_Oconcat(X58,c_List_Oreplicate(tc_List_Olist(X58),X98,c_List_Olist_ONil(X58))) = c_List_Olist_ONil(X58),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_concat__replicate__trivial) ).

fof(fact_nat__diff__split__asm,axiom,
    ! [X24,X6,X18] :
      ( hBOOL(hAPP(X18,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X6),X24)))
    <=> ~ ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),X24))
            & ~ hBOOL(hAPP(X18,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
          | ? [X158] :
              ( X6 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),X158)
              & ~ hBOOL(hAPP(X18,X158)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__diff__split__asm) ).

fof(fact_distinct_Osimps_I2_J,axiom,
    ! [X239,X25,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239)))
    <=> ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X239)))
        & hBOOL(hAPP(c_List_Odistinct(X5),X239)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct_Osimps_I2_J) ).

fof(fact_length__rotate,axiom,
    ! [X242,X57,X58] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),hAPP(c_List_Orotate(X58,X57),X242)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__rotate) ).

fof(fact_dropWhile_Osimps_I1_J,axiom,
    ! [X18,X5] : c_List_OdropWhile(X5,X18,c_List_Olist_ONil(X5)) = c_List_Olist_ONil(X5),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dropWhile_Osimps_I1_J) ).

fof(fact_Diff__insert__absorb,axiom,
    ! [X21,X25,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = X21 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__insert__absorb) ).

fof(fact_setsum__insert,axiom,
    ! [X2,X6,X205,X5,X20] :
      ( class_Groups_Ocomm__monoid__add(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X205))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X205))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X2),hAPP(hAPP(c_Set_Oinsert(X5),X6),X205)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20),hAPP(X2,X6)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X2),X205)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__insert) ).

fof(fact_setsum_Oinsert,axiom,
    ! [X1,X25,X21,X5,X20] :
      ( class_Groups_Ocomm__monoid__add(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X1),hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20),hAPP(X1,X25)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X1),X21)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum_Oinsert) ).

fof(fact_setprod_Oinsert,axiom,
    ! [X1,X25,X21,X5,X20] :
      ( class_Groups_Ocomm__monoid__mult(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X1),hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20),hAPP(X1,X25)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X1),X21)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod_Oinsert) ).

fof(fact_setprod__insert,axiom,
    ! [X2,X6,X21,X5,X20] :
      ( class_Groups_Ocomm__monoid__mult(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X21))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X2),hAPP(hAPP(c_Set_Oinsert(X5),X6),X21)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20),hAPP(X2,X6)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X2),X21)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__insert) ).

fof(fact_drop__upt,axiom,
    ! [X97,X98,X72] : hAPP(hAPP(c_List_Odrop(tc_Nat_Onat),X72),c_List_Oupt(X98,X97)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),X72),X97),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__upt) ).

fof(fact_filter__empty__conv,axiom,
    ! [X239,X18,X5] :
      ( hAPP(c_List_Ofilter(X5,X18),X239) = c_List_Olist_ONil(X5)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X239)))
         => ~ hBOOL(hAPP(X18,X3)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter__empty__conv) ).

fof(fact_not__int__zless__negative,axiom,
    ! [X72,X57] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X57)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X72)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__int__zless__negative) ).

fof(fact_set__rotate,axiom,
    ! [X239,X50,X5] : hAPP(c_List_Oset(X5),hAPP(c_List_Orotate(X5,X50),X239)) = hAPP(c_List_Oset(X5),X239),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__rotate) ).

fof(fact_sup1CI,axiom,
    ! [X5,X21,X25,X113] :
      ( ( ~ hBOOL(hAPP(X113,X25))
       => hBOOL(hAPP(X21,X25)) )
     => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113),X25)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup1CI) ).

fof(fact_partition__P,axiom,
    ! [X278,X279,X239,X18,X5] :
      ( c_List_Opartition(X5,X18,X239) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X279),X278)
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X279)))
           => hBOOL(hAPP(X18,X3)) )
        & ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X278)))
           => ~ hBOOL(hAPP(X18,X3)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_partition__P) ).

fof(fact_trancl__domain,axiom,
    ! [X171,X5] : hAPP(c_Relation_ODomain(X5,X5),c_Transitive__Closure_Otrancl(X5,X171)) = hAPP(c_Relation_ODomain(X5,X5),X171),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__domain) ).

fof(fact_trancl__range,axiom,
    ! [X171,X5] : hAPP(c_Relation_ORange(X5,X5),c_Transitive__Closure_Otrancl(X5,X171)) = hAPP(c_Relation_ORange(X5,X5),X171),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__range) ).

fof(fact_le__nat__number__of,axiom,
    ! [X168,X123] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X123)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X168)))
    <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X123),X168))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X123),c_Int_OPls)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__nat__number__of) ).

fof(fact_diff__bin__simps_I7_J,axiom,
    ! [X99,X96] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(X96)),c_Int_OBit0(X99)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X96),X99)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__bin__simps_I7_J) ).

fof(fact_add__Bit0__Bit0,axiom,
    ! [X99,X96] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(X96)),c_Int_OBit0(X99)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X96),X99)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Bit0__Bit0) ).

fof(fact_folding__one_Oeq__fold_H,axiom,
    ! [X25,X21,X205,X2,X5] :
      ( c_Finite__Set_Ofolding__one(X5,X2,X205)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => hAPP(X205,hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,X2),X25),X21) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one_Oeq__fold_H) ).

fof(fact_Abs__Integ__cases,axiom,
    ! [X25] :
      ~ ! [X177] :
          ( X25 = hAPP(c_Int_OAbs__Integ,X177)
         => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X177),c_Int_OInteg)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Abs__Integ__cases) ).

fof(fact_upt__conv__Cons,axiom,
    ! [X97,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),X97))
     => c_List_Oupt(X98,X97) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X98),c_List_Oupt(hAPP(c_Nat_OSuc,X98),X97)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_upt__conv__Cons) ).

fof(fact_filter__insort__triv,axiom,
    ! [X239,X2,X5,X25,X18,X20] :
      ( class_Orderings_Olinorder(X20)
     => ( ~ hBOOL(hAPP(X18,X25))
       => hAPP(c_List_Ofilter(X5,X18),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X20,X2),X25),X239)) = hAPP(c_List_Ofilter(X5,X18),X239) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter__insort__triv) ).

fof(fact_min__max_OInf__fin_Oeq__fold_H,axiom,
    ! [X25,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omin(X5)),X25),X21) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Oeq__fold_H) ).

fof(fact_min__max_OSup__fin_Oeq__fold_H,axiom,
    ! [X25,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omax(X5)),X25),X21) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Oeq__fold_H) ).

fof(fact_not__psubset__empty,axiom,
    ! [X21,X5] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X21),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__psubset__empty) ).

fof(fact_fold1__eq__fold,axiom,
    ! [X6,X21,X5] :
      ( class_Groups_Oab__semigroup__mult(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X21))
         => hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),hAPP(hAPP(c_Set_Oinsert(X5),X6),X21)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Groups_Otimes__class_Otimes(X5)),X6),X21) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__eq__fold) ).

fof(fact_number__of__Bit0,axiom,
    ! [X128,X58] :
      ( class_Int_Onumber__ring(X58)
     => hAPP(c_Int_Onumber__class_Onumber__of(X58),c_Int_OBit0(X128)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),c_Groups_Ozero__class_Ozero(X58)),hAPP(c_Int_Onumber__class_Onumber__of(X58),X128))),hAPP(c_Int_Onumber__class_Onumber__of(X58),X128)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__Bit0) ).

fof(fact_map__nth,axiom,
    ! [X239,X5] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X5),hAPP(c_List_Onth(X5),X239)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239))) = X239,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__nth) ).

fof(fact_le__infE,axiom,
    ! [X90,X62,X66,X58] :
      ( class_Lattices_Osemilattice__inf(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X66),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X62),X90)))
       => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X66),X62))
           => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X66),X90)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__infE) ).

fof(fact_min__max_Ole__infE,axiom,
    ! [X90,X62,X66,X58] :
      ( class_Orderings_Olinorder(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X66),hAPP(hAPP(c_Orderings_Oord__class_Omin(X58),X62),X90)))
       => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X66),X62))
           => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X66),X90)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ole__infE) ).

fof(fact_length__remove1,axiom,
    ! [X239,X25,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X239)))
       => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_Oremove1(X5,X25,X239)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X239)))
       => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_Oremove1(X5,X25,X239)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__remove1) ).

fof(fact_Int__insert__left__if0,axiom,
    ! [X113,X112,X6,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X112))
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X6),X113)),X112) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X113),X112) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__insert__left__if0) ).

fof(fact_nat__of__aux__code,axiom,
    ! [X57,X98] :
      ( ( X98 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => c_Code__Numeral_Onat__of__aux(X98,X57) = X57 )
      & ( X98 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => c_Code__Numeral_Onat__of__aux(X98,X57) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X98),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,X57)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__of__aux__code) ).

fof(fact_nat__of__aux__def,axiom,
    ! [X57,X98] : c_Code__Numeral_Onat__of__aux(X98,X57) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X98)),X57),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__of__aux__def) ).

fof(fact_sym__trancl,axiom,
    ! [X171,X5] :
      ( c_Relation_Osym(X5,X171)
     => c_Relation_Osym(X5,c_Transitive__Closure_Otrancl(X5,X171)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sym__trancl) ).

fof(fact_wf__trancl,axiom,
    ! [X171,X5] :
      ( c_Wellfounded_Owf(X5,X171)
     => c_Wellfounded_Owf(X5,c_Transitive__Closure_Otrancl(X5,X171)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__trancl) ).

fof(fact_R__O__Id,axiom,
    ! [X32,X20,X5] : hAPP(hAPP(c_Relation_Orel__comp(X5,X20,X20),X32),c_Relation_OId(X20)) = X32,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_R__O__Id) ).

fof(fact_trancl__unfold__right,axiom,
    ! [X171,X5] : c_Transitive__Closure_Otrancl(X5,X171) = hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),c_Transitive__Closure_Ortrancl(X5,X171)),X171),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__unfold__right) ).

fof(fact_trancl__rtrancl__absorb,axiom,
    ! [X32,X5] : c_Transitive__Closure_Ortrancl(X5,c_Transitive__Closure_Otrancl(X5,X32)) = c_Transitive__Closure_Ortrancl(X5,X32),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__rtrancl__absorb) ).

fof(fact_concat_Osimps_I1_J,axiom,
    ! [X58] : c_List_Oconcat(X58,c_List_Olist_ONil(tc_List_Olist(X58))) = c_List_Olist_ONil(X58),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_concat_Osimps_I1_J) ).

fof(fact_Min_Oeq__fold_H,axiom,
    ! [X25,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => c_Big__Operators_Olinorder__class_OMin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omin(X5)),X25),X21) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min_Oeq__fold_H) ).

fof(fact_Max_Oeq__fold_H,axiom,
    ! [X25,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => c_Big__Operators_Olinorder__class_OMax(X5,hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omax(X5)),X25),X21) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max_Oeq__fold_H) ).

fof(fact_Sup__fin_Oeq__fold_H,axiom,
    ! [X25,X21,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => c_Big__Operators_Olattice__class_OSup__fin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Lattices_Osemilattice__sup__class_Osup(X5)),X25),X21) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_Oeq__fold_H) ).

fof(fact_Inf__fin_Oeq__fold_H,axiom,
    ! [X25,X21,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => c_Big__Operators_Olattice__class_OInf__fin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Lattices_Osemilattice__inf__class_Oinf(X5)),X25),X21) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_Oeq__fold_H) ).

fof(fact_trans__trancl,axiom,
    ! [X171,X5] : c_Relation_Otrans(X5,c_Transitive__Closure_Otrancl(X5,X171)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__trancl) ).

fof(fact_eq__nat__number__of,axiom,
    ! [X168,X123] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X123) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X168)
    <=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X123)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X168)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X123)))
         => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X168)))
             => hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X123) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
            & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X168)))
             => X123 = X168 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__nat__number__of) ).

fof(fact_abs__number__of,axiom,
    ! [X66,X58] :
      ( ( class_Int_Onumber__ring(X58)
        & class_Rings_Olinordered__idom(X58) )
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(c_Int_Onumber__class_Onumber__of(X58),X66)),c_Groups_Ozero__class_Ozero(X58)))
         => hAPP(c_Groups_Oabs__class_Oabs(X58),hAPP(c_Int_Onumber__class_Onumber__of(X58),X66)) = hAPP(c_Groups_Ouminus__class_Ouminus(X58),hAPP(c_Int_Onumber__class_Onumber__of(X58),X66)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(c_Int_Onumber__class_Onumber__of(X58),X66)),c_Groups_Ozero__class_Ozero(X58)))
         => hAPP(c_Groups_Oabs__class_Oabs(X58),hAPP(c_Int_Onumber__class_Onumber__of(X58),X66)) = hAPP(c_Int_Onumber__class_Onumber__of(X58),X66) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__number__of) ).

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

fof(fact_mod__nat__number__of,axiom,
    ! [X164,X136] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)))
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X164)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)))
       => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X164)))
           => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X164)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136) )
          & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X164)))
           => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X164)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X164))) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__nat__number__of) ).

fof(fact_min__max_OInf__fin_Oinsert,axiom,
    ! [X25,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X25),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X21)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Oinsert) ).

fof(fact_min__max_OSup__fin_Oinsert,axiom,
    ! [X25,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X25),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X21)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Oinsert) ).

fof(fact_mult__Bit0,axiom,
    ! [X99,X96] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(X96)),X99) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X96),X99)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__Bit0) ).

fof(fact_takeWhile__append1,axiom,
    ! [X251,X18,X239,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X239)))
     => ( ~ hBOOL(hAPP(X18,X25))
       => c_List_OtakeWhile(X5,X18,hAPP(hAPP(c_List_Oappend(X5),X239),X251)) = c_List_OtakeWhile(X5,X18,X239) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_takeWhile__append1) ).

fof(fact_power__nat__number__of__number__of,axiom,
    ! [X128,X136] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)))
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X128)) = 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),X128)) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)))
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X128)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X128))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__nat__number__of__number__of) ).

fof(fact_div__nat__number__of,axiom,
    ! [X164,X136] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X164)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X164)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X164))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__nat__number__of) ).

fof(fact_fold1__insert,axiom,
    ! [X25,X21,X5] :
      ( class_Groups_Oab__semigroup__mult(X5)
     => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
         => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
           => hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X25),hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),X21)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__insert) ).

fof(fact_Suc__diff__number__of,axiom,
    ! [X72,X136] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X136))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X72)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X72),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(X136))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__diff__number__of) ).

fof(fact_ex__least__nat__less,axiom,
    ! [X50,X18] :
      ( ~ hBOOL(hAPP(X18,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
     => ( hBOOL(hAPP(X18,X50))
       => ? [X100] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X100),X50))
            & ! [X146] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X146),X100))
               => ~ hBOOL(hAPP(X18,X146)) )
            & hBOOL(hAPP(X18,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X100),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ex__least__nat__less) ).

fof(fact_greaterThanAtMost__upt,axiom,
    ! [X95,X50] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X50,X95) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,X50),hAPP(c_Nat_OSuc,X95))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThanAtMost__upt) ).

fof(fact_rel__simps_I21_J,axiom,
    ! [X87] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X87)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I21_J) ).

fof(fact_rel__simps_I4_J,axiom,
    ! [X87] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X87)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I4_J) ).

fof(fact_rel__simps_I25_J,axiom,
    ! [X87] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X87)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I25_J) ).

fof(fact_rel__simps_I8_J,axiom,
    ! [X87] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X87)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I8_J) ).

fof(fact_Int__insert__right__if0,axiom,
    ! [X113,X21,X6,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X21))
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X6),X113)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__insert__right__if0) ).

fof(fact_rotate__id,axiom,
    ! [X242,X58,X57] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X57,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
     => hAPP(c_List_Orotate(X58,X57),X242) = X242 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate__id) ).

fof(fact_rotate__is__Nil__conv,axiom,
    ! [X239,X50,X5] :
      ( hAPP(c_List_Orotate(X5,X50),X239) = c_List_Olist_ONil(X5)
    <=> X239 = c_List_Olist_ONil(X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate__is__Nil__conv) ).

fof(fact_simp__from__to,axiom,
    ! [X82,X157] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X157),X82))
       => c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X82,X157) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X157),X82))
       => c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X82,X157) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),X82),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X82),c_Groups_Oone__class_Oone(tc_Int_Oint)),X157)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_simp__from__to) ).

fof(fact_double__number__of__Bit0,axiom,
    ! [X128,X58] :
      ( class_Int_Onumber__ring(X58)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),c_Groups_Oone__class_Oone(X58)),c_Groups_Oone__class_Oone(X58))),hAPP(c_Int_Onumber__class_Onumber__of(X58),X128)) = hAPP(c_Int_Onumber__class_Onumber__of(X58),c_Int_OBit0(X128)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__number__of__Bit0) ).

fof(fact_insertCI,axiom,
    ! [X24,X113,X6,X5] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X113))
       => X6 = X24 )
     => hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(hAPP(c_Set_Oinsert(X5),X24),X113))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertCI) ).

fof(fact_Bit1__def,axiom,
    ! [X96] : c_Int_OBit1(X96) = 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)),X96)),X96),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bit1__def) ).

fof(fact_internal__split__conv,axiom,
    ! [X24,X6,X23,X5,X116,X20] : hAPP(hAPP(c_Product__Type_Ointernal__split(X20,X116,X5),X23),hAPP(hAPP(c_Product__Type_OPair(X20,X116),X6),X24)) = hAPP(hAPP(X23,X6),X24),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_internal__split__conv) ).

fof(fact_internal__split__def,axiom,
    ! [X116,X20,X5] : c_Product__Type_Ointernal__split(X5,X20,X116) = c_Product__Type_Oprod_Oprod__case(X5,X20,X116),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_internal__split__def) ).

fof(fact_map__replicate__trivial,axiom,
    ! [X82,X25,X5] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X5),hAPP(c_COMBK(X5,tc_Nat_Onat),X25)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X82)) = c_List_Oreplicate(X5,X82,X25),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__replicate__trivial) ).

fof(fact_ComplI,axiom,
    ! [X21,X23,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X23),X21))
     => hBOOL(hAPP(hAPP(c_member(X5),X23),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X21))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ComplI) ).

fof(fact_vimage__const,axiom,
    ! [X20,X21,X23,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X23),X21))
       => hAPP(c_Set_Ovimage(X20,X5,hAPP(c_COMBK(X5,X20),X23)),X21) = c_Orderings_Otop__class_Otop(tc_fun(X20,tc_HOL_Obool)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X23),X21))
       => hAPP(c_Set_Ovimage(X20,X5,hAPP(c_COMBK(X5,X20),X23)),X21) = c_Orderings_Obot__class_Obot(tc_fun(X20,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__const) ).

fof(fact_folding__one_Oinsert,axiom,
    ! [X25,X21,X205,X2,X5] :
      ( c_Finite__Set_Ofolding__one(X5,X2,X205)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(X205,hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(hAPP(X2,X25),hAPP(X205,X21)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one_Oinsert) ).

fof(fact_map__Suc__upt,axiom,
    ! [X50,X95] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),c_List_Oupt(X95,X50)) = c_List_Oupt(hAPP(c_Nat_OSuc,X95),hAPP(c_Nat_OSuc,X50)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__Suc__upt) ).

fof(fact_divmod__int__def,axiom,
    ! [X90,X62] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X62))
       => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X90))
           => c_Divides_Odivmod__int(X62,X90) = c_Divides_OposDivAlg(X62,X90) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X90))
           => ( ( X62 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
               => c_Divides_Odivmod__int(X62,X90) = 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)) )
              & ( X62 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
               => c_Divides_Odivmod__int(X62,X90) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X62),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X90))) ) ) ) ) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X62))
       => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X90))
           => c_Divides_Odivmod__int(X62,X90) = c_Divides_OnegDivAlg(X62,X90) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X90))
           => c_Divides_Odivmod__int(X62,X90) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X62),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X90))) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__int__def) ).

fof(fact_takeWhile__tail,axiom,
    ! [X156,X239,X5,X25,X18] :
      ( ~ hBOOL(hAPP(X18,X25))
     => c_List_OtakeWhile(X5,X18,hAPP(hAPP(c_List_Oappend(X5),X239),hAPP(hAPP(c_List_Olist_OCons(X5),X25),X156))) = c_List_OtakeWhile(X5,X18,X239) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_takeWhile__tail) ).

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

fof(fact_numeral__1__eq__1,axiom,
    ! [X58] :
      ( class_Int_Onumber__ring(X58)
     => hAPP(c_Int_Onumber__class_Onumber__of(X58),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(X58) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_numeral__1__eq__1) ).

fof(fact_semiring__norm_I110_J,axiom,
    ! [X58] :
      ( class_Int_Onumber__ring(X58)
     => c_Groups_Oone__class_Oone(X58) = hAPP(c_Int_Onumber__class_Onumber__of(X58),c_Int_OBit1(c_Int_OPls)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_semiring__norm_I110_J) ).

fof(fact_not__less__eq__eq,axiom,
    ! [X50,X95] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X50))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X50)),X95)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__eq__eq) ).

fof(fact_abs__not__less__zero,axiom,
    ! [X62,X58] :
      ( class_Groups_Oordered__ab__group__add__abs(X58)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(c_Groups_Oabs__class_Oabs(X58),X62)),c_Groups_Ozero__class_Ozero(X58))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__not__less__zero) ).

fof(fact_of__nat__less__0__iff,axiom,
    ! [X72,X58] :
      ( class_Rings_Olinordered__semidom(X58)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X58),X72)),c_Groups_Ozero__class_Ozero(X58))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__less__0__iff) ).

fof(fact_iszero__number__of__Bit0,axiom,
    ! [X121,X5] :
      ( ( class_Int_Onumber__ring(X5)
        & class_Int_Oring__char__0(X5) )
     => ( c_Int_Oiszero(X5,hAPP(c_Int_Onumber__class_Onumber__of(X5),c_Int_OBit0(X121)))
      <=> c_Int_Oiszero(X5,hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_iszero__number__of__Bit0) ).

fof(fact_add__nat__number__of,axiom,
    ! [X164,X136] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X136),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X164)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X164) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X136),c_Int_OPls))
       => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X164),c_Int_OPls))
           => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X164)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X164),c_Int_OPls))
           => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X164)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X136),X164)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nat__number__of) ).

fof(fact_power__nat__number__of,axiom,
    ! [X57,X136] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)))
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)),X57) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X57) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)))
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)),X57) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)),X57)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__nat__number__of) ).

fof(fact_diff__bin__simps_I3_J,axiom,
    ! [X99] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X99)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),X99)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__bin__simps_I3_J) ).

fof(fact_minus__shift__def,axiom,
    ! [X134,X99,X96] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X96),X99))
       => c_Random_Ominus__shift(X134,X96,X99) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X134),X96)),X99) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X96),X99))
       => c_Random_Ominus__shift(X134,X96,X99) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X96),X99) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__shift__def) ).

fof(fact_split__zmod,axiom,
    ! [X87,X50,X18] :
      ( hBOOL(hAPP(X18,c_Divides_Odiv__class_Omod(tc_Int_Oint,X50,X87)))
    <=> ( ( X87 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hBOOL(hAPP(X18,X50)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X87))
         => ! [X146,X101] :
              ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X101))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X101),X87))
                & X50 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X87),X146)),X101) )
             => hBOOL(hAPP(X18,X101)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X87),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => ! [X146,X101] :
              ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X87),X101))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X101),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                & X50 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X87),X146)),X101) )
             => hBOOL(hAPP(X18,X101)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__zmod) ).

fof(fact_upto_Osimps,axiom,
    ! [X97,X98] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X98),X97))
       => c_List_Oupto(X98,X97) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),X98),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X98),c_Groups_Oone__class_Oone(tc_Int_Oint)),X97)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X98),X97))
       => c_List_Oupto(X98,X97) = c_List_Olist_ONil(tc_Int_Oint) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_upto_Osimps) ).

fof(fact_rel__simps_I49_J,axiom,
    ! [X99,X96] : c_Int_OBit0(X96) != c_Int_OBit1(X99),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I49_J) ).

fof(fact_rel__simps_I50_J,axiom,
    ! [X99,X96] : c_Int_OBit1(X96) != c_Int_OBit0(X99),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I50_J) ).

fof(fact_divmod__nat__div__mod,axiom,
    ! [X57,X72] : c_Divides_Odivmod__nat(X72,X57) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X72),X57)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X72,X57)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__div__mod) ).

fof(fact_code__numeral_Osimps_I5_J,axiom,
    ! [X174,X89,X19,X5] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X5,X19,X89,c_Code__Numeral_OSuc__code__numeral(X174)) = hAPP(X89,X174),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_code__numeral_Osimps_I5_J) ).

fof(fact_greaterThanLessThan__upt,axiom,
    ! [X95,X50] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X50,X95) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,X50),X95)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThanLessThan__upt) ).

fof(fact_remdups_Osimps_I2_J,axiom,
    ! [X239,X25,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X239)))
       => c_List_Oremdups(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239)) = c_List_Oremdups(X5,X239) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X239)))
       => c_List_Oremdups(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239)) = hAPP(hAPP(c_List_Olist_OCons(X5),X25),c_List_Oremdups(X5,X239)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_remdups_Osimps_I2_J) ).

fof(fact_of__int__of__nat,axiom,
    ! [X96,X58] :
      ( class_Rings_Oring__1(X58)
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X96),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => hAPP(c_Int_Oring__1__class_Oof__int(X58),X96) = hAPP(c_Groups_Ouminus__class_Ouminus(X58),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X58),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X96)))) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X96),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => hAPP(c_Int_Oring__1__class_Oof__int(X58),X96) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X58),hAPP(c_Int_Onat,X96)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__of__nat) ).

fof(fact_small__lazy_H_Osimps,axiom,
    ! [X98,X91] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X91),X98))
       => c_Lazy__Sequence_Osmall__lazy_H(X91,X98) = c_Lazy__Sequence_Oempty(tc_Int_Oint) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X91),X98))
       => c_Lazy__Sequence_Osmall__lazy_H(X91,X98) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),X98),c_Lazy__Sequence_Osmall__lazy_H(X91,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X98),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_small__lazy_H_Osimps) ).

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

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

fof(fact_Min_Oinsert,axiom,
    ! [X25,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => c_Big__Operators_Olinorder__class_OMin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X25),c_Big__Operators_Olinorder__class_OMin(X5,X21)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min_Oinsert) ).

fof(fact_Max_Oinsert,axiom,
    ! [X25,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => c_Big__Operators_Olinorder__class_OMax(X5,hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X25),c_Big__Operators_Olinorder__class_OMax(X5,X21)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max_Oinsert) ).

fof(fact_Sup__fin_Oinsert,axiom,
    ! [X25,X21,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => c_Big__Operators_Olattice__class_OSup__fin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X25),c_Big__Operators_Olattice__class_OSup__fin(X5,X21)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_Oinsert) ).

fof(fact_Inf__fin_Oinsert,axiom,
    ! [X25,X21,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => c_Big__Operators_Olattice__class_OInf__fin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X25),c_Big__Operators_Olattice__class_OInf__fin(X5,X21)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_Oinsert) ).

fof(fact_rtrancl__trancl__absorb,axiom,
    ! [X32,X5] : c_Transitive__Closure_Otrancl(X5,c_Transitive__Closure_Ortrancl(X5,X32)) = c_Transitive__Closure_Ortrancl(X5,X32),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__trancl__absorb) ).

fof(fact_sublist__singleton,axiom,
    ! [X25,X5,X21] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X21))
       => c_List_Osublist(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X25),c_List_Olist_ONil(X5)),X21) = hAPP(hAPP(c_List_Olist_OCons(X5),X25),c_List_Olist_ONil(X5)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X21))
       => c_List_Osublist(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X25),c_List_Olist_ONil(X5)),X21) = c_List_Olist_ONil(X5) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sublist__singleton) ).

fof(fact_in__set__member,axiom,
    ! [X239,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X239)))
    <=> hBOOL(hAPP(hAPP(c_List_Omember(X5),X239),X25)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__set__member) ).

fof(fact_List_Omember__def,axiom,
    ! [X25,X239,X5] :
      ( hBOOL(hAPP(hAPP(c_List_Omember(X5),X239),X25))
    <=> hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X239))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_List_Omember__def) ).

fof(fact_one__mod__nat__number__of,axiom,
    ! [X164] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X164)))
       => 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),X164)) = 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),X164)))
       => 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),X164)) = 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),X164))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__mod__nat__number__of) ).

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

fof(fact_less__le__not__le,axiom,
    ! [X33,X25,X5] :
      ( class_Orderings_Opreorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X25),X33))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X25),X33))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X33),X25)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__le__not__le) ).

fof(fact_card_Oinsert,axiom,
    ! [X25,X21,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
       => hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X5),X21)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card_Oinsert) ).

fof(fact_split__zdiv,axiom,
    ! [X87,X50,X18] :
      ( hBOOL(hAPP(X18,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X50),X87)))
    <=> ( ( X87 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hBOOL(hAPP(X18,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)),X87))
         => ! [X146] :
              ( ? [X101] :
                  ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X101))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X101),X87))
                  & X50 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X87),X146)),X101) )
             => hBOOL(hAPP(X18,X146)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X87),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => ! [X146] :
              ( ? [X101] :
                  ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X87),X101))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X101),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                  & X50 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X87),X146)),X101) )
             => hBOOL(hAPP(X18,X146)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__zdiv) ).

fof(fact_insert__ident,axiom,
    ! [X113,X21,X25,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X113))
       => ( hAPP(hAPP(c_Set_Oinsert(X5),X25),X21) = hAPP(hAPP(c_Set_Oinsert(X5),X25),X113)
        <=> X21 = X113 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__ident) ).

fof(fact_card__insert__if,axiom,
    ! [X25,X21,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
     => ( ( hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(c_Finite__Set_Ocard(X5),X21) )
        & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X5),X21)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__insert__if) ).

fof(fact_last__upt,axiom,
    ! [X97,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),X97))
     => c_List_Olast(tc_Nat_Onat,c_List_Oupt(X98,X97)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X97),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__upt) ).

fof(fact_Suc__code__numeral__minus__one,axiom,
    ! [X57] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(X57)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = X57,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__code__numeral__minus__one) ).

fof(fact_not__less__eq,axiom,
    ! [X50,X95] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),X50))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X50),hAPP(c_Nat_OSuc,X95))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__eq) ).

fof(fact_distinct__upt,axiom,
    ! [X97,X98] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(X98,X97))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__upt) ).

fof(fact_relpow_Osimps_I1_J,axiom,
    ! [X32,X5] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X32) = c_Relation_OId(X5),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_relpow_Osimps_I1_J) ).

fof(fact_takeWhile_Osimps_I2_J,axiom,
    ! [X239,X5,X25,X18] :
      ( ( hBOOL(hAPP(X18,X25))
       => c_List_OtakeWhile(X5,X18,hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239)) = hAPP(hAPP(c_List_Olist_OCons(X5),X25),c_List_OtakeWhile(X5,X18,X239)) )
      & ( ~ hBOOL(hAPP(X18,X25))
       => c_List_OtakeWhile(X5,X18,hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239)) = c_List_Olist_ONil(X5) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_takeWhile_Osimps_I2_J) ).

fof(fact_int__less__0__conv,axiom,
    ! [X96] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X96)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__less__0__conv) ).

fof(fact_rel__simps_I43_J,axiom,
    ! [X156] :
      ( c_Int_OMin = c_Int_OBit1(X156)
    <=> c_Int_OMin = X156 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I43_J) ).

fof(fact_rel__simps_I47_J,axiom,
    ! [X87] :
      ( c_Int_OBit1(X87) = c_Int_OMin
    <=> X87 = c_Int_OMin ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I47_J) ).

fof(fact_rel__simps_I46_J,axiom,
    ! [X96] : c_Int_OBit1(X96) != c_Int_OPls,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I46_J) ).

fof(fact_rel__simps_I39_J,axiom,
    ! [X99] : c_Int_OPls != c_Int_OBit1(X99),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I39_J) ).

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

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

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

fof(fact_of__nat__number__of__lemma,axiom,
    ! [X136,X58] :
      ( class_Int_Onumber__ring(X58)
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)))
         => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X58),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)) = hAPP(c_Int_Onumber__class_Onumber__of(X58),X136) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)))
         => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X58),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)) = c_Groups_Ozero__class_Ozero(X58) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__number__of__lemma) ).

fof(fact_card__insert__disjoint,axiom,
    ! [X25,X21,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
       => hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X5),X21)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__insert__disjoint) ).

fof(fact_linorder__antisym__conv2,axiom,
    ! [X33,X25,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X25),X33))
       => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X25),X33))
        <=> X25 = X33 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__antisym__conv2) ).

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

fof(fact_evalc_OWhileFalse,axiom,
    ! [X23,X76,X24] :
      ( ~ hBOOL(hAPP(X24,X76))
     => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X24,X23)),X76),X76)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_OWhileFalse) ).

fof(fact_List_Oinsert__def,axiom,
    ! [X239,X25,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X239)))
       => c_List_Oinsert(X5,X25,X239) = X239 )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X239)))
       => c_List_Oinsert(X5,X25,X239) = hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_List_Oinsert__def) ).

fof(fact_xt1_I9_J,axiom,
    ! [X62,X90,X58] :
      ( class_Orderings_Oorder(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X90),X62))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X62),X90)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I9_J) ).

fof(fact_order__less__not__sym,axiom,
    ! [X65,X66,X58] :
      ( class_Orderings_Opreorder(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X66),X65))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X65),X66)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__not__sym) ).

fof(fact_order__less__imp__not__less,axiom,
    ! [X65,X66,X58] :
      ( class_Orderings_Opreorder(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X66),X65))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X65),X66)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__less) ).

fof(fact_order__less__asym_H,axiom,
    ! [X90,X62,X58] :
      ( class_Orderings_Opreorder(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X62),X90))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X90),X62)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__asym_H) ).

fof(fact_order__less__asym,axiom,
    ! [X65,X66,X58] :
      ( class_Orderings_Opreorder(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X66),X65))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X65),X66)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__asym) ).

fof(fact_linorder__not__le,axiom,
    ! [X33,X25,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X25),X33))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X33),X25)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__not__le) ).

fof(fact_leD,axiom,
    ! [X66,X65,X58] :
      ( class_Orderings_Olinorder(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X65),X66))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X66),X65)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_leD) ).

fof(fact_linorder__not__less,axiom,
    ! [X33,X25,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X25),X33))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X33),X25)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__not__less) ).

fof(fact_not__less__iff__gr__or__eq,axiom,
    ! [X33,X25,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X25),X33))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X33),X25))
          | X25 = X33 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__iff__gr__or__eq) ).

fof(fact_mult__nat__number__of,axiom,
    ! [X164,X136] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X136),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X164)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X136),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X164)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X136),X164)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__nat__number__of) ).

fof(fact_hd__upt,axiom,
    ! [X97,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),X97))
     => hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(X98,X97)) = X98 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hd__upt) ).

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

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

fof(fact_le__SucE,axiom,
    ! [X57,X72] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X72),hAPP(c_Nat_OSuc,X57)))
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X72),X57))
       => X72 = hAPP(c_Nat_OSuc,X57) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__SucE) ).

fof(fact_atLeastAtMost__upt,axiom,
    ! [X95,X50] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X50,X95) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X50,hAPP(c_Nat_OSuc,X95))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastAtMost__upt) ).

fof(fact_atLeastLessThanSuc,axiom,
    ! [X50,X95] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X50))
       => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X95),hAPP(c_Nat_OSuc,X50)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X50),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X95),X50)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X50))
       => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X95),hAPP(c_Nat_OSuc,X50)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThanSuc) ).

fof(fact_filter_Osimps_I2_J,axiom,
    ! [X239,X5,X25,X18] :
      ( ( hBOOL(hAPP(X18,X25))
       => hAPP(c_List_Ofilter(X5,X18),hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239)) = hAPP(hAPP(c_List_Olist_OCons(X5),X25),hAPP(c_List_Ofilter(X5,X18),X239)) )
      & ( ~ hBOOL(hAPP(X18,X25))
       => hAPP(c_List_Ofilter(X5,X18),hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239)) = hAPP(c_List_Ofilter(X5,X18),X239) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter_Osimps_I2_J) ).

fof(fact_less__SucE,axiom,
    ! [X57,X72] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X72),hAPP(c_Nat_OSuc,X57)))
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X72),X57))
       => X72 = X57 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__SucE) ).

fof(fact_less__antisym,axiom,
    ! [X72,X57] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X57),X72))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X57),hAPP(c_Nat_OSuc,X72)))
       => X72 = X57 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__antisym) ).

fof(fact_not__less__less__Suc__eq,axiom,
    ! [X95,X50] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X50),X95))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X50),hAPP(c_Nat_OSuc,X95)))
      <=> X50 = X95 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__less__Suc__eq) ).

fof(fact_divmod__nat__rel__divmod__nat,axiom,
    ! [X57,X72] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X72,X57),c_Divides_Odivmod__nat(X72,X57))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__rel__divmod__nat) ).

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

fof(fact_atMost__upto,axiom,
    ! [X50] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X50) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,X50))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atMost__upto) ).

fof(fact_number__of__pred,axiom,
    ! [X128,X58] :
      ( class_Int_Onumber__ring(X58)
     => hAPP(c_Int_Onumber__class_Onumber__of(X58),c_Int_Opred(X128)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(c_Groups_Ouminus__class_Ouminus(X58),c_Groups_Oone__class_Oone(X58))),hAPP(c_Int_Onumber__class_Onumber__of(X58),X128)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__pred) ).

fof(fact_evaln_OWhileFalse,axiom,
    ! [X50,X23,X76,X24] :
      ( ~ hBOOL(hAPP(X24,X76))
     => c_Natural_Oevaln(c_Com_Ocom_OWhile(X24,X23),X76,X50,X76) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_OWhileFalse) ).

fof(fact_trancl__id,axiom,
    ! [X171,X5] :
      ( c_Relation_Otrans(X5,X171)
     => c_Transitive__Closure_Otrancl(X5,X171) = X171 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__id) ).

fof(fact_atLeastatMost__empty__iff2,axiom,
    ! [X24,X6,X5] :
      ( class_Orderings_Oorder(X5)
     => ( c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,X24)
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),X24)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastatMost__empty__iff2) ).

fof(fact_greaterThanAtMost__empty__iff2,axiom,
    ! [X156,X87,X5] :
      ( class_Orderings_Oorder(X5)
     => ( c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X87,X156)
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X87),X156)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThanAtMost__empty__iff2) ).

fof(fact_atLeastatMost__empty__iff,axiom,
    ! [X24,X6,X5] :
      ( class_Orderings_Oorder(X5)
     => ( c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,X24) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),X24)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastatMost__empty__iff) ).

fof(fact_greaterThanAtMost__empty__iff,axiom,
    ! [X156,X87,X5] :
      ( class_Orderings_Oorder(X5)
     => ( c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X87,X156) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X87),X156)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThanAtMost__empty__iff) ).

fof(fact_divmod__nat__base,axiom,
    ! [X57,X72] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X72),X57))
     => c_Divides_Odivmod__nat(X72,X57) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X72) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__base) ).

fof(fact_equalityE,axiom,
    ! [X5,X113,X21] :
      ( X21 = X113
     => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),X113))
         => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X113),X21)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityE) ).

fof(fact_Suc__n__not__le__n,axiom,
    ! [X57] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X57)),X57)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__not__le__n) ).

fof(fact_z3div__def,axiom,
    ! [X96,X99] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X99))
       => c_SMT_Oz3div(X96,X99) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X96),X99) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X99))
       => c_SMT_Oz3div(X96,X99) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X96),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X99))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_z3div__def) ).

fof(fact_mod__if,axiom,
    ! [X57,X72] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X72),X57))
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,X72,X57) = X72 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X72),X57))
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,X72,X57) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X72),X57),X57) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__if) ).

fof(fact_mod__geq,axiom,
    ! [X57,X72] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X72),X57))
     => c_Divides_Odiv__class_Omod(tc_Nat_Onat,X72,X57) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X72),X57),X57) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__geq) ).

fof(fact_not__in__set__insert,axiom,
    ! [X239,X25,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X239)))
     => c_List_Oinsert(X5,X25,X239) = hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__in__set__insert) ).

fof(fact_linorder__antisym__conv1,axiom,
    ! [X33,X25,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X25),X33))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X25),X33))
        <=> X25 = X33 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__antisym__conv1) ).

fof(fact_atLeastLessThan__empty__iff,axiom,
    ! [X24,X6,X5] :
      ( class_Orderings_Oorder(X5)
     => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X6),X24) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),X24)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__empty__iff) ).

fof(fact_atLeastLessThan__empty__iff2,axiom,
    ! [X24,X6,X5] :
      ( class_Orderings_Oorder(X5)
     => ( c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X6),X24)
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),X24)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__empty__iff2) ).

fof(fact_part__equivpE,axiom,
    ! [X32,X5] :
      ( c_Equiv__Relations_Opart__equivp(X5,X32)
     => ~ ( ? [X3] : hBOOL(hAPP(hAPP(X32,X3),X3))
         => ( c_Predicate_Osymp(X5,X32)
           => ~ c_Predicate_Otransp(X5,X32) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_part__equivpE) ).

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

fof(fact_code__numeral_Osize_I2_J,axiom,
    ! [X172] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(X172)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(X172)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_code__numeral_Osize_I2_J) ).

fof(fact_minus__Bit0,axiom,
    ! [X96] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(X96)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X96)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__Bit0) ).

fof(fact_filter__replicate,axiom,
    ! [X50,X5,X25,X18] :
      ( ( hBOOL(hAPP(X18,X25))
       => hAPP(c_List_Ofilter(X5,X18),c_List_Oreplicate(X5,X50,X25)) = c_List_Oreplicate(X5,X50,X25) )
      & ( ~ hBOOL(hAPP(X18,X25))
       => hAPP(c_List_Ofilter(X5,X18),c_List_Oreplicate(X5,X50,X25)) = c_List_Olist_ONil(X5) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter__replicate) ).

fof(fact_transfer__nat__int__list__return__embed,axiom,
    ! [X99] :
      ( c_List_Onat__list(X99)
     => c_List_Oembed__list(c_List_Oreturn__list(X99)) = X99 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__list__return__embed) ).

fof(fact_all__not__in__conv,axiom,
    ! [X21,X5] :
      ( ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(X5),X3),X21))
    <=> X21 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_all__not__in__conv) ).

fof(fact_remove1__idem,axiom,
    ! [X239,X25,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X239)))
     => c_List_Oremove1(X5,X25,X239) = X239 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_remove1__idem) ).

fof(fact_length__upt,axiom,
    ! [X97,X98] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),c_List_Oupt(X98,X97)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X97),X98),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__upt) ).

fof(fact_sgn__if,axiom,
    ! [X66,X58] :
      ( class_Groups_Osgn__if(X58)
     => ( ( X66 = c_Groups_Ozero__class_Ozero(X58)
         => c_Groups_Osgn__class_Osgn(X58,X66) = c_Groups_Ozero__class_Ozero(X58) )
        & ( X66 != c_Groups_Ozero__class_Ozero(X58)
         => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),X66))
             => c_Groups_Osgn__class_Osgn(X58,X66) = c_Groups_Oone__class_Oone(X58) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),X66))
             => c_Groups_Osgn__class_Osgn(X58,X66) = hAPP(c_Groups_Ouminus__class_Ouminus(X58),c_Groups_Oone__class_Oone(X58)) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__if) ).

fof(fact_upt__conv__Nil,axiom,
    ! [X98,X97] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X97),X98))
     => c_List_Oupt(X98,X97) = c_List_Olist_ONil(tc_Nat_Onat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_upt__conv__Nil) ).

fof(fact_upt__eq__Nil__conv,axiom,
    ! [X157,X82] :
      ( c_List_Oupt(X82,X157) = c_List_Olist_ONil(tc_Nat_Onat)
    <=> ( X157 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X157),X82)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_upt__eq__Nil__conv) ).

fof(fact_z3mod__def,axiom,
    ! [X96,X99] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X99))
       => c_SMT_Oz3mod(X96,X99) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X96,X99) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X99))
       => c_SMT_Oz3mod(X96,X99) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X96,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X99)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_z3mod__def) ).

fof(fact_abs__if,axiom,
    ! [X62,X58] :
      ( class_Groups_Oabs__if(X58)
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X62),c_Groups_Ozero__class_Ozero(X58)))
         => hAPP(c_Groups_Oabs__class_Oabs(X58),X62) = hAPP(c_Groups_Ouminus__class_Ouminus(X58),X62) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X62),c_Groups_Ozero__class_Ozero(X58)))
         => hAPP(c_Groups_Oabs__class_Oabs(X58),X62) = X62 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__if) ).

fof(fact_not__one__le__zero,axiom,
    ! [X58] :
      ( class_Rings_Olinordered__semidom(X58)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Oone__class_Oone(X58)),c_Groups_Ozero__class_Ozero(X58))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__one__le__zero) ).

fof(fact_not__one__less__zero,axiom,
    ! [X58] :
      ( class_Rings_Olinordered__semidom(X58)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Oone__class_Oone(X58)),c_Groups_Ozero__class_Ozero(X58))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__one__less__zero) ).

fof(fact_add__diff__inverse,axiom,
    ! [X57,X72] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X72),X57))
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X57),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X72),X57)) = X72 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__diff__inverse) ).

fof(fact_atLeast__upt,axiom,
    ! [X50] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X50) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X50)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeast__upt) ).

fof(fact_linorder__neqE__linordered__idom,axiom,
    ! [X65,X66,X58] :
      ( class_Rings_Olinordered__idom(X58)
     => ( X66 != X65
       => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X66),X65))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X65),X66)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE__linordered__idom) ).

fof(fact_linorder__antisym__conv3,axiom,
    ! [X25,X33,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X33),X25))
       => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X25),X33))
        <=> X25 = X33 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__antisym__conv3) ).

fof(fact_linorder__neqE,axiom,
    ! [X65,X66,X58] :
      ( class_Orderings_Olinorder(X58)
     => ( X66 != X65
       => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X66),X65))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X65),X66)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE) ).

fof(fact_linorder__cases,axiom,
    ! [X65,X66,X58] :
      ( class_Orderings_Olinorder(X58)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X66),X65))
       => ( X66 != X65
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X65),X66)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__cases) ).

fof(fact_linorder__le__cases,axiom,
    ! [X65,X66,X58] :
      ( class_Orderings_Olinorder(X58)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X66),X65))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X65),X66)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__le__cases) ).

fof(fact_leI,axiom,
    ! [X65,X66,X58] :
      ( class_Orderings_Olinorder(X58)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X66),X65))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X65),X66)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_leI) ).

fof(fact_not__leE,axiom,
    ! [X66,X65,X58] :
      ( class_Orderings_Olinorder(X58)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X65),X66))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X66),X65)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__leE) ).

fof(fact_set__upt,axiom,
    ! [X157,X82] : hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X82,X157)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X82),X157),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__upt) ).

fof(fact_atLeastLessThan__upt,axiom,
    ! [X157,X82] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X82),X157) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X82,X157)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__upt) ).

fof(fact_succ__pred,axiom,
    ! [X66] : c_Int_Osucc(c_Int_Opred(X66)) = X66,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_succ__pred) ).

fof(fact_number__of__succ,axiom,
    ! [X96,X58] :
      ( class_Int_Onumber__ring(X58)
     => hAPP(c_Int_Onumber__class_Onumber__of(X58),c_Int_Osucc(X96)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),c_Groups_Oone__class_Oone(X58)),hAPP(c_Int_Onumber__class_Onumber__of(X58),X96)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__succ) ).

fof(fact_equals0D,axiom,
    ! [X6,X5,X21] :
      ( X21 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
     => ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X21)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equals0D) ).

fof(fact_not__neg__eq__ge__0,axiom,
    ! [X25] :
      ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X25))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__neg__eq__ge__0) ).

fof(fact_of__nat__cases,axiom,
    ! [X25] :
      ~ ! [X177] :
          ( X25 = hAPP(c_Code__Numeral_Oof__nat,X177)
         => ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X177),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__cases) ).

fof(fact_nat__eq__iff,axiom,
    ! [X95,X121] :
      ( hAPP(c_Int_Onat,X121) = X95
    <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X121))
         => X121 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X95) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X121))
         => X95 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__eq__iff) ).

fof(fact_nat__eq__iff2,axiom,
    ! [X121,X95] :
      ( X95 = hAPP(c_Int_Onat,X121)
    <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X121))
         => X121 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X95) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X121))
         => X95 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__eq__iff2) ).

fof(fact_int__nat__eq,axiom,
    ! [X94] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X94))
       => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X94)) = X94 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X94))
       => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X94)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__nat__eq) ).

fof(fact_tsub__def,axiom,
    ! [X66,X65] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X65),X66))
       => c_Nat__Transfer_Otsub(X66,X65) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X66),X65) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X65),X66))
       => c_Nat__Transfer_Otsub(X66,X65) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tsub__def) ).

fof(fact_of__nat__number__of__eq,axiom,
    ! [X136,X58] :
      ( class_Int_Onumber__ring(X58)
     => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)))
         => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X58),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)) = c_Groups_Ozero__class_Ozero(X58) )
        & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)))
         => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X58),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)) = hAPP(c_Int_Onumber__class_Onumber__of(X58),X136) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__number__of__eq) ).

fof(fact_mod__nat__def,axiom,
    ! [X57,X72] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X72,X57) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(X72,X57)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__nat__def) ).

fof(fact_remove1__filter__not,axiom,
    ! [X239,X5,X25,X18] :
      ( ~ hBOOL(hAPP(X18,X25))
     => c_List_Oremove1(X5,X25,hAPP(c_List_Ofilter(X5,X18),X239)) = hAPP(c_List_Ofilter(X5,X18),X239) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_remove1__filter__not) ).

fof(fact_div__nat__def,axiom,
    ! [X57,X72] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X72),X57) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(X72,X57)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__nat__def) ).

fof(fact_int__nat__number__of,axiom,
    ! [X136] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)))
       => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)))
       => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__nat__number__of) ).

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

fof(fact_linorder__neqE__nat,axiom,
    ! [X65,X66] :
      ( X66 != X65
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X66),X65))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X65),X66)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE__nat) ).

fof(fact_divmod__nat__eq,axiom,
    ! [X182,X57,X72] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X72,X57),X182))
     => c_Divides_Odivmod__nat(X72,X57) = X182 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__eq) ).

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

fof(fact_sorted__upt,axiom,
    ! [X97,X98] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(X98,X97)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__upt) ).

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

fof(fact_order__less__irrefl,axiom,
    ! [X66,X58] :
      ( class_Orderings_Opreorder(X58)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X66),X66)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__irrefl) ).

fof(fact_beyond__def,axiom,
    ! [X99,X96] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X96),X99))
       => c_Quickcheck_Obeyond(X96,X99) = X99 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X96),X99))
       => c_Quickcheck_Obeyond(X96,X99) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_beyond__def) ).

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

fof(fact_less__nat__zero__code,axiom,
    ! [X57] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X57),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__nat__zero__code) ).

fof(fact_not__less0,axiom,
    ! [X57] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X57),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less0) ).

fof(fact_less__zeroE,axiom,
    ! [X57] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X57),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__zeroE) ).

fof(fact_divmod__nat__zero,axiom,
    ! [X72] : c_Divides_Odivmod__nat(X72,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)),X72),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__zero) ).

fof(fact_less__not__refl,axiom,
    ! [X57] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X57),X57)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl) ).

fof(fact_less__irrefl__nat,axiom,
    ! [X57] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X57),X57)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__irrefl__nat) ).

fof(fact_rel__simps_I48_J,axiom,
    ! [X156,X87] :
      ( c_Int_OBit0(X87) = c_Int_OBit0(X156)
    <=> X87 = X156 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I48_J) ).

fof(fact_setsum_Oinfinite,axiom,
    ! [X1,X21,X5,X20] :
      ( class_Groups_Ocomm__monoid__add(X20)
     => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X1),X21) = c_Groups_Ozero__class_Ozero(X20) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum_Oinfinite) ).

fof(fact_setsum__infinite,axiom,
    ! [X2,X21,X5,X20] :
      ( class_Groups_Ocomm__monoid__add(X20)
     => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X2),X21) = c_Groups_Ozero__class_Ozero(X20) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__infinite) ).

fof(fact_setprod_Oinfinite,axiom,
    ! [X1,X21,X5,X20] :
      ( class_Groups_Ocomm__monoid__mult(X20)
     => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X1),X21) = c_Groups_Oone__class_Oone(X20) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod_Oinfinite) ).

fof(fact_setprod__infinite,axiom,
    ! [X2,X21,X5,X20] :
      ( class_Groups_Ocomm__monoid__mult(X20)
     => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X2),X21) = c_Groups_Oone__class_Oone(X20) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__infinite) ).

fof(fact_not__neg__int,axiom,
    ! [X57] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X57))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__neg__int) ).

fof(fact_equivE,axiom,
    ! [X171,X21,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X21,X171)
     => ~ ( c_Relation_Orefl__on(X5,X21,X171)
         => ( c_Relation_Osym(X5,X171)
           => ~ c_Relation_Otrans(X5,X171) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equivE) ).

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

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

fof(help_c__fimplies__3,axiom,
    ! [X16,X18] :
      ( ~ hBOOL(hAPP(hAPP(c_fimplies,X18),X16))
      | ~ hBOOL(X18)
      | hBOOL(X16) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fimplies__3) ).

fof(fact_card__eq__0__iff,axiom,
    ! [X21,X5] :
      ( hAPP(c_Finite__Set_Ocard(X5),X21) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> ( X21 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__eq__0__iff) ).

fof(help_c__fdisj__3,axiom,
    ! [X16,X18] :
      ( ~ hBOOL(hAPP(hAPP(c_fdisj,X18),X16))
      | hBOOL(X18)
      | hBOOL(X16) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fdisj__3) ).

fof(help_c__fconj__2,axiom,
    ! [X16,X18] :
      ( ~ hBOOL(hAPP(hAPP(c_fconj,X18),X16))
      | hBOOL(X18) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fconj__2) ).

fof(help_c__fconj__3,axiom,
    ! [X16,X18] :
      ( ~ hBOOL(hAPP(hAPP(c_fconj,X18),X16))
      | hBOOL(X16) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fconj__3) ).

fof(fact_empty__Collect__eq,axiom,
    ! [X18,X5] :
      ( c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X5),X18)
    <=> ! [X3] : ~ hBOOL(hAPP(X18,X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__Collect__eq) ).

fof(fact_Collect__empty__eq,axiom,
    ! [X18,X5] :
      ( hAPP(c_Set_OCollect(X5),X18) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
    <=> ! [X3] : ~ hBOOL(hAPP(X18,X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__empty__eq) ).

fof(help_c__fequal__1,axiom,
    ! [X33,X25] :
      ( ~ hBOOL(hAPP(hAPP(c_fequal,X25),X33))
      | X25 = X33 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fequal__1) ).

fof(fact_nat__of__code,axiom,
    ! [X98] : hAPP(c_Code__Numeral_Onat__of,X98) = c_Code__Numeral_Onat__of__aux(X98,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__of__code) ).

fof(fact_list__ex1__simps_I1_J,axiom,
    ! [X18,X5] : ~ c_List_Olist__ex1(X5,X18,c_List_Olist_ONil(X5)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__ex1__simps_I1_J) ).

fof(fact_list__ex__simps_I2_J,axiom,
    ! [X18,X5] : ~ c_List_Olist__ex(X5,X18,c_List_Olist_ONil(X5)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__ex__simps_I2_J) ).

fof(fact_succ__def,axiom,
    ! [X96] : c_Int_Osucc(X96) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X96),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_succ__def) ).

fof(fact_pred__def,axiom,
    ! [X96] : c_Int_Opred(X96) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X96),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__def) ).

fof(fact_upt__0,axiom,
    ! [X98] : c_List_Oupt(X98,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_upt__0) ).

fof(help_c__fconj__1,axiom,
    ! [X16,X18] :
      ( ~ hBOOL(X18)
      | ~ hBOOL(X16)
      | hBOOL(hAPP(hAPP(c_fconj,X18),X16)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fconj__1) ).

fof(fact_add__Min,axiom,
    ! [X96] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),X96) = c_Int_Opred(X96),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Min) ).

fof(fact_nonzero__number__of__Min,axiom,
    ! [X58] :
      ( class_Int_Onumber__ring(X58)
     => ~ c_Int_Oiszero(X58,hAPP(c_Int_Onumber__class_Onumber__of(X58),c_Int_OMin)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__number__of__Min) ).

fof(help_c__fdisj__1,axiom,
    ! [X16,X18] :
      ( ~ hBOOL(X18)
      | hBOOL(hAPP(hAPP(c_fdisj,X18),X16)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fdisj__1) ).

fof(help_c__fdisj__2,axiom,
    ! [X18,X16] :
      ( ~ hBOOL(X16)
      | hBOOL(hAPP(hAPP(c_fdisj,X18),X16)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fdisj__2) ).

fof(help_c__fimplies__2,axiom,
    ! [X18,X16] :
      ( ~ hBOOL(X16)
      | hBOOL(hAPP(hAPP(c_fimplies,X18),X16)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fimplies__2) ).

fof(fact_rel__simps_I38_J,axiom,
    ! [X156] :
      ( c_Int_OPls = c_Int_OBit0(X156)
    <=> c_Int_OPls = X156 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I38_J) ).

fof(fact_rel__simps_I44_J,axiom,
    ! [X87] :
      ( c_Int_OBit0(X87) = c_Int_OPls
    <=> X87 = c_Int_OPls ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I44_J) ).

fof(fact_rel__simps_I45_J,axiom,
    ! [X96] : c_Int_OBit0(X96) != c_Int_OMin,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I45_J) ).

fof(fact_rel__simps_I42_J,axiom,
    ! [X99] : c_Int_OMin != c_Int_OBit0(X99),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I42_J) ).

fof(fact_not__neg__nat,axiom,
    ! [X94] :
      ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X94))
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X94)) = X94 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__neg__nat) ).

fof(fact_card__infinite,axiom,
    ! [X21,X5] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
     => hAPP(c_Finite__Set_Ocard(X5),X21) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__infinite) ).

fof(help_c__fNot__1,axiom,
    ! [X18] :
      ( ~ hBOOL(hAPP(c_fNot,X18))
      | ~ hBOOL(X18) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fNot__1) ).

fof(fact_not__iszero__1,axiom,
    ! [X58] :
      ( class_Rings_Osemiring__1(X58)
     => ~ c_Int_Oiszero(X58,c_Groups_Oone__class_Oone(X58)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__iszero__1) ).

fof(fact_equivpE,axiom,
    ! [X32,X5] :
      ( c_Equiv__Relations_Oequivp(X5,X32)
     => ~ ( c_Predicate_Oreflp(X5,X32)
         => ( c_Predicate_Osymp(X5,X32)
           => ~ c_Predicate_Otransp(X5,X32) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equivpE) ).

fof(help_c__fNot__2,axiom,
    ! [X18] :
      ( ~ ~ hBOOL(X18)
      | hBOOL(hAPP(c_fNot,X18)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fNot__2) ).

fof(fact_UN__equiv__class__type2,axiom,
    ! [X113,X223,X224,X2,X116,X213,X214,X20,X215,X216,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X216,X215)
     => ( c_Equiv__Relations_Oequiv(X20,X214,X213)
       => ( c_Equiv__Relations_Ocongruent2(X5,X20,tc_fun(X116,tc_HOL_Obool),X215,X213,X2)
         => ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X224),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X216),X215)))
           => ( hBOOL(hAPP(hAPP(c_member(tc_fun(X20,tc_HOL_Obool)),X223),hAPP(hAPP(c_Equiv__Relations_Oquotient(X20),X214),X213)))
             => ( ! [X138] :
                    ( hBOOL(hAPP(hAPP(c_member(X5),X138),X216))
                   => ! [X225] :
                        ( hBOOL(hAPP(hAPP(c_member(X20),X225),X214))
                       => hBOOL(hAPP(hAPP(c_member(tc_fun(X116,tc_HOL_Obool)),hAPP(hAPP(X2,X138),X225)),X113)) ) )
               => hBOOL(hAPP(hAPP(c_member(tc_fun(X116,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X116,tc_HOL_Obool)),X224),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_fun(X116,tc_HOL_Obool)),tc_fun(X116,tc_HOL_Obool),X5),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,tc_fun(X116,tc_HOL_Obool)),X223)),X2))),X113)) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__equiv__class__type2) ).

fof(fact_setsum__mult__setsum__if__inj,axiom,
    ! [X113,X21,X1,X2,X20,X5,X116] :
      ( class_Rings_Osemiring__0(X116)
     => ( c_Fun_Oinj__on(tc_prod(X5,X20),X116,hAPP(c_Product__Type_Oprod_Oprod__case(X5,X20,X116),hAPP(hAPP(c_COMBC(X5,tc_fun(X20,X116),tc_fun(X20,X116)),hAPP(hAPP(c_COMBB(tc_fun(X116,X116),tc_fun(tc_fun(X20,X116),tc_fun(X20,X116)),X5),c_COMBB(X116,X116,X20)),hAPP(hAPP(c_COMBB(X116,tc_fun(X116,X116),X5),c_Groups_Otimes__class_Otimes(X116)),X2))),X1)),hAPP(hAPP(c_Product__Type_OSigma(X5,X20),X21),hAPP(c_COMBK(tc_fun(X20,tc_HOL_Obool),X5),X113)))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X116),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X116),X2),X21)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X20,X116),X1),X113)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X116,X116),c_Fun_Oid(X116)),hAPP(c_Set_OCollect(X116),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X116),c_HOL_OEx(X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X20,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool),X116),hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(X20))),hAPP(hAPP(c_COMBC(X116,tc_fun(X5,tc_fun(X20,tc_HOL_Obool)),tc_fun(X5,tc_fun(X20,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool))),tc_fun(tc_fun(X5,tc_fun(X20,tc_HOL_Obool)),tc_fun(X5,tc_fun(X20,tc_HOL_Obool))),X116),c_COMBS(X5,tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X20,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X5,tc_fun(tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool))),X116),hAPP(c_COMBB(tc_fun(X20,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),X5),c_COMBS(X20,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X20,tc_HOL_Obool)),tc_fun(X5,tc_fun(X20,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X116),hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X20),c_fconj))),hAPP(hAPP(c_COMBC(X116,tc_fun(X5,tc_fun(X20,X116)),tc_fun(X5,tc_fun(X20,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X20,X116),tc_fun(X20,tc_HOL_Obool)),tc_fun(tc_fun(X5,tc_fun(X20,X116)),tc_fun(X5,tc_fun(X20,tc_HOL_Obool))),X116),c_COMBB(tc_fun(X20,X116),tc_fun(X20,tc_HOL_Obool),X5)),hAPP(hAPP(c_COMBB(tc_fun(X116,tc_HOL_Obool),tc_fun(tc_fun(X20,X116),tc_fun(X20,tc_HOL_Obool)),X116),c_COMBB(X116,tc_HOL_Obool,X20)),c_fequal))),hAPP(hAPP(c_COMBC(X5,tc_fun(X20,X116),tc_fun(X20,X116)),hAPP(hAPP(c_COMBB(tc_fun(X116,X116),tc_fun(tc_fun(X20,X116),tc_fun(X20,X116)),X5),c_COMBB(X116,X116,X20)),hAPP(hAPP(c_COMBB(X116,tc_fun(X116,X116),X5),c_Groups_Otimes__class_Otimes(X116)),X2))),X1)))))),hAPP(hAPP(c_COMBC(X5,tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),X5),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X20)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X21)))),hAPP(hAPP(c_COMBC(X20,tc_fun(X20,tc_HOL_Obool),tc_HOL_Obool),c_member(X20)),X113))))))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__mult__setsum__if__inj) ).

fof(fact_rel__comp__def,axiom,
    ! [X76,X171,X20,X116,X5] : hAPP(hAPP(c_Relation_Orel__comp(X5,X116,X20),X171),X76) = hAPP(c_Set_OCollect(tc_prod(X5,X20)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X20,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_fun(X116,tc_HOL_Obool)),tc_fun(X20,tc_HOL_Obool),X5),hAPP(c_COMBB(tc_fun(X116,tc_HOL_Obool),tc_HOL_Obool,X20),c_HOL_OEx(X116))),hAPP(hAPP(c_COMBC(X5,tc_fun(X20,tc_fun(X116,tc_HOL_Obool)),tc_fun(X20,tc_fun(X116,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X116,tc_HOL_Obool),tc_fun(X116,tc_HOL_Obool)),tc_fun(tc_fun(X20,tc_fun(X116,tc_HOL_Obool)),tc_fun(X20,tc_fun(X116,tc_HOL_Obool))),X5),c_COMBB(tc_fun(X116,tc_HOL_Obool),tc_fun(X116,tc_HOL_Obool),X20)),hAPP(hAPP(c_COMBB(tc_fun(X116,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X116,tc_HOL_Obool),tc_fun(X116,tc_HOL_Obool)),X5),c_COMBS(X116,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X116,tc_HOL_Obool),tc_fun(X116,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X116),c_fconj)),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X116),tc_HOL_Obool),tc_fun(X116,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X116,tc_fun(tc_fun(tc_prod(X5,X116),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X116),tc_HOL_Obool),tc_fun(X116,tc_HOL_Obool)),X5),c_COMBC(X116,tc_fun(tc_prod(X5,X116),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X116,tc_prod(X5,X116)),tc_fun(X116,tc_fun(tc_fun(tc_prod(X5,X116),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X116),tc_fun(tc_fun(tc_prod(X5,X116),tc_HOL_Obool),tc_HOL_Obool),X116),c_member(tc_prod(X5,X116)))),c_Product__Type_OPair(X5,X116)))),X171))))),hAPP(hAPP(c_COMBC(X20,tc_fun(tc_prod(X116,X20),tc_HOL_Obool),tc_fun(X116,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X116,tc_fun(tc_fun(tc_prod(X116,X20),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X116,X20),tc_HOL_Obool),tc_fun(X116,tc_HOL_Obool)),X20),c_COMBC(X116,tc_fun(tc_prod(X116,X20),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X116,tc_prod(X116,X20)),tc_fun(X116,tc_fun(tc_fun(tc_prod(X116,X20),tc_HOL_Obool),tc_HOL_Obool)),X20),hAPP(c_COMBB(tc_prod(X116,X20),tc_fun(tc_fun(tc_prod(X116,X20),tc_HOL_Obool),tc_HOL_Obool),X116),c_member(tc_prod(X116,X20)))),hAPP(c_COMBC(X116,X20,tc_prod(X116,X20)),c_Product__Type_OPair(X116,X20))))),X76))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__comp__def) ).

fof(fact_min__max_Osup__Inf2__distrib,axiom,
    ! [X113,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X113))
           => ( X113 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X21)),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X113)) = c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool),X5),hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(X5))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),tc_fun(tc_fun(X5,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_fun(X5,tc_HOL_Obool))),X5),c_COMBS(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X5,tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),X5),hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X5),hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_fun(X5,X5)),tc_fun(X5,tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),tc_fun(tc_fun(X5,tc_fun(X5,X5)),tc_fun(X5,tc_fun(X5,tc_HOL_Obool))),X5),c_COMBB(tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool),X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBB(X5,tc_HOL_Obool,X5)),c_fequal))),c_Orderings_Oord__class_Omax(X5)))))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X21)))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X113))))))) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup__Inf2__distrib) ).

fof(fact_min__max_Oinf__Sup2__distrib,axiom,
    ! [X113,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X113))
           => ( X113 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X21)),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X113)) = c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool),X5),hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(X5))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),tc_fun(tc_fun(X5,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_fun(X5,tc_HOL_Obool))),X5),c_COMBS(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X5,tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),X5),hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X5),hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_fun(X5,X5)),tc_fun(X5,tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),tc_fun(tc_fun(X5,tc_fun(X5,X5)),tc_fun(X5,tc_fun(X5,tc_HOL_Obool))),X5),c_COMBB(tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool),X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBB(X5,tc_HOL_Obool,X5)),c_fequal))),c_Orderings_Oord__class_Omin(X5)))))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X21)))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X113))))))) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__Sup2__distrib) ).

fof(fact_inf__Sup2__distrib,axiom,
    ! [X113,X21,X5] :
      ( class_Lattices_Odistrib__lattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X113))
           => ( X113 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),c_Big__Operators_Olattice__class_OSup__fin(X5,X21)),c_Big__Operators_Olattice__class_OSup__fin(X5,X113)) = c_Big__Operators_Olattice__class_OSup__fin(X5,hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool),X5),hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(X5))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),tc_fun(tc_fun(X5,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_fun(X5,tc_HOL_Obool))),X5),c_COMBS(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X5,tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),X5),hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X5),hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_fun(X5,X5)),tc_fun(X5,tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),tc_fun(tc_fun(X5,tc_fun(X5,X5)),tc_fun(X5,tc_fun(X5,tc_HOL_Obool))),X5),c_COMBB(tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool),X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBB(X5,tc_HOL_Obool,X5)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(X5)))))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X21)))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X113))))))) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__Sup2__distrib) ).

fof(fact_sup__Inf2__distrib,axiom,
    ! [X113,X21,X5] :
      ( class_Lattices_Odistrib__lattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X113))
           => ( X113 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),c_Big__Operators_Olattice__class_OInf__fin(X5,X21)),c_Big__Operators_Olattice__class_OInf__fin(X5,X113)) = c_Big__Operators_Olattice__class_OInf__fin(X5,hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool),X5),hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(X5))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),tc_fun(tc_fun(X5,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_fun(X5,tc_HOL_Obool))),X5),c_COMBS(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X5,tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),X5),hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X5),hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_fun(X5,X5)),tc_fun(X5,tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),tc_fun(tc_fun(X5,tc_fun(X5,X5)),tc_fun(X5,tc_fun(X5,tc_HOL_Obool))),X5),c_COMBB(tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool),X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBB(X5,tc_HOL_Obool,X5)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(X5)))))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X21)))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X113))))))) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__Inf2__distrib) ).

fof(fact_set__Cons__def,axiom,
    ! [X198,X21,X5] : c_List_Oset__Cons(X5,X21,X198) = hAPP(c_Set_OCollect(tc_List_Olist(X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(X5)),c_HOL_OEx(X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool),tc_List_Olist(X5)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(tc_List_Olist(X5)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_fun(X5,tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),tc_fun(X5,tc_fun(tc_List_Olist(X5),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_fun(tc_List_Olist(X5),tc_HOL_Obool))),tc_fun(tc_fun(X5,tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),tc_fun(X5,tc_fun(tc_List_Olist(X5),tc_HOL_Obool))),tc_List_Olist(X5)),c_COMBS(X5,tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_fun(tc_List_Olist(X5),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_List_Olist(X5),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X5,tc_fun(tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_fun(tc_List_Olist(X5),tc_HOL_Obool))),tc_List_Olist(X5)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X5),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),X5),c_COMBS(tc_List_Olist(X5),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),tc_fun(X5,tc_fun(tc_List_Olist(X5),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(X5)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_fun(tc_List_Olist(X5),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X5)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_fun(X5,tc_fun(tc_List_Olist(X5),tc_List_Olist(X5))),tc_fun(X5,tc_fun(tc_List_Olist(X5),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(X5),tc_List_Olist(X5)),tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),tc_fun(tc_fun(X5,tc_fun(tc_List_Olist(X5),tc_List_Olist(X5))),tc_fun(X5,tc_fun(tc_List_Olist(X5),tc_HOL_Obool))),tc_List_Olist(X5)),c_COMBB(tc_fun(tc_List_Olist(X5),tc_List_Olist(X5)),tc_fun(tc_List_Olist(X5),tc_HOL_Obool),X5)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X5),tc_List_Olist(X5)),tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),tc_List_Olist(X5)),c_COMBB(tc_List_Olist(X5),tc_HOL_Obool,tc_List_Olist(X5))),c_fequal))),c_List_Olist_OCons(X5)))))),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),X5),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X5))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X21)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(X5))),X198)))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__Cons__def) ).

fof(fact_image__INT,axiom,
    ! [X157,X113,X21,X116,X112,X2,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,X2,X112)
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X116),X3),X21))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(X113,X3)),X112)) )
       => ( hBOOL(hAPP(hAPP(c_member(X116),X157),X21))
         => hAPP(c_Set_Oimage(X5,X20,X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X116,tc_fun(X5,tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X116,tc_fun(X20,tc_HOL_Obool)),X21),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool),X116),c_Set_Oimage(X5,X20,X2)),X113)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__INT) ).

fof(fact_inf__Int__eq2,axiom,
    ! [X33,X25,X192,X32,X20,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_fun(X20,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_fun(tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),X5),c_COMBC(X20,tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_prod(X5,X20)),tc_fun(X20,tc_fun(tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X20),tc_fun(tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_HOL_Obool),X20),c_member(tc_prod(X5,X20)))),c_Product__Type_OPair(X5,X20)))),X32)),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_fun(tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),X5),c_COMBC(X20,tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_prod(X5,X20)),tc_fun(X20,tc_fun(tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X20),tc_fun(tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_HOL_Obool),X20),c_member(tc_prod(X5,X20)))),c_Product__Type_OPair(X5,X20)))),X192)),X25),X33))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X20)),hAPP(hAPP(c_Product__Type_OPair(X5,X20),X25),X33)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X5,X20),tc_HOL_Obool)),X32),X192))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__Int__eq2) ).

fof(fact_sup__Un__eq2,axiom,
    ! [X33,X25,X192,X32,X20,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_fun(X20,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_fun(tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),X5),c_COMBC(X20,tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_prod(X5,X20)),tc_fun(X20,tc_fun(tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X20),tc_fun(tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_HOL_Obool),X20),c_member(tc_prod(X5,X20)))),c_Product__Type_OPair(X5,X20)))),X32)),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_fun(tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),X5),c_COMBC(X20,tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_prod(X5,X20)),tc_fun(X20,tc_fun(tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X20),tc_fun(tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_HOL_Obool),X20),c_member(tc_prod(X5,X20)))),c_Product__Type_OPair(X5,X20)))),X192)),X25),X33))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X20)),hAPP(hAPP(c_Product__Type_OPair(X5,X20),X25),X33)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X20),tc_HOL_Obool)),X32),X192))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__Un__eq2) ).

fof(fact_lenlex__conv,axiom,
    ! [X171,X5] : c_List_Olenlex(X5,X171) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X5),tc_List_Olist(X5),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(X5),tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X5),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),tc_List_Olist(X5)),c_COMBS(tc_List_Olist(X5),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_fun(tc_List_Olist(X5),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(X5)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X5)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_fun(tc_List_Olist(X5),tc_Nat_Onat),tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X5),tc_Nat_Onat),tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),tc_List_Olist(X5)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X5))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X5)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X5))))),c_Nat_Osize__class_Osize(tc_List_Olist(X5)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(X5),tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X5),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),tc_List_Olist(X5)),c_COMBS(tc_List_Olist(X5),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_fun(tc_List_Olist(X5),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(X5)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X5)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_fun(tc_List_Olist(X5),tc_Nat_Onat),tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X5),tc_Nat_Onat),tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),tc_List_Olist(X5)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X5))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X5)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X5))))),c_Nat_Osize__class_Osize(tc_List_Olist(X5)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_fun(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_HOL_Obool),tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X5),tc_fun(tc_fun(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_HOL_Obool),tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),tc_List_Olist(X5)),c_COMBC(tc_List_Olist(X5),tc_fun(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),tc_fun(tc_List_Olist(X5),tc_fun(tc_fun(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(X5)),hAPP(c_COMBB(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_fun(tc_fun(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X5)),c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))))),c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5))))),c_List_Olex(X5,X171)))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lenlex__conv) ).

fof(fact_foldl__apply,axiom,
    ! [X76,X1,X122,X2,X20,X116,X239,X5] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X239)))
         => hAPP(c_Fun_Ocomp(X116,X116,X20,hAPP(X2,X3)),X122) = hAPP(c_Fun_Ocomp(X20,X116,X20,X122),hAPP(X1,X3)) )
     => hAPP(c_List_Ofoldl(X116,X5,hAPP(c_COMBC(X5,X116,X116),X2),hAPP(X122,X76)),X239) = hAPP(X122,hAPP(c_List_Ofoldl(X20,X5,hAPP(c_COMBC(X5,X20,X20),X1),X76),X239)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldl__apply) ).

fof(fact_INF__INT__eq2,axiom,
    ! [X33,X25,X171,X116,X20,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X20,tc_fun(X116,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X20,X116),tc_HOL_Obool),tc_fun(X20,tc_fun(X116,tc_HOL_Obool)),X5),hAPP(c_COMBC(X20,tc_fun(tc_prod(X20,X116),tc_HOL_Obool),tc_fun(X116,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X116,tc_fun(tc_fun(tc_prod(X20,X116),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X20,X116),tc_HOL_Obool),tc_fun(X116,tc_HOL_Obool)),X20),c_COMBC(X116,tc_fun(tc_prod(X20,X116),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X116,tc_prod(X20,X116)),tc_fun(X116,tc_fun(tc_fun(tc_prod(X20,X116),tc_HOL_Obool),tc_HOL_Obool)),X20),hAPP(c_COMBB(tc_prod(X20,X116),tc_fun(tc_fun(tc_prod(X20,X116),tc_HOL_Obool),tc_HOL_Obool),X116),c_member(tc_prod(X20,X116)))),c_Product__Type_OPair(X20,X116))))),X171)),X25),X33))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(X20,X116)),hAPP(hAPP(c_Product__Type_OPair(X20,X116),X25),X33)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(tc_prod(X20,X116),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),X171))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF__INT__eq2) ).

fof(fact_SUP__UN__eq2,axiom,
    ! [X33,X25,X171,X116,X20,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X20,tc_fun(X116,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X20,X116),tc_HOL_Obool),tc_fun(X20,tc_fun(X116,tc_HOL_Obool)),X5),hAPP(c_COMBC(X20,tc_fun(tc_prod(X20,X116),tc_HOL_Obool),tc_fun(X116,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X116,tc_fun(tc_fun(tc_prod(X20,X116),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X20,X116),tc_HOL_Obool),tc_fun(X116,tc_HOL_Obool)),X20),c_COMBC(X116,tc_fun(tc_prod(X20,X116),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X116,tc_prod(X20,X116)),tc_fun(X116,tc_fun(tc_fun(tc_prod(X20,X116),tc_HOL_Obool),tc_HOL_Obool)),X20),hAPP(c_COMBB(tc_prod(X20,X116),tc_fun(tc_fun(tc_prod(X20,X116),tc_HOL_Obool),tc_HOL_Obool),X116),c_member(tc_prod(X20,X116)))),c_Product__Type_OPair(X20,X116))))),X171)),X25),X33))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(X20,X116)),hAPP(hAPP(c_Product__Type_OPair(X20,X116),X25),X33)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(tc_prod(X20,X116),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),X171))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUP__UN__eq2) ).

fof(fact_pred__comp__rel__comp__eq,axiom,
    ! [X33,X25,X76,X171,X116,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X5,X20,X116,hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_fun(tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),X5),c_COMBC(X20,tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_prod(X5,X20)),tc_fun(X20,tc_fun(tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X20),tc_fun(tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_HOL_Obool),X20),c_member(tc_prod(X5,X20)))),c_Product__Type_OPair(X5,X20)))),X171),hAPP(hAPP(c_COMBC(X20,tc_fun(tc_prod(X20,X116),tc_HOL_Obool),tc_fun(X116,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X116,tc_fun(tc_fun(tc_prod(X20,X116),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X20,X116),tc_HOL_Obool),tc_fun(X116,tc_HOL_Obool)),X20),c_COMBC(X116,tc_fun(tc_prod(X20,X116),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X116,tc_prod(X20,X116)),tc_fun(X116,tc_fun(tc_fun(tc_prod(X20,X116),tc_HOL_Obool),tc_HOL_Obool)),X20),hAPP(c_COMBB(tc_prod(X20,X116),tc_fun(tc_fun(tc_prod(X20,X116),tc_HOL_Obool),tc_HOL_Obool),X116),c_member(tc_prod(X20,X116)))),c_Product__Type_OPair(X20,X116)))),X76)),X25),X33))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X116)),hAPP(hAPP(c_Product__Type_OPair(X5,X116),X25),X33)),hAPP(hAPP(c_Relation_Orel__comp(X5,X20,X116),X171),X76))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__comp__rel__comp__eq) ).

fof(fact_UN__equiv__class__inject,axiom,
    ! [X196,X194,X2,X20,X171,X21,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X21,X171)
     => ( c_Equiv__Relations_Ocongruent(X5,tc_fun(X20,tc_HOL_Obool),X171,X2)
       => ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X20,tc_HOL_Obool)),X194),X2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X20,tc_HOL_Obool)),X196),X2)
         => ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X194),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X21),X171)))
           => ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X196),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X21),X171)))
             => ( ! [X3] :
                    ( hBOOL(hAPP(hAPP(c_member(X5),X3),X21))
                   => ! [X177] :
                        ( hBOOL(hAPP(hAPP(c_member(X5),X177),X21))
                       => ( hAPP(X2,X3) = hAPP(X2,X177)
                         => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X177)),X171)) ) ) )
               => X194 = X196 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__equiv__class__inject) ).

fof(fact_hoare__derivs_OBody,axiom,
    ! [X200,X16,X18,X4,X5] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool)),X4),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X5),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(X5,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X5)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X5,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X5))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X5,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X5))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(X5)),X18)),c_Com_Ocom_OBODY)),X16)),X200)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X5),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(X5,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X5)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X5,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X5))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X5,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X5))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(X5)),X18)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),X16)),X200))
     => c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X5),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(X5,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X5)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X5,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X5))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X5,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X5))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(X5)),X18)),c_Com_Ocom_OBODY)),X16)),X200)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hoare__derivs_OBody) ).

fof(fact_finite__image__set,axiom,
    ! [X2,X20,X18,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(c_Set_OCollect(X5),X18)))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X20),hAPP(c_Set_OCollect(X20),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X20),c_HOL_OEx(X5)),hAPP(hAPP(c_COMBC(X20,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X20),c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X20),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj)),hAPP(hAPP(c_COMBC(X20,tc_fun(X5,X20),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_fun(tc_fun(X5,X20),tc_fun(X5,tc_HOL_Obool)),X20),c_COMBB(X20,tc_HOL_Obool,X5)),c_fequal)),X2)))),X18))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__image__set) ).

fof(fact_setsum__reindex__cong,axiom,
    ! [X122,X1,X113,X21,X2,X20,X5,X116] :
      ( class_Groups_Ocomm__monoid__add(X116)
     => ( c_Fun_Oinj__on(X5,X20,X2,X21)
       => ( X113 = hAPP(c_Set_Oimage(X5,X20,X2),X21)
         => ( ! [X187] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X187),X21))
               => hAPP(X1,X187) = hAPP(X122,hAPP(X2,X187)) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X20,X116),X122),X113) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X116),X1),X21) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__reindex__cong) ).

fof(fact_Body1,axiom,
    ! [X17,X200,X16,X18,X4,X5] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool)),X4),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X5),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(X5,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X5)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X5,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X5))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X5,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X5))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(X5)),X18)),c_Com_Ocom_OBODY)),X16)),X200)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X5),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(X5,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X5)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X5,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X5))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X5,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X5))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(X5)),X18)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),X16)),X200))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X17),X200))
       => c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X5)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),hAPP(X18,X17)),hAPP(c_Com_Ocom_OBODY,X17)),hAPP(X16,X17))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool)))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Body1) ).

fof(fact_conversep__converse__eq,axiom,
    ! [X33,X25,X171,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X5,X20,hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_fun(tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),X5),c_COMBC(X20,tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_prod(X5,X20)),tc_fun(X20,tc_fun(tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X20),tc_fun(tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_HOL_Obool),X20),c_member(tc_prod(X5,X20)))),c_Product__Type_OPair(X5,X20)))),X171)),X25),X33))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(X20,X5)),hAPP(hAPP(c_Product__Type_OPair(X20,X5),X25),X33)),hAPP(c_Relation_Oconverse(X5,X20),X171))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_conversep__converse__eq) ).

fof(fact_strong__setprod__reindex__cong,axiom,
    ! [X122,X1,X113,X21,X2,X20,X5,X116] :
      ( class_Groups_Ocomm__monoid__mult(X116)
     => ( c_Fun_Oinj__on(X5,X20,X2,X21)
       => ( X113 = hAPP(c_Set_Oimage(X5,X20,X2),X21)
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X3),X21))
               => hAPP(X1,X3) = hAPP(hAPP(c_Fun_Ocomp(X20,X116,X5,X122),X2),X3) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X20,X116),X122),X113) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X116),X1),X21) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_strong__setprod__reindex__cong) ).

fof(fact_setsum__ivl__cong,axiom,
    ! [X1,X2,X22,X24,X23,X6,X5,X20] :
      ( ( class_Groups_Ocomm__monoid__add(X20)
        & class_Orderings_Oord(X5) )
     => ( X6 = X23
       => ( X24 = X22
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X23),X3))
               => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X3),X22))
                 => hAPP(X2,X3) = hAPP(X1,X3) ) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X6),X24)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X1),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X23),X22)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__ivl__cong) ).

fof(fact_minus__int__def,axiom,
    ! [X120] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X120) = 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,X120)),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/sandbox/benchmark/theBenchmark.p',fact_minus__int__def) ).

fof(fact_exE__realizer,axiom,
    ! [X116,X2,X16,X160,X5,X20,X18] :
      ( hBOOL(hAPP(hAPP(X18,hAPP(c_Product__Type_Osnd(X20,X5),X160)),hAPP(c_Product__Type_Ofst(X20,X5),X160)))
     => ( ! [X3,X177] :
            ( hBOOL(hAPP(hAPP(X18,X177),X3))
           => hBOOL(hAPP(X16,hAPP(hAPP(X2,X3),X177))) )
       => hBOOL(hAPP(X16,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X20,X5,X116),X2),X160))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_exE__realizer) ).

fof(fact_rp__inv__image__def,axiom,
    ! [X20,X5] : c_FunDef_Orp__inv__image(X5,X20) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_fun(X20,X5),tc_prod(tc_fun(tc_prod(X20,X20),tc_HOL_Obool),tc_fun(tc_prod(X20,X20),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_fun(X20,X5),tc_fun(tc_prod(X20,X20),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_fun(X20,X5),tc_prod(tc_fun(tc_prod(X20,X20),tc_HOL_Obool),tc_fun(tc_prod(X20,X20),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(X20,X5),tc_fun(tc_prod(X20,X20),tc_HOL_Obool)),tc_fun(tc_fun(X20,X5),tc_prod(tc_fun(tc_prod(X20,X20),tc_HOL_Obool),tc_fun(tc_prod(X20,X20),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_fun(X20,X5),tc_fun(tc_prod(X20,X20),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_fun(X20,X5),tc_prod(tc_fun(tc_prod(X20,X20),tc_HOL_Obool),tc_fun(tc_prod(X20,X20),tc_HOL_Obool))))),tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(X20,X5),tc_fun(tc_prod(X20,X20),tc_HOL_Obool)),tc_fun(tc_fun(X20,X5),tc_prod(tc_fun(tc_prod(X20,X20),tc_HOL_Obool),tc_fun(tc_prod(X20,X20),tc_HOL_Obool))),tc_fun(tc_prod(X5,X5),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X20,X5),tc_fun(tc_fun(tc_prod(X20,X20),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X20,X20),tc_HOL_Obool),tc_fun(tc_prod(X20,X20),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(X20,X5),tc_fun(tc_prod(X20,X20),tc_HOL_Obool)),tc_fun(tc_fun(X20,X5),tc_prod(tc_fun(tc_prod(X20,X20),tc_HOL_Obool),tc_fun(tc_prod(X20,X20),tc_HOL_Obool)))),tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_COMBS(tc_fun(X20,X5),tc_fun(tc_prod(X20,X20),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X20,X20),tc_HOL_Obool),tc_fun(tc_prod(X20,X20),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X20,X5),tc_fun(tc_prod(X20,X20),tc_HOL_Obool)),tc_fun(tc_fun(X20,X5),tc_fun(tc_fun(tc_prod(X20,X20),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X20,X20),tc_HOL_Obool),tc_fun(tc_prod(X20,X20),tc_HOL_Obool)))),tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(X20,X20),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X20,X20),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X20,X20),tc_HOL_Obool),tc_fun(tc_prod(X20,X20),tc_HOL_Obool))),tc_fun(X20,X5)),c_Product__Type_OPair(tc_fun(tc_prod(X20,X20),tc_HOL_Obool),tc_fun(tc_prod(X20,X20),tc_HOL_Obool)))),c_Relation_Oinv__image(X5,X20))))),c_Relation_Oinv__image(X5,X20))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rp__inv__image__def) ).

fof(fact_inv__image__def,axiom,
    ! [X2,X171,X5,X20] : hAPP(hAPP(c_Relation_Oinv__image(X20,X5),X171),X2) = hAPP(c_Set_OCollect(tc_prod(X5,X5)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X5,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X20,X20),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_fun(tc_prod(X20,X20),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X20,X20),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBC(X5,tc_fun(tc_prod(X20,X20),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_prod(X20,X20)),tc_fun(X5,tc_fun(tc_fun(tc_prod(X20,X20),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X20,X20),tc_fun(tc_fun(tc_prod(X20,X20),tc_HOL_Obool),tc_HOL_Obool),X5),c_member(tc_prod(X20,X20)))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,X20),tc_fun(X5,tc_prod(X20,X20))),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_prod(X20,X20)),tc_fun(tc_fun(X5,X20),tc_fun(X5,tc_prod(X20,X20))),X5),c_COMBB(X20,tc_prod(X20,X20),X5)),hAPP(hAPP(c_COMBB(X20,tc_fun(X20,tc_prod(X20,X20)),X5),c_Product__Type_OPair(X20,X20)),X2))),X2)))),X171))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__image__def) ).

fof(fact_set__zip,axiom,
    ! [X251,X239,X20,X5] : hAPP(c_List_Oset(tc_prod(X5,X20)),hAPP(hAPP(c_List_Ozip(X5,X20),X239),X251)) = hAPP(c_Set_OCollect(tc_prod(X5,X20)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(X5,X20)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(X5,X20),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(X5,X20)),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_prod(X5,X20)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(tc_prod(X5,X20),tc_fun(tc_Nat_Onat,tc_prod(X5,X20)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(X5,X20)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(X5,X20)),c_COMBB(tc_prod(X5,X20),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X20,tc_prod(X5,X20)),hAPP(hAPP(c_COMBB(X5,tc_fun(X20,tc_prod(X5,X20)),tc_Nat_Onat),c_Product__Type_OPair(X5,X20)),hAPP(c_List_Onth(X5),X239))),hAPP(c_List_Onth(X20),X251)))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X20)),X251)))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__zip) ).

fof(fact_LoopF,axiom,
    ! [X23,X24,X18,X4,X5] : c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X5)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),X5),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj)),X18))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate),c_fNot),X24))),c_Com_Ocom_OWhile(X24,X23)),X18)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_LoopF) ).

fof(fact_pred__subset__eq2,axiom,
    ! [X192,X32,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_fun(X20,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_fun(tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),X5),c_COMBC(X20,tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_prod(X5,X20)),tc_fun(X20,tc_fun(tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X20),tc_fun(tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_HOL_Obool),X20),c_member(tc_prod(X5,X20)))),c_Product__Type_OPair(X5,X20)))),X32)),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_fun(tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),X5),c_COMBC(X20,tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_prod(X5,X20)),tc_fun(X20,tc_fun(tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X20),tc_fun(tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_HOL_Obool),X20),c_member(tc_prod(X5,X20)))),c_Product__Type_OPair(X5,X20)))),X192)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X20),tc_HOL_Obool)),X32),X192)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__subset__eq2) ).

fof(fact_Pow__Compl,axiom,
    ! [X21,X5] : hAPP(c_Set_OPow(X5),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X21)) = hAPP(c_Set_OCollect(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(X5,tc_HOL_Obool)),c_HOL_OEx(tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),c_COMBS(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,tc_fun(X5,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(X5,tc_HOL_Obool)),hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X21)),c_Set_OPow(X5))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__Compl) ).

fof(fact_UN__equiv__class__type,axiom,
    ! [X113,X194,X2,X20,X171,X21,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X21,X171)
     => ( c_Equiv__Relations_Ocongruent(X5,tc_fun(X20,tc_HOL_Obool),X171,X2)
       => ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X194),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X21),X171)))
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X3),X21))
               => hBOOL(hAPP(hAPP(c_member(tc_fun(X20,tc_HOL_Obool)),hAPP(X2,X3)),X113)) )
           => hBOOL(hAPP(hAPP(c_member(tc_fun(X20,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X20,tc_HOL_Obool)),X194),X2)),X113)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__equiv__class__type) ).

fof(fact_INF2__I,axiom,
    ! [X116,X20,X23,X24,X113,X21,X5] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),X21))
         => hBOOL(hAPP(hAPP(hAPP(X113,X3),X24),X23)) )
     => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X20,tc_fun(X116,tc_HOL_Obool))),X21),X113),X24),X23)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF2__I) ).

fof(fact_INF2__iff,axiom,
    ! [X23,X24,X113,X21,X116,X20,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X20,tc_fun(X116,tc_HOL_Obool))),X21),X113),X24),X23))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),X21))
         => hBOOL(hAPP(hAPP(hAPP(X113,X3),X24),X23)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF2__iff) ).

fof(fact_min__max_Osup__Inf1__distrib,axiom,
    ! [X25,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X25),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X21)) = c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(X5)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBB(X5,tc_HOL_Obool,X5)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(X5),X25))))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X21))))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup__Inf1__distrib) ).

fof(fact_min__max_Oinf__Sup1__distrib,axiom,
    ! [X25,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X25),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X21)) = c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(X5)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBB(X5,tc_HOL_Obool,X5)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(X5),X25))))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X21))))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__Sup1__distrib) ).

fof(fact_inf__Sup1__distrib,axiom,
    ! [X25,X21,X5] :
      ( class_Lattices_Odistrib__lattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X25),c_Big__Operators_Olattice__class_OSup__fin(X5,X21)) = c_Big__Operators_Olattice__class_OSup__fin(X5,hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(X5)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBB(X5,tc_HOL_Obool,X5)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X25))))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X21))))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__Sup1__distrib) ).

fof(fact_sup__Inf1__distrib,axiom,
    ! [X25,X21,X5] :
      ( class_Lattices_Odistrib__lattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X25),c_Big__Operators_Olattice__class_OInf__fin(X5,X21)) = c_Big__Operators_Olattice__class_OInf__fin(X5,hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(X5)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBB(X5,tc_HOL_Obool,X5)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X25))))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X21))))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__Inf1__distrib) ).

fof(fact_add__Min__commute,axiom,
    ! [X87,X207,X5] :
      ( class_Groups_Olinordered__ab__semigroup__add(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X207))
       => ( X207 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X87),c_Big__Operators_Olinorder__class_OMin(X5,X207)) = c_Big__Operators_Olinorder__class_OMin(X5,hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(X5)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBB(X5,tc_HOL_Obool,X5)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(X5),X87))))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X207))))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Min__commute) ).

fof(fact_add__Max__commute,axiom,
    ! [X87,X207,X5] :
      ( class_Groups_Olinordered__ab__semigroup__add(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X207))
       => ( X207 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X87),c_Big__Operators_Olinorder__class_OMax(X5,X207)) = c_Big__Operators_Olinorder__class_OMax(X5,hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(X5)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBB(X5,tc_HOL_Obool,X5)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(X5),X87))))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X207))))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Max__commute) ).

fof(fact_escape,axiom,
    ! [X16,X23,X4,X5,X18] :
      ( ! [X29,X30] :
          ( hBOOL(hAPP(hAPP(X18,X29),X30))
         => c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X5)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),X5),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),X30))),X23),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),X5),hAPP(X16,X29)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool)))) )
     => c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X5)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),X18),X23),X16)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_escape) ).

fof(fact_listrel__iff__zip,axiom,
    ! [X171,X251,X239,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X239),X251)),c_List_Olistrel(X5,X171)))
    <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X251)
        & ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X3),hAPP(c_List_Oset(tc_prod(X5,X5)),hAPP(hAPP(c_List_Ozip(X5,X5),X239),X251))))
           => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5,X5,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBC(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_prod(X5,X5)),tc_fun(X5,tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X5),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool),X5),c_member(tc_prod(X5,X5)))),c_Product__Type_OPair(X5,X5)))),X171)),X3)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__iff__zip) ).

fof(fact_DomainP__Domain__eq,axiom,
    ! [X25,X171,X20,X5] :
      ( hBOOL(hAPP(c_Predicate_ODomainP(X5,X20,hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_fun(tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),X5),c_COMBC(X20,tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_prod(X5,X20)),tc_fun(X20,tc_fun(tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X20),tc_fun(tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_HOL_Obool),X20),c_member(tc_prod(X5,X20)))),c_Product__Type_OPair(X5,X20)))),X171)),X25))
    <=> hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_Relation_ODomain(X5,X20),X171))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DomainP__Domain__eq) ).

fof(fact_RangeP__Range__eq,axiom,
    ! [X25,X171,X20,X5] :
      ( hBOOL(hAPP(c_Predicate_ORangeP(X5,X20,hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_fun(tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),X5),c_COMBC(X20,tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_prod(X5,X20)),tc_fun(X20,tc_fun(tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X20),tc_fun(tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_HOL_Obool),X20),c_member(tc_prod(X5,X20)))),c_Product__Type_OPair(X5,X20)))),X171)),X25))
    <=> hBOOL(hAPP(hAPP(c_member(X20),X25),hAPP(c_Relation_ORange(X5,X20),X171))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_RangeP__Range__eq) ).

fof(fact_accp__acc__eq,axiom,
    ! [X25,X171,X5] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(X5,hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBC(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_prod(X5,X5)),tc_fun(X5,tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X5),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool),X5),c_member(tc_prod(X5,X5)))),c_Product__Type_OPair(X5,X5)))),X171)),X25))
    <=> hBOOL(hAPP(hAPP(c_member(X5),X25),c_Wellfounded_Oacc(X5,X171))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_accp__acc__eq) ).

fof(fact_lazy__sequence__size__code,axiom,
    ! [X277,X76,X5] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X5,X76),X277) = c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(X5,tc_Lazy__Sequence_Olazy__sequence(X5)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(X5,tc_Lazy__Sequence_Olazy__sequence(X5),tc_Nat_Onat),hAPP(hAPP(c_COMBC(X5,tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(X5),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X5),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(X5),tc_Nat_Onat)),X5),c_COMBC(tc_Lazy__Sequence_Olazy__sequence(X5),tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X5),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(X5),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),X5),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(X5)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat))),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_Lazy__Sequence_Olazy__sequence(X5),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(X5),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X5),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(X5),tc_Nat_Onat)),X5),c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Lazy__Sequence_Olazy__sequence(X5))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),X5),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X76))),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X5,X76))))),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Lazy__Sequence_Oyield(X5),X277)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lazy__sequence__size__code) ).

fof(fact_conseq12,axiom,
    ! [X16,X18,X28,X23,X31,X4,X5] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X5)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),X31),X23),X28)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool))))
     => ( ! [X29,X30] :
            ( hBOOL(hAPP(hAPP(X18,X29),X30))
           => ! [X70] :
                ( ! [X71] :
                    ( hBOOL(hAPP(hAPP(X31,X71),X30))
                   => hBOOL(hAPP(hAPP(X28,X71),X70)) )
               => hBOOL(hAPP(hAPP(X16,X29),X70)) ) )
       => c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X5)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),X18),X23),X16)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool)))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_conseq12) ).

fof(fact_fold__graph_H_Oequations_I2_J,axiom,
    ! [X59,X27,X26,X60,X63,X20,X5] :
      ( c_Nitpick_Ofold__graph_H(X5,X20,X63,X60,X26,hAPP(hAPP(X63,X27),X59))
    <=> ( ( X26 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
          & hAPP(hAPP(X63,X27),X59) = X60 )
        | ? [X3,X177] :
            ( hAPP(hAPP(X63,X27),X59) = hAPP(hAPP(X63,X3),X177)
            & hBOOL(hAPP(hAPP(c_member(X5),X3),X26))
            & c_Nitpick_Ofold__graph_H(X5,X20,X63,X60,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X26),hAPP(hAPP(c_Set_Oinsert(X5),X3),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),X177) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__graph_H_Oequations_I2_J) ).

fof(fact_SUP2__iff,axiom,
    ! [X23,X24,X113,X21,X116,X20,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X20,tc_fun(X116,tc_HOL_Obool))),X21),X113),X24),X23))
    <=> ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),X21))
          & hBOOL(hAPP(hAPP(hAPP(X113,X3),X24),X23)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUP2__iff) ).

fof(fact_partition_Osimps_I2_J,axiom,
    ! [X239,X25,X18,X5] : c_List_Opartition(X5,X18,hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X5),tc_List_Olist(X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_COMBS(tc_List_Olist(X5),tc_fun(tc_List_Olist(X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),tc_fun(tc_List_Olist(X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X5),tc_fun(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))),tc_fun(tc_fun(tc_List_Olist(X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),tc_fun(tc_List_Olist(X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))),tc_List_Olist(X5)),c_COMBS(tc_List_Olist(X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),tc_fun(tc_List_Olist(X5),tc_fun(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))),tc_List_Olist(X5)),hAPP(c_COMBB(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_fun(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),tc_List_Olist(X5)),hAPP(c_If(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(X18,X25)))),hAPP(hAPP(c_COMBB(tc_List_Olist(X5),tc_fun(tc_List_Olist(X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),tc_List_Olist(X5)),c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(c_List_Olist_OCons(X5),X25))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_fun(tc_List_Olist(X5),tc_List_Olist(X5)),tc_fun(tc_List_Olist(X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),tc_fun(tc_fun(tc_List_Olist(X5),tc_List_Olist(X5)),tc_fun(tc_List_Olist(X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))),tc_List_Olist(X5)),c_COMBB(tc_List_Olist(X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_List_Olist(X5))),c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)))),hAPP(c_List_Olist_OCons(X5),X25)))),c_List_Opartition(X5,X18,X239)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_partition_Osimps_I2_J) ).

fof(fact_hoare__derivs_Oequations_I8_J,axiom,
    ! [X60,X63,X26,X27,X5] : c_Hoare__Mirabelle_Ohoare__derivs(X5,X27,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X5)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),X5),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),X26)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),X63)),X60))),c_Com_Ocom_OAss(X63,X60)),X26)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hoare__derivs_Oequations_I8_J) ).

fof(fact_Ass,axiom,
    ! [X6,X194,X18,X4,X5] : c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X5)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),X5),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),X18)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),X194)),X6))),c_Com_Ocom_OAss(X194,X6)),X18)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ass) ).

fof(fact_lexn_Osimps_I2_J,axiom,
    ! [X50,X171,X5] : hAPP(c_List_Olexn(X5,X171),hAPP(c_Nat_OSuc,X50)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(X5,tc_List_Olist(X5)),tc_prod(X5,tc_List_Olist(X5))),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),c_Product__Type_Omap__pair(tc_prod(X5,tc_List_Olist(X5)),tc_List_Olist(X5),tc_prod(X5,tc_List_Olist(X5)),tc_List_Olist(X5),hAPP(c_Product__Type_Oprod_Oprod__case(X5,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olist_OCons(X5)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olist_OCons(X5)))),c_Wellfounded_Olex__prod(X5,tc_List_Olist(X5),X171,hAPP(c_List_Olexn(X5,X171),X50)))),hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X5),tc_List_Olist(X5),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),tc_List_Olist(X5)),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X5))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X5)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X5)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X5)))),hAPP(c_Nat_OSuc,X50))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X5)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X5)))),hAPP(c_Nat_OSuc,X50)))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexn_Osimps_I2_J) ).

fof(fact_set__sublist,axiom,
    ! [X221,X239,X5] : hAPP(c_List_Oset(X5),c_List_Osublist(X5,X239,X221)) = hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X5),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_Nat_Onat,X5),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,X5),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X5),c_COMBB(X5,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(X5),X239))))),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X221))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__sublist) ).

fof(fact_setsum__multicount__gen,axiom,
    ! [X87,X32,X15,X20,X76,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X76))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X20),X15))
       => ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X20),X3),X15))
             => hAPP(c_Finite__Set_Ocard(X5),hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X76))),hAPP(hAPP(c_COMBC(X5,X20,tc_HOL_Obool),X32),X3)))) = hAPP(X87,X3) )
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_Nat_Onat,X5),c_Finite__Set_Ocard(X20)),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool),X5),c_Set_OCollect(X20)),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool),X5),hAPP(c_COMBS(X20,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X20),c_fconj),hAPP(hAPP(c_COMBC(X20,tc_fun(X20,tc_HOL_Obool),tc_HOL_Obool),c_member(X20)),X15)))),X32)))),X76) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X20,tc_Nat_Onat),X87),X15) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__multicount__gen) ).

fof(fact_set__conv__nth,axiom,
    ! [X239,X5] : hAPP(c_List_Oset(X5),X239) = hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X5),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_Nat_Onat,X5),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,X5),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X5),c_COMBB(X5,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(X5),X239))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__conv__nth) ).

fof(fact_Sigma__def,axiom,
    ! [X113,X21,X20,X5] : hAPP(hAPP(c_Product__Type_OSigma(X5,X20),X21),X113) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(tc_prod(X5,X20),tc_HOL_Obool)),X21),hAPP(hAPP(c_COMBS(X5,tc_fun(X20,tc_fun(tc_prod(X5,X20),tc_HOL_Obool)),tc_fun(tc_prod(X5,X20),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_fun(tc_fun(X20,tc_fun(tc_prod(X5,X20),tc_HOL_Obool)),tc_fun(tc_prod(X5,X20),tc_HOL_Obool)),X5),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,tc_fun(tc_prod(X5,X20),tc_HOL_Obool))),X113)),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_fun(X20,tc_fun(tc_prod(X5,X20),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_fun(tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_fun(tc_prod(X5,X20),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_fun(X20,tc_fun(tc_prod(X5,X20),tc_HOL_Obool))),X5),c_COMBC(X20,tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_fun(tc_prod(X5,X20),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_prod(X5,X20)),tc_fun(X20,tc_fun(tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_fun(tc_prod(X5,X20),tc_HOL_Obool))),X5),hAPP(c_COMBB(tc_prod(X5,X20),tc_fun(tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_fun(tc_prod(X5,X20),tc_HOL_Obool)),X20),c_Set_Oinsert(tc_prod(X5,X20)))),c_Product__Type_OPair(X5,X20)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X20),tc_HOL_Obool))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__def) ).

fof(fact_setsum__multicount,axiom,
    ! [X87,X32,X212,X20,X192,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X192))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X20),X212))
       => ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X20),X3),X212))
             => hAPP(c_Finite__Set_Ocard(X5),hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X192))),hAPP(hAPP(c_COMBC(X5,X20,tc_HOL_Obool),X32),X3)))) = X87 )
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_Nat_Onat,X5),c_Finite__Set_Ocard(X20)),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool),X5),c_Set_OCollect(X20)),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool),X5),hAPP(c_COMBS(X20,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X20),c_fconj),hAPP(hAPP(c_COMBC(X20,tc_fun(X20,tc_HOL_Obool),tc_HOL_Obool),c_member(X20)),X212)))),X32)))),X192) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X87),hAPP(c_Finite__Set_Ocard(X20),X212)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__multicount) ).

fof(fact_setsum__setsum__restrict,axiom,
    ! [X32,X2,X212,X20,X192,X5,X116] :
      ( class_Groups_Ocomm__monoid__add(X116)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X192))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X20),X212))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X116),hAPP(hAPP(c_COMBS(X5,tc_fun(X20,tc_HOL_Obool),X116),hAPP(hAPP(c_COMBB(tc_fun(X20,X116),tc_fun(tc_fun(X20,tc_HOL_Obool),X116),X5),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X20,X116)),X2)),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool),X5),c_Set_OCollect(X20)),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool),X5),hAPP(c_COMBS(X20,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X20),c_fconj),hAPP(hAPP(c_COMBC(X20,tc_fun(X20,tc_HOL_Obool),tc_HOL_Obool),c_member(X20)),X212)))),X32)))),X192) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X20,X116),hAPP(hAPP(c_COMBS(X20,tc_fun(X5,tc_HOL_Obool),X116),hAPP(hAPP(c_COMBB(tc_fun(X5,X116),tc_fun(tc_fun(X5,tc_HOL_Obool),X116),X20),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X116)),hAPP(c_COMBC(X5,X20,X116),X2))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X20),c_Set_OCollect(X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X20),hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X192)))),hAPP(c_COMBC(X5,X20,tc_HOL_Obool),X32))))),X212) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__setsum__restrict) ).

fof(fact_anamorph_Osimps,axiom,
    ! [X25,X2,X5,X20,X87] :
      ( ( X87 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => hAPP(hAPP(c_Lazy__Sequence_Oanamorph(X20,X5,X2),X87),X25) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),X20),c_List_Olist_ONil(X5)),X25) )
      & ( X87 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => hAPP(hAPP(c_Lazy__Sequence_Oanamorph(X20,X5,X2),X87),X25) = c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(X5),X20),tc_prod(X5,X20),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),X20),c_List_Olist_ONil(X5)),X25),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X20,tc_prod(tc_List_Olist(X5),X20)),hAPP(hAPP(c_COMBC(X5,tc_fun(X20,tc_prod(tc_List_Olist(X5),X20)),tc_fun(X20,tc_prod(tc_List_Olist(X5),X20))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(X5),X20),tc_prod(tc_List_Olist(X5),X20)),tc_fun(tc_fun(X20,tc_prod(tc_List_Olist(X5),X20)),tc_fun(X20,tc_prod(tc_List_Olist(X5),X20))),X5),c_COMBB(tc_prod(tc_List_Olist(X5),X20),tc_prod(tc_List_Olist(X5),X20),X20)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X5),tc_fun(X20,tc_prod(tc_List_Olist(X5),X20))),tc_fun(tc_prod(tc_List_Olist(X5),X20),tc_prod(tc_List_Olist(X5),X20)),X5),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X5),X20,tc_prod(tc_List_Olist(X5),X20))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X5),tc_List_Olist(X5)),tc_fun(tc_List_Olist(X5),tc_fun(X20,tc_prod(tc_List_Olist(X5),X20))),X5),hAPP(c_COMBB(tc_List_Olist(X5),tc_fun(X20,tc_prod(tc_List_Olist(X5),X20)),tc_List_Olist(X5)),c_Product__Type_OPair(tc_List_Olist(X5),X20))),c_List_Olist_OCons(X5))))),hAPP(c_Lazy__Sequence_Oanamorph(X20,X5,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X87),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))))),hAPP(X2,X25)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_anamorph_Osimps) ).

fof(fact_sequence__trans,axiom,
    ! [X87,X82,X171,X2,X5] :
      ( ! [X146] : hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),hAPP(X2,hAPP(c_Nat_OSuc,X146))),hAPP(X2,X146))),c_Transitive__Closure_Ortrancl(X5,X171)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),hAPP(X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X82),X87))),hAPP(X2,X82))),c_Transitive__Closure_Ortrancl(X5,X171))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sequence__trans) ).

fof(fact_fun__lub__def,axiom,
    ! [X25,X21,X311,X116,X5,X20] : c_Partial__Function_Ofun__lub(X20,X5,X116,X311,X21,X25) = hAPP(X311,hAPP(c_Set_OCollect(X20),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X116,X20),tc_HOL_Obool),tc_HOL_Obool,X20),c_HOL_OEx(tc_fun(X116,X20))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X116,X20),tc_HOL_Obool),tc_fun(tc_fun(X116,X20),tc_HOL_Obool),X20),hAPP(c_COMBS(tc_fun(X116,X20),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X116,X20)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(X116,X20),tc_fun(tc_fun(X116,X20),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X116,X20))),X21)))),hAPP(hAPP(c_COMBC(X20,tc_fun(tc_fun(X116,X20),X20),tc_fun(tc_fun(X116,X20),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X116,X20),X20),tc_fun(tc_fun(X116,X20),tc_HOL_Obool)),X20),c_COMBB(X20,tc_HOL_Obool,tc_fun(X116,X20))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(X116,X20),X116,X20),c_COMBI(tc_fun(X116,X20))),X25)))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__lub__def) ).

fof(fact_Inf__fun__def,axiom,
    ! [X25,X21,X20,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X20,X5),X21),X25) = c_Complete__Lattice_OInf__class_OInf(X5,hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X20,X5),tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(tc_fun(X20,X5))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X20,X5),tc_HOL_Obool),tc_fun(tc_fun(X20,X5),tc_HOL_Obool),X5),hAPP(c_COMBS(tc_fun(X20,X5),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X20,X5)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(X20,X5),tc_fun(tc_fun(X20,X5),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X20,X5))),X21)))),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_fun(X20,X5),X5),tc_fun(tc_fun(X20,X5),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X20,X5),X5),tc_fun(tc_fun(X20,X5),tc_HOL_Obool)),X5),c_COMBB(X5,tc_HOL_Obool,tc_fun(X20,X5))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(X20,X5),X20,X5),c_COMBI(tc_fun(X20,X5))),X25)))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fun__def) ).

fof(fact_Inf__apply,axiom,
    ! [X25,X21,X20,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X20,X5),X21),X25) = c_Complete__Lattice_OInf__class_OInf(X5,hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X20,X5),tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(tc_fun(X20,X5))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X20,X5),tc_HOL_Obool),tc_fun(tc_fun(X20,X5),tc_HOL_Obool),X5),hAPP(c_COMBS(tc_fun(X20,X5),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X20,X5)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(X20,X5),tc_fun(tc_fun(X20,X5),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X20,X5))),X21)))),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_fun(X20,X5),X5),tc_fun(tc_fun(X20,X5),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X20,X5),X5),tc_fun(tc_fun(X20,X5),tc_HOL_Obool)),X5),c_COMBB(X5,tc_HOL_Obool,tc_fun(X20,X5))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(X20,X5),X20,X5),c_COMBI(tc_fun(X20,X5))),X25)))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__apply) ).

fof(fact_Sup__apply,axiom,
    ! [X25,X21,X20,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X20,X5),X21),X25) = c_Complete__Lattice_OSup__class_OSup(X5,hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X20,X5),tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(tc_fun(X20,X5))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X20,X5),tc_HOL_Obool),tc_fun(tc_fun(X20,X5),tc_HOL_Obool),X5),hAPP(c_COMBS(tc_fun(X20,X5),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X20,X5)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(X20,X5),tc_fun(tc_fun(X20,X5),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X20,X5))),X21)))),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_fun(X20,X5),X5),tc_fun(tc_fun(X20,X5),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X20,X5),X5),tc_fun(tc_fun(X20,X5),tc_HOL_Obool)),X5),c_COMBB(X5,tc_HOL_Obool,tc_fun(X20,X5))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(X20,X5),X20,X5),c_COMBI(tc_fun(X20,X5))),X25)))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__apply) ).

fof(fact_Sup__fun__def,axiom,
    ! [X25,X21,X20,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X20,X5),X21),X25) = c_Complete__Lattice_OSup__class_OSup(X5,hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X20,X5),tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(tc_fun(X20,X5))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X20,X5),tc_HOL_Obool),tc_fun(tc_fun(X20,X5),tc_HOL_Obool),X5),hAPP(c_COMBS(tc_fun(X20,X5),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X20,X5)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(X20,X5),tc_fun(tc_fun(X20,X5),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X20,X5))),X21)))),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_fun(X20,X5),X5),tc_fun(tc_fun(X20,X5),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X20,X5),X5),tc_fun(tc_fun(X20,X5),tc_HOL_Obool)),X5),c_COMBB(X5,tc_HOL_Obool,tc_fun(X20,X5))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(X20,X5),X20,X5),c_COMBI(tc_fun(X20,X5))),X25)))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fun__def) ).

fof(fact_divmod__int__rel__def,axiom,
    ! [X24,X6] : c_Divides_Odivmod__int__rel(X6,X24) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fequal,X6))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24)))))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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)),X24))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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)),X24))))),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)),X24)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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),X24))),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/sandbox/benchmark/theBenchmark.p',fact_divmod__int__rel__def) ).

fof(fact_setsum__product,axiom,
    ! [X113,X1,X116,X21,X2,X20,X5] :
      ( class_Rings_Osemiring__0(X5)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X20,X5),X2),X21)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X116,X5),X1),X113)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X20,X5),hAPP(hAPP(c_COMBC(X20,tc_fun(X116,tc_HOL_Obool),X5),hAPP(hAPP(c_COMBB(tc_fun(X116,X5),tc_fun(tc_fun(X116,tc_HOL_Obool),X5),X20),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X116,X5)),hAPP(hAPP(c_COMBC(X20,tc_fun(X116,X5),tc_fun(X116,X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,X5),tc_fun(tc_fun(X116,X5),tc_fun(X116,X5)),X20),c_COMBB(X5,X5,X116)),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X20),c_Groups_Otimes__class_Otimes(X5)),X2))),X1))),X113)),X21) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__product) ).

fof(fact_fold__image__Sigma,axiom,
    ! [X1,X113,X20,X21,X5,X116] :
      ( class_Groups_Ocomm__monoid__mult(X116)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),X21))
             => hBOOL(hAPP(c_Finite__Set_Ofinite(X20),hAPP(X113,X3))) )
         => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X116,X5,c_Groups_Otimes__class_Otimes(X116)),hAPP(hAPP(c_COMBS(X5,tc_fun(X20,tc_HOL_Obool),X116),hAPP(hAPP(c_COMBC(X5,X116,tc_fun(tc_fun(X20,tc_HOL_Obool),X116)),hAPP(hAPP(c_COMBB(tc_fun(X20,X116),tc_fun(X116,tc_fun(tc_fun(X20,tc_HOL_Obool),X116)),X5),c_Finite__Set_Ofold__image(X116,X20,c_Groups_Otimes__class_Otimes(X116))),X1)),c_Groups_Oone__class_Oone(X116))),X113)),c_Groups_Oone__class_Oone(X116)),X21) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X116,tc_prod(X5,X20),c_Groups_Otimes__class_Otimes(X116)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X20,X116),X1)),c_Groups_Oone__class_Oone(X116)),hAPP(hAPP(c_Product__Type_OSigma(X5,X20),X21),X113)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__image__Sigma) ).

fof(fact_finite__lists__length__le,axiom,
    ! [X50,X21,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X5)),hAPP(c_Set_OCollect(tc_List_Olist(X5)),hAPP(hAPP(c_COMBS(tc_List_Olist(X5),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X5)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X5)),c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool))),c_List_Oset(X5))),X21))),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X5)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X5)))),X50))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__lists__length__le) ).

fof(fact_finite__lists__length__eq,axiom,
    ! [X50,X21,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X5)),hAPP(c_Set_OCollect(tc_List_Olist(X5)),hAPP(hAPP(c_COMBS(tc_List_Olist(X5),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X5)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X5)),c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool))),c_List_Oset(X5))),X21))),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X5)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X5)))),X50))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__lists__length__eq) ).

fof(fact_folding__image__simple_Ounion__inter__neutral,axiom,
    ! [X113,X21,X205,X1,X120,X2,X20,X5] :
      ( c_Finite__Set_Ofolding__image__simple(X5,X20,X2,X120,X1,X205)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X20),X21))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X20),X113))
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X20),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20,tc_HOL_Obool)),X21),X113)))
               => hAPP(X1,X3) = X120 )
           => hAPP(X205,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20,tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(X2,hAPP(X205,X21)),hAPP(X205,X113)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple_Ounion__inter__neutral) ).

fof(fact_nat__def,axiom,
    ! [X120] : hAPP(c_Int_Onat,X120) = 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,X120)),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/sandbox/benchmark/theBenchmark.p',fact_nat__def) ).

fof(fact_nat__intermed__int__val,axiom,
    ! [X87,X2,X50,X95] :
      ( ! [X146] :
          ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X146))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X146),X50)) )
         => 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),X146),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X2,X146)))),c_Groups_Oone__class_Oone(tc_Int_Oint))) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),X50))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X2,X95)),X87))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X87),hAPP(X2,X50)))
           => ? [X146] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X146))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X146),X50))
                & hAPP(X2,X146) = X87 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__intermed__int__val) ).

fof(fact_finite__Collect__bex,axiom,
    ! [X16,X20,X21,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X20),hAPP(c_Set_OCollect(X20),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X20),c_HOL_OEx(X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X20),hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X21)))),X16)))))
      <=> ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X21))
           => hBOOL(hAPP(c_Finite__Set_Ofinite(X20),hAPP(c_Set_OCollect(X20),hAPP(hAPP(c_COMBC(X20,X5,tc_HOL_Obool),X16),X3)))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Collect__bex) ).

fof(fact_Sigma__mono,axiom,
    ! [X144,X113,X20,X112,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),X112))
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X21))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20,tc_HOL_Obool)),hAPP(X113,X3)),hAPP(X144,X3))) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X20),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X5,X20),X21),X113)),hAPP(hAPP(c_Product__Type_OSigma(X5,X20),X112),X144))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__mono) ).

fof(fact_mem__splitI2,axiom,
    ! [X23,X120,X116,X20,X5,X160] :
      ( ! [X187,X188] :
          ( X160 = hAPP(hAPP(c_Product__Type_OPair(X5,X20),X187),X188)
         => hBOOL(hAPP(hAPP(c_member(X116),X120),hAPP(hAPP(X23,X187),X188))) )
     => hBOOL(hAPP(hAPP(c_member(X116),X120),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5,X20,tc_fun(X116,tc_HOL_Obool)),X23),X160))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__splitI2) ).

fof(fact_converse__def,axiom,
    ! [X171,X5,X20] : hAPP(c_Relation_Oconverse(X20,X5),X171) = hAPP(c_Set_OCollect(tc_prod(X5,X20)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X20,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X20,X5),tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_fun(tc_fun(tc_prod(X20,X5),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X20,X5),tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),X5),c_COMBC(X20,tc_fun(tc_prod(X20,X5),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_prod(X20,X5)),tc_fun(X20,tc_fun(tc_fun(tc_prod(X20,X5),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X20,X5),tc_fun(tc_fun(tc_prod(X20,X5),tc_HOL_Obool),tc_HOL_Obool),X20),c_member(tc_prod(X20,X5)))),hAPP(c_COMBC(X20,X5,tc_prod(X20,X5)),c_Product__Type_OPair(X20,X5))))),X171))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__def) ).

fof(fact_fold__image__UN__disjoint,axiom,
    ! [X1,X21,X20,X221,X5,X116] :
      ( class_Groups_Ocomm__monoid__mult(X116)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X221))
       => ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),X221))
             => hBOOL(hAPP(c_Finite__Set_Ofinite(X20),hAPP(X21,X3))) )
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X3),X221))
               => ! [X204] :
                    ( hBOOL(hAPP(hAPP(c_member(X5),X204),X221))
                   => ( X3 != X204
                     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20,tc_HOL_Obool)),hAPP(X21,X3)),hAPP(X21,X204)) = c_Orderings_Obot__class_Obot(tc_fun(X20,tc_HOL_Obool)) ) ) )
           => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X116,X20,c_Groups_Otimes__class_Otimes(X116)),X1),c_Groups_Oone__class_Oone(X116)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X20,tc_HOL_Obool)),X221),X21)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X116,X5,c_Groups_Otimes__class_Otimes(X116)),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),X116,X5),hAPP(hAPP(c_Finite__Set_Ofold__image(X116,X20,c_Groups_Otimes__class_Otimes(X116)),X1),c_Groups_Oone__class_Oone(X116))),X21)),c_Groups_Oone__class_Oone(X116)),X221) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__image__UN__disjoint) ).

fof(fact_INT__eq,axiom,
    ! [X113,X21,X5,X20] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X20,tc_fun(X5,tc_HOL_Obool)),X21),X113) = c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),hAPP(c_Set_OCollect(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_HOL_Obool,tc_fun(X5,tc_HOL_Obool)),c_HOL_OEx(X20)),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(c_COMBS(X20,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X20),c_fconj),hAPP(hAPP(c_COMBC(X20,tc_fun(X20,tc_HOL_Obool),tc_HOL_Obool),c_member(X20)),X21)))),hAPP(hAPP(c_COMBC(tc_fun(X5,tc_HOL_Obool),tc_fun(X20,tc_fun(X5,tc_HOL_Obool)),tc_fun(X20,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X20,tc_fun(X5,tc_HOL_Obool)),tc_fun(X20,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X20)),c_fequal)),X113))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__eq) ).

fof(fact_UN__eq,axiom,
    ! [X113,X21,X5,X20] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,tc_fun(X5,tc_HOL_Obool)),X21),X113) = c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),hAPP(c_Set_OCollect(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_HOL_Obool,tc_fun(X5,tc_HOL_Obool)),c_HOL_OEx(X20)),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(c_COMBS(X20,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X20),c_fconj),hAPP(hAPP(c_COMBC(X20,tc_fun(X20,tc_HOL_Obool),tc_HOL_Obool),c_member(X20)),X21)))),hAPP(hAPP(c_COMBC(tc_fun(X5,tc_HOL_Obool),tc_fun(X20,tc_fun(X5,tc_HOL_Obool)),tc_fun(X20,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X20,tc_fun(X5,tc_HOL_Obool)),tc_fun(X20,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X20)),c_fequal)),X113))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__eq) ).

fof(fact_part__equivp__typedef,axiom,
    ! [X32,X5] :
      ( c_Equiv__Relations_Opart__equivp(X5,X32)
     => ? [X158] : hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X158),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,tc_fun(X5,tc_HOL_Obool)),c_HOL_OEx(X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBS(X5,X5,tc_HOL_Obool),X32),c_COMBI(X5))))),hAPP(hAPP(c_COMBC(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X5,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X5)),c_fequal)),X32))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_part__equivp__typedef) ).

fof(fact_card__less__Suc,axiom,
    ! [X82,X210] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X210))
     => 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)),X210))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X82))))) = 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)),X210))),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,X82))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__less__Suc) ).

fof(fact_setsum__image__gen,axiom,
    ! [X2,X116,X1,X192,X5,X20] :
      ( class_Groups_Ocomm__monoid__add(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X192))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X1),X192) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X116,X20),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),X20,X116),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X1)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X116),c_Set_OCollect(X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X116),hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X192)))),hAPP(c_COMBC(X5,X116,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X116,tc_fun(X116,tc_HOL_Obool),X5),c_fequal),X2)))))),hAPP(c_Set_Oimage(X5,X116,X2),X192)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__image__gen) ).

fof(fact_refl__on__def_H,axiom,
    ! [X171,X21,X5] :
      ( c_Relation_Orefl__on(X5,X21,X171)
    <=> ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X3),X171))
           => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5,X5,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X21)))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X21))),X3)) )
        & ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X21))
           => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X3)),X171)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__on__def_H) ).

fof(fact_zip__Cons,axiom,
    ! [X251,X33,X239,X20,X5] : hAPP(hAPP(c_List_Ozip(X5,X20),X239),hAPP(hAPP(c_List_Olist_OCons(X20),X33),X251)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(X5,X20)),X5,c_List_Olist_ONil(tc_prod(X5,X20)),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_List_Olist(X5),tc_List_Olist(tc_prod(X5,X20))),tc_fun(tc_List_Olist(X5),tc_List_Olist(tc_prod(X5,X20)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(X5,X20)),tc_List_Olist(tc_prod(X5,X20))),tc_fun(tc_fun(tc_List_Olist(X5),tc_List_Olist(tc_prod(X5,X20))),tc_fun(tc_List_Olist(X5),tc_List_Olist(tc_prod(X5,X20)))),X5),c_COMBB(tc_List_Olist(tc_prod(X5,X20)),tc_List_Olist(tc_prod(X5,X20)),tc_List_Olist(X5))),hAPP(hAPP(c_COMBB(tc_prod(X5,X20),tc_fun(tc_List_Olist(tc_prod(X5,X20)),tc_List_Olist(tc_prod(X5,X20))),X5),c_List_Olist_OCons(tc_prod(X5,X20))),hAPP(hAPP(c_COMBC(X5,X20,tc_prod(X5,X20)),c_Product__Type_OPair(X5,X20)),X33)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_List_Olist(X20),tc_List_Olist(tc_prod(X5,X20))),c_List_Ozip(X5,X20)),X251))),X239),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__Cons) ).

fof(fact_max__extp__max__ext__eq,axiom,
    ! [X199,X25,X32,X5] :
      ( c_Wellfounded_Omax__extp(X5,hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBC(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_prod(X5,X5)),tc_fun(X5,tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X5),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool),X5),c_member(tc_prod(X5,X5)))),c_Product__Type_OPair(X5,X5)))),X32),X25,X199)
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X25),X199)),c_Wellfounded_Omax__ext(X5,X32))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__extp__max__ext__eq) ).

fof(fact_listrelp__listrel__eq,axiom,
    ! [X199,X25,X171,X5] :
      ( c_List_Olistrelp(X5,hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBC(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_prod(X5,X5)),tc_fun(X5,tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X5),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool),X5),c_member(tc_prod(X5,X5)))),c_Product__Type_OPair(X5,X5)))),X171),X25,X199)
    <=> 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)),X25),X199)),c_List_Olistrel(X5,X171))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrelp__listrel__eq) ).

fof(fact_UN__Times__distrib,axiom,
    ! [X205,X234,X113,X21,X20,X5,X115,X116] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(X116,X115),tc_fun(tc_prod(X5,X20),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X116,X115),X21),hAPP(c_COMBK(tc_fun(X115,tc_HOL_Obool),X116),X113))),hAPP(c_Product__Type_Oprod_Oprod__case(X116,X115,tc_fun(tc_prod(X5,X20),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X116,tc_fun(X115,tc_fun(X5,tc_fun(X20,tc_HOL_Obool))),tc_fun(X115,tc_fun(tc_prod(X5,X20),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,tc_fun(X20,tc_HOL_Obool)),tc_fun(tc_prod(X5,X20),tc_HOL_Obool)),tc_fun(tc_fun(X115,tc_fun(X5,tc_fun(X20,tc_HOL_Obool))),tc_fun(X115,tc_fun(tc_prod(X5,X20),tc_HOL_Obool))),X116),c_COMBB(tc_fun(X5,tc_fun(X20,tc_HOL_Obool)),tc_fun(tc_prod(X5,X20),tc_HOL_Obool),X115)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_fun(X20,tc_HOL_Obool)),tc_fun(tc_prod(X5,X20),tc_HOL_Obool)),X116),c_Product__Type_OSigma(X5,X20)),X234))),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_fun(X5,tc_fun(X20,tc_HOL_Obool)),X115),c_COMBK(tc_fun(X20,tc_HOL_Obool),X5)),X205)))) = hAPP(hAPP(c_Product__Type_OSigma(X5,X20),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X116,tc_fun(X5,tc_HOL_Obool)),X21),X234)),hAPP(c_COMBK(tc_fun(X20,tc_HOL_Obool),X5),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X115,tc_fun(X20,tc_HOL_Obool)),X113),X205))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__Times__distrib) ).

fof(fact_equivp__equiv,axiom,
    ! [X21,X5] :
      ( c_Equiv__Relations_Oequiv(X5,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X21)
    <=> c_Equiv__Relations_Oequivp(X5,hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBC(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_prod(X5,X5)),tc_fun(X5,tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X5),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool),X5),c_member(tc_prod(X5,X5)))),c_Product__Type_OPair(X5,X5)))),X21)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equivp__equiv) ).

fof(fact_wfP__wf__eq,axiom,
    ! [X171,X5] :
      ( c_Wellfounded_OwfP(X5,hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBC(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_prod(X5,X5)),tc_fun(X5,tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X5),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool),X5),c_member(tc_prod(X5,X5)))),c_Product__Type_OPair(X5,X5)))),X171))
    <=> c_Wellfounded_Owf(X5,X171) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfP__wf__eq) ).

fof(fact_pred__equals__eq2,axiom,
    ! [X192,X32,X20,X5] :
      ( hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_fun(tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),X5),c_COMBC(X20,tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_prod(X5,X20)),tc_fun(X20,tc_fun(tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X20),tc_fun(tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_HOL_Obool),X20),c_member(tc_prod(X5,X20)))),c_Product__Type_OPair(X5,X20)))),X32) = hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_fun(tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),X5),c_COMBC(X20,tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_prod(X5,X20)),tc_fun(X20,tc_fun(tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_prod(X5,X20),tc_fun(tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_HOL_Obool),X20),c_member(tc_prod(X5,X20)))),c_Product__Type_OPair(X5,X20)))),X192)
    <=> X32 = X192 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__equals__eq2) ).

fof(fact_map__zip__map2,axiom,
    ! [X251,X1,X115,X239,X2,X5,X116,X20] : hAPP(hAPP(c_List_Omap(tc_prod(X20,X116),X5),X2),hAPP(hAPP(c_List_Ozip(X20,X116),X239),hAPP(hAPP(c_List_Omap(X115,X116),X1),X251))) = hAPP(hAPP(c_List_Omap(tc_prod(X20,X115),X5),hAPP(c_Product__Type_Oprod_Oprod__case(X20,X115,X5),hAPP(hAPP(c_COMBB(tc_fun(X115,tc_prod(X20,X116)),tc_fun(X115,X5),X20),hAPP(c_COMBB(tc_prod(X20,X116),X5,X115),X2)),hAPP(hAPP(c_COMBC(X20,tc_fun(X115,X116),tc_fun(X115,tc_prod(X20,X116))),hAPP(hAPP(c_COMBB(tc_fun(X116,tc_prod(X20,X116)),tc_fun(tc_fun(X115,X116),tc_fun(X115,tc_prod(X20,X116))),X20),c_COMBB(X116,tc_prod(X20,X116),X115)),c_Product__Type_OPair(X20,X116))),X1)))),hAPP(hAPP(c_List_Ozip(X20,X115),X239),X251)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__zip__map2) ).

fof(fact_fun__left__comm_Ofold__graph__insertE__aux,axiom,
    ! [X6,X33,X21,X120,X2,X20,X5] :
      ( c_Finite__Set_Ofun__left__comm(X5,X20,X2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X20,X2,X120,X21),X33))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X21))
         => ? [X295] :
              ( X33 = hAPP(hAPP(X2,X6),X295)
              & hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X20,X2,X120,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),X295)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__graph__insertE__aux) ).

fof(fact_zip__Cons1,axiom,
    ! [X251,X239,X25,X20,X5] : hAPP(hAPP(c_List_Ozip(X5,X20),hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239)),X251) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(X5,X20)),X20,c_List_Olist_ONil(tc_prod(X5,X20)),hAPP(hAPP(c_COMBC(X20,tc_fun(tc_List_Olist(X20),tc_List_Olist(tc_prod(X5,X20))),tc_fun(tc_List_Olist(X20),tc_List_Olist(tc_prod(X5,X20)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(X5,X20)),tc_List_Olist(tc_prod(X5,X20))),tc_fun(tc_fun(tc_List_Olist(X20),tc_List_Olist(tc_prod(X5,X20))),tc_fun(tc_List_Olist(X20),tc_List_Olist(tc_prod(X5,X20)))),X20),c_COMBB(tc_List_Olist(tc_prod(X5,X20)),tc_List_Olist(tc_prod(X5,X20)),tc_List_Olist(X20))),hAPP(hAPP(c_COMBB(tc_prod(X5,X20),tc_fun(tc_List_Olist(tc_prod(X5,X20)),tc_List_Olist(tc_prod(X5,X20))),X20),c_List_Olist_OCons(tc_prod(X5,X20))),hAPP(c_Product__Type_OPair(X5,X20),X25)))),hAPP(c_List_Ozip(X5,X20),X239))),X251),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__Cons1) ).

fof(fact_wf__if__measure,axiom,
    ! [X5,X1,X2,X18] :
      ( ! [X3] :
          ( hBOOL(hAPP(X18,X3))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X2,hAPP(X1,X3))),hAPP(X2,X3))) )
     => c_Wellfounded_Owf(X5,hAPP(c_Set_OCollect(tc_prod(X5,X5)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X5,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X5),hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),X18))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,X5),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBB(X5,tc_HOL_Obool,X5)),c_fequal)),X1))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__if__measure) ).

fof(fact_max__ext__compat,axiom,
    ! [X192,X32,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),X32),X192)),X32))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Wellfounded_Omax__ext(X5,X32)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(X5,X192)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(X5,X32))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__ext__compat) ).

fof(fact_min__ext__compat,axiom,
    ! [X192,X32,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),X32),X192)),X32))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Wellfounded_Omin__ext(X5,X32)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(X5,X192)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(X5,X32))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__ext__compat) ).

fof(fact_hoare__derivs_OIf,axiom,
    ! [X22,X16,X23,X24,X18,X4,X5] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X5)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),c_Hoare__Mirabelle_Opeek__and(X5,X18,X24)),X23),X16)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool))))
     => ( c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X5)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),c_Hoare__Mirabelle_Opeek__and(X5,X18,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),X24))),X22),X16)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool))))
       => c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X5)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),X18),c_Com_Ocom_OCond(X24,X23,X22)),X16)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool)))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hoare__derivs_OIf) ).

fof(fact_conseq1,axiom,
    ! [X18,X16,X23,X31,X4,X5] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X5)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),X31),X23),X16)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool))))
     => ( ! [X29,X30] :
            ( hBOOL(hAPP(hAPP(X18,X29),X30))
           => hBOOL(hAPP(hAPP(X31,X29),X30)) )
       => c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X5)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),X18),X23),X16)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool)))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_conseq1) ).

fof(fact_conseq2,axiom,
    ! [X16,X28,X23,X18,X4,X5] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X5)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),X18),X23),X28)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool))))
     => ( ! [X29,X30] :
            ( hBOOL(hAPP(hAPP(X28,X29),X30))
           => hBOOL(hAPP(hAPP(X16,X29),X30)) )
       => c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X5)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),X18),X23),X16)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool)))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_conseq2) ).

fof(fact_setsum__restrict__set_H,axiom,
    ! [X113,X2,X21,X5,X20] :
      ( class_Groups_Ocomm__monoid__add(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X2),hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X21))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X113)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),hAPP(hAPP(c_COMBC(X5,X20,X20),hAPP(hAPP(c_COMBS(X5,X20,tc_fun(X20,X20)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X20,tc_fun(X20,X20)),X5),c_If(X20)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X113))),X2)),c_Groups_Ozero__class_Ozero(X20))),X21) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__restrict__set_H) ).

fof(fact_zip__map__map,axiom,
    ! [X251,X1,X115,X239,X2,X116,X20,X5] : hAPP(hAPP(c_List_Ozip(X5,X20),hAPP(hAPP(c_List_Omap(X116,X5),X2),X239)),hAPP(hAPP(c_List_Omap(X115,X20),X1),X251)) = hAPP(hAPP(c_List_Omap(tc_prod(X116,X115),tc_prod(X5,X20)),hAPP(c_Product__Type_Oprod_Oprod__case(X116,X115,tc_prod(X5,X20)),hAPP(hAPP(c_COMBC(X116,tc_fun(X115,X20),tc_fun(X115,tc_prod(X5,X20))),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_prod(X5,X20)),tc_fun(tc_fun(X115,X20),tc_fun(X115,tc_prod(X5,X20))),X116),c_COMBB(X20,tc_prod(X5,X20),X115)),hAPP(hAPP(c_COMBB(X5,tc_fun(X20,tc_prod(X5,X20)),X116),c_Product__Type_OPair(X5,X20)),X2))),X1))),hAPP(hAPP(c_List_Ozip(X116,X115),X239),X251)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__map__map) ).

fof(fact_finite__psubset__def,axiom,
    ! [X5] : c_Wellfounded_Ofinite__psubset(X5) = hAPP(c_Set_OCollect(tc_prod(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),c_COMBS(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool))))),c_Finite__Set_Ofinite(X5)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__psubset__def) ).

fof(fact_map__pair__imageI,axiom,
    ! [X1,X2,X115,X116,X32,X24,X6,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X20)),hAPP(hAPP(c_Product__Type_OPair(X5,X20),X6),X24)),X32))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X116,X115)),hAPP(hAPP(c_Product__Type_OPair(X116,X115),hAPP(X2,X6)),hAPP(X1,X24))),hAPP(c_Set_Oimage(tc_prod(X5,X20),tc_prod(X116,X115),c_Product__Type_Omap__pair(X5,X116,X20,X115,X2,X1)),X32))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__pair__imageI) ).

fof(fact_New__Random__Sequence_Oneg__decr__bind__def,axiom,
    ! [X292,X293,X294,X2,X32,X5,X20] : c_New__Random__Sequence_Oneg__decr__bind(X20,X5,X32,X2,X294,X293,X292) = c_New__DSequence_Oneg__decr__bind(X20,X5,hAPP(hAPP(hAPP(X32,X294),X293),X292),hAPP(hAPP(c_COMBC(X20,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X5)))),hAPP(hAPP(c_COMBC(X20,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X5))))),hAPP(hAPP(c_COMBC(X20,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X5)))))),X2),X294)),X293)),X292)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_New__Random__Sequence_Oneg__decr__bind__def) ).

fof(fact_INTER__def,axiom,
    ! [X113,X21,X5,X20] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X20,tc_fun(X5,tc_HOL_Obool)),X21),X113) = hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OAll(X20)),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool),X5),hAPP(c_COMBS(X20,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X20),c_fimplies),hAPP(hAPP(c_COMBC(X20,tc_fun(X20,tc_HOL_Obool),tc_HOL_Obool),c_member(X20)),X21)))),hAPP(hAPP(c_COMBC(X5,tc_fun(X20,tc_fun(X5,tc_HOL_Obool)),tc_fun(X20,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X20,tc_fun(X5,tc_HOL_Obool)),tc_fun(X20,tc_HOL_Obool)),X5),c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X20)),c_member(X5))),X113)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INTER__def) ).

fof(fact_congruent__def,axiom,
    ! [X2,X171,X20,X5] :
      ( c_Equiv__Relations_Ocongruent(X5,X20,X171,X2)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X3),X171))
         => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5,X5,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,X20),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_fun(tc_fun(X5,X20),tc_fun(X5,tc_HOL_Obool)),X5),c_COMBB(X20,tc_HOL_Obool,X5)),hAPP(hAPP(c_COMBB(X20,tc_fun(X20,tc_HOL_Obool),X5),c_fequal),X2))),X2)),X3)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_congruent__def) ).

fof(fact_finite__Collect__bounded__ex,axiom,
    ! [X16,X20,X18,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(c_Set_OCollect(X5),X18)))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X20),hAPP(c_Set_OCollect(X20),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X20),c_HOL_OEx(X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X20),hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),X18))),X16)))))
      <=> ! [X177] :
            ( hBOOL(hAPP(X18,X177))
           => hBOOL(hAPP(c_Finite__Set_Ofinite(X20),hAPP(c_Set_OCollect(X20),hAPP(hAPP(c_COMBC(X20,X5,tc_HOL_Obool),X16),X177)))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Collect__bounded__ex) ).

fof(fact_setsum__Sigma,axiom,
    ! [X2,X113,X20,X21,X5,X116] :
      ( class_Groups_Ocomm__monoid__add(X116)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),X21))
             => hBOOL(hAPP(c_Finite__Set_Ofinite(X20),hAPP(X113,X3))) )
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X116),hAPP(hAPP(c_COMBS(X5,tc_fun(X20,tc_HOL_Obool),X116),hAPP(hAPP(c_COMBB(tc_fun(X20,X116),tc_fun(tc_fun(X20,tc_HOL_Obool),X116),X5),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X20,X116)),X2)),X113)),X21) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(X5,X20),X116),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X20,X116),X2)),hAPP(hAPP(c_Product__Type_OSigma(X5,X20),X21),X113)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__Sigma) ).

fof(fact_setprod__Sigma,axiom,
    ! [X2,X113,X20,X21,X5,X116] :
      ( class_Groups_Ocomm__monoid__mult(X116)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),X21))
             => hBOOL(hAPP(c_Finite__Set_Ofinite(X20),hAPP(X113,X3))) )
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X116),hAPP(hAPP(c_COMBS(X5,tc_fun(X20,tc_HOL_Obool),X116),hAPP(hAPP(c_COMBB(tc_fun(X20,X116),tc_fun(tc_fun(X20,tc_HOL_Obool),X116),X5),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X20,X116)),X2)),X113)),X21) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(X5,X20),X116),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X20,X116),X2)),hAPP(hAPP(c_Product__Type_OSigma(X5,X20),X21),X113)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__Sigma) ).

fof(fact_setsum__restrict__set,axiom,
    ! [X113,X2,X21,X5,X20] :
      ( class_Groups_Ocomm__monoid__add(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),hAPP(hAPP(c_COMBC(X5,X20,X20),hAPP(hAPP(c_COMBS(X5,X20,tc_fun(X20,X20)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X20,tc_fun(X20,X20)),X5),c_If(X20)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X113))),X2)),c_Groups_Ozero__class_Ozero(X20))),X21) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__restrict__set) ).

fof(fact_UN__finite2__subset,axiom,
    ! [X113,X87,X21,X5] :
      ( ! [X69] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X69)),X21)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X69),X87))),X113)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X21)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X113))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__finite2__subset) ).

fof(fact_New__Random__Sequence_Opos__decr__bind__def,axiom,
    ! [X292,X293,X294,X2,X32,X5,X20] : c_New__Random__Sequence_Opos__decr__bind(X20,X5,X32,X2,X294,X293,X292) = c_New__DSequence_Opos__decr__bind(X20,X5,hAPP(hAPP(hAPP(X32,X294),X293),X292),hAPP(hAPP(c_COMBC(X20,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X5))),hAPP(hAPP(c_COMBC(X20,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X5)))),hAPP(hAPP(c_COMBC(X20,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X5))))),X2),X294)),X293)),X292)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_New__Random__Sequence_Opos__decr__bind__def) ).

fof(fact_image__split__eq__Sigma,axiom,
    ! [X21,X1,X2,X20,X5,X116] : hAPP(c_Set_Oimage(X116,tc_prod(X5,X20),hAPP(hAPP(c_COMBS(X116,X20,tc_prod(X5,X20)),hAPP(hAPP(c_COMBB(X5,tc_fun(X20,tc_prod(X5,X20)),X116),c_Product__Type_OPair(X5,X20)),X2)),X1)),X21) = hAPP(hAPP(c_Product__Type_OSigma(X5,X20),hAPP(c_Set_Oimage(X116,X5,X2),X21)),hAPP(hAPP(c_COMBB(tc_fun(X116,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool),X5),c_Set_Oimage(X116,X20,X1)),hAPP(hAPP(c_COMBC(X5,tc_fun(X116,tc_HOL_Obool),tc_fun(X116,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X116,tc_HOL_Obool),tc_fun(tc_fun(X116,tc_HOL_Obool),tc_fun(X116,tc_HOL_Obool)),X5),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X116,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X116,tc_HOL_Obool),X5),c_Set_Ovimage(X116,X5,X2)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Set_Oinsert(X5)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))),X21))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__split__eq__Sigma) ).

fof(fact_small__lazy__list_Osimps,axiom,
    ! [X22,X5] :
      ( class_Lazy__Sequence_Osmall__lazy(X5)
     => c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(X5),X22) = c_Lazy__Sequence_Oappend(tc_List_Olist(X5),hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(X5)),c_List_Olist_ONil(X5)),hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X5))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22)),hAPP(c_Lazy__Sequence_Obind(tc_prod(X5,tc_List_Olist(X5)),tc_List_Olist(X5),c_Lazy__Sequence_Oproduct(X5,tc_List_Olist(X5),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X22),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X22),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Product__Type_Oprod_Oprod__case(X5,tc_List_Olist(X5),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X5))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X5),tc_List_Olist(X5)),tc_fun(tc_List_Olist(X5),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X5))),X5),hAPP(c_COMBB(tc_List_Olist(X5),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X5)),tc_List_Olist(X5)),c_Lazy__Sequence_Osingle(tc_List_Olist(X5)))),c_List_Olist_OCons(X5))))),c_Lazy__Sequence_Oempty(tc_List_Olist(X5)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_small__lazy__list_Osimps) ).

fof(fact_Sup__Inf,axiom,
    ! [X21,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => c_Complete__Lattice_OSup__class_OSup(X5,X21) = c_Complete__Lattice_OInf__class_OInf(X5,hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OAll(X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X5),hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fimplies),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X21)))),hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X5)))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__Inf) ).

fof(fact_setsum__nonneg__leq__bound,axiom,
    ! [X82,X113,X2,X76,X5,X20] :
      ( class_Groups_Oordered__ab__group__add(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X76))
       => ( ! [X146] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X146),X76))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20),c_Groups_Ozero__class_Ozero(X20)),hAPP(X2,X146))) )
         => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X2),X76) = X113
           => ( hBOOL(hAPP(hAPP(c_member(X5),X82),X76))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20),hAPP(X2,X82)),X113)) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__nonneg__leq__bound) ).

fof(fact_Inf__Sup,axiom,
    ! [X21,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => c_Complete__Lattice_OInf__class_OInf(X5,X21) = c_Complete__Lattice_OSup__class_OSup(X5,hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OAll(X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X5),hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fimplies),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X21)))),c_Orderings_Oord__class_Oless__eq(X5))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__Sup) ).

fof(fact_Int__UN__distrib2,axiom,
    ! [X113,X222,X116,X21,X221,X20,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,tc_fun(X5,tc_HOL_Obool)),X221),X21)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X116,tc_fun(X5,tc_HOL_Obool)),X222),X113)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,tc_fun(X5,tc_HOL_Obool)),X221),hAPP(hAPP(c_COMBB(tc_fun(X116,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool),X20),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X116,tc_fun(X5,tc_HOL_Obool)),X222)),hAPP(hAPP(c_COMBC(X20,tc_fun(X116,tc_fun(X5,tc_HOL_Obool)),tc_fun(X116,tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),tc_fun(tc_fun(X116,tc_fun(X5,tc_HOL_Obool)),tc_fun(X116,tc_fun(X5,tc_HOL_Obool))),X20),c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X116)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X20),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool))),X21))),X113))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__UN__distrib2) ).

fof(fact_Un__INT__distrib2,axiom,
    ! [X113,X222,X116,X21,X221,X20,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X20,tc_fun(X5,tc_HOL_Obool)),X221),X21)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X116,tc_fun(X5,tc_HOL_Obool)),X222),X113)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X20,tc_fun(X5,tc_HOL_Obool)),X221),hAPP(hAPP(c_COMBB(tc_fun(X116,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool),X20),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X116,tc_fun(X5,tc_HOL_Obool)),X222)),hAPP(hAPP(c_COMBC(X20,tc_fun(X116,tc_fun(X5,tc_HOL_Obool)),tc_fun(X116,tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),tc_fun(tc_fun(X116,tc_fun(X5,tc_HOL_Obool)),tc_fun(X116,tc_fun(X5,tc_HOL_Obool))),X20),c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X116)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X20),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool))),X21))),X113))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__INT__distrib2) ).

fof(fact_neg__bind__def,axiom,
    ! [X292,X293,X294,X2,X32,X5,X20] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(X20,X5,X32,X2),X294),X293),X292) = c_New__DSequence_Oneg__bind(X20,X5,hAPP(hAPP(hAPP(X32,X294),X293),X292),hAPP(hAPP(c_COMBC(X20,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X5)))),hAPP(hAPP(c_COMBC(X20,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X5))))),hAPP(hAPP(c_COMBC(X20,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X5)))))),X2),X294)),X293)),X292)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__bind__def) ).

fof(fact_Inter__eq,axiom,
    ! [X21,X5] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),X21) = hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OAll(tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),X5),hAPP(c_COMBS(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X5,tc_HOL_Obool))),X21)))),c_member(X5)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__eq) ).

fof(fact_Union__eq,axiom,
    ! [X21,X5] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X21) = hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),X5),hAPP(c_COMBS(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X5,tc_HOL_Obool))),X21)))),c_member(X5)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__eq) ).

fof(fact_rtrancl__Un__separatorE,axiom,
    ! [X16,X18,X24,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X24)),c_Transitive__Closure_Ortrancl(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X18),X16))))
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X3)),c_Transitive__Closure_Ortrancl(X5,X18)))
           => ! [X177] :
                ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X177)),X16))
               => X3 = X177 ) )
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X24)),c_Transitive__Closure_Ortrancl(X5,X18))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__Un__separatorE) ).

fof(fact_rtrancl__Un__separator__converseE,axiom,
    ! [X16,X18,X24,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X24)),c_Transitive__Closure_Ortrancl(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X18),X16))))
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X24)),c_Transitive__Closure_Ortrancl(X5,X18)))
           => ! [X177] :
                ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X177),X3)),X16))
               => X177 = X3 ) )
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X24)),c_Transitive__Closure_Ortrancl(X5,X18))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__Un__separator__converseE) ).

fof(fact_zip__map2,axiom,
    ! [X251,X2,X116,X239,X20,X5] : hAPP(hAPP(c_List_Ozip(X5,X20),X239),hAPP(hAPP(c_List_Omap(X116,X20),X2),X251)) = hAPP(hAPP(c_List_Omap(tc_prod(X5,X116),tc_prod(X5,X20)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X116,tc_prod(X5,X20)),hAPP(hAPP(c_COMBC(X5,tc_fun(X116,X20),tc_fun(X116,tc_prod(X5,X20))),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_prod(X5,X20)),tc_fun(tc_fun(X116,X20),tc_fun(X116,tc_prod(X5,X20))),X5),c_COMBB(X20,tc_prod(X5,X20),X116)),c_Product__Type_OPair(X5,X20))),X2))),hAPP(hAPP(c_List_Ozip(X5,X116),X239),X251)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__map2) ).

fof(fact_nat0__intermed__int__val,axiom,
    ! [X87,X2,X50] :
      ( ! [X146] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X146),X50))
         => 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),X146),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X2,X146)))),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))),X87))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X87),hAPP(X2,X50)))
         => ? [X146] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X146),X50))
              & hAPP(X2,X146) = X87 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat0__intermed__int__val) ).

fof(fact_int__val__lemma,axiom,
    ! [X87,X2,X50] :
      ( ! [X146] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X146),X50))
         => 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),X146),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X2,X146)))),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))),X87))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X87),hAPP(X2,X50)))
         => ? [X146] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X146),X50))
              & hAPP(X2,X146) = X87 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__val__lemma) ).

fof(fact_inj__vimage__singleton,axiom,
    ! [X6,X2,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X5,X20,X2),hAPP(hAPP(c_Set_Oinsert(X20),X6),c_Orderings_Obot__class_Obot(tc_fun(X20,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(X5),c_HOL_OThe(X5,hAPP(hAPP(c_COMBC(X5,X20,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X20,tc_fun(X20,tc_HOL_Obool),X5),c_fequal),X2)),X6))),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__vimage__singleton) ).

fof(fact_pos__bind__def,axiom,
    ! [X292,X293,X294,X2,X32,X5,X20] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(X20,X5,X32,X2),X294),X293),X292) = c_New__DSequence_Opos__bind(X20,X5,hAPP(hAPP(hAPP(X32,X294),X293),X292),hAPP(hAPP(c_COMBC(X20,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X5))),hAPP(hAPP(c_COMBC(X20,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X5)))),hAPP(hAPP(c_COMBC(X20,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X5))))),X2),X294)),X293)),X292)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__bind__def) ).

fof(fact_Nitpick_Oprod__def,axiom,
    ! [X113,X21,X20,X5] : c_Nitpick_Oprod(X5,X20,X21,X113) = hAPP(c_Set_OCollect(tc_prod(X5,X20)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X20,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X5,tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),X5),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X20)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X21)))),hAPP(hAPP(c_COMBC(X20,tc_fun(X20,tc_HOL_Obool),tc_HOL_Obool),c_member(X20)),X113)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Oprod__def) ).

fof(fact_map__pair_Ocompositionality,axiom,
    ! [X235,X82,X122,X206,X114,X1,X2,X20,X115,X5,X116] : hAPP(c_Product__Type_Omap__pair(X116,X5,X115,X20,X2,X1),hAPP(c_Product__Type_Omap__pair(X114,X116,X206,X115,X122,X82),X235)) = hAPP(c_Product__Type_Omap__pair(X114,X5,X206,X20,hAPP(c_Fun_Ocomp(X116,X5,X114,X2),X122),hAPP(c_Fun_Ocomp(X115,X20,X206,X1),X82)),X235),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__pair_Ocompositionality) ).

fof(fact_le,axiom,
    ! [X123,X159,X33,X25] :
      ( 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),X25),X33)),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),X159),X123)),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),X25),X123)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X159),X33))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le) ).

fof(fact_less,axiom,
    ! [X123,X159,X33,X25] :
      ( 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),X25),X33)),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),X159),X123)),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),X25),X123)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X159),X33))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less) ).

fof(fact_setsum__reindex__nonzero,axiom,
    ! [X20,X122,X2,X192,X5,X116] :
      ( class_Groups_Ocomm__monoid__add(X116)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X192))
       => ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),X192))
             => ! [X177] :
                  ( hBOOL(hAPP(hAPP(c_member(X5),X177),X192))
                 => ( X3 != X177
                   => ( hAPP(X2,X3) = hAPP(X2,X177)
                     => hAPP(X122,hAPP(X2,X3)) = c_Groups_Ozero__class_Ozero(X116) ) ) ) )
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X20,X116),X122),hAPP(c_Set_Oimage(X5,X20,X2),X192)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X116),hAPP(c_Fun_Ocomp(X20,X116,X5,X122),X2)),X192) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__reindex__nonzero) ).

fof(fact_if__image__distrib,axiom,
    ! [X192,X1,X2,X18,X5,X20] : hAPP(c_Set_Oimage(X20,X5,hAPP(hAPP(c_COMBS(X20,X5,X5),hAPP(hAPP(c_COMBS(X20,X5,tc_fun(X5,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5,tc_fun(X5,X5)),X20),c_If(X5)),X18)),X2)),X1)),X192) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Oimage(X20,X5,X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20,tc_HOL_Obool)),X192),hAPP(c_Set_OCollect(X20),X18)))),hAPP(c_Set_Oimage(X20,X5,X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20,tc_HOL_Obool)),X192),hAPP(c_Set_OCollect(X20),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X20),c_fNot),X18))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_if__image__distrib) ).

fof(fact_mult,axiom,
    ! [X123,X159,X33,X25] : 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),X25),X33)),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),X159),X123)),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),X25),X159)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X123))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25),X123)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X159)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult) ).

fof(fact_fold__image__cong,axiom,
    ! [X120,X122,X1,X21,X5,X20] :
      ( class_Groups_Oab__semigroup__mult(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),X21))
             => hAPP(X1,X3) = hAPP(X122,X3) )
         => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X20,X5,c_Groups_Otimes__class_Otimes(X20)),X1),X120),X21) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X20,X5,c_Groups_Otimes__class_Otimes(X20)),X122),X120),X21) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__image__cong) ).

fof(fact_wf__map__pair__image,axiom,
    ! [X2,X20,X171,X5] :
      ( c_Wellfounded_Owf(X5,X171)
     => ( c_Fun_Oinj__on(X5,X20,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
       => c_Wellfounded_Owf(X20,hAPP(c_Set_Oimage(tc_prod(X5,X5),tc_prod(X20,X20),c_Product__Type_Omap__pair(X5,X20,X5,X20,X2,X2)),X171)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__map__pair__image) ).

fof(fact_inj__on__INTER,axiom,
    ! [X21,X2,X116,X20,X5,X221] :
      ( X221 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
     => ( ! [X146] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X146),X221))
           => c_Fun_Oinj__on(X20,X116,X2,hAPP(X21,X146)) )
       => c_Fun_Oinj__on(X20,X116,X2,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X20,tc_HOL_Obool)),X221),X21)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__INTER) ).

fof(fact_listsum__mono,axiom,
    ! [X1,X2,X239,X5,X20] :
      ( ( class_Groups_Omonoid__add(X20)
        & class_Groups_Oordered__ab__semigroup__add(X20) )
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X239)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20),hAPP(X2,X3)),hAPP(X1,X3))) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20),hAPP(c_List_Omonoid__add__class_Olistsum(X20),hAPP(hAPP(c_List_Omap(X5,X20),X2),X239))),hAPP(c_List_Omonoid__add__class_Olistsum(X20),hAPP(hAPP(c_List_Omap(X5,X20),X1),X239)))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__mono) ).

fof(fact_list__all2__all__nthI,axiom,
    ! [X18,X24,X20,X6,X5] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X6) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X20)),X24)
     => ( ! [X69] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X69),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X6)))
           => hBOOL(hAPP(hAPP(X18,hAPP(hAPP(c_List_Onth(X5),X6),X69)),hAPP(hAPP(c_List_Onth(X20),X24),X69))) )
       => c_List_Olist__all2(X5,X20,X18,X6,X24) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__all2__all__nthI) ).

fof(fact_list__all2__conv__all__nth,axiom,
    ! [X251,X239,X18,X20,X5] :
      ( c_List_Olist__all2(X5,X20,X18,X239,X251)
    <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X20)),X251)
        & ! [X146] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X146),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239)))
           => hBOOL(hAPP(hAPP(X18,hAPP(hAPP(c_List_Onth(X5),X239),X146)),hAPP(hAPP(c_List_Onth(X20),X251),X146))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__all2__conv__all__nth) ).

fof(fact_setsum__strict__mono,axiom,
    ! [X1,X2,X21,X5,X20] :
      ( ( class_Groups_Ocomm__monoid__add(X20)
        & class_Groups_Oordered__cancel__ab__semigroup__add(X20) )
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X3),X21))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20),hAPP(X2,X3)),hAPP(X1,X3))) )
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X2),X21)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X1),X21))) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__strict__mono) ).

fof(fact_setsum__cases,axiom,
    ! [X1,X2,X18,X21,X5,X20] :
      ( class_Groups_Ocomm__monoid__add(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),hAPP(hAPP(c_COMBS(X5,X20,X20),hAPP(hAPP(c_COMBS(X5,X20,tc_fun(X20,X20)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X20,tc_fun(X20,X20)),X5),c_If(X20)),X18)),X2)),X1)),X21) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(c_Set_OCollect(X5),X18)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_OCollect(X5),X18))))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__cases) ).

fof(fact_folding__one__idem_Ohom__commute,axiom,
    ! [X207,X122,X205,X2,X5] :
      ( c_Finite__Set_Ofolding__one__idem(X5,X2,X205)
     => ( ! [X3,X177] : hAPP(X122,hAPP(hAPP(X2,X3),X177)) = hAPP(hAPP(X2,hAPP(X122,X3)),hAPP(X122,X177))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X207))
         => ( X207 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(X122,hAPP(X205,X207)) = hAPP(X205,hAPP(c_Set_Oimage(X5,X5,X122),X207)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Ohom__commute) ).

fof(fact_set__n__lists,axiom,
    ! [X239,X50,X5] : hAPP(c_List_Oset(tc_List_Olist(X5)),c_Enum_On__lists(X5,X50,X239)) = hAPP(c_Set_OCollect(tc_List_Olist(X5)),hAPP(hAPP(c_COMBS(tc_List_Olist(X5),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X5)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X5)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X5)))),X50))),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X5)),c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool))),c_List_Oset(X5))),hAPP(c_List_Oset(X5),X239)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__n__lists) ).

fof(fact_map__pair_Ocomp,axiom,
    ! [X82,X122,X1,X2,X20,X5,X115,X116,X206,X114] : hAPP(c_Fun_Ocomp(tc_prod(X114,X206),tc_prod(X116,X115),tc_prod(X5,X20),c_Product__Type_Omap__pair(X114,X116,X206,X115,X2,X1)),c_Product__Type_Omap__pair(X5,X114,X20,X206,X122,X82)) = c_Product__Type_Omap__pair(X5,X116,X20,X115,hAPP(c_Fun_Ocomp(X114,X116,X5,X2),X122),hAPP(c_Fun_Ocomp(X206,X115,X20,X1),X82)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__pair_Ocomp) ).

fof(fact_map__pair__compose,axiom,
    ! [X236,X237,X206,X89,X19,X114,X115,X20,X116,X5] : c_Product__Type_Omap__pair(X5,X116,X20,X115,hAPP(c_Fun_Ocomp(X114,X116,X5,X19),X89),hAPP(c_Fun_Ocomp(X206,X115,X20,X237),X236)) = hAPP(c_Fun_Ocomp(tc_prod(X114,X206),tc_prod(X116,X115),tc_prod(X5,X20),c_Product__Type_Omap__pair(X114,X116,X206,X115,X19,X237)),c_Product__Type_Omap__pair(X5,X114,X20,X206,X89,X236)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__pair__compose) ).

fof(fact_listrel__iff__nth,axiom,
    ! [X171,X251,X239,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X239),X251)),c_List_Olistrel(X5,X171)))
    <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X251)
        & ! [X69] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X69),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239)))
           => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),hAPP(hAPP(c_List_Onth(X5),X239),X69)),hAPP(hAPP(c_List_Onth(X5),X251),X69))),X171)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__iff__nth) ).

fof(fact_rel__pow__Suc__D2,axiom,
    ! [X32,X50,X120,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X120)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),hAPP(c_Nat_OSuc,X50)),X32)))
     => ? [X177] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X177)),X32))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X177),X120)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X50),X32))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__pow__Suc__D2) ).

fof(fact_quotient__def,axiom,
    ! [X171,X21,X5] : hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X21),X171) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),X21),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),X5),c_Set_Oinsert(tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X5),c_Relation_OImage(X5,X5,X171)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Set_Oinsert(X5)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)))),
    file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J) ).

fof(fact_Image__iff,axiom,
    ! [X21,X171,X20,X24,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X24),hAPP(c_Relation_OImage(X20,X5,X171),X21)))
    <=> ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X20),X3),X21))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(X20,X5)),hAPP(hAPP(c_Product__Type_OPair(X20,X5),X3),X24)),X171)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__iff) ).

fof(fact_folding__one_Oclosed,axiom,
    ! [X21,X205,X2,X5] :
      ( c_Finite__Set_Ofolding__one(X5,X2,X205)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( ! [X3,X177] : hBOOL(hAPP(hAPP(c_member(X5),hAPP(hAPP(X2,X3),X177)),hAPP(hAPP(c_Set_Oinsert(X5),X3),hAPP(hAPP(c_Set_Oinsert(X5),X177),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))
           => hBOOL(hAPP(hAPP(c_member(X5),hAPP(X205,X21)),X21)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one_Oclosed) ).

fof(fact_Image__Collect__split,axiom,
    ! [X21,X18,X5,X20] : hAPP(c_Relation_OImage(X20,X5,hAPP(c_Set_OCollect(tc_prod(X20,X5)),hAPP(c_Product__Type_Oprod_Oprod__case(X20,X5,tc_HOL_Obool),X18))),X21) = hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(X20)),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool),X5),hAPP(c_COMBS(X20,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X20),c_fconj),hAPP(hAPP(c_COMBC(X20,tc_fun(X20,tc_HOL_Obool),tc_HOL_Obool),c_member(X20)),X21)))),hAPP(c_COMBC(X20,X5,tc_HOL_Obool),X18)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__Collect__split) ).

fof(fact_quotient__diff1,axiom,
    ! [X6,X21,X171,X5] :
      ( c_Fun_Oinj__on(X5,tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),X5),c_Equiv__Relations_Oquotient(X5)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Set_Oinsert(X5)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),X171),X21)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X21))
       => hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),X171) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X21),X171)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),X171)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotient__diff1) ).

fof(fact_Collect__ball__eq,axiom,
    ! [X18,X21,X20,X5] : hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OAll(X20)),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool),X5),hAPP(c_COMBS(X20,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X20),c_fimplies),hAPP(hAPP(c_COMBC(X20,tc_fun(X20,tc_HOL_Obool),tc_HOL_Obool),c_member(X20)),X21)))),X18))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X20,tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X20),c_Set_OCollect(X5)),hAPP(c_COMBC(X5,X20,tc_HOL_Obool),X18))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__ball__eq) ).

fof(fact_sublist__append,axiom,
    ! [X21,X244,X156,X5] : c_List_Osublist(X5,hAPP(hAPP(c_List_Oappend(X5),X156),X244),X21) = hAPP(hAPP(c_List_Oappend(X5),c_List_Osublist(X5,X156,X21)),c_List_Osublist(X5,X244,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X156)))),X21)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sublist__append) ).

fof(fact_zip__obtain__same__length,axiom,
    ! [X18,X251,X20,X239,X5] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),hAPP(hAPP(c_List_Otake(X5),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X20)),X251))),X239)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X20)),hAPP(hAPP(c_List_Otake(X20),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X20)),X251))),X251))
       => hBOOL(hAPP(X18,hAPP(hAPP(c_List_Ozip(X5,X20),hAPP(hAPP(c_List_Otake(X5),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X20)),X251))),X239)),hAPP(hAPP(c_List_Otake(X20),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X20)),X251))),X251)))) )
     => hBOOL(hAPP(X18,hAPP(hAPP(c_List_Ozip(X5,X20),X239),X251))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__obtain__same__length) ).

fof(fact_card__quotient__disjoint,axiom,
    ! [X171,X21,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
     => ( c_Fun_Oinj__on(X5,tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),X5),c_Equiv__Relations_Oquotient(X5)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Set_Oinsert(X5)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),X171),X21)
       => hAPP(c_Finite__Set_Ocard(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X21),X171)) = hAPP(c_Finite__Set_Ocard(X5),X21) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__quotient__disjoint) ).

fof(fact_arith__series__general,axiom,
    ! [X50,X22,X6,X5] :
      ( class_Rings_Ocomm__semiring__1(X5)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),c_Groups_Oone__class_Oone(X5)),c_Groups_Oone__class_Oone(X5))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),hAPP(hAPP(c_COMBB(X5,X5,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(X5),X6)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(X5)),c_Nat_Osemiring__1__class_Oof__nat(X5))),X22))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X50))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X50)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X50),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X22)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_arith__series__general) ).

fof(fact_reduction__pair__def,axiom,
    ! [X18,X5] :
      ( c_FunDef_Oreduction__pair(X5,X18)
    <=> ( c_Wellfounded_Owf(X5,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X18))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X18)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X18))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X18))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_reduction__pair__def) ).

fof(fact_UN__subset__iff,axiom,
    ! [X113,X21,X221,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,tc_fun(X5,tc_HOL_Obool)),X221),X21)),X113))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X20),X3),X221))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(X21,X3)),X113)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__subset__iff) ).

fof(fact_setsum__bounded,axiom,
    ! [X231,X2,X21,X5,X20] :
      ( ( class_Groups_Oordered__ab__semigroup__add(X20)
        & class_Rings_Osemiring__1(X20) )
     => ( ! [X146] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X146),X21))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20),hAPP(X2,X146)),X231)) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X2),X21)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20),hAPP(c_Finite__Set_Ocard(X5),X21))),X231))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__bounded) ).

fof(fact_map__pair__def,axiom,
    ! [X1,X2,X115,X20,X116,X5] : c_Product__Type_Omap__pair(X5,X116,X20,X115,X2,X1) = hAPP(c_Product__Type_Oprod_Oprod__case(X5,X20,tc_prod(X116,X115)),hAPP(hAPP(c_COMBC(X5,tc_fun(X20,X115),tc_fun(X20,tc_prod(X116,X115))),hAPP(hAPP(c_COMBB(tc_fun(X115,tc_prod(X116,X115)),tc_fun(tc_fun(X20,X115),tc_fun(X20,tc_prod(X116,X115))),X5),c_COMBB(X115,tc_prod(X116,X115),X20)),hAPP(hAPP(c_COMBB(X116,tc_fun(X115,tc_prod(X116,X115)),X5),c_Product__Type_OPair(X116,X115)),X2))),X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__pair__def) ).

fof(fact_decr__lemma,axiom,
    ! [X94,X66,X91] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X91))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X66),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),X66),X94))),c_Groups_Oone__class_Oone(tc_Int_Oint))),X91))),X94)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_decr__lemma) ).

fof(fact_SUP__le__iff,axiom,
    ! [X159,X210,X21,X20,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,X5),X21),X210)),X159))
      <=> ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X20),X3),X21))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(X210,X3)),X159)) ) ) ),
    file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__numerals_I4_J) ).

fof(fact_lexord__take__index__conv,axiom,
    ! [X171,X33,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X25),X33)),c_List_Olexord(X5,X171)))
    <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X25)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X33)))
          & hAPP(hAPP(c_List_Otake(X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X25)),X33) = X25 )
        | ? [X146] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X146),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X25)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X33))))
            & hAPP(hAPP(c_List_Otake(X5),X146),X25) = hAPP(hAPP(c_List_Otake(X5),X146),X33)
            & hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),hAPP(hAPP(c_List_Onth(X5),X25),X146)),hAPP(hAPP(c_List_Onth(X5),X33),X146))),X171)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexord__take__index__conv) ).

fof(fact_SetCompr__Sigma__eq,axiom,
    ! [X16,X18,X20,X5] : hAPP(c_Set_OCollect(tc_prod(X5,X20)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X20,tc_HOL_Obool),hAPP(hAPP(c_COMBS(X5,tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),X5),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X20)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),X18))),X16))) = hAPP(hAPP(c_Product__Type_OSigma(X5,X20),hAPP(c_Set_OCollect(X5),X18)),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool),X5),c_Set_OCollect(X20)),X16)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SetCompr__Sigma__eq) ).

fof(fact_card__less,axiom,
    ! [X82,X210] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X210))
     => 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)),X210))),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,X82))))) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__less) ).

fof(fact_Eps__split__eq,axiom,
    ! [X33,X25,X20,X5] : c_Hilbert__Choice_OEps(tc_prod(X5,X20),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X20,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X5,tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),X5),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X20)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(c_fequal,X25)))),hAPP(c_fequal,X33)))) = hAPP(hAPP(c_Product__Type_OPair(X5,X20),X25),X33),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Eps__split__eq) ).

fof(fact_The__split__eq,axiom,
    ! [X33,X25,X20,X5] : c_HOL_OThe(tc_prod(X5,X20),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X20,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X5,tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),X5),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X20)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(c_fequal,X25)))),hAPP(c_fequal,X33)))) = hAPP(hAPP(c_Product__Type_OPair(X5,X20),X25),X33),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_The__split__eq) ).

fof(fact_setsum__commute,axiom,
    ! [X21,X113,X2,X116,X20,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X20,X5),hAPP(hAPP(c_COMBC(X20,tc_fun(X116,tc_HOL_Obool),X5),hAPP(hAPP(c_COMBB(tc_fun(X116,X5),tc_fun(tc_fun(X116,tc_HOL_Obool),X5),X20),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X116,X5)),X2)),X113)),X21) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X116,X5),hAPP(hAPP(c_COMBC(X116,tc_fun(X20,tc_HOL_Obool),X5),hAPP(hAPP(c_COMBB(tc_fun(X20,X5),tc_fun(tc_fun(X20,tc_HOL_Obool),X5),X116),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X20,X5)),hAPP(c_COMBC(X20,X116,X5),X2))),X21)),X113) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__commute) ).

fof(fact_Collect__split,axiom,
    ! [X16,X18,X20,X5] : hAPP(c_Set_OCollect(tc_prod(X5,X20)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X20,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X5,tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),X5),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X20)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),X18))),X16))) = hAPP(hAPP(c_Product__Type_OSigma(X5,X20),hAPP(c_Set_OCollect(X5),X18)),hAPP(c_COMBK(tc_fun(X20,tc_HOL_Obool),X5),hAPP(c_Set_OCollect(X20),X16))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__split) ).

fof(fact_image__eq__fold__image,axiom,
    ! [X2,X20,X21,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
     => hAPP(c_Set_Oimage(X5,X20,X2),X21) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(X20,tc_HOL_Obool),X5,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X5,tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X20,tc_fun(tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),X5),c_Set_Oinsert(X20)),X2)),c_Orderings_Obot__class_Obot(tc_fun(X20,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(X20,tc_HOL_Obool))),X21) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__eq__fold__image) ).

fof(fact_card__Diff2__less,axiom,
    ! [X33,X25,X21,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X33),X21))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(X5),X33),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X5),X21))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Diff2__less) ).

fof(fact_Id__on__def_H,axiom,
    ! [X21,X5] : c_Relation_OId__on(X5,X21) = hAPP(c_Product__Type_Oprod_Oprod__case(X5,X5,tc_HOL_Obool),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(X5,tc_HOL_Obool)),X5),c_COMBC(X5,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X5),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj)),c_fequal))),X21)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Id__on__def_H) ).

fof(fact_int__ge__less__than__def,axiom,
    ! [X22] : c_Int_Oint__ge__less__than(X22) = 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),X22)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__ge__less__than__def) ).

fof(fact_scomp__scomp,axiom,
    ! [X122,X1,X2,X206,X114,X20,X115,X116,X5] : hAPP(hAPP(c_Product__Type_Oscomp(X5,X116,X115,X20),hAPP(hAPP(c_Product__Type_Oscomp(X5,X114,X206,tc_prod(X116,X115)),X2),X1)),X122) = hAPP(hAPP(c_Product__Type_Oscomp(X5,X114,X206,X20),X2),hAPP(hAPP(c_COMBC(X114,tc_fun(X116,tc_fun(X115,X20)),tc_fun(X206,X20)),hAPP(hAPP(c_COMBB(tc_fun(X206,tc_prod(X116,X115)),tc_fun(tc_fun(X116,tc_fun(X115,X20)),tc_fun(X206,X20)),X114),c_Product__Type_Oscomp(X206,X116,X115,X20)),X1)),X122)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_scomp__scomp) ).

fof(fact_wmax__insertI,axiom,
    ! [X198,X25,X197,X33] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X33),X197))
     => ( 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)),X25),X33)),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)),X198),X197)),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)),X25),X198)),X197)),c_FunDef_Omax__weak)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wmax__insertI) ).

fof(fact_smax__insertI,axiom,
    ! [X194,X25,X196,X33] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X33),X196))
     => ( 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)),X25),X33)),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)),X194),X196)),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)),X25),X194)),X196)),c_FunDef_Omax__strict)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smax__insertI) ).

fof(fact_sorted__map__same,axiom,
    ! [X239,X1,X2,X20,X5] :
      ( class_Orderings_Olinorder(X5)
     => c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Omap(X20,X5),X2),hAPP(c_List_Ofilter(X20,hAPP(hAPP(c_COMBC(X20,X5,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,tc_HOL_Obool),X20),c_fequal),X2)),hAPP(X1,X239))),X239))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__map__same) ).

fof(fact_Loop,axiom,
    ! [X23,X24,X18,X4,X5] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X5)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),c_Hoare__Mirabelle_Opeek__and(X5,X18,X24)),X23),X18)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool))))
     => c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X5)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),X18),c_Com_Ocom_OWhile(X24,X23)),c_Hoare__Mirabelle_Opeek__and(X5,X18,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),X24)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Loop) ).

fof(fact_max__ext_Osimps,axiom,
    ! [X32,X26,X27,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X27),X26)),c_Wellfounded_Omax__ext(X5,X32)))
    <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X27))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X26))
        & X26 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
        & ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X27))
           => ? [X204] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X204),X26))
                & hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X204)),X32)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__ext_Osimps) ).

fof(fact_wf__union__merge,axiom,
    ! [X192,X32,X5] :
      ( c_Wellfounded_Owf(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X32),X192))
    <=> c_Wellfounded_Owf(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),X32),X32)),hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),X192),X32))),X192)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__union__merge) ).

fof(fact_map__pair__surj__on,axiom,
    ! [X238,X113,X1,X116,X115,X202,X21,X2,X5,X20] :
      ( hAPP(c_Set_Oimage(X20,X5,X2),X21) = X202
     => ( hAPP(c_Set_Oimage(X115,X116,X1),X113) = X238
       => hAPP(c_Set_Oimage(tc_prod(X20,X115),tc_prod(X5,X116),c_Product__Type_Omap__pair(X20,X5,X115,X116,X2,X1)),hAPP(hAPP(c_Product__Type_OSigma(X20,X115),X21),hAPP(c_COMBK(tc_fun(X115,tc_HOL_Obool),X20),X113))) = hAPP(hAPP(c_Product__Type_OSigma(X5,X116),X202),hAPP(c_COMBK(tc_fun(X116,tc_HOL_Obool),X5),X238)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__pair__surj__on) ).

fof(fact_wmin__insertI,axiom,
    ! [X197,X33,X198,X25] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X25),X198))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X25),X33)),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)),X198),X197)),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)),X198),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X33),X197))),c_FunDef_Omin__weak)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wmin__insertI) ).

fof(fact_smin__insertI,axiom,
    ! [X197,X33,X198,X25] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X25),X198))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X25),X33)),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)),X198),X197)),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)),X198),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X33),X197))),c_FunDef_Omin__strict)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smin__insertI) ).

fof(fact_insert__fold1SetE,axiom,
    ! [X25,X194,X6,X2,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(X5,X2,hAPP(hAPP(c_Set_Oinsert(X5),X6),X194)),X25))
     => ~ ! [X187,X226] :
            ( hAPP(hAPP(c_Set_Oinsert(X5),X6),X194) = hAPP(hAPP(c_Set_Oinsert(X5),X187),X226)
           => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X5,X2,X187,X226),X25))
             => hBOOL(hAPP(hAPP(c_member(X5),X187),X226)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__fold1SetE) ).

fof(fact_listrel1__iff__update,axiom,
    ! [X171,X251,X239,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X239),X251)),c_List_Olistrel1(X5,X171)))
    <=> ? [X177,X69] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),hAPP(hAPP(c_List_Onth(X5),X239),X69)),X177)),X171))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X69),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239)))
          & X251 = hAPP(hAPP(c_List_Olist__update(X5,X239),X69),X177) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel1__iff__update) ).

fof(fact_map__pair__surj,axiom,
    ! [X1,X116,X115,X2,X5,X20] :
      ( hAPP(c_Set_Oimage(X20,X5,X2),c_Orderings_Otop__class_Otop(tc_fun(X20,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))
     => ( hAPP(c_Set_Oimage(X115,X116,X1),c_Orderings_Otop__class_Otop(tc_fun(X115,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X116,tc_HOL_Obool))
       => hAPP(c_Set_Oimage(tc_prod(X20,X115),tc_prod(X5,X116),c_Product__Type_Omap__pair(X20,X5,X115,X116,X2,X1)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X20,X115),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X5,X116),tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__pair__surj) ).

fof(fact_minus__fold__remove,axiom,
    ! [X113,X21,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X113),X21) = hAPP(hAPP(c_Finite__Set_Ofold(X5,tc_fun(X5,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),hAPP(c_COMBC(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Set_Oinsert(X5)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),X113),X21) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__fold__remove) ).

fof(fact_fst__map__pair,axiom,
    ! [X25,X1,X2,X115,X116,X20,X5] : hAPP(c_Product__Type_Ofst(X5,X20),hAPP(c_Product__Type_Omap__pair(X116,X5,X115,X20,X2,X1),X25)) = hAPP(X2,hAPP(c_Product__Type_Ofst(X116,X115),X25)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fst__map__pair) ).

fof(fact_snd__prod__fun,axiom,
    ! [X25,X1,X2,X115,X116,X5,X20] : hAPP(c_Product__Type_Osnd(X20,X5),hAPP(c_Product__Type_Omap__pair(X116,X20,X115,X5,X2,X1),X25)) = hAPP(X1,hAPP(c_Product__Type_Osnd(X116,X115),X25)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_snd__prod__fun) ).

fof(fact_lexord__linear,axiom,
    ! [X33,X25,X171,X5] :
      ( ! [X187,X188] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X187),X188)),X171))
          | X187 = X188
          | hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X188),X187)),X171)) )
     => ( 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)),X25),X33)),c_List_Olexord(X5,X171)))
        | X25 = X33
        | 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)),X33),X25)),c_List_Olexord(X5,X171))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexord__linear) ).

fof(fact_add,axiom,
    ! [X123,X159,X33,X25] : 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),X25),X33)),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),X159),X123)),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),X25),X159)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X123))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add) ).

fof(fact_Id__on__def,axiom,
    ! [X21,X5] : c_Relation_OId__on(X5,X21) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X21),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_prod(X5,X5),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X5),c_Set_Oinsert(tc_prod(X5,X5))),hAPP(hAPP(c_COMBS(X5,X5,tc_prod(X5,X5)),c_Product__Type_OPair(X5,X5)),c_COMBI(X5)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Id__on__def) ).

fof(fact_conversep__noteq,axiom,
    ! [X33,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X5,X5,hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X5),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot)),c_fequal)),X25),X33))
    <=> X25 != X33 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_conversep__noteq) ).

fof(fact_map__zip__map,axiom,
    ! [X251,X239,X1,X115,X2,X5,X116,X20] : hAPP(hAPP(c_List_Omap(tc_prod(X20,X116),X5),X2),hAPP(hAPP(c_List_Ozip(X20,X116),hAPP(hAPP(c_List_Omap(X115,X20),X1),X239)),X251)) = hAPP(hAPP(c_List_Omap(tc_prod(X115,X116),X5),hAPP(c_Product__Type_Oprod_Oprod__case(X115,X116,X5),hAPP(hAPP(c_COMBB(tc_fun(X116,tc_prod(X20,X116)),tc_fun(X116,X5),X115),hAPP(c_COMBB(tc_prod(X20,X116),X5,X116),X2)),hAPP(hAPP(c_COMBB(X20,tc_fun(X116,tc_prod(X20,X116)),X115),c_Product__Type_OPair(X20,X116)),X1)))),hAPP(hAPP(c_List_Ozip(X115,X116),X239),X251)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__zip__map) ).

fof(fact_order__fun_I2_J,axiom,
    ! [X1,X2,X5,X20] :
      ( ( class_Orderings_Oorder(X20)
        & class_Enum_Oenum(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,X20)),X2),X1))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X20)),X2),X1))
          & hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X5),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),hAPP(hAPP(c_COMBS(X5,X20,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X20,tc_fun(X20,tc_HOL_Obool),X5),c_fequal),X2)),X1)))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__fun_I2_J) ).

fof(fact_sublist__Cons,axiom,
    ! [X21,X156,X25,X5] : c_List_Osublist(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X25),X156),X21) = hAPP(hAPP(c_List_Oappend(X5),hAPP(hAPP(hAPP(c_If(tc_List_Olist(X5)),hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X21)),hAPP(hAPP(c_List_Olist_OCons(X5),X25),c_List_Olist_ONil(X5))),c_List_Olist_ONil(X5))),c_List_Osublist(X5,X156,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)),X21)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sublist__Cons) ).

fof(fact_nth__nth__transpose__sorted,axiom,
    ! [X157,X82,X239,X5] :
      ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X5),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X5))),X239)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X82),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5))),c_List_Otranspose(X5,X239))))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X157),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5))),hAPP(c_List_Ofilter(tc_List_Olist(X5),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X5)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X82)),c_Nat_Osize__class_Osize(tc_List_Olist(X5)))),X239))))
         => hAPP(hAPP(c_List_Onth(X5),hAPP(hAPP(c_List_Onth(tc_List_Olist(X5)),c_List_Otranspose(X5,X239)),X82)),X157) = hAPP(hAPP(c_List_Onth(X5),hAPP(hAPP(c_List_Onth(tc_List_Olist(X5)),X239),X157)),X82) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__nth__transpose__sorted) ).

fof(fact_INF__less__iff,axiom,
    ! [X6,X2,X21,X20,X5] :
      ( ( class_Complete__Lattice_Ocomplete__lattice(X5)
        & class_Orderings_Olinorder(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X20,X5),X21),X2)),X6))
      <=> ? [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X20),X3),X21))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(X2,X3)),X6)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF__less__iff) ).

fof(fact_ball__UN,axiom,
    ! [X18,X113,X21,X20,X5] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,tc_fun(X5,tc_HOL_Obool)),X21),X113)))
         => hBOOL(hAPP(X18,X3)) )
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X20),X3),X21))
         => ! [X204] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X204),hAPP(X113,X3)))
             => hBOOL(hAPP(X18,X204)) ) ) ),
    file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J) ).

fof(fact_max__ext__additive,axiom,
    ! [X144,X112,X32,X113,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X21),X113)),c_Wellfounded_Omax__ext(X5,X32)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X112),X144)),c_Wellfounded_Omax__ext(X5,X32)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X112)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X113),X144))),c_Wellfounded_Omax__ext(X5,X32))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__ext__additive) ).

fof(fact_SigmaE,axiom,
    ! [X113,X21,X23,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X20)),X23),hAPP(hAPP(c_Product__Type_OSigma(X5,X20),X21),X113)))
     => ~ ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X21))
           => ! [X177] :
                ( hBOOL(hAPP(hAPP(c_member(X20),X177),hAPP(X113,X3)))
               => X23 != hAPP(hAPP(c_Product__Type_OPair(X5,X20),X3),X177) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SigmaE) ).

fof(fact_foldl__map,axiom,
    ! [X239,X2,X116,X6,X1,X20,X5] : hAPP(c_List_Ofoldl(X5,X20,X1,X6),hAPP(hAPP(c_List_Omap(X116,X20),X2),X239)) = hAPP(c_List_Ofoldl(X5,X116,hAPP(hAPP(c_COMBC(X5,tc_fun(X116,X20),tc_fun(X116,X5)),hAPP(hAPP(c_COMBB(tc_fun(X20,X5),tc_fun(tc_fun(X116,X20),tc_fun(X116,X5)),X5),c_COMBB(X20,X5,X116)),X1)),X2),X6),X239),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldl__map) ).

fof(fact_rel__comp__UNION__distrib2,axiom,
    ! [X76,X171,X221,X115,X20,X116,X5] : hAPP(hAPP(c_Relation_Orel__comp(X5,X116,X20),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X115,tc_fun(tc_prod(X5,X116),tc_HOL_Obool)),X221),X171)),X76) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X115,tc_fun(tc_prod(X5,X20),tc_HOL_Obool)),X221),hAPP(hAPP(c_COMBC(X115,tc_fun(tc_prod(X116,X20),tc_HOL_Obool),tc_fun(tc_prod(X5,X20),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X5,X116),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X116,X20),tc_HOL_Obool),tc_fun(tc_prod(X5,X20),tc_HOL_Obool)),X115),c_Relation_Orel__comp(X5,X116,X20)),X171)),X76)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__comp__UNION__distrib2) ).

fof(fact_finite__Collect__disjI,axiom,
    ! [X16,X18,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fdisj),X18)),X16))))
    <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(c_Set_OCollect(X5),X18)))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(c_Set_OCollect(X5),X16))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Collect__disjI) ).

fof(fact_inj__transfer,axiom,
    ! [X25,X18,X2,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => ( ! [X177] :
            ( hBOOL(hAPP(hAPP(c_member(X20),X177),hAPP(c_Set_Oimage(X5,X20,X2),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))))
           => hBOOL(hAPP(X18,hAPP(c_Hilbert__Choice_Oinv__into(X5,X20,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X2),X177))) )
       => hBOOL(hAPP(X18,X25)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__transfer) ).

fof(fact_enum__all__prod__def,axiom,
    ! [X18,X5,X20] :
      ( ( class_Enum_Oenum(X20)
        & class_Enum_Oenum(X5) )
     => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(X5,X20)),X18))
      <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X5),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_HOL_Obool,X5),c_Enum_Oenum__class_Oenum__all(X20)),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_prod(X5,X20)),tc_fun(X20,tc_HOL_Obool),X5),hAPP(c_COMBB(tc_prod(X5,X20),tc_HOL_Obool,X20),X18)),c_Product__Type_OPair(X5,X20))))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_enum__all__prod__def) ).

fof(fact_enum__ex__prod__def,axiom,
    ! [X18,X5,X20] :
      ( ( class_Enum_Oenum(X20)
        & class_Enum_Oenum(X5) )
     => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(X5,X20)),X18))
      <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X5),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_HOL_Obool,X5),c_Enum_Oenum__class_Oenum__ex(X20)),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_prod(X5,X20)),tc_fun(X20,tc_HOL_Obool),X5),hAPP(c_COMBB(tc_prod(X5,X20),tc_HOL_Obool,X20),X18)),c_Product__Type_OPair(X5,X20))))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_enum__ex__prod__def) ).

fof(fact_listsp__conj__eq,axiom,
    ! [X25,X113,X21,X5] :
      ( hBOOL(hAPP(c_List_Olistsp(X5,hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),X21)),X113)),X25))
    <=> ( hBOOL(hAPP(c_List_Olistsp(X5,X21),X25))
        & hBOOL(hAPP(c_List_Olistsp(X5,X113),X25)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsp__conj__eq) ).

fof(fact_lists__IntI,axiom,
    ! [X113,X21,X156,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X156),c_List_Olists(X5,X21)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X156),c_List_Olists(X5,X113)))
       => hBOOL(hAPP(c_List_Olistsp(X5,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X21)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X113))),X156)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lists__IntI) ).

fof(fact_UN__equiv__class2,axiom,
    ! [X26,X27,X2,X116,X213,X214,X20,X215,X216,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X216,X215)
     => ( c_Equiv__Relations_Oequiv(X20,X214,X213)
       => ( c_Equiv__Relations_Ocongruent2(X5,X20,tc_fun(X116,tc_HOL_Obool),X215,X213,X2)
         => ( hBOOL(hAPP(hAPP(c_member(X5),X27),X216))
           => ( hBOOL(hAPP(hAPP(c_member(X20),X26),X214))
             => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X116,tc_HOL_Obool)),hAPP(c_Relation_OImage(X5,X5,X215),hAPP(hAPP(c_Set_Oinsert(X5),X27),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_fun(X116,tc_HOL_Obool)),tc_fun(X116,tc_HOL_Obool),X5),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,tc_fun(X116,tc_HOL_Obool)),hAPP(c_Relation_OImage(X20,X20,X213),hAPP(hAPP(c_Set_Oinsert(X20),X26),c_Orderings_Obot__class_Obot(tc_fun(X20,tc_HOL_Obool)))))),X2)) = hAPP(hAPP(X2,X27),X26) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__equiv__class2) ).

fof(fact_length__sublist,axiom,
    ! [X221,X239,X5] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_Osublist(X5,X239,X221)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X221)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__sublist) ).

fof(fact_length__filter__conv__card,axiom,
    ! [X239,X160,X5] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),hAPP(c_List_Ofilter(X5,X160),X239)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239)))),hAPP(hAPP(c_COMBB(X5,tc_HOL_Obool,tc_Nat_Onat),X160),hAPP(c_List_Onth(X5),X239))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__filter__conv__card) ).

fof(fact_fold__image__distrib,axiom,
    ! [X122,X1,X21,X5,X20] :
      ( class_Groups_Ocomm__monoid__mult(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X20,X5,c_Groups_Otimes__class_Otimes(X20)),hAPP(hAPP(c_COMBS(X5,X20,X20),hAPP(hAPP(c_COMBB(X20,tc_fun(X20,X20),X5),c_Groups_Otimes__class_Otimes(X20)),X1)),X122)),c_Groups_Oone__class_Oone(X20)),X21) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X20,X5,c_Groups_Otimes__class_Otimes(X20)),X1),c_Groups_Oone__class_Oone(X20)),X21)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X20,X5,c_Groups_Otimes__class_Otimes(X20)),X122),c_Groups_Oone__class_Oone(X20)),X21)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__image__distrib) ).

fof(fact_snoc__listrel1__snoc__iff,axiom,
    ! [X171,X33,X251,X25,X239,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(hAPP(c_List_Oappend(X5),X239),hAPP(hAPP(c_List_Olist_OCons(X5),X25),c_List_Olist_ONil(X5)))),hAPP(hAPP(c_List_Oappend(X5),X251),hAPP(hAPP(c_List_Olist_OCons(X5),X33),c_List_Olist_ONil(X5))))),c_List_Olistrel1(X5,X171)))
    <=> ( ( 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)),X239),X251)),c_List_Olistrel1(X5,X171)))
          & X25 = X33 )
        | ( X239 = X251
          & hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X33)),X171)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_snoc__listrel1__snoc__iff) ).

fof(fact_list__all2__map2,axiom,
    ! [X280,X2,X116,X273,X18,X20,X5] :
      ( c_List_Olist__all2(X5,X20,X18,X273,hAPP(hAPP(c_List_Omap(X116,X20),X2),X280))
    <=> c_List_Olist__all2(X5,X116,hAPP(hAPP(c_COMBC(X5,tc_fun(X116,X20),tc_fun(X116,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_fun(tc_fun(X116,X20),tc_fun(X116,tc_HOL_Obool)),X5),c_COMBB(X20,tc_HOL_Obool,X116)),X18)),X2),X273,X280) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__all2__map2) ).

fof(fact_UN__finite2__eq,axiom,
    ! [X113,X87,X21,X5] :
      ( ! [X69] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X69)),X21) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X69),X87))),X113)
     => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X21) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X113) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__finite2__eq) ).

fof(fact_max__ext_Ointros,axiom,
    ! [X32,X196,X194,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X194))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X196))
       => ( X196 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X3),X194))
               => ? [X204] :
                    ( hBOOL(hAPP(hAPP(c_member(X5),X204),X196))
                    & hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X204)),X32)) ) )
           => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X194),X196)),c_Wellfounded_Omax__ext(X5,X32))) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__ext_Ointros) ).

fof(fact_pred__comp_Oequations,axiom,
    ! [X63,X27,X76,X171,X116,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X5,X20,X116,X171,X76),X27),X63))
    <=> ? [X188] :
          ( hBOOL(hAPP(hAPP(X171,X27),X188))
          & hBOOL(hAPP(hAPP(X76,X188),X63)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__comp_Oequations) ).

fof(fact_wf__no__infinite__down__chainE,axiom,
    ! [X2,X171,X5] :
      ( c_Wellfounded_Owf(X5,X171)
     => ~ ! [X100] : hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),hAPP(X2,hAPP(c_Nat_OSuc,X100))),hAPP(X2,X100))),X171)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__no__infinite__down__chainE) ).

fof(fact_wf__iff__no__infinite__down__chain,axiom,
    ! [X171,X5] :
      ( c_Wellfounded_Owf(X5,X171)
    <=> ~ ? [X227] :
          ! [X146] : hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),hAPP(X227,hAPP(c_Nat_OSuc,X146))),hAPP(X227,X146))),X171)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__iff__no__infinite__down__chain) ).

fof(fact_congruent2__implies__congruent__UN,axiom,
    ! [X6,X2,X116,X213,X214,X20,X215,X216,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X216,X215)
     => ( c_Equiv__Relations_Oequiv(X20,X214,X213)
       => ( c_Equiv__Relations_Ocongruent2(X5,X20,tc_fun(X116,tc_HOL_Obool),X215,X213,X2)
         => ( hBOOL(hAPP(hAPP(c_member(X20),X6),X214))
           => c_Equiv__Relations_Ocongruent(X5,tc_fun(X116,tc_HOL_Obool),X215,hAPP(hAPP(c_COMBB(tc_fun(X20,tc_fun(X116,tc_HOL_Obool)),tc_fun(X116,tc_HOL_Obool),X5),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,tc_fun(X116,tc_HOL_Obool)),hAPP(c_Relation_OImage(X20,X20,X213),hAPP(hAPP(c_Set_Oinsert(X20),X6),c_Orderings_Obot__class_Obot(tc_fun(X20,tc_HOL_Obool)))))),X2)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_congruent2__implies__congruent__UN) ).

fof(fact_Diff1__fold__graph,axiom,
    ! [X33,X25,X21,X120,X2,X20,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X20,X2,X120,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),X33))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
       => hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X20,X2,X120,X21),hAPP(hAPP(X2,X25),X33))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff1__fold__graph) ).

fof(fact_setsum__mono3,axiom,
    ! [X2,X21,X113,X5,X20] :
      ( ( class_Groups_Ocomm__monoid__add(X20)
        & class_Groups_Oordered__ab__semigroup__add(X20) )
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X113))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),X113))
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X113),X21)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20),c_Groups_Ozero__class_Ozero(X20)),hAPP(X2,X3))) )
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X2),X21)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X2),X113))) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__mono3) ).

fof(fact_setsum__mono2,axiom,
    ! [X2,X21,X113,X5,X20] :
      ( class_Groups_Oordered__comm__monoid__add(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X113))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),X113))
         => ( ! [X188] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X188),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X113),X21)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20),c_Groups_Ozero__class_Ozero(X20)),hAPP(X2,X188))) )
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X2),X21)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X2),X113))) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__mono2) ).

fof(fact_INF__INT__eq,axiom,
    ! [X25,X171,X20,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X20,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool),X5),hAPP(c_COMBC(X20,tc_fun(X20,tc_HOL_Obool),tc_HOL_Obool),c_member(X20))),X171)),X25))
    <=> hBOOL(hAPP(hAPP(c_member(X20),X25),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X20,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),X171))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF__INT__eq) ).

fof(fact_SUP__UN__eq,axiom,
    ! [X25,X171,X20,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X20,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool),X5),hAPP(c_COMBC(X20,tc_fun(X20,tc_HOL_Obool),tc_HOL_Obool),c_member(X20))),X171)),X25))
    <=> hBOOL(hAPP(hAPP(c_member(X20),X25),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X20,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),X171))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUP__UN__eq) ).

fof(fact_le__add__iff1,axiom,
    ! [X22,X24,X23,X155,X6,X5] :
      ( class_Rings_Oordered__ring(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X155)),X23)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X24),X155)),X22)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X6),X24)),X155)),X23)),X22)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add__iff1) ).

fof(fact_less__add__iff1,axiom,
    ! [X22,X24,X23,X155,X6,X5] :
      ( class_Rings_Oordered__ring(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X155)),X23)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X24),X155)),X22)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X6),X24)),X155)),X23)),X22)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__iff1) ).

fof(fact_fold__graph_H_Ointros_I2_J,axiom,
    ! [X33,X120,X2,X20,X21,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
     => ( c_Nitpick_Ofold__graph_H(X5,X20,X2,X120,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),X33)
       => c_Nitpick_Ofold__graph_H(X5,X20,X2,X120,X21,hAPP(hAPP(X2,X25),X33)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__graph_H_Ointros_I2_J) ).

fof(fact_INT__subset__iff,axiom,
    ! [X21,X221,X20,X113,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X113),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X20,tc_fun(X5,tc_HOL_Obool)),X221),X21)))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X20),X3),X221))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X113),hAPP(X21,X3))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__subset__iff) ).

fof(fact_refl__on__INTER,axiom,
    ! [X171,X21,X20,X192,X5] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),X192))
         => c_Relation_Orefl__on(X20,hAPP(X21,X3),hAPP(X171,X3)) )
     => c_Relation_Orefl__on(X20,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X20,tc_HOL_Obool)),X192),X21),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(tc_prod(X20,X20),tc_HOL_Obool)),X192),X171)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__on__INTER) ).

fof(fact_zminus1__lemma,axiom,
    ! [X171,X153,X24,X6] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X6,X24),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X153),X171)))
     => hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X6),X24),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,X171),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X153)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X153)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,X171),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),X24),X171))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zminus1__lemma) ).

fof(fact_INT__iff,axiom,
    ! [X113,X21,X20,X24,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X24),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X20,tc_fun(X5,tc_HOL_Obool)),X21),X113)))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X20),X3),X21))
         => hBOOL(hAPP(hAPP(c_member(X5),X24),hAPP(X113,X3))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__iff) ).

fof(fact_vimage__Times,axiom,
    ! [X113,X21,X2,X116,X20,X5] : hAPP(c_Set_Ovimage(X5,tc_prod(X20,X116),X2),hAPP(hAPP(c_Product__Type_OSigma(X20,X116),X21),hAPP(c_COMBK(tc_fun(X116,tc_HOL_Obool),X20),X113))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X5,X20,hAPP(c_Fun_Ocomp(tc_prod(X20,X116),X20,X5,c_Product__Type_Ofst(X20,X116)),X2)),X21)),hAPP(c_Set_Ovimage(X5,X116,hAPP(c_Fun_Ocomp(tc_prod(X20,X116),X116,X5,c_Product__Type_Osnd(X20,X116)),X2)),X113)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__Times) ).

fof(fact_size__code,axiom,
    ! [X277,X5] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X5)),X277) = c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(X5,tc_Lazy__Sequence_Olazy__sequence(X5)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(X5,tc_Lazy__Sequence_Olazy__sequence(X5),tc_Nat_Onat),hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X5),tc_Nat_Onat),X5),hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(X5),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(X5)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X5)))),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(c_Lazy__Sequence_Oyield(X5),X277)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_size__code) ).

fof(fact_in__lex__prod,axiom,
    ! [X76,X171,X179,X180,X24,X6,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X5,X20),tc_prod(X5,X20))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X5,X20),tc_prod(X5,X20)),hAPP(hAPP(c_Product__Type_OPair(X5,X20),X6),X24)),hAPP(hAPP(c_Product__Type_OPair(X5,X20),X180),X179))),c_Wellfounded_Olex__prod(X5,X20,X171,X76)))
    <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X180)),X171))
        | ( X6 = X180
          & hBOOL(hAPP(hAPP(c_member(tc_prod(X20,X20)),hAPP(hAPP(c_Product__Type_OPair(X20,X20),X24),X179)),X76)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__lex__prod) ).

fof(fact_INF1__iff,axiom,
    ! [X24,X113,X21,X20,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X20,tc_HOL_Obool)),X21),X113),X24))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),X21))
         => hBOOL(hAPP(hAPP(X113,X3),X24)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF1__iff) ).

fof(fact_finite__M__bounded__by__nat,axiom,
    ! [X82,X18] : 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),X18)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X82))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__M__bounded__by__nat) ).

fof(fact_incr__lemma,axiom,
    ! [X66,X94,X91] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X91))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X94),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X66),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),X66),X94))),c_Groups_Oone__class_Oone(tc_Int_Oint))),X91)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_incr__lemma) ).

fof(fact_le__INF__iff,axiom,
    ! [X210,X21,X20,X159,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X159),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X20,X5),X21),X210)))
      <=> ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X20),X3),X21))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X159),hAPP(X210,X3))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__INF__iff) ).

fof(fact_insort__is__Cons,axiom,
    ! [X6,X2,X239,X5,X20] :
      ( class_Orderings_Olinorder(X20)
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X239)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20),hAPP(X2,X6)),hAPP(X2,X3))) )
       => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X20,X2),X6),X239) = hAPP(hAPP(c_List_Olist_OCons(X5),X6),X239) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insort__is__Cons) ).

fof(fact_setsum__nonneg__0,axiom,
    ! [X82,X2,X76,X5,X20] :
      ( class_Groups_Oordered__ab__group__add(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X76))
       => ( ! [X146] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X146),X76))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20),c_Groups_Ozero__class_Ozero(X20)),hAPP(X2,X146))) )
         => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X2),X76) = c_Groups_Ozero__class_Ozero(X20)
           => ( hBOOL(hAPP(hAPP(c_member(X5),X82),X76))
             => hAPP(X2,X82) = c_Groups_Ozero__class_Ozero(X20) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__nonneg__0) ).

fof(fact_inv__into__def,axiom,
    ! [X25,X2,X21,X20,X5] : hAPP(c_Hilbert__Choice_Oinv__into(X5,X20,X21,X2),X25) = c_Hilbert__Choice_OEps(X5,hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X21))),hAPP(hAPP(c_COMBC(X5,X20,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X20,tc_fun(X20,tc_HOL_Obool),X5),c_fequal),X2)),X25))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__into__def) ).

fof(fact_the__inv__into__def,axiom,
    ! [X25,X2,X21,X20,X5] : hAPP(c_Fun_Othe__inv__into(X5,X20,X21,X2),X25) = c_HOL_OThe(X5,hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X21))),hAPP(hAPP(c_COMBC(X5,X20,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X20,tc_fun(X20,tc_HOL_Obool),X5),c_fequal),X2)),X25))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__inv__into__def) ).

fof(fact_listrel1E,axiom,
    ! [X171,X251,X239,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X239),X251)),c_List_Olistrel1(X5,X171)))
     => ~ ! [X3,X177] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X177)),X171))
           => ! [X252,X260] :
                ( X239 = hAPP(hAPP(c_List_Oappend(X5),X252),hAPP(hAPP(c_List_Olist_OCons(X5),X3),X260))
               => X251 != hAPP(hAPP(c_List_Oappend(X5),X252),hAPP(hAPP(c_List_Olist_OCons(X5),X177),X260)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel1E) ).

fof(fact_fun__left__comm_Ofold__graph__determ,axiom,
    ! [X33,X25,X21,X120,X2,X20,X5] :
      ( c_Finite__Set_Ofun__left__comm(X5,X20,X2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X20,X2,X120,X21),X25))
       => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X20,X2,X120,X21),X33))
         => X33 = X25 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__graph__determ) ).

fof(fact_listsum__subtractf,axiom,
    ! [X239,X1,X2,X20,X5] :
      ( class_Groups_Oab__group__add(X5)
     => hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X20,X5),hAPP(hAPP(c_COMBS(X20,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X20),c_Groups_Ominus__class_Ominus(X5)),X2)),X1)),X239)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X20,X5),X2),X239))),hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X20,X5),X1),X239))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__subtractf) ).

fof(fact_listsum__addf,axiom,
    ! [X239,X1,X2,X20,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X20,X5),hAPP(hAPP(c_COMBS(X20,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X20),c_Groups_Oplus__class_Oplus(X5)),X2)),X1)),X239)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X20,X5),X2),X239))),hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X20,X5),X1),X239))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__addf) ).

fof(fact_UN__Pow__subset,axiom,
    ! [X113,X21,X20,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),X21),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),X20),c_Set_OPow(X5)),X113))),hAPP(c_Set_OPow(X5),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,tc_fun(X5,tc_HOL_Obool)),X21),X113)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__Pow__subset) ).

fof(fact_nat__le__add__iff1,axiom,
    ! [X50,X95,X159,X82,X157] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X157),X82))
     => ( 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),X82),X159)),X95)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X157),X159)),X50)))
      <=> 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),X82),X157)),X159)),X95)),X50)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__add__iff1) ).

fof(fact_nat__less__add__iff1,axiom,
    ! [X50,X95,X159,X82,X157] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X157),X82))
     => ( 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),X82),X159)),X95)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X157),X159)),X50)))
      <=> 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),X82),X157)),X159)),X95)),X50)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__add__iff1) ).

fof(fact_listsum__mult__const,axiom,
    ! [X239,X23,X2,X20,X5] :
      ( class_Rings_Osemiring__0(X5)
     => hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X20,X5),hAPP(hAPP(c_COMBC(X20,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X20),c_Groups_Otimes__class_Otimes(X5)),X2)),X23)),X239)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X20,X5),X2),X239))),X23) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__mult__const) ).

fof(fact_int__ge__less__than2__def,axiom,
    ! [X22] : c_Int_Oint__ge__less__than2(X22) = 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),X22)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__ge__less__than2__def) ).

fof(fact_fold__image__Un__one,axiom,
    ! [X2,X212,X192,X5,X20] :
      ( class_Groups_Ocomm__monoid__mult(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X192))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X212))
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X192),X212)))
               => hAPP(X2,X3) = c_Groups_Oone__class_Oone(X20) )
           => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X20,X5,c_Groups_Otimes__class_Otimes(X20)),X2),c_Groups_Oone__class_Oone(X20)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X192),X212)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X20,X5,c_Groups_Otimes__class_Otimes(X20)),X2),c_Groups_Oone__class_Oone(X20)),X192)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X20,X5,c_Groups_Otimes__class_Otimes(X20)),X2),c_Groups_Oone__class_Oone(X20)),X212)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__image__Un__one) ).

fof(fact_inf__Int__eq,axiom,
    ! [X25,X192,X32,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X32)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X192)),X25))
    <=> hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X32),X192))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__Int__eq) ).

fof(fact_sup__Un__eq,axiom,
    ! [X25,X192,X32,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X32)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X192)),X25))
    <=> hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X32),X192))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__Un__eq) ).

fof(fact_insert__Collect,axiom,
    ! [X18,X6,X5] : hAPP(hAPP(c_Set_Oinsert(X5),X6),hAPP(c_Set_OCollect(X5),X18)) = hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X6)))),X18)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__Collect) ).

fof(fact_equiv__class__nondisjoint,axiom,
    ! [X24,X6,X25,X171,X21,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X21,X171)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_OImage(X5,X5,X171),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X5,X5,X171),hAPP(hAPP(c_Set_Oinsert(X5),X24),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X24)),X171)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equiv__class__nondisjoint) ).

fof(fact_measures__def,axiom,
    ! [X290,X5] : c_List_Omeasures(X5,X290) = hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat),X5),c_List_Olex(tc_Nat_Onat,c_Wellfounded_Oless__than)),hAPP(hAPP(c_COMBC(X5,tc_List_Olist(tc_fun(X5,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,tc_Nat_Onat),tc_Nat_Onat),tc_fun(tc_List_Olist(tc_fun(X5,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),X5),c_List_Omap(tc_fun(X5,tc_Nat_Onat),tc_Nat_Onat)),hAPP(c_COMBC(tc_fun(X5,tc_Nat_Onat),X5,tc_Nat_Onat),c_COMBI(tc_fun(X5,tc_Nat_Onat))))),X290)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_measures__def) ).

fof(fact_divmod__nat__rel__add1__eq,axiom,
    ! [X183,X184,X90,X185,X186,X56,X62] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X62,X56),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X186),X185)))
     => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X90,X56),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X184),X183)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X56))
         => hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X62),X90),X56),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),X186),X184)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X185),X183)),X56))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X185),X183),X56)))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__rel__add1__eq) ).

fof(fact_Random__Sequence_Omap__def,axiom,
    ! [X18,X2,X5,X20] : c_Random__Sequence_Omap(X20,X5,X2,X18) = c_Random__Sequence_Obind(X20,X5,X18,hAPP(c_Fun_Ocomp(X5,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))))),X20,c_Random__Sequence_Osingle(X5)),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Random__Sequence_Omap__def) ).

fof(fact_setprod__Un,axiom,
    ! [X2,X113,X21,X5,X20] :
      ( class_Fields_Ofield(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X113))
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113)))
               => hAPP(X2,X3) != c_Groups_Ozero__class_Ozero(X20) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X20),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X2),X21)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X2),X113))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113))) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__Un) ).

fof(fact_zadd1__lemma,axiom,
    ! [X183,X184,X90,X185,X186,X56,X62] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X62,X56),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X186),X185)))
     => ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X90,X56),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X184),X183)))
       => ( X56 != 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),X62),X90),X56),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),X186),X184)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X185),X183)),X56))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X185),X183),X56)))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd1__lemma) ).

fof(fact_setsum__cartesian__product,axiom,
    ! [X21,X113,X2,X116,X20,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X20,X5),hAPP(hAPP(c_COMBC(X20,tc_fun(X116,tc_HOL_Obool),X5),hAPP(hAPP(c_COMBB(tc_fun(X116,X5),tc_fun(tc_fun(X116,tc_HOL_Obool),X5),X20),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X116,X5)),X2)),X113)),X21) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(X20,X116),X5),hAPP(c_Product__Type_Oprod_Oprod__case(X20,X116,X5),X2)),hAPP(hAPP(c_Product__Type_OSigma(X20,X116),X21),hAPP(c_COMBK(tc_fun(X116,tc_HOL_Obool),X20),X113))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__cartesian__product) ).

fof(fact_setprod__cartesian__product,axiom,
    ! [X21,X113,X2,X116,X20,X5] :
      ( class_Groups_Ocomm__monoid__mult(X5)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X20,X5),hAPP(hAPP(c_COMBC(X20,tc_fun(X116,tc_HOL_Obool),X5),hAPP(hAPP(c_COMBB(tc_fun(X116,X5),tc_fun(tc_fun(X116,tc_HOL_Obool),X5),X20),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X116,X5)),X2)),X113)),X21) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(X20,X116),X5),hAPP(c_Product__Type_Oprod_Oprod__case(X20,X116,X5),X2)),hAPP(hAPP(c_Product__Type_OSigma(X20,X116),X21),hAPP(c_COMBK(tc_fun(X116,tc_HOL_Obool),X20),X113))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__cartesian__product) ).

fof(fact_map__pair__inj__on,axiom,
    ! [X113,X1,X115,X116,X21,X2,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,X2,X21)
     => ( c_Fun_Oinj__on(X116,X115,X1,X113)
       => c_Fun_Oinj__on(tc_prod(X5,X116),tc_prod(X20,X115),c_Product__Type_Omap__pair(X5,X20,X116,X115,X2,X1),hAPP(hAPP(c_Product__Type_OSigma(X5,X116),X21),hAPP(c_COMBK(tc_fun(X116,tc_HOL_Obool),X5),X113))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__pair__inj__on) ).

fof(fact_divmod__nat__rel__mult1__eq,axiom,
    ! [X62,X134,X140,X56,X90] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X90,X56),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X140),X134)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X56))
       => hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X62),X90),X56),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),X62),X140)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X62),X134)),X56))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X62),X134),X56)))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__rel__mult1__eq) ).

fof(fact_lift__Suc__mono__less__iff,axiom,
    ! [X95,X50,X2,X5] :
      ( class_Orderings_Oorder(X5)
     => ( ! [X69] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(X2,X69)),hAPP(X2,hAPP(c_Nat_OSuc,X69))))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(X2,X50)),hAPP(X2,X95)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X50),X95)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lift__Suc__mono__less__iff) ).

fof(fact_lift__Suc__mono__less,axiom,
    ! [X109,X50,X2,X5] :
      ( class_Orderings_Oorder(X5)
     => ( ! [X69] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(X2,X69)),hAPP(X2,hAPP(c_Nat_OSuc,X69))))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X50),X109))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(X2,X50)),hAPP(X2,X109))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lift__Suc__mono__less) ).

fof(fact_zmult1__lemma,axiom,
    ! [X62,X134,X140,X56,X90] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X90,X56),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X140),X134)))
     => ( X56 != 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),X62),X90),X56),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),X62),X140)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X62),X134)),X56))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X62),X134),X56)))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult1__lemma) ).

fof(fact_,axiom,
    ! [X110,X104,X20,X5] : c_Lazy__Sequence_Oproduct(X5,X20,X104,X110) = hAPP(c_Lazy__Sequence_Obind(X5,tc_prod(X5,X20),X104),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_Lazy__Sequence_Olazy__sequence(tc_prod(X5,X20))),tc_Lazy__Sequence_Olazy__sequence(tc_prod(X5,X20)),X5),c_Lazy__Sequence_Obind(X20,tc_prod(X5,X20),X110)),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_prod(X5,X20)),tc_fun(X20,tc_Lazy__Sequence_Olazy__sequence(tc_prod(X5,X20))),X5),hAPP(c_COMBB(tc_prod(X5,X20),tc_Lazy__Sequence_Olazy__sequence(tc_prod(X5,X20)),X20),c_Lazy__Sequence_Osingle(tc_prod(X5,X20)))),c_Product__Type_OPair(X5,X20)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_) ).

fof(fact_Ex__inj__on__UNION__Sigma,axiom,
    ! [X21,X221,X20,X5] :
    ? [X227] :
      ( c_Fun_Oinj__on(X5,tc_prod(X20,X5),X227,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,tc_fun(X5,tc_HOL_Obool)),X221),X21))
      & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X20,X5),tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,tc_prod(X20,X5),X227),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,tc_fun(X5,tc_HOL_Obool)),X221),X21))),hAPP(hAPP(c_Product__Type_OSigma(X20,X5),X221),X21))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ex__inj__on__UNION__Sigma) ).

fof(fact_sublist__shift__lemma__Suc,axiom,
    ! [X287,X239,X18,X5] : hAPP(hAPP(c_List_Omap(tc_prod(X5,tc_Nat_Onat),X5),c_Product__Type_Ofst(X5,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X5,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(X5,tc_Nat_Onat)),X18),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(X5,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(X5,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(X5,tc_Nat_Onat),X239),X287))) = hAPP(hAPP(c_List_Omap(tc_prod(X5,tc_Nat_Onat),X5),c_Product__Type_Ofst(X5,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X5,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(X5,tc_Nat_Onat)),X18),c_Product__Type_Osnd(X5,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(X5,tc_Nat_Onat),X239),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),X287)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sublist__shift__lemma__Suc) ).

fof(fact_fst__comp__map__pair,axiom,
    ! [X1,X2,X20,X5,X115,X116] : hAPP(c_Fun_Ocomp(tc_prod(X116,X115),X116,tc_prod(X5,X20),c_Product__Type_Ofst(X116,X115)),c_Product__Type_Omap__pair(X5,X116,X20,X115,X2,X1)) = hAPP(c_Fun_Ocomp(X5,X116,tc_prod(X5,X20),X2),c_Product__Type_Ofst(X5,X20)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fst__comp__map__pair) ).

fof(fact_snd__comp__map__pair,axiom,
    ! [X1,X2,X20,X5,X116,X115] : hAPP(c_Fun_Ocomp(tc_prod(X115,X116),X116,tc_prod(X5,X20),c_Product__Type_Osnd(X115,X116)),c_Product__Type_Omap__pair(X5,X115,X20,X116,X2,X1)) = hAPP(c_Fun_Ocomp(X20,X116,tc_prod(X5,X20),X1),c_Product__Type_Osnd(X5,X20)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_snd__comp__map__pair) ).

fof(fact_INT__extend__simps_I9_J,axiom,
    ! [X112,X113,X116,X21,X5,X20] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X20,tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_COMBC(X20,tc_fun(X116,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X116,tc_HOL_Obool),tc_fun(tc_fun(X116,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),X20),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X116,tc_fun(X5,tc_HOL_Obool))),X113)),X112)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X116,tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,tc_fun(X116,tc_HOL_Obool)),X21),X113)),X112),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__extend__simps_I9_J) ).

fof(fact_UN__extend__simps_I9_J,axiom,
    ! [X112,X113,X116,X21,X5,X20] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_COMBC(X20,tc_fun(X116,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X116,tc_HOL_Obool),tc_fun(tc_fun(X116,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),X20),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X116,tc_fun(X5,tc_HOL_Obool))),X113)),X112)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X116,tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,tc_fun(X116,tc_HOL_Obool)),X21),X113)),X112),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__extend__simps_I9_J) ).

fof(fact_INT__simps_I9_J,axiom,
    ! [X112,X113,X21,X116,X5,X20] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X20,tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X116,tc_fun(X20,tc_HOL_Obool)),X21),X113)),X112) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X116,tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_COMBC(X116,tc_fun(X20,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_fun(tc_fun(X20,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),X116),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X20,tc_fun(X5,tc_HOL_Obool))),X113)),X112)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__simps_I9_J) ).

fof(fact_UN__simps_I9_J,axiom,
    ! [X112,X113,X21,X116,X5,X20] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X116,tc_fun(X20,tc_HOL_Obool)),X21),X113)),X112) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X116,tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_COMBC(X116,tc_fun(X20,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_fun(tc_fun(X20,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),X116),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,tc_fun(X5,tc_HOL_Obool))),X113)),X112)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__simps_I9_J) ).

fof(fact_UN__UN__flatten,axiom,
    ! [X112,X113,X21,X116,X5,X20] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X116,tc_fun(X20,tc_HOL_Obool)),X21),X113)),X112) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X116,tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_COMBC(X116,tc_fun(X20,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_fun(tc_fun(X20,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),X116),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,tc_fun(X5,tc_HOL_Obool))),X113)),X112)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__UN__flatten) ).

fof(fact_finite__less__ub,axiom,
    ! [X159,X2] :
      ( ! [X69] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X69),hAPP(X2,X69)))
     => 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)),X159)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__less__ub) ).

fof(fact_congruent2D,axiom,
    ! [X217,X218,X219,X220,X2,X213,X215,X116,X20,X5] :
      ( c_Equiv__Relations_Ocongruent2(X5,X20,X116,X215,X213,X2)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X220),X219)),X215))
       => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X20,X20)),hAPP(hAPP(c_Product__Type_OPair(X20,X20),X218),X217)),X213))
         => hAPP(hAPP(X2,X220),X218) = hAPP(hAPP(X2,X219),X217) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_congruent2D) ).

fof(fact_Int__Collect__mono,axiom,
    ! [X16,X18,X113,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),X113))
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X21))
           => ( hBOOL(hAPP(X18,X3))
             => hBOOL(hAPP(X16,X3)) ) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(c_Set_OCollect(X5),X18))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X113),hAPP(c_Set_OCollect(X5),X16)))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__Collect__mono) ).

fof(fact_UN__finite__subset,axiom,
    ! [X112,X21,X5] :
      ( ! [X69] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X69)),X21)),X112))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X21)),X112)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__finite__subset) ).

fof(fact_set__diff__eq,axiom,
    ! [X113,X21,X5] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),X113) = hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X21))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X113)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__diff__eq) ).

fof(fact_finite__Collect__conjI,axiom,
    ! [X16,X18,X5] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(c_Set_OCollect(X5),X18)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(c_Set_OCollect(X5),X16))) )
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),X18)),X16)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Collect__conjI) ).

fof(fact_UN__UN__finite__eq,axiom,
    ! [X21,X5] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X5,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),X21)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X21),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__UN__finite__eq) ).

fof(fact_map__pair__simp,axiom,
    ! [X24,X6,X1,X2,X20,X115,X5,X116] : hAPP(c_Product__Type_Omap__pair(X116,X5,X115,X20,X2,X1),hAPP(hAPP(c_Product__Type_OPair(X116,X115),X6),X24)) = hAPP(hAPP(c_Product__Type_OPair(X5,X20),hAPP(X2,X6)),hAPP(X1,X24)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__pair__simp) ).

fof(fact_list__all2I,axiom,
    ! [X18,X24,X6,X20,X5] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X20)),X3),hAPP(c_List_Oset(tc_prod(X5,X20)),hAPP(hAPP(c_List_Ozip(X5,X20),X6),X24))))
         => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5,X20,tc_HOL_Obool),X18),X3)) )
     => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X6) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X20)),X24)
       => c_List_Olist__all2(X5,X20,X18,X6,X24) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__all2I) ).

fof(fact_list__all2__def,axiom,
    ! [X251,X239,X18,X20,X5] :
      ( c_List_Olist__all2(X5,X20,X18,X239,X251)
    <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X20)),X251)
        & ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X20)),X3),hAPP(c_List_Oset(tc_prod(X5,X20)),hAPP(hAPP(c_List_Ozip(X5,X20),X239),X251))))
           => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5,X20,tc_HOL_Obool),X18),X3)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__all2__def) ).

fof(fact_map__pair__ident,axiom,
    ! [X120,X20,X5] : hAPP(c_Product__Type_Omap__pair(X5,X5,X20,X20,c_COMBI(X5),c_COMBI(X20)),X120) = X120,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__pair__ident) ).

fof(fact_folding__image__simple_Ounion__inter,axiom,
    ! [X113,X21,X205,X1,X120,X2,X20,X5] :
      ( c_Finite__Set_Ofolding__image__simple(X5,X20,X2,X120,X1,X205)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X20),X21))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X20),X113))
         => hAPP(hAPP(X2,hAPP(X205,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20,tc_HOL_Obool)),X21),X113))),hAPP(X205,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20,tc_HOL_Obool)),X21),X113))) = hAPP(hAPP(X2,hAPP(X205,X21)),hAPP(X205,X113)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple_Ounion__inter) ).

fof(fact_setsum_Ounion__inter__neutral,axiom,
    ! [X1,X113,X21,X5,X20] :
      ( class_Groups_Ocomm__monoid__add(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X113))
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113)))
               => hAPP(X1,X3) = c_Groups_Ozero__class_Ozero(X20) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X1),X21)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X1),X113)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum_Ounion__inter__neutral) ).

fof(fact_setsum__Un__zero,axiom,
    ! [X2,X212,X192,X5,X20] :
      ( class_Groups_Ocomm__monoid__add(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X192))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X212))
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X192),X212)))
               => hAPP(X2,X3) = c_Groups_Ozero__class_Ozero(X20) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X192),X212)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X2),X192)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X2),X212)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__Un__zero) ).

fof(fact_setprod_Ounion__inter__neutral,axiom,
    ! [X1,X113,X21,X5,X20] :
      ( class_Groups_Ocomm__monoid__mult(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X113))
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113)))
               => hAPP(X1,X3) = c_Groups_Oone__class_Oone(X20) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X1),X21)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X1),X113)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod_Ounion__inter__neutral) ).

fof(fact_setprod__Un__one,axiom,
    ! [X2,X212,X192,X5,X20] :
      ( class_Groups_Ocomm__monoid__mult(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X192))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X212))
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X192),X212)))
               => hAPP(X2,X3) = c_Groups_Oone__class_Oone(X20) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X192),X212)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X2),X192)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X2),X212)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__Un__one) ).

fof(fact_Image__singleton,axiom,
    ! [X6,X171,X5,X20] : hAPP(c_Relation_OImage(X20,X5,X171),hAPP(hAPP(c_Set_Oinsert(X20),X6),c_Orderings_Obot__class_Obot(tc_fun(X20,tc_HOL_Obool)))) = hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X20,X5),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X20,X5),tc_fun(tc_fun(tc_prod(X20,X5),tc_HOL_Obool),tc_HOL_Obool),X5),c_member(tc_prod(X20,X5))),hAPP(c_Product__Type_OPair(X20,X5),X6))),X171)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__singleton) ).

fof(fact_folding__image__simple_Oremove,axiom,
    ! [X25,X21,X205,X1,X120,X2,X20,X5] :
      ( c_Finite__Set_Ofolding__image__simple(X5,X20,X2,X120,X1,X205)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X20),X21))
       => ( hBOOL(hAPP(hAPP(c_member(X20),X25),X21))
         => hAPP(X205,X21) = hAPP(hAPP(X2,hAPP(X1,X25)),hAPP(X205,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X20),X25),c_Orderings_Obot__class_Obot(tc_fun(X20,tc_HOL_Obool)))))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple_Oremove) ).

fof(fact_subset__image__iff,axiom,
    ! [X21,X2,X20,X113,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X113),hAPP(c_Set_Oimage(X20,X5,X2),X21)))
    <=> ? [X201] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20,tc_HOL_Obool)),X201),X21))
          & X113 = hAPP(c_Set_Oimage(X20,X5,X2),X201) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__image__iff) ).

fof(fact_UN__iff,axiom,
    ! [X113,X21,X20,X24,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X24),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,tc_fun(X5,tc_HOL_Obool)),X21),X113)))
    <=> ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X20),X3),X21))
          & hBOOL(hAPP(hAPP(c_member(X5),X24),hAPP(X113,X3))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__iff) ).

fof(fact_folding__image__simple_Oinsert__remove,axiom,
    ! [X25,X21,X205,X1,X120,X2,X20,X5] :
      ( c_Finite__Set_Ofolding__image__simple(X5,X20,X2,X120,X1,X205)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X20),X21))
       => hAPP(X205,hAPP(hAPP(c_Set_Oinsert(X20),X25),X21)) = hAPP(hAPP(X2,hAPP(X1,X25)),hAPP(X205,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X20),X25),c_Orderings_Obot__class_Obot(tc_fun(X20,tc_HOL_Obool)))))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple_Oinsert__remove) ).

fof(fact_inv__into__comp,axiom,
    ! [X25,X21,X1,X116,X2,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,X2,hAPP(c_Set_Oimage(X116,X5,X1),X21))
     => ( c_Fun_Oinj__on(X116,X5,X1,X21)
       => ( hBOOL(hAPP(hAPP(c_member(X20),X25),hAPP(c_Set_Oimage(X5,X20,X2),hAPP(c_Set_Oimage(X116,X5,X1),X21))))
         => hAPP(c_Hilbert__Choice_Oinv__into(X116,X20,X21,hAPP(c_Fun_Ocomp(X5,X20,X116,X2),X1)),X25) = hAPP(hAPP(c_Fun_Ocomp(X5,X116,X20,c_Hilbert__Choice_Oinv__into(X116,X5,X21,X1)),c_Hilbert__Choice_Oinv__into(X5,X20,hAPP(c_Set_Oimage(X116,X5,X1),X21),X2)),X25) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__into__comp) ).

fof(fact_the__inv__into__comp,axiom,
    ! [X25,X21,X1,X116,X2,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,X2,hAPP(c_Set_Oimage(X116,X5,X1),X21))
     => ( c_Fun_Oinj__on(X116,X5,X1,X21)
       => ( hBOOL(hAPP(hAPP(c_member(X20),X25),hAPP(c_Set_Oimage(X5,X20,X2),hAPP(c_Set_Oimage(X116,X5,X1),X21))))
         => hAPP(c_Fun_Othe__inv__into(X116,X20,X21,hAPP(c_Fun_Ocomp(X5,X20,X116,X2),X1)),X25) = hAPP(hAPP(c_Fun_Ocomp(X5,X116,X20,c_Fun_Othe__inv__into(X116,X5,X21,X1)),c_Fun_Othe__inv__into(X5,X20,hAPP(c_Set_Oimage(X116,X5,X1),X21),X2)),X25) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__inv__into__comp) ).

fof(fact_setsum__mono__zero__right,axiom,
    ! [X2,X192,X212,X5,X20] :
      ( class_Groups_Ocomm__monoid__add(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X212))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X192),X212))
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X212),X192)))
               => hAPP(X2,X3) = c_Groups_Ozero__class_Ozero(X20) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X2),X212) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X2),X192) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__mono__zero__right) ).

fof(fact_setsum__mono__zero__left,axiom,
    ! [X2,X192,X212,X5,X20] :
      ( class_Groups_Ocomm__monoid__add(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X212))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X192),X212))
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X212),X192)))
               => hAPP(X2,X3) = c_Groups_Ozero__class_Ozero(X20) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X2),X192) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X2),X212) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__mono__zero__left) ).

fof(fact_setprod__mono__one__left,axiom,
    ! [X2,X192,X212,X5,X20] :
      ( class_Groups_Ocomm__monoid__mult(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X212))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X192),X212))
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X212),X192)))
               => hAPP(X2,X3) = c_Groups_Oone__class_Oone(X20) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X2),X192) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X2),X212) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__mono__one__left) ).

fof(fact_setprod__mono__one__right,axiom,
    ! [X2,X192,X212,X5,X20] :
      ( class_Groups_Ocomm__monoid__mult(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X212))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X192),X212))
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X212),X192)))
               => hAPP(X2,X3) = c_Groups_Oone__class_Oone(X20) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X2),X212) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X2),X192) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__mono__one__right) ).

fof(fact_SUP1__iff,axiom,
    ! [X24,X113,X21,X20,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X20,tc_HOL_Obool)),X21),X113),X24))
    <=> ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),X21))
          & hBOOL(hAPP(hAPP(X113,X3),X24)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUP1__iff) ).

fof(fact_order__fun_I1_J,axiom,
    ! [X1,X2,X5,X20] :
      ( ( class_Orderings_Oorder(X20)
        & class_Enum_Oenum(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X20)),X2),X1))
      <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X5),hAPP(hAPP(c_COMBS(X5,X20,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X20,tc_fun(X20,tc_HOL_Obool),X5),c_Orderings_Oord__class_Oless__eq(X20)),X2)),X1))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__fun_I1_J) ).

fof(fact_rtrancl__imp__UN__rel__pow,axiom,
    ! [X32,X160,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X160),c_Transitive__Closure_Ortrancl(X5,X32)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X160),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool)),X32)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__imp__UN__rel__pow) ).

fof(fact_Int__Inter__image,axiom,
    ! [X113,X21,X112,X5,X20] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X20,tc_fun(X5,tc_HOL_Obool)),X112),hAPP(hAPP(c_COMBS(X20,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X20),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool))),X21)),X113)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),hAPP(c_Set_Oimage(X20,tc_fun(X5,tc_HOL_Obool),X21),X112))),c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),hAPP(c_Set_Oimage(X20,tc_fun(X5,tc_HOL_Obool),X113),X112))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__Inter__image) ).

fof(fact_Un__Union__image,axiom,
    ! [X113,X21,X112,X5,X20] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,tc_fun(X5,tc_HOL_Obool)),X112),hAPP(hAPP(c_COMBS(X20,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X20),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool))),X21)),X113)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),hAPP(c_Set_Oimage(X20,tc_fun(X5,tc_HOL_Obool),X21),X112))),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),hAPP(c_Set_Oimage(X20,tc_fun(X5,tc_HOL_Obool),X113),X112))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Union__image) ).

fof(fact_lexord__append__left__rightI,axiom,
    ! [X33,X25,X159,X171,X24,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X24)),X171))
     => 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),X159),hAPP(hAPP(c_List_Olist_OCons(X5),X6),X25))),hAPP(hAPP(c_List_Oappend(X5),X159),hAPP(hAPP(c_List_Olist_OCons(X5),X24),X33)))),c_List_Olexord(X5,X171))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexord__append__left__rightI) ).

fof(fact_intrel__iff,axiom,
    ! [X123,X159,X33,X25] :
      ( 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),X25),X33)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X159),X123))),c_Int_Ointrel))
    <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),X123) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X159),X33) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_intrel__iff) ).

fof(fact_same__fstI,axiom,
    ! [X5,X32,X33,X195,X20,X25,X18] :
      ( hBOOL(hAPP(X18,X25))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X20,X20)),hAPP(hAPP(c_Product__Type_OPair(X20,X20),X195),X33)),hAPP(X32,X25)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X5,X20),tc_prod(X5,X20))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X5,X20),tc_prod(X5,X20)),hAPP(hAPP(c_Product__Type_OPair(X5,X20),X25),X195)),hAPP(hAPP(c_Product__Type_OPair(X5,X20),X25),X33))),c_Recdef_Osame__fst(X5,X20,X18,X32))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_same__fstI) ).

fof(fact_less__SUP__iff,axiom,
    ! [X2,X21,X20,X6,X5] :
      ( ( class_Complete__Lattice_Ocomplete__lattice(X5)
        & class_Orderings_Olinorder(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,X5),X21),X2)))
      <=> ? [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X20),X3),X21))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),hAPP(X2,X3))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__SUP__iff) ).

fof(fact_split__twice,axiom,
    ! [X160,X1,X114,X115,X2,X5,X116,X20] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X20,X116,X5),X2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X115,X114,tc_prod(X20,X116)),X1),X160)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X115,X114,X5),hAPP(hAPP(c_COMBB(tc_fun(X114,tc_prod(X20,X116)),tc_fun(X114,X5),X115),hAPP(c_COMBB(tc_prod(X20,X116),X5,X114),hAPP(c_Product__Type_Oprod_Oprod__case(X20,X116,X5),X2))),X1)),X160),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__twice) ).

fof(fact_list__size__pointwise,axiom,
    ! [X1,X2,X239,X5] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X239)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X2,X3)),hAPP(X1,X3))) )
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(X5,X2,X239)),c_List_Olist_Olist__size(X5,X1,X239))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__size__pointwise) ).

fof(fact_inj__graph,axiom,
    ! [X20,X5] : c_Fun_Oinj__on(tc_fun(X5,X20),tc_fun(tc_prod(X5,X20),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_fun(X5,X20)),c_Set_OCollect(tc_prod(X5,X20))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X20,tc_HOL_Obool)),tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_fun(X5,X20)),c_Product__Type_Oprod_Oprod__case(X5,X20,tc_HOL_Obool)),hAPP(c_COMBB(X20,tc_fun(X20,tc_HOL_Obool),X5),hAPP(c_COMBC(X20,X20,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X5,X20),tc_HOL_Obool))),
    file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J) ).

fof(fact_max__extp_Osimps,axiom,
    ! [X26,X27,X32,X5] :
      ( c_Wellfounded_Omax__extp(X5,X32,X27,X26)
    <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X27))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X26))
        & X26 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
        & ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X27))
           => ? [X204] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X204),X26))
                & hBOOL(hAPP(hAPP(X32,X3),X204)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__extp_Osimps) ).

fof(fact_max__extp_Oequations,axiom,
    ! [X26,X27,X32,X5] :
      ( c_Wellfounded_Omax__extp(X5,X32,X27,X26)
    <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X27))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X26))
        & X26 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
        & ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X27))
           => ? [X204] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X204),X26))
                & hBOOL(hAPP(hAPP(X32,X3),X204)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__extp_Oequations) ).

fof(fact_Int__def,axiom,
    ! [X113,X21,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113) = hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X21))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X113))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__def) ).

fof(fact_Un__def,axiom,
    ! [X113,X21,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113) = hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fdisj),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X21))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X113))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__def) ).

fof(fact_folding__image__simple_Ounion__disjoint,axiom,
    ! [X113,X21,X205,X1,X120,X2,X20,X5] :
      ( c_Finite__Set_Ofolding__image__simple(X5,X20,X2,X120,X1,X205)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X20),X21))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X20),X113))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20,tc_HOL_Obool)),X21),X113) = c_Orderings_Obot__class_Obot(tc_fun(X20,tc_HOL_Obool))
           => hAPP(X205,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20,tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(X2,hAPP(X205,X21)),hAPP(X205,X113)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple_Ounion__disjoint) ).

fof(fact_le__add__iff2,axiom,
    ! [X22,X24,X23,X155,X6,X5] :
      ( class_Rings_Oordered__ring(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X155)),X23)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X24),X155)),X22)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X23),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X24),X6)),X155)),X22))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add__iff2) ).

fof(fact_less__add__iff2,axiom,
    ! [X22,X24,X23,X155,X6,X5] :
      ( class_Rings_Oordered__ring(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X155)),X23)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X24),X155)),X22)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X24),X6)),X155)),X22))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__iff2) ).

fof(fact_Image__INT__subset,axiom,
    ! [X113,X21,X116,X171,X20,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_OImage(X20,X5,X171),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X116,tc_fun(X20,tc_HOL_Obool)),X21),X113))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X116,tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X116),c_Relation_OImage(X20,X5,X171)),X113)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__INT__subset) ).

fof(fact_folding__image__simple__idem_Osubset__idem,axiom,
    ! [X113,X21,X205,X1,X120,X2,X20,X5] :
      ( c_Finite__Set_Ofolding__image__simple__idem(X5,X20,X2,X120,X1,X205)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X20),X21))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20,tc_HOL_Obool)),X113),X21))
         => hAPP(hAPP(X2,hAPP(X205,X113)),hAPP(X205,X21)) = hAPP(X205,X21) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Osubset__idem) ).

fof(fact_le__fun__def,axiom,
    ! [X1,X2,X5,X20] :
      ( class_Orderings_Oord(X20)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X20)),X2),X1))
      <=> ! [X3] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20),hAPP(X2,X3)),hAPP(X1,X3))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__fun__def) ).

fof(fact_folding__image__simple_Oeq__fold__g,axiom,
    ! [X21,X205,X1,X120,X2,X20,X5] :
      ( c_Finite__Set_Ofolding__image__simple(X5,X20,X2,X120,X1,X205)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X20),X21))
       => hAPP(X205,X21) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X5,X20,X2),X1),X120),X21) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple_Oeq__fold__g) ).

fof(fact_map__eq__conv,axiom,
    ! [X1,X239,X2,X5,X20] :
      ( hAPP(hAPP(c_List_Omap(X20,X5),X2),X239) = hAPP(hAPP(c_List_Omap(X20,X5),X1),X239)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X20),X3),hAPP(c_List_Oset(X20),X239)))
         => hAPP(X2,X3) = hAPP(X1,X3) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__eq__conv) ).

fof(fact_pred__comp_Ointros,axiom,
    ! [X116,X20,X5,X23,X76,X24,X6,X171] :
      ( hBOOL(hAPP(hAPP(X171,X6),X24))
     => ( hBOOL(hAPP(hAPP(X76,X24),X23))
       => hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X5,X20,X116,X171,X76),X6),X23)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__comp_Ointros) ).

fof(fact_folding__image__simple__idem_Ounion__idem,axiom,
    ! [X113,X21,X205,X1,X120,X2,X20,X5] :
      ( c_Finite__Set_Ofolding__image__simple__idem(X5,X20,X2,X120,X1,X205)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X20),X21))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X20),X113))
         => hAPP(X205,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20,tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(X2,hAPP(X205,X21)),hAPP(X205,X113)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Ounion__idem) ).

fof(fact_congruent2__implies__congruent,axiom,
    ! [X6,X2,X213,X116,X20,X215,X21,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X21,X215)
     => ( c_Equiv__Relations_Ocongruent2(X5,X20,X116,X215,X213,X2)
       => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X21))
         => c_Equiv__Relations_Ocongruent(X20,X116,X213,hAPP(X2,X6)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_congruent2__implies__congruent) ).

fof(fact_append__eq__append__conv2,axiom,
    ! [X13,X250,X251,X239,X5] :
      ( hAPP(hAPP(c_List_Oappend(X5),X239),X251) = hAPP(hAPP(c_List_Oappend(X5),X250),X13)
    <=> ? [X252] :
          ( ( X239 = hAPP(hAPP(c_List_Oappend(X5),X250),X252)
            & hAPP(hAPP(c_List_Oappend(X5),X252),X251) = X13 )
          | ( hAPP(hAPP(c_List_Oappend(X5),X239),X252) = X250
            & X251 = hAPP(hAPP(c_List_Oappend(X5),X252),X13) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__eq__append__conv2) ).

fof(fact_inj__on__iff__card__le,axiom,
    ! [X113,X20,X21,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X20),X113))
       => ( ? [X227] :
              ( c_Fun_Oinj__on(X5,X20,X227,X21)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X20,X227),X21)),X113)) )
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X21)),hAPP(c_Finite__Set_Ocard(X20),X113))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__iff__card__le) ).

fof(fact_folding__image__simple__idem_Oin__idem,axiom,
    ! [X25,X21,X205,X1,X120,X2,X20,X5] :
      ( c_Finite__Set_Ofolding__image__simple__idem(X5,X20,X2,X120,X1,X205)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X20),X21))
       => ( hBOOL(hAPP(hAPP(c_member(X20),X25),X21))
         => hAPP(hAPP(X2,hAPP(X1,X25)),hAPP(X205,X21)) = hAPP(X205,X21) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oin__idem) ).

fof(fact_sublists_Osimps_I2_J,axiom,
    ! [X239,X25,X5] : c_Enum_Osublists(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(X5)),tc_List_Olist(tc_List_Olist(X5))),c_Enum_Osublists(X5,X239)),hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(X5)),tc_List_Olist(tc_List_Olist(X5)),tc_List_Olist(tc_List_Olist(X5))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(X5)),tc_fun(tc_List_Olist(tc_List_Olist(X5)),tc_List_Olist(tc_List_Olist(X5))),tc_List_Olist(tc_List_Olist(X5))),c_List_Oappend(tc_List_Olist(X5))),hAPP(c_List_Omap(tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(c_List_Olist_OCons(X5),X25)))),c_COMBI(tc_List_Olist(tc_List_Olist(X5))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sublists_Osimps_I2_J) ).

fof(fact_folding__image__simple__idem_Oinsert__idem,axiom,
    ! [X25,X21,X205,X1,X120,X2,X20,X5] :
      ( c_Finite__Set_Ofolding__image__simple__idem(X5,X20,X2,X120,X1,X205)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X20),X21))
       => hAPP(X205,hAPP(hAPP(c_Set_Oinsert(X20),X25),X21)) = hAPP(hAPP(X2,hAPP(X1,X25)),hAPP(X205,X21)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oinsert__idem) ).

fof(fact_INT__Int__distrib,axiom,
    ! [X113,X21,X221,X5,X20] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X20,tc_fun(X5,tc_HOL_Obool)),X221),hAPP(hAPP(c_COMBS(X20,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X20),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool))),X21)),X113)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X20,tc_fun(X5,tc_HOL_Obool)),X221),X21)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X20,tc_fun(X5,tc_HOL_Obool)),X221),X113)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__Int__distrib) ).

fof(fact_UN__Un__distrib,axiom,
    ! [X113,X21,X221,X5,X20] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,tc_fun(X5,tc_HOL_Obool)),X221),hAPP(hAPP(c_COMBS(X20,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X20),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool))),X21)),X113)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,tc_fun(X5,tc_HOL_Obool)),X221),X21)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,tc_fun(X5,tc_HOL_Obool)),X221),X113)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__Un__distrib) ).

fof(fact_folding__image__simple_Oempty,axiom,
    ! [X205,X1,X120,X2,X20,X5] :
      ( c_Finite__Set_Ofolding__image__simple(X5,X20,X2,X120,X1,X205)
     => hAPP(X205,c_Orderings_Obot__class_Obot(tc_fun(X20,tc_HOL_Obool))) = X120 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple_Oempty) ).

fof(fact_folding__image__simple__idem_Oidem,axiom,
    ! [X25,X205,X1,X120,X2,X20,X5] :
      ( c_Finite__Set_Ofolding__image__simple__idem(X5,X20,X2,X120,X1,X205)
     => hAPP(hAPP(X2,X25),X25) = X25 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oidem) ).

fof(fact_smax__emptyI,axiom,
    ! [X196] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X196))
     => ( X196 != 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))),X196)),c_FunDef_Omax__strict)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smax__emptyI) ).

fof(fact_set__filter,axiom,
    ! [X239,X18,X5] : hAPP(c_List_Oset(X5),hAPP(c_List_Ofilter(X5,X18),X239)) = hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),hAPP(c_List_Oset(X5),X239)))),X18)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__filter) ).

fof(fact_sum__diff__distrib,axiom,
    ! [X50,X18,X16] :
      ( ! [X3] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(X16,X3)),hAPP(X18,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),X18),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X50))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X16),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X50))) = 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)),X18)),X16)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X50)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__diff__distrib) ).

fof(fact_inj__on__iff__surj,axiom,
    ! [X202,X20,X5,X21] :
      ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
     => ( ? [X227] :
            ( c_Fun_Oinj__on(X5,X20,X227,X21)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X20,X227),X21)),X202)) )
      <=> ? [X229] : hAPP(c_Set_Oimage(X20,X5,X229),X202) = X21 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__iff__surj) ).

fof(fact_Range__iff,axiom,
    ! [X171,X20,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(c_Relation_ORange(X20,X5),X171)))
    <=> ? [X177] : hBOOL(hAPP(hAPP(c_member(tc_prod(X20,X5)),hAPP(hAPP(c_Product__Type_OPair(X20,X5),X177),X6)),X171)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__iff) ).

fof(fact_wmax__emptyI,axiom,
    ! [X194] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X194))
     => 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))),X194)),c_FunDef_Omax__weak)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wmax__emptyI) ).

fof(fact_INT__simps_I1_J,axiom,
    ! [X113,X21,X20,X5,X112] :
      ( ( X112 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X20,tc_HOL_Obool)),X112),hAPP(hAPP(c_COMBC(X5,tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_fun(tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),X5),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20,tc_HOL_Obool))),X21)),X113)) = c_Orderings_Otop__class_Otop(tc_fun(X20,tc_HOL_Obool)) )
      & ( X112 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X20,tc_HOL_Obool)),X112),hAPP(hAPP(c_COMBC(X5,tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_fun(tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),X5),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20,tc_HOL_Obool))),X21)),X113)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X20,tc_HOL_Obool)),X112),X21)),X113) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__simps_I1_J) ).

fof(fact_INT__simps_I3_J,axiom,
    ! [X113,X21,X20,X5,X112] :
      ( ( X112 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X20,tc_HOL_Obool)),X112),hAPP(hAPP(c_COMBC(X5,tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_fun(tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),X5),c_Groups_Ominus__class_Ominus(tc_fun(X20,tc_HOL_Obool))),X21)),X113)) = c_Orderings_Otop__class_Otop(tc_fun(X20,tc_HOL_Obool)) )
      & ( X112 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X20,tc_HOL_Obool)),X112),hAPP(hAPP(c_COMBC(X5,tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_fun(tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),X5),c_Groups_Ominus__class_Ominus(tc_fun(X20,tc_HOL_Obool))),X21)),X113)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X20,tc_HOL_Obool)),X112),X21)),X113) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__simps_I3_J) ).

fof(fact_UN__simps_I2_J,axiom,
    ! [X113,X21,X20,X5,X112] :
      ( ( X112 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X20,tc_HOL_Obool)),X112),hAPP(hAPP(c_COMBC(X5,tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_fun(tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),X5),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20,tc_HOL_Obool))),X21)),X113)) = c_Orderings_Obot__class_Obot(tc_fun(X20,tc_HOL_Obool)) )
      & ( X112 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X20,tc_HOL_Obool)),X112),hAPP(hAPP(c_COMBC(X5,tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_fun(tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),X5),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20,tc_HOL_Obool))),X21)),X113)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X20,tc_HOL_Obool)),X112),X21)),X113) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__simps_I2_J) ).

fof(fact_INT__extend__simps_I1_J,axiom,
    ! [X113,X21,X20,X5,X112] :
      ( ( X112 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X20,tc_HOL_Obool)),X112),X21)),X113) = X113 )
      & ( X112 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X20,tc_HOL_Obool)),X112),X21)),X113) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X20,tc_HOL_Obool)),X112),hAPP(hAPP(c_COMBC(X5,tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_fun(tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),X5),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20,tc_HOL_Obool))),X21)),X113)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__extend__simps_I1_J) ).

fof(fact_UN__extend__simps_I2_J,axiom,
    ! [X113,X21,X20,X5,X112] :
      ( ( X112 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X20,tc_HOL_Obool)),X112),X21)),X113) = X113 )
      & ( X112 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X20,tc_HOL_Obool)),X112),X21)),X113) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X20,tc_HOL_Obool)),X112),hAPP(hAPP(c_COMBC(X5,tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_fun(tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),X5),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20,tc_HOL_Obool))),X21)),X113)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__extend__simps_I2_J) ).

fof(fact_INT__extend__simps_I3_J,axiom,
    ! [X113,X21,X20,X5,X112] :
      ( ( X112 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X20,tc_HOL_Obool)),X112),X21)),X113) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X20,tc_HOL_Obool))),X113) )
      & ( X112 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X20,tc_HOL_Obool)),X112),X21)),X113) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X20,tc_HOL_Obool)),X112),hAPP(hAPP(c_COMBC(X5,tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_fun(tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),X5),c_Groups_Ominus__class_Ominus(tc_fun(X20,tc_HOL_Obool))),X21)),X113)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__extend__simps_I3_J) ).

fof(fact_INT__simps_I6_J,axiom,
    ! [X113,X21,X112,X5,X20] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X20,tc_fun(X5,tc_HOL_Obool)),X112),hAPP(hAPP(c_COMBC(X20,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X20),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool))),X21)),X113)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X20,tc_fun(X5,tc_HOL_Obool)),X112),X21)),X113),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__simps_I6_J) ).

fof(fact_UN__simps_I4_J,axiom,
    ! [X113,X21,X112,X5,X20] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,tc_fun(X5,tc_HOL_Obool)),X112),hAPP(hAPP(c_COMBC(X20,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X20),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool))),X21)),X113)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,tc_fun(X5,tc_HOL_Obool)),X112),X21)),X113),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__simps_I4_J) ).

fof(fact_UN__simps_I6_J,axiom,
    ! [X113,X21,X112,X5,X20] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,tc_fun(X5,tc_HOL_Obool)),X112),hAPP(hAPP(c_COMBC(X20,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X20),c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool))),X21)),X113)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,tc_fun(X5,tc_HOL_Obool)),X112),X21)),X113),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__simps_I6_J) ).

fof(fact_UN__extend__simps_I4_J,axiom,
    ! [X113,X21,X112,X20,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,tc_fun(X5,tc_HOL_Obool)),X112),X21)),X113) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,tc_fun(X5,tc_HOL_Obool)),X112),hAPP(hAPP(c_COMBC(X20,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X20),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool))),X21)),X113)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__extend__simps_I4_J) ).

fof(fact_INT__extend__simps_I6_J,axiom,
    ! [X113,X21,X112,X20,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X20,tc_fun(X5,tc_HOL_Obool)),X112),X21)),X113) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X20,tc_fun(X5,tc_HOL_Obool)),X112),hAPP(hAPP(c_COMBC(X20,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X20),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool))),X21)),X113)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__extend__simps_I6_J) ).

fof(fact_UN__extend__simps_I6_J,axiom,
    ! [X113,X21,X112,X20,X5] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,tc_fun(X5,tc_HOL_Obool)),X112),X21)),X113) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,tc_fun(X5,tc_HOL_Obool)),X112),hAPP(hAPP(c_COMBC(X20,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X20),c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool))),X21)),X113)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__extend__simps_I6_J) ).

fof(fact_rel__comp__subset__Sigma,axiom,
    ! [X112,X76,X116,X113,X21,X171,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X20),tc_HOL_Obool)),X171),hAPP(hAPP(c_Product__Type_OSigma(X5,X20),X21),hAPP(c_COMBK(tc_fun(X20,tc_HOL_Obool),X5),X113))))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X20,X116),tc_HOL_Obool)),X76),hAPP(hAPP(c_Product__Type_OSigma(X20,X116),X113),hAPP(c_COMBK(tc_fun(X116,tc_HOL_Obool),X20),X112))))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X116),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X5,X20,X116),X171),X76)),hAPP(hAPP(c_Product__Type_OSigma(X5,X116),X21),hAPP(c_COMBK(tc_fun(X116,tc_HOL_Obool),X5),X112)))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__comp__subset__Sigma) ).

fof(fact_Cons__listrel1__Cons,axiom,
    ! [X171,X251,X33,X239,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239)),hAPP(hAPP(c_List_Olist_OCons(X5),X33),X251))),c_List_Olistrel1(X5,X171)))
    <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X33)),X171))
          & X239 = X251 )
        | ( X25 = X33
          & 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)),X239),X251)),c_List_Olistrel1(X5,X171))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Cons__listrel1__Cons) ).

fof(fact_lexord__cons__cons,axiom,
    ! [X171,X33,X24,X25,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(hAPP(c_List_Olist_OCons(X5),X6),X25)),hAPP(hAPP(c_List_Olist_OCons(X5),X24),X33))),c_List_Olexord(X5,X171)))
    <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X24)),X171))
        | ( X6 = X24
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X25),X33)),c_List_Olexord(X5,X171))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexord__cons__cons) ).

fof(fact_Cons__in__lex,axiom,
    ! [X171,X251,X33,X239,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239)),hAPP(hAPP(c_List_Olist_OCons(X5),X33),X251))),c_List_Olex(X5,X171)))
    <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X33)),X171))
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X251) )
        | ( X25 = X33
          & 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)),X239),X251)),c_List_Olex(X5,X171))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Cons__in__lex) ).

fof(fact_Sigma__Int__distrib2,axiom,
    ! [X113,X21,X221,X20,X5] : hAPP(hAPP(c_Product__Type_OSigma(X5,X20),X221),hAPP(hAPP(c_COMBS(X5,tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_fun(tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),X5),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20,tc_HOL_Obool))),X21)),X113)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X5,X20),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X5,X20),X221),X21)),hAPP(hAPP(c_Product__Type_OSigma(X5,X20),X221),X113)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__Int__distrib2) ).

fof(fact_Sigma__Un__distrib2,axiom,
    ! [X113,X21,X221,X20,X5] : hAPP(hAPP(c_Product__Type_OSigma(X5,X20),X221),hAPP(hAPP(c_COMBS(X5,tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_fun(tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),X5),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20,tc_HOL_Obool))),X21)),X113)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X20),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X5,X20),X221),X21)),hAPP(hAPP(c_Product__Type_OSigma(X5,X20),X221),X113)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__Un__distrib2) ).

fof(fact_Sigma__Diff__distrib2,axiom,
    ! [X113,X21,X221,X20,X5] : hAPP(hAPP(c_Product__Type_OSigma(X5,X20),X221),hAPP(hAPP(c_COMBS(X5,tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_fun(tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),X5),c_Groups_Ominus__class_Ominus(tc_fun(X20,tc_HOL_Obool))),X21)),X113)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X5,X20),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X5,X20),X221),X21)),hAPP(hAPP(c_Product__Type_OSigma(X5,X20),X221),X113)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__Diff__distrib2) ).

fof(fact_abs__diff__triangle__ineq,axiom,
    ! [X91,X56,X90,X62,X58] :
      ( class_Groups_Oordered__ab__group__add__abs(X58)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(c_Groups_Oabs__class_Oabs(X58),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),X90)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X56),X91)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(c_Groups_Oabs__class_Oabs(X58),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X58),X62),X56))),hAPP(c_Groups_Oabs__class_Oabs(X58),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X58),X90),X91))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__diff__triangle__ineq) ).

fof(fact_nat__le__add__iff2,axiom,
    ! [X50,X95,X159,X157,X82] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X82),X157))
     => ( 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),X82),X159)),X95)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X157),X159)),X50)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),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),X157),X82)),X159)),X50))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__add__iff2) ).

fof(fact_nat__less__add__iff2,axiom,
    ! [X50,X95,X159,X157,X82] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X82),X157))
     => ( 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),X82),X159)),X95)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X157),X159)),X50)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),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),X157),X82)),X159)),X50))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__add__iff2) ).

fof(fact_folding__image_Odistrib,axiom,
    ! [X122,X1,X21,X205,X120,X2,X20,X5] :
      ( c_Finite__Set_Ofolding__image(X5,X20,X2,X120,X205)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X20),X21))
       => hAPP(hAPP(X205,hAPP(hAPP(c_COMBS(X20,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X20),X2),X1)),X122)),X21) = hAPP(hAPP(X2,hAPP(hAPP(X205,X1),X21)),hAPP(hAPP(X205,X122),X21)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image_Odistrib) ).

fof(fact_fold__image__Un__Int,axiom,
    ! [X1,X113,X21,X5,X20] :
      ( class_Groups_Ocomm__monoid__mult(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X113))
         => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X20,X5,c_Groups_Otimes__class_Otimes(X20)),X1),c_Groups_Oone__class_Oone(X20)),X21)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X20,X5,c_Groups_Otimes__class_Otimes(X20)),X1),c_Groups_Oone__class_Oone(X20)),X113)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X20,X5,c_Groups_Otimes__class_Otimes(X20)),X1),c_Groups_Oone__class_Oone(X20)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X20,X5,c_Groups_Otimes__class_Otimes(X20)),X1),c_Groups_Oone__class_Oone(X20)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__image__Un__Int) ).

fof(fact_arith__series__nat,axiom,
    ! [X50,X22,X6] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),X22))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X50))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X50),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X50),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X22)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_arith__series__nat) ).

fof(fact_Un__Int__crazy,axiom,
    ! [X112,X113,X21,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X113),X112))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X112),X21)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X113),X112))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X112),X21)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Int__crazy) ).

fof(fact_rtrancl__listrel1__ConsI2,axiom,
    ! [X251,X239,X171,X33,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X33)),c_Transitive__Closure_Ortrancl(X5,X171)))
     => ( 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)),X239),X251)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X5),c_List_Olistrel1(X5,X171))))
       => 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),X25),X239)),hAPP(hAPP(c_List_Olist_OCons(X5),X33),X251))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X5),c_List_Olistrel1(X5,X171)))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__listrel1__ConsI2) ).

fof(fact_image__diff__subset,axiom,
    ! [X113,X21,X2,X20,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Oimage(X20,X5,X2),X21)),hAPP(c_Set_Oimage(X20,X5,X2),X113))),hAPP(c_Set_Oimage(X20,X5,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20,tc_HOL_Obool)),X21),X113)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__diff__subset) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J,axiom,
    ! [X18] : hAPP(c_Set_OCollect(tc_Nat_Onat),X18) = 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),X18),c_Int_Onat)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J) ).

fof(fact_lenlex__def,axiom,
    ! [X171,X5] : c_List_Olenlex(X5,X171) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(X5)),tc_List_Olist(X5)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(X5),c_Wellfounded_Oless__than,c_List_Olex(X5,X171))),hAPP(hAPP(c_COMBS(tc_List_Olist(X5),tc_List_Olist(X5),tc_prod(tc_Nat_Onat,tc_List_Olist(X5))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(X5),tc_prod(tc_Nat_Onat,tc_List_Olist(X5))),tc_List_Olist(X5)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(X5))),c_Nat_Osize__class_Osize(tc_List_Olist(X5)))),c_COMBI(tc_List_Olist(X5)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lenlex__def) ).

fof(fact_refl__onI,axiom,
    ! [X21,X171,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X171),hAPP(hAPP(c_Product__Type_OSigma(X5,X5),X21),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X5),X21))))
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X21))
           => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X3)),X171)) )
       => c_Relation_Orefl__on(X5,X21,X171) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__onI) ).

fof(fact_refl__on__def,axiom,
    ! [X171,X21,X5] :
      ( c_Relation_Orefl__on(X5,X21,X171)
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X171),hAPP(hAPP(c_Product__Type_OSigma(X5,X5),X21),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X5),X21))))
        & ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X21))
           => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X3)),X171)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__on__def) ).

fof(fact_insert__compr,axiom,
    ! [X113,X6,X5] : hAPP(hAPP(c_Set_Oinsert(X5),X6),X113) = hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fdisj),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X6))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X113))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__compr) ).

fof(fact_insert__compr__raw,axiom,
    ! [X113,X6,X5] : hAPP(hAPP(c_Set_Oinsert(X5),X6),X113) = hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fdisj),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X6))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X113))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__compr__raw) ).

fof(fact_listrel_OCons,axiom,
    ! [X251,X239,X171,X33,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X33)),X171))
     => ( 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)),X239),X251)),c_List_Olistrel(X5,X171)))
       => 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),X25),X239)),hAPP(hAPP(c_List_Olist_OCons(X5),X33),X251))),c_List_Olistrel(X5,X171))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel_OCons) ).

fof(fact_smin__emptyI,axiom,
    ! [X194] :
      ( X194 != 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)),X194),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/sandbox/benchmark/theBenchmark.p',fact_smin__emptyI) ).

fof(fact_minus,axiom,
    ! [X33,X25] : 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),X25),X33)),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),X33),X25)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus) ).

fof(fact_wmin__emptyI,axiom,
    ! [X194] : 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)),X194),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/sandbox/benchmark/theBenchmark.p',fact_wmin__emptyI) ).

fof(fact_fun__left__comm_Ofold__equality,axiom,
    ! [X33,X21,X120,X2,X20,X5] :
      ( c_Finite__Set_Ofun__left__comm(X5,X20,X2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X20,X2,X120,X21),X33))
       => hAPP(hAPP(c_Finite__Set_Ofold(X5,X20,X2),X120),X21) = X33 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__equality) ).

fof(fact_empty__fold__graphE,axiom,
    ! [X25,X120,X2,X20,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X20,X2,X120,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),X25))
     => X25 = X120 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__fold__graphE) ).

fof(fact_subset__equiv__class,axiom,
    ! [X6,X24,X171,X21,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X21,X171)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_OImage(X5,X5,X171),hAPP(hAPP(c_Set_Oinsert(X5),X24),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X5,X5,X171),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X24),X21))
         => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X24)),X171)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__equiv__class) ).

fof(fact_BodyN,axiom,
    ! [X4,X16,X17,X18,X5] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(X5,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X5)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),X18),hAPP(c_Com_Ocom_OBODY,X17)),X16)),X4),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X5)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),X18),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X17))),X16)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool))))
     => c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X5)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),X18),hAPP(c_Com_Ocom_OBODY,X17)),X16)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_BodyN) ).

fof(fact_ord_OatLeastLessThan__iff,axiom,
    ! [X159,X156,X209,X208,X82,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X82),c_SetInterval_Oord_OatLeastLessThan(X5,X208,X209,X156,X159)))
    <=> ( hBOOL(hAPP(hAPP(X208,X156),X82))
        & hBOOL(hAPP(hAPP(X209,X82),X159)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord_OatLeastLessThan__iff) ).

fof(fact_ord_OgreaterThanAtMost__iff,axiom,
    ! [X159,X156,X209,X208,X82,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X82),c_SetInterval_Oord_OgreaterThanAtMost(X5,X208,X209,X156,X159)))
    <=> ( hBOOL(hAPP(hAPP(X209,X156),X82))
        & hBOOL(hAPP(hAPP(X208,X82),X159)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord_OgreaterThanAtMost__iff) ).

fof(fact_transfer__nat__int__sum__prod__cong_I1_J,axiom,
    ! [X1,X2,X113,X21,X5] :
      ( ( class_Groups_Ocomm__monoid__add(X5)
        & class_Groups_Ocomm__monoid__mult(X5) )
     => ( X21 = X113
       => ( c_Nat__Transfer_Onat__set(X113)
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
               => hAPP(X2,X3) = hAPP(X1,X3) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X5),X2),X21) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X5),X1),X113) ) ) ) ),
    file('/export/starexec/sandbox/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,X113,X21,X5] :
      ( ( class_Groups_Ocomm__monoid__add(X5)
        & class_Groups_Ocomm__monoid__mult(X5) )
     => ( X21 = X113
       => ( c_Nat__Transfer_Onat__set(X113)
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
               => hAPP(X2,X3) = hAPP(X1,X3) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X5),X2),X21) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X5),X1),X113) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__sum__prod__cong_I2_J) ).

fof(fact_select__weigth__drop__zero,axiom,
    ! [X239,X5] : c_Random_Oselect__weight(X5,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,X5),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,X5,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,X5)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),X239)) = c_Random_Oselect__weight(X5,X239),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_select__weigth__drop__zero) ).

fof(fact_pick__drop__zero,axiom,
    ! [X239,X5] : c_Random_Opick(X5,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,X5),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,X5,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,X5)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),X239)) = c_Random_Opick(X5,X239),
    file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__numerals_I3_J) ).

fof(fact_o__inv__distrib,axiom,
    ! [X1,X116,X2,X20,X5] :
      ( c_Fun_Obij__betw(X5,X20,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X20,tc_HOL_Obool)))
     => ( c_Fun_Obij__betw(X116,X5,X1,c_Orderings_Otop__class_Otop(tc_fun(X116,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
       => c_Hilbert__Choice_Oinv__into(X116,X20,c_Orderings_Otop__class_Otop(tc_fun(X116,tc_HOL_Obool)),hAPP(c_Fun_Ocomp(X5,X20,X116,X2),X1)) = hAPP(c_Fun_Ocomp(X5,X116,X20,c_Hilbert__Choice_Oinv__into(X116,X5,c_Orderings_Otop__class_Otop(tc_fun(X116,tc_HOL_Obool)),X1)),c_Hilbert__Choice_Oinv__into(X5,X20,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__inv__distrib) ).

fof(fact_Domain__Int__subset,axiom,
    ! [X113,X21,X20,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X5,X20),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X5,X20),tc_HOL_Obool)),X21),X113))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X5,X20),X21)),hAPP(c_Relation_ODomain(X5,X20),X113)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__Int__subset) ).

fof(fact_Range__Int__subset,axiom,
    ! [X113,X21,X20,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_ORange(X20,X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X20,X5),tc_HOL_Obool)),X21),X113))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_ORange(X20,X5),X21)),hAPP(c_Relation_ORange(X20,X5),X113)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__Int__subset) ).

fof(fact_setsum_Odistrib,axiom,
    ! [X122,X1,X21,X5,X20] :
      ( class_Groups_Ocomm__monoid__add(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),hAPP(hAPP(c_COMBS(X5,X20,X20),hAPP(hAPP(c_COMBB(X20,tc_fun(X20,X20),X5),c_Groups_Oplus__class_Oplus(X20)),X1)),X122)),X21) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X1),X21)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X122),X21)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum_Odistrib) ).

fof(fact_setprod__dividef,axiom,
    ! [X1,X2,X21,X5,X20] :
      ( class_Fields_Ofield__inverse__zero(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),hAPP(hAPP(c_COMBS(X5,X20,X20),hAPP(hAPP(c_COMBB(X20,tc_fun(X20,X20),X5),c_Rings_Oinverse__class_Odivide(X20)),X2)),X1)),X21) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X20),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X2),X21)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X1),X21)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__dividef) ).

fof(fact_setprod_Odistrib,axiom,
    ! [X122,X1,X21,X5,X20] :
      ( class_Groups_Ocomm__monoid__mult(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),hAPP(hAPP(c_COMBS(X5,X20,X20),hAPP(hAPP(c_COMBB(X20,tc_fun(X20,X20),X5),c_Groups_Otimes__class_Otimes(X20)),X1)),X122)),X21) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X1),X21)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X122),X21)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod_Odistrib) ).

fof(fact_fold__graph__imp__finite,axiom,
    ! [X25,X21,X120,X2,X20,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X20,X2,X120,X21),X25))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__graph__imp__finite) ).

fof(fact_rotate1__def,axiom,
    ! [X239,X5] : hAPP(c_List_Orotate1(X5),X239) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(X5),X5,c_List_Olist_ONil(X5),hAPP(hAPP(c_COMBB(tc_List_Olist(X5),tc_fun(tc_List_Olist(X5),tc_List_Olist(X5)),X5),hAPP(c_COMBC(tc_List_Olist(X5),tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Oappend(X5))),hAPP(hAPP(c_COMBC(X5,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olist_OCons(X5)),c_List_Olist_ONil(X5)))),X239),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate1__def) ).

fof(fact_setsum__subtractf,axiom,
    ! [X21,X1,X2,X20,X5] :
      ( class_Groups_Oab__group__add(X5)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X20,X5),hAPP(hAPP(c_COMBS(X20,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X20),c_Groups_Ominus__class_Ominus(X5)),X2)),X1)),X21) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X20,X5),X2),X21)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X20,X5),X1),X21)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__subtractf) ).

fof(fact_setsum__addf,axiom,
    ! [X21,X1,X2,X20,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X20,X5),hAPP(hAPP(c_COMBS(X20,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X20),c_Groups_Oplus__class_Oplus(X5)),X2)),X1)),X21) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X20,X5),X2),X21)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X20,X5),X1),X21)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__addf) ).

fof(fact_setprod__timesf,axiom,
    ! [X21,X1,X2,X20,X5] :
      ( class_Groups_Ocomm__monoid__mult(X5)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X20,X5),hAPP(hAPP(c_COMBS(X20,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X20),c_Groups_Otimes__class_Otimes(X5)),X2)),X1)),X21) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X20,X5),X2),X21)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X20,X5),X1),X21)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__timesf) ).

fof(fact_divmod__nat__rel__mult2__eq,axiom,
    ! [X56,X134,X140,X90,X62] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X62,X90),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X140),X134)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X90))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X56))
         => hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X62,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X90),X56)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X140),X56)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X90),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X140,X56))),X134)))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__rel__mult2__eq) ).

fof(fact_lists__Int__eq,axiom,
    ! [X113,X21,X5] : c_List_Olistsp(X5,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X21)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X113))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(X5))),c_List_Olists(X5,X21))),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(X5))),c_List_Olists(X5,X113))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lists__Int__eq) ).

fof(fact_select__weight__def,axiom,
    ! [X239,X5] : c_Random_Oselect__weight(X5,X239) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X5,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X5),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X5)),X239)))),hAPP(hAPP(c_COMBB(X5,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X5,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(X5,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Opick(X5,X239))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_select__weight__def) ).

fof(fact_insert__times__insert,axiom,
    ! [X113,X24,X21,X6,X20,X5] : hAPP(hAPP(c_Product__Type_OSigma(X5,X20),hAPP(hAPP(c_Set_Oinsert(X5),X6),X21)),hAPP(c_COMBK(tc_fun(X20,tc_HOL_Obool),X5),hAPP(hAPP(c_Set_Oinsert(X20),X24),X113))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(X5,X20)),hAPP(hAPP(c_Product__Type_OPair(X5,X20),X6),X24)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X20),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X5,X20),X21),hAPP(c_COMBK(tc_fun(X20,tc_HOL_Obool),X5),hAPP(hAPP(c_Set_Oinsert(X20),X24),X113)))),hAPP(hAPP(c_Product__Type_OSigma(X5,X20),hAPP(hAPP(c_Set_Oinsert(X5),X6),X21)),hAPP(c_COMBK(tc_fun(X20,tc_HOL_Obool),X5),X113)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__times__insert) ).

fof(fact_setsum__divide__distrib,axiom,
    ! [X171,X21,X2,X20,X5] :
      ( class_Fields_Ofield(X5)
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X20,X5),X2),X21)),X171) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X20,X5),hAPP(hAPP(c_COMBC(X20,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X20),c_Rings_Oinverse__class_Odivide(X5)),X2)),X171)),X21) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__divide__distrib) ).

fof(fact_setsum__left__distrib,axiom,
    ! [X171,X21,X2,X20,X5] :
      ( class_Rings_Osemiring__0(X5)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X20,X5),X2),X21)),X171) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X20,X5),hAPP(hAPP(c_COMBC(X20,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X20),c_Groups_Otimes__class_Otimes(X5)),X2)),X171)),X21) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__left__distrib) ).

fof(fact_zmult2__lemma,axiom,
    ! [X56,X134,X140,X90,X62] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X62,X90),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X140),X134)))
     => ( X90 != 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)),X56))
         => hBOOL(hAPP(c_Divides_Odivmod__int__rel(X62,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X90),X56)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X140),X56)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X90),c_Divides_Odiv__class_Omod(tc_Int_Oint,X140,X56))),X134)))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult2__lemma) ).

fof(fact_listrel__rtrancl__trans,axiom,
    ! [X250,X171,X251,X239,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X239),X251)),c_List_Olistrel(X5,c_Transitive__Closure_Ortrancl(X5,X171))))
     => ( 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)),X251),X250)),c_List_Olistrel(X5,c_Transitive__Closure_Ortrancl(X5,X171))))
       => 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)),X239),X250)),c_List_Olistrel(X5,c_Transitive__Closure_Ortrancl(X5,X171)))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__rtrancl__trans) ).

fof(fact_pred__subset__eq,axiom,
    ! [X192,X32,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X32)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X192)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X32),X192)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__subset__eq) ).

fof(fact_reduction__pair__lemma,axiom,
    ! [X192,X32,X18,X5] :
      ( c_FunDef_Oreduction__pair(X5,X18)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X32),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X18)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X192),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X18)))
         => ( c_Wellfounded_Owf(X5,X192)
           => c_Wellfounded_Owf(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X32),X192)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_reduction__pair__lemma) ).

fof(fact_Union__Int__subset,axiom,
    ! [X113,X21,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),X21),X113))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X21)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X113)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__Int__subset) ).

fof(fact_fun__upd__twist,axiom,
    ! [X22,X24,X95,X20,X5,X23,X6] :
      ( X6 != X23
     => c_Fun_Ofun__upd(X5,X20,c_Fun_Ofun__upd(X5,X20,X95,X6,X24),X23,X22) = c_Fun_Ofun__upd(X5,X20,c_Fun_Ofun__upd(X5,X20,X95,X23,X22),X6,X24) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__twist) ).

fof(fact_Image__subset__eq,axiom,
    ! [X113,X21,X171,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_OImage(X20,X5,X171),X21)),X113))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20,tc_HOL_Obool)),X21),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20,tc_HOL_Obool)),hAPP(c_Relation_OImage(X5,X20,hAPP(c_Relation_Oconverse(X20,X5),X171)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X113))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__subset__eq) ).

fof(fact_image__eq__UN,axiom,
    ! [X21,X2,X5,X20] : hAPP(c_Set_Oimage(X20,X5,X2),X21) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_COMBC(X20,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X5,tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X20),c_Set_Oinsert(X5)),X2)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__eq__UN) ).

fof(fact_rtrancl__listrel1__ConsI1,axiom,
    ! [X25,X171,X251,X239,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X239),X251)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X5),c_List_Olistrel1(X5,X171))))
     => 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),X25),X239)),hAPP(hAPP(c_List_Olist_OCons(X5),X25),X251))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X5),c_List_Olistrel1(X5,X171)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__listrel1__ConsI1) ).

fof(fact_pair__leqI2,axiom,
    ! [X15,X76,X24,X6] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X6),X24))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X76),X15))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X6),X76)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X24),X15))),c_FunDef_Opair__leq)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__leqI2) ).

fof(fact_pair__lessI2,axiom,
    ! [X15,X76,X24,X6] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X6),X24))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X76),X15))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X6),X76)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X24),X15))),c_FunDef_Opair__less)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__lessI2) ).

fof(fact_rtrancl__Un__subset,axiom,
    ! [X192,X32,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X5,X32)),c_Transitive__Closure_Ortrancl(X5,X192))),c_Transitive__Closure_Ortrancl(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X32),X192)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__Un__subset) ).

fof(fact_lexord__trans,axiom,
    ! [X120,X171,X33,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X25),X33)),c_List_Olexord(X5,X171)))
     => ( 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)),X33),X120)),c_List_Olexord(X5,X171)))
       => ( c_Relation_Otrans(X5,X171)
         => 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)),X25),X120)),c_List_Olexord(X5,X171))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexord__trans) ).

fof(fact_Image__Int__subset,axiom,
    ! [X113,X21,X32,X20,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_OImage(X20,X5,X32),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20,tc_HOL_Obool)),X21),X113))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_OImage(X20,X5,X32),X21)),hAPP(c_Relation_OImage(X20,X5,X32),X113)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__Int__subset) ).

fof(fact_image__Int__subset,axiom,
    ! [X113,X21,X2,X20,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Oimage(X20,X5,X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20,tc_HOL_Obool)),X21),X113))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Oimage(X20,X5,X2),X21)),hAPP(c_Set_Oimage(X20,X5,X2),X113)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__Int__subset) ).

fof(fact_transfer__nat__int__set__cong,axiom,
    ! [X31,X18] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
         => ( hBOOL(hAPP(X18,X3))
          <=> hBOOL(hAPP(X31,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)))),X18)) = 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)))),X31)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__set__cong) ).

fof(fact_pair__leqI1,axiom,
    ! [X15,X76,X24,X6] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),X24))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X6),X76)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X24),X15))),c_FunDef_Opair__leq)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__leqI1) ).

fof(fact_pair__lessI1,axiom,
    ! [X15,X76,X24,X6] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),X24))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X6),X76)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X24),X15))),c_FunDef_Opair__less)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__lessI1) ).

fof(fact_lists__eq__set,axiom,
    ! [X21,X5] : c_List_Olists(X5,X21) = hAPP(c_Set_OCollect(tc_List_Olist(X5)),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X5)),c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool))),c_List_Oset(X5))),X21)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lists__eq__set) ).

fof(fact_append__listrel1I,axiom,
    ! [X258,X259,X171,X251,X239,X5] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X239),X251)),c_List_Olistrel1(X5,X171)))
          & X259 = X258 )
        | ( X239 = X251
          & 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)),X259),X258)),c_List_Olistrel1(X5,X171))) ) )
     => 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),X239),X259)),hAPP(hAPP(c_List_Oappend(X5),X251),X258))),c_List_Olistrel1(X5,X171))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__listrel1I) ).

fof(fact_listrel1I2,axiom,
    ! [X25,X171,X251,X239,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X239),X251)),c_List_Olistrel1(X5,X171)))
     => 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),X25),X239)),hAPP(hAPP(c_List_Olist_OCons(X5),X25),X251))),c_List_Olistrel1(X5,X171))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel1I2) ).

fof(fact_lexord__append__leftI,axiom,
    ! [X25,X171,X123,X159,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X159),X123)),c_List_Olexord(X5,X171)))
     => 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),X25),X159)),hAPP(hAPP(c_List_Oappend(X5),X25),X123))),c_List_Olexord(X5,X171))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexord__append__leftI) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J,axiom,
    ! [X18] : 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)))),X18))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J) ).

fof(fact_zip__map1,axiom,
    ! [X251,X239,X2,X116,X20,X5] : hAPP(hAPP(c_List_Ozip(X5,X20),hAPP(hAPP(c_List_Omap(X116,X5),X2),X239)),X251) = hAPP(hAPP(c_List_Omap(tc_prod(X116,X20),tc_prod(X5,X20)),hAPP(c_Product__Type_Oprod_Oprod__case(X116,X20,tc_prod(X5,X20)),hAPP(hAPP(c_COMBB(X5,tc_fun(X20,tc_prod(X5,X20)),X116),c_Product__Type_OPair(X5,X20)),X2))),hAPP(hAPP(c_List_Ozip(X116,X20),X239),X251)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__map1) ).

fof(fact_mlex__prod__def,axiom,
    ! [X32,X2,X5] : c_Wellfounded_Omlex__prod(X5,X2,X32) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,X5),X5),c_Wellfounded_Olex__prod(tc_Nat_Onat,X5,c_Wellfounded_Oless__than,X32)),hAPP(hAPP(c_COMBS(X5,X5,tc_prod(tc_Nat_Onat,X5)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X5,tc_prod(tc_Nat_Onat,X5)),X5),c_Product__Type_OPair(tc_Nat_Onat,X5)),X2)),c_COMBI(X5))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mlex__prod__def) ).

fof(fact_finite__empty__induct,axiom,
    ! [X18,X21,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
     => ( hBOOL(hAPP(X18,X21))
       => ( ! [X187,X226] :
              ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X226))
             => ( hBOOL(hAPP(hAPP(c_member(X5),X187),X226))
               => ( hBOOL(hAPP(X18,X226))
                 => hBOOL(hAPP(X18,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X226),hAPP(hAPP(c_Set_Oinsert(X5),X187),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ) )
         => hBOOL(hAPP(X18,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__empty__induct) ).

fof(fact_Times__subset__cancel2,axiom,
    ! [X113,X21,X20,X112,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X25),X112))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X20,X5),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X20,X5),X21),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X20),X112))),hAPP(hAPP(c_Product__Type_OSigma(X20,X5),X113),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X20),X112))))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20,tc_HOL_Obool)),X21),X113)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Times__subset__cancel2) ).

fof(fact_rel__pow__Suc__I2,axiom,
    ! [X50,X120,X32,X33,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X33)),X32))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X33),X120)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X50),X32)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X120)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),hAPP(c_Nat_OSuc,X50)),X32))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__pow__Suc__I2) ).

fof(fact_rel__pow__Suc__I,axiom,
    ! [X120,X32,X50,X33,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X33)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X50),X32)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X33),X120)),X32))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X120)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),hAPP(c_Nat_OSuc,X50)),X32))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__pow__Suc__I) ).

fof(fact_image__Pow__mono,axiom,
    ! [X113,X21,X2,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Oimage(X20,X5,X2),X21)),X113))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_fun(X20,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),c_Set_Oimage(X20,X5,X2)),hAPP(c_Set_OPow(X20),X21))),hAPP(c_Set_OPow(X5),X113))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__Pow__mono) ).

fof(fact_select__weight__member,axiom,
    ! [X76,X239,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X5),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X5)),X239))))
     => hBOOL(hAPP(hAPP(c_member(X5),hAPP(c_Product__Type_Ofst(X5,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect__weight(X5,X239),X76))),hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X5),X5),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X5)),X239)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_select__weight__member) ).

fof(fact_setsum__abs,axiom,
    ! [X21,X2,X20,X5] :
      ( class_Groups_Oordered__ab__group__add__abs(X5)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Groups_Oabs__class_Oabs(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X20,X5),X2),X21))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X20,X5),hAPP(hAPP(c_COMBB(X5,X5,X20),c_Groups_Oabs__class_Oabs(X5)),X2)),X21))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__abs) ).

fof(fact_set__minus__filter__out,axiom,
    ! [X33,X239,X5] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),X239)),hAPP(hAPP(c_Set_Oinsert(X5),X33),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = hAPP(c_List_Oset(X5),hAPP(c_List_Ofilter(X5,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X33))),X239)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__minus__filter__out) ).

fof(fact_filter__filter,axiom,
    ! [X239,X16,X18,X5] : hAPP(c_List_Ofilter(X5,X18),hAPP(c_List_Ofilter(X5,X16),X239)) = hAPP(c_List_Ofilter(X5,hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),X16)),X18)),X239),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter__filter) ).

fof(fact_Domain__Diff__subset,axiom,
    ! [X113,X21,X20,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X5,X20),X21)),hAPP(c_Relation_ODomain(X5,X20),X113))),hAPP(c_Relation_ODomain(X5,X20),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X5,X20),tc_HOL_Obool)),X21),X113)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__Diff__subset) ).

fof(fact_Range__Diff__subset,axiom,
    ! [X113,X21,X20,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_ORange(X20,X5),X21)),hAPP(c_Relation_ORange(X20,X5),X113))),hAPP(c_Relation_ORange(X20,X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X20,X5),tc_HOL_Obool)),X21),X113)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__Diff__subset) ).

fof(fact_fun__left__comm__idem__remove,axiom,
    ! [X5] : c_Finite__Set_Ofun__left__comm__idem(X5,tc_fun(X5,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5),hAPP(c_COMBC(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Set_Oinsert(X5)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__idem__remove) ).

fof(fact_card__Diff1__less,axiom,
    ! [X25,X21,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X5),X21))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Diff1__less) ).

fof(fact_split__comp__eq,axiom,
    ! [X1,X2,X115,X116,X20,X5] : hAPP(hAPP(c_COMBS(tc_prod(X5,X20),X20,X116),hAPP(hAPP(c_COMBB(X115,tc_fun(X20,X116),tc_prod(X5,X20)),X2),hAPP(hAPP(c_COMBB(X5,X115,tc_prod(X5,X20)),X1),c_Product__Type_Ofst(X5,X20)))),c_Product__Type_Osnd(X5,X20)) = hAPP(c_Product__Type_Oprod_Oprod__case(X5,X20,X116),hAPP(hAPP(c_COMBB(X115,tc_fun(X20,X116),X5),X2),X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__comp__eq) ).

fof(fact_insort__key__remove1,axiom,
    ! [X2,X239,X6,X5,X20] :
      ( class_Orderings_Olinorder(X20)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(c_List_Oset(X5),X239)))
       => ( c_List_Olinorder__class_Osorted(X20,hAPP(hAPP(c_List_Omap(X5,X20),X2),X239))
         => ( hAPP(c_List_Ohd(X5),hAPP(c_List_Ofilter(X5,hAPP(hAPP(c_COMBB(X20,tc_HOL_Obool,X5),hAPP(c_fequal,hAPP(X2,X6))),X2)),X239)) = X6
           => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X20,X2),X6),c_List_Oremove1(X5,X6,X239)) = X239 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insort__key__remove1) ).

fof(fact_bij__betw__Disj__Un,axiom,
    ! [X2,X238,X202,X20,X113,X21,X5] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
     => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20,tc_HOL_Obool)),X202),X238) = c_Orderings_Obot__class_Obot(tc_fun(X20,tc_HOL_Obool))
       => ( c_Fun_Obij__betw(X5,X20,X2,X21,X202)
         => ( c_Fun_Obij__betw(X5,X20,X2,X113,X238)
           => c_Fun_Obij__betw(X5,X20,X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20,tc_HOL_Obool)),X202),X238)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__betw__Disj__Un) ).

fof(fact_equiv__intrel__iff,axiom,
    ! [X33,X25] :
      ( 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)),X25),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)),X33),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)),X25),X33)),c_Int_Ointrel)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equiv__intrel__iff) ).

fof(fact_setsum__UNION__zero,axiom,
    ! [X2,X192,X5,X20] :
      ( class_Groups_Ocomm__monoid__add(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X5,tc_HOL_Obool)),X192))
       => ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X3),X192))
             => hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X3)) )
         => ( ! [X308] :
                ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X308),X192))
               => ! [X309] :
                    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X309),X192))
                   => ( X308 != X309
                     => ! [X3] :
                          ( hBOOL(hAPP(hAPP(c_member(X5),X3),X308))
                         => ( hBOOL(hAPP(hAPP(c_member(X5),X3),X309))
                           => hAPP(X2,X3) = c_Groups_Ozero__class_Ozero(X20) ) ) ) ) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X192)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X5,tc_HOL_Obool),X20),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X2)),X192) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__UNION__zero) ).

fof(fact_fold__graph_H_Ointros_I1_J,axiom,
    ! [X120,X2,X20,X5] : c_Nitpick_Ofold__graph_H(X5,X20,X2,X120,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),X120),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__graph_H_Ointros_I1_J) ).

fof(fact_fold__graph_H_Oequations_I1_J,axiom,
    ! [X26,X27,X20,X5] : c_Nitpick_Ofold__graph_H(X5,X20,X27,X26,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),X26),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__graph_H_Oequations_I1_J) ).

fof(fact_map__pair_Oid,axiom,
    ! [X20,X5] : c_Product__Type_Omap__pair(X5,X5,X20,X20,c_Fun_Oid(X5),c_Fun_Oid(X20)) = c_Fun_Oid(tc_prod(X5,X20)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__pair_Oid) ).

fof(fact_map__pair_Oidentity,axiom,
    ! [X20,X5] : c_Product__Type_Omap__pair(X5,X5,X20,X20,c_COMBI(X5),c_COMBI(X20)) = c_Fun_Oid(tc_prod(X5,X20)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__pair_Oidentity) ).

fof(fact_fun__left__comm_Ofold__graph__fold,axiom,
    ! [X120,X21,X2,X20,X5] :
      ( c_Finite__Set_Ofun__left__comm(X5,X20,X2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X20,X2,X120,X21),hAPP(hAPP(c_Finite__Set_Ofold(X5,X20,X2),X120),X21))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__graph__fold) ).

fof(fact_negateSnd__def,axiom,
    c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negateSnd__def) ).

fof(fact_card__Diff1__le,axiom,
    ! [X25,X21,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X5),X21))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Diff1__le) ).

fof(fact_rel__comp__mono,axiom,
    ! [X76,X243,X116,X171,X203,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X20),tc_HOL_Obool)),X203),X171))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X20,X116),tc_HOL_Obool)),X243),X76))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X116),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X5,X20,X116),X203),X243)),hAPP(hAPP(c_Relation_Orel__comp(X5,X20,X116),X171),X76))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__comp__mono) ).

fof(fact_equiv__class__subset,axiom,
    ! [X24,X6,X171,X21,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X21,X171)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X24)),X171))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_OImage(X5,X5,X171),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X5,X5,X171),hAPP(hAPP(c_Set_Oinsert(X5),X24),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equiv__class__subset) ).

fof(fact_the__inv__into__into,axiom,
    ! [X113,X25,X21,X2,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,X2,X21)
     => ( hBOOL(hAPP(hAPP(c_member(X20),X25),hAPP(c_Set_Oimage(X5,X20,X2),X21)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),X113))
         => hBOOL(hAPP(hAPP(c_member(X5),hAPP(c_Fun_Othe__inv__into(X5,X20,X21,X2),X25)),X113)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__inv__into__into) ).

fof(fact_finite__range__imageI,axiom,
    ! [X2,X116,X1,X20,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(c_Set_Oimage(X20,X5,X1),c_Orderings_Otop__class_Otop(tc_fun(X20,tc_HOL_Obool)))))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X116),hAPP(c_Set_Oimage(X20,X116,hAPP(hAPP(c_COMBB(X5,X116,X20),X2),X1)),c_Orderings_Otop__class_Otop(tc_fun(X20,tc_HOL_Obool))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__range__imageI) ).

fof(fact_Inter__Un__subset,axiom,
    ! [X113,X21,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),X21)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),X113))),c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),X21),X113)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__Un__subset) ).

fof(fact_listrel__subset,axiom,
    ! [X21,X171,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X171),hAPP(hAPP(c_Product__Type_OSigma(X5,X5),X21),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X5),X21))))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_HOL_Obool)),c_List_Olistrel(X5,X171)),hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olists(X5,X21)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X5),tc_HOL_Obool),tc_List_Olist(X5)),c_List_Olists(X5,X21))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__subset) ).

fof(fact_fold__image__reindex,axiom,
    ! [X120,X1,X122,X20,X21,X5,X116] :
      ( class_Groups_Oab__semigroup__mult(X116)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( c_Fun_Oinj__on(X5,X20,X122,X21)
         => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X116,X20,c_Groups_Otimes__class_Otimes(X116)),X1),X120),hAPP(c_Set_Oimage(X5,X20,X122),X21)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X116,X5,c_Groups_Otimes__class_Otimes(X116)),hAPP(c_Fun_Ocomp(X20,X116,X5,X1),X122)),X120),X21) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__image__reindex) ).

fof(fact_zmult2__lemma__aux4,axiom,
    ! [X140,X90,X134,X56] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X56))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X134))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X134),X90))
         => 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),X90),c_Divides_Odiv__class_Omod(tc_Int_Oint,X140,X56))),X134)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X90),X56))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult2__lemma__aux4) ).

fof(fact_fold__sup__le__sup,axiom,
    ! [X23,X24,X21,X5] :
      ( class_Lattices_Osemilattice__sup(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),X21))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X3),X24)) )
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Lattices_Osemilattice__sup__class_Osup(X5)),X23),X21)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X24),X23))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__sup__le__sup) ).

fof(fact_min__max_Ofold__sup__le__sup,axiom,
    ! [X23,X24,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),X21))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X3),X24)) )
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omax(X5)),X23),X21)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X24),X23))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ofold__sup__le__sup) ).

fof(fact_bij__betw__combine,axiom,
    ! [X144,X112,X113,X21,X2,X20,X5] :
      ( c_Fun_Obij__betw(X5,X20,X2,X21,X113)
     => ( c_Fun_Obij__betw(X5,X20,X2,X112,X144)
       => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20,tc_HOL_Obool)),X113),X144) = c_Orderings_Obot__class_Obot(tc_fun(X20,tc_HOL_Obool))
         => c_Fun_Obij__betw(X5,X20,X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X112),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20,tc_HOL_Obool)),X113),X144)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__betw__combine) ).

fof(fact_listrel1I1,axiom,
    ! [X239,X171,X33,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X33)),X171))
     => 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),X25),X239)),hAPP(hAPP(c_List_Olist_OCons(X5),X33),X239))),c_List_Olistrel1(X5,X171))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel1I1) ).

fof(fact_transpose__column,axiom,
    ! [X82,X239,X5] :
      ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X5),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X5))),X239)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X82),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5))),X239)))
       => hAPP(hAPP(c_List_Omap(tc_List_Olist(X5),X5),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_Nat_Onat,X5),c_List_Onth(X5)),X82)),hAPP(c_List_Ofilter(tc_List_Olist(X5),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X5)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X82)),c_Nat_Osize__class_Osize(tc_List_Olist(X5)))),c_List_Otranspose(X5,X239))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(X5)),X239),X82) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose__column) ).

fof(fact_split__paired__Eps,axiom,
    ! [X18,X20,X5] : c_Hilbert__Choice_OEps(tc_prod(X5,X20),X18) = c_Hilbert__Choice_OEps(tc_prod(X5,X20),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X20,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_prod(X5,X20)),tc_fun(X20,tc_HOL_Obool),X5),hAPP(c_COMBB(tc_prod(X5,X20),tc_HOL_Obool,X20),X18)),c_Product__Type_OPair(X5,X20)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__paired__Eps) ).

fof(fact_split__paired__The,axiom,
    ! [X18,X20,X5] : c_HOL_OThe(tc_prod(X5,X20),X18) = c_HOL_OThe(tc_prod(X5,X20),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X20,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_prod(X5,X20)),tc_fun(X20,tc_HOL_Obool),X5),hAPP(c_COMBB(tc_prod(X5,X20),tc_HOL_Obool,X20),X18)),c_Product__Type_OPair(X5,X20)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__paired__The) ).

fof(fact_Comp,axiom,
    ! [X32,X22,X16,X23,X18,X4,X5] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X5)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),X18),X23),X16)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool))))
     => ( c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X5)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),X16),X22),X32)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool))))
       => c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X5)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),X18),c_Com_Ocom_OSemi(X23,X22)),X32)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool)))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Comp) ).

fof(fact_total__on__def,axiom,
    ! [X171,X21,X5] :
      ( c_Relation_Ototal__on(X5,X21,X171)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),X21))
         => ! [X204] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X204),X21))
             => ( X3 != X204
               => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X204)),X171))
                  | hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X204),X3)),X171)) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_total__on__def) ).

fof(fact_mod__lemma,axiom,
    ! [X140,X90,X134,X56] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X56))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X134),X90))
       => 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),X90),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X140,X56))),X134)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X90),X56))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__lemma) ).

fof(fact_single__valued__confluent,axiom,
    ! [X120,X33,X25,X171,X5] :
      ( c_Relation_Osingle__valued(X5,X5,X171)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X33)),c_Transitive__Closure_Ortrancl(X5,X171)))
       => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X120)),c_Transitive__Closure_Ortrancl(X5,X171)))
         => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X33),X120)),c_Transitive__Closure_Ortrancl(X5,X171)))
            | hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X120),X33)),c_Transitive__Closure_Ortrancl(X5,X171))) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valued__confluent) ).

fof(fact_reduction__pairI,axiom,
    ! [X192,X32,X5] :
      ( c_Wellfounded_Owf(X5,X32)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),X32),X192)),X32))
       => c_FunDef_Oreduction__pair(X5,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X32),X192)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_reduction__pairI) ).

fof(fact_zmult2__lemma__aux2,axiom,
    ! [X140,X134,X90,X56] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X56))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X90),X134))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X134),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),X90),c_Divides_Odiv__class_Omod(tc_Int_Oint,X140,X56))),X134)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult2__lemma__aux2) ).

fof(fact_select__def,axiom,
    ! [X239,X5] : c_Random_Oselect(X5,X239) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X5,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239)))),hAPP(hAPP(c_COMBB(X5,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X5,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(X5,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X5,tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Onth(X5),X239)),c_Code__Numeral_Onat__of))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_select__def) ).

fof(fact_of__int,axiom,
    ! [X157,X82,X5] :
      ( class_Rings_Oring__1(X5)
     => hAPP(c_Int_Oring__1__class_Oof__int(X5),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X82),X157)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X82)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X157)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int) ).

fof(fact_diff__single__insert,axiom,
    ! [X113,X25,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),X113))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),X113))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__single__insert) ).

fof(fact_nat,axiom,
    ! [X33,X25] : 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),X25),X33)),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),X25),X33),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat) ).

fof(fact_inj__on__Un,axiom,
    ! [X113,X21,X2,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113))
    <=> ( c_Fun_Oinj__on(X5,X20,X2,X21)
        & c_Fun_Oinj__on(X5,X20,X2,X113)
        & hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X20,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),X113))),hAPP(c_Set_Oimage(X5,X20,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X113),X21))) = c_Orderings_Obot__class_Obot(tc_fun(X20,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__Un) ).

fof(fact_in__finite__psubset,axiom,
    ! [X113,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X21),X113)),c_Wellfounded_Ofinite__psubset(X5)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X21),X113))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X113)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__finite__psubset) ).

fof(fact_Domain__iff,axiom,
    ! [X171,X20,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(c_Relation_ODomain(X5,X20),X171)))
    <=> ? [X177] : hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X20)),hAPP(hAPP(c_Product__Type_OPair(X5,X20),X6),X177)),X171)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__iff) ).

fof(fact_Un__Pow__subset,axiom,
    ! [X113,X21,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X5),X21)),hAPP(c_Set_OPow(X5),X113))),hAPP(c_Set_OPow(X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Pow__subset) ).

fof(fact_o__inv__o__cancel,axiom,
    ! [X1,X116,X2,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => hAPP(c_Fun_Ocomp(X20,X116,X5,hAPP(c_Fun_Ocomp(X5,X116,X20,X1),c_Hilbert__Choice_Oinv__into(X5,X20,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X2))),X2) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__inv__o__cancel) ).

fof(conj_1,conjecture,
    c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),v_G),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).

fof(fact_nat__diff__add__eq1,axiom,
    ! [X57,X72,X55,X98,X97] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X97),X98))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X98),X55)),X72)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X97),X55)),X57)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X98),X97)),X55)),X72)),X57) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__diff__add__eq1) ).

fof(fact_pick__member,axiom,
    ! [X239,X5,X82] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X82),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X5),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X5)),X239))))
     => hBOOL(hAPP(hAPP(c_member(X5),hAPP(c_Random_Opick(X5,X239),X82)),hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X5),X5),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X5)),X239)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pick__member) ).

fof(fact_rel__compI,axiom,
    ! [X76,X23,X116,X171,X24,X6,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X20)),hAPP(hAPP(c_Product__Type_OPair(X5,X20),X6),X24)),X171))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X20,X116)),hAPP(hAPP(c_Product__Type_OPair(X20,X116),X24),X23)),X76))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X116)),hAPP(hAPP(c_Product__Type_OPair(X5,X116),X6),X23)),hAPP(hAPP(c_Relation_Orel__comp(X5,X20,X116),X171),X76))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__compI) ).

fof(fact_sorted__insort__insert__key,axiom,
    ! [X25,X239,X2,X20,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Omap(X20,X5),X2),X239))
       => c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Omap(X20,X5),X2),c_List_Olinorder__class_Oinsort__insert__key(X20,X5,X2,X25,X239))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__insort__insert__key) ).

fof(fact_list__all2__append,axiom,
    ! [X258,X259,X18,X251,X20,X239,X5] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X20)),X251)
     => ( c_List_Olist__all2(X5,X20,X18,hAPP(hAPP(c_List_Oappend(X5),X239),X259),hAPP(hAPP(c_List_Oappend(X20),X251),X258))
      <=> ( c_List_Olist__all2(X5,X20,X18,X239,X251)
          & c_List_Olist__all2(X5,X20,X18,X259,X258) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__all2__append) ).

fof(fact_bex__Un,axiom,
    ! [X18,X113,X21,X5] :
      ( ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113)))
          & hBOOL(hAPP(X18,X3)) )
    <=> ( ? [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X21))
            & hBOOL(hAPP(X18,X3)) )
        | ? [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X113))
            & hBOOL(hAPP(X18,X3)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bex__Un) ).

fof(fact_ball__Un,axiom,
    ! [X18,X113,X21,X5] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113)))
         => hBOOL(hAPP(X18,X3)) )
    <=> ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X21))
           => hBOOL(hAPP(X18,X3)) )
        & ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X113))
           => hBOOL(hAPP(X18,X3)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ball__Un) ).

fof(fact_INF2__D,axiom,
    ! [X6,X23,X24,X113,X21,X116,X20,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X20,tc_fun(X116,tc_HOL_Obool))),X21),X113),X24),X23))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X21))
       => hBOOL(hAPP(hAPP(hAPP(X113,X6),X24),X23)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF2__D) ).

fof(fact_list__all2__appendI,axiom,
    ! [X22,X23,X24,X6,X18,X20,X5] :
      ( c_List_Olist__all2(X5,X20,X18,X6,X24)
     => ( c_List_Olist__all2(X5,X20,X18,X23,X22)
       => c_List_Olist__all2(X5,X20,X18,hAPP(hAPP(c_List_Oappend(X5),X6),X23),hAPP(hAPP(c_List_Oappend(X20),X24),X22)) ) ),
    file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_nat__2) ).

fof(fact_fun__upd__comp,axiom,
    ! [X33,X25,X1,X2,X5,X20,X116] : hAPP(c_Fun_Ocomp(X116,X20,X5,X2),c_Fun_Ofun__upd(X5,X116,X1,X25,X33)) = c_Fun_Ofun__upd(X5,X20,hAPP(c_Fun_Ocomp(X116,X20,X5,X2),X1),X25,hAPP(X2,X33)),
    file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J) ).

fof(fact_vimage__def,axiom,
    ! [X113,X2,X20,X5] : hAPP(c_Set_Ovimage(X5,X20,X2),X113) = hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBC(X5,tc_fun(X20,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(X20,tc_fun(tc_fun(X20,tc_HOL_Obool),tc_HOL_Obool),X5),c_member(X20)),X2)),X113)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__def) ).

fof(fact_zip__append2,axiom,
    ! [X248,X241,X242,X5,X58] : hAPP(hAPP(c_List_Ozip(X58,X5),X242),hAPP(hAPP(c_List_Oappend(X5),X241),X248)) = hAPP(hAPP(c_List_Oappend(tc_prod(X58,X5)),hAPP(hAPP(c_List_Ozip(X58,X5),hAPP(hAPP(c_List_Otake(X58),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X241)),X242)),X241)),hAPP(hAPP(c_List_Ozip(X58,X5),hAPP(hAPP(c_List_Odrop(X58),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X241)),X242)),X248)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__append2) ).

fof(fact_in__listrel1__converse,axiom,
    ! [X171,X33,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X25),X33)),c_List_Olistrel1(X5,hAPP(c_Relation_Oconverse(X5,X5),X171))))
    <=> 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)),X25),X33)),hAPP(c_Relation_Oconverse(tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel1(X5,X171)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__listrel1__converse) ).

fof(fact_Cons__eq__append__conv,axiom,
    ! [X250,X251,X239,X25,X5] :
      ( hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239) = hAPP(hAPP(c_List_Oappend(X5),X251),X250)
    <=> ( ( X251 = c_List_Olist_ONil(X5)
          & hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239) = X250 )
        | ? [X257] :
            ( hAPP(hAPP(c_List_Olist_OCons(X5),X25),X257) = X251
            & X239 = hAPP(hAPP(c_List_Oappend(X5),X257),X250) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Cons__eq__append__conv) ).

fof(fact_append__eq__Cons__conv,axiom,
    ! [X239,X25,X250,X251,X5] :
      ( hAPP(hAPP(c_List_Oappend(X5),X251),X250) = hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239)
    <=> ( ( X251 = c_List_Olist_ONil(X5)
          & X250 = hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239) )
        | ? [X257] :
            ( X251 = hAPP(hAPP(c_List_Olist_OCons(X5),X25),X257)
            & hAPP(hAPP(c_List_Oappend(X5),X257),X250) = X239 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__eq__Cons__conv) ).

fof(fact_inv__into__into,axiom,
    ! [X21,X2,X20,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_Set_Oimage(X20,X5,X2),X21)))
     => hBOOL(hAPP(hAPP(c_member(X20),hAPP(c_Hilbert__Choice_Oinv__into(X20,X5,X21,X2),X25)),X21)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__into__into) ).

fof(fact_min__max_OInf__fin_Oclosed,axiom,
    ! [X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( ! [X3,X177] : hBOOL(hAPP(hAPP(c_member(X5),hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X3),X177)),hAPP(hAPP(c_Set_Oinsert(X5),X3),hAPP(hAPP(c_Set_Oinsert(X5),X177),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))
           => hBOOL(hAPP(hAPP(c_member(X5),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X21)),X21)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Oclosed) ).

fof(fact_min__max_OSup__fin_Oclosed,axiom,
    ! [X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( ! [X3,X177] : hBOOL(hAPP(hAPP(c_member(X5),hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X3),X177)),hAPP(hAPP(c_Set_Oinsert(X5),X3),hAPP(hAPP(c_Set_Oinsert(X5),X177),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))
           => hBOOL(hAPP(hAPP(c_member(X5),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X21)),X21)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Oclosed) ).

fof(fact_triple__valid__def2,axiom,
    ! [X16,X23,X18,X50,X5] :
      ( c_Hoare__Mirabelle_Otriple__valid(X5,X50,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),X18),X23),X16))
    <=> ! [X29,X30] :
          ( hBOOL(hAPP(hAPP(X18,X29),X30))
         => ! [X70] :
              ( c_Natural_Oevaln(X23,X30,X50,X70)
             => hBOOL(hAPP(hAPP(X16,X29),X70)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_triple__valid__def2) ).

fof(fact_card__SigmaI,axiom,
    ! [X113,X20,X21,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X21))
           => hBOOL(hAPP(c_Finite__Set_Ofinite(X20),hAPP(X113,X3))) )
       => hAPP(c_Finite__Set_Ocard(tc_prod(X5,X20)),hAPP(hAPP(c_Product__Type_OSigma(X5,X20),X21),X113)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_Nat_Onat,X5),c_Finite__Set_Ocard(X20)),X113)),X21) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__SigmaI) ).

fof(fact_fold__graph_OemptyI,axiom,
    ! [X120,X2,X20,X5] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X20,X2,X120,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),X120)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__graph_OemptyI) ).

fof(fact_fold__graph_Oequations_I1_J,axiom,
    ! [X120,X2,X20,X5] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X20,X2,X120,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),X120)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__graph_Oequations_I1_J) ).

fof(fact_wf__union__compatible,axiom,
    ! [X192,X32,X5] :
      ( c_Wellfounded_Owf(X5,X32)
     => ( c_Wellfounded_Owf(X5,X192)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),X32),X192)),X32))
         => c_Wellfounded_Owf(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X32),X192)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__union__compatible) ).

fof(fact_fold1__in,axiom,
    ! [X21,X5] :
      ( class_Groups_Oab__semigroup__mult(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( ! [X3,X177] : hBOOL(hAPP(hAPP(c_member(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X3),X177)),hAPP(hAPP(c_Set_Oinsert(X5),X3),hAPP(hAPP(c_Set_Oinsert(X5),X177),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))
           => hBOOL(hAPP(hAPP(c_member(X5),hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),X21)),X21)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__in) ).

fof(fact_unique__quotient__lemma,axiom,
    ! [X134,X140,X141,X142,X90] :
      ( 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),X90),X142)),X141)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X90),X140)),X134)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X141))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X141),X90))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X134),X90))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X142),X140)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_unique__quotient__lemma) ).

fof(fact_unique__quotient__lemma__neg,axiom,
    ! [X134,X140,X141,X142,X90] :
      ( 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),X90),X142)),X141)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X90),X140)),X134)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X134),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X90),X134))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X90),X141))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X140),X142)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_unique__quotient__lemma__neg) ).

fof(fact_distinct__insort__insert,axiom,
    ! [X25,X2,X239,X5,X20] :
      ( class_Orderings_Olinorder(X20)
     => ( hBOOL(hAPP(c_List_Odistinct(X5),X239))
       => hBOOL(hAPP(c_List_Odistinct(X5),c_List_Olinorder__class_Oinsort__insert__key(X5,X20,X2,X25,X239))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__insort__insert) ).

fof(fact_nth__transpose,axiom,
    ! [X239,X5,X82] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X82),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5))),c_List_Otranspose(X5,X239))))
     => hAPP(hAPP(c_List_Onth(tc_List_Olist(X5)),c_List_Otranspose(X5,X239)),X82) = hAPP(hAPP(c_List_Omap(tc_List_Olist(X5),X5),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_Nat_Onat,X5),c_List_Onth(X5)),X82)),hAPP(c_List_Ofilter(tc_List_Olist(X5),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X5)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X82)),c_Nat_Osize__class_Osize(tc_List_Olist(X5)))),X239)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__transpose) ).

fof(fact_Powp__Pow__eq,axiom,
    ! [X25,X21,X5] :
      ( hBOOL(hAPP(c_Predicate_OPowp(X5,hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X21)),X25))
    <=> hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X25),hAPP(c_Set_OPow(X5),X21))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Powp__Pow__eq) ).

fof(fact_card__bij__eq,axiom,
    ! [X1,X113,X21,X2,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,X2,X21)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X20,X2),X21)),X113))
       => ( c_Fun_Oinj__on(X20,X5,X1,X113)
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Oimage(X20,X5,X1),X113)),X21))
           => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
             => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X20),X113))
               => hAPP(c_Finite__Set_Ocard(X5),X21) = hAPP(c_Finite__Set_Ocard(X20),X113) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__bij__eq) ).

fof(fact_Eps__split,axiom,
    ! [X18,X20,X5] : c_Hilbert__Choice_OEps(tc_prod(X5,X20),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X20,tc_HOL_Obool),X18)) = c_Hilbert__Choice_OEps(tc_prod(X5,X20),hAPP(hAPP(c_COMBS(tc_prod(X5,X20),X20,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X5,tc_fun(X20,tc_HOL_Obool),tc_prod(X5,X20)),X18),c_Product__Type_Ofst(X5,X20))),c_Product__Type_Osnd(X5,X20))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Eps__split) ).

fof(fact_The__split,axiom,
    ! [X18,X20,X5] : c_HOL_OThe(tc_prod(X5,X20),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X20,tc_HOL_Obool),X18)) = c_HOL_OThe(tc_prod(X5,X20),hAPP(hAPP(c_COMBS(tc_prod(X5,X20),X20,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X5,tc_fun(X20,tc_HOL_Obool),tc_prod(X5,X20)),X18),c_Product__Type_Ofst(X5,X20))),c_Product__Type_Osnd(X5,X20))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_The__split) ).

fof(fact_in__measures_I2_J,axiom,
    ! [X290,X2,X33,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X33)),c_List_Omeasures(X5,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X5,tc_Nat_Onat)),X2),X290))))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X2,X25)),hAPP(X2,X33)))
        | ( hAPP(X2,X25) = hAPP(X2,X33)
          & hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X33)),c_List_Omeasures(X5,X290))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__measures_I2_J) ).

fof(fact_div__mod__equality,axiom,
    ! [X56,X90,X62,X58] :
      ( class_Divides_Osemiring__div(X58)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X58),X62),X90)),X90)),c_Divides_Odiv__class_Omod(X58,X62,X90))),X56) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),X56) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mod__equality) ).

fof(fact_fun__upd__upd,axiom,
    ! [X120,X33,X25,X2,X20,X5] : c_Fun_Ofun__upd(X5,X20,c_Fun_Ofun__upd(X5,X20,X2,X25,X33),X25,X120) = c_Fun_Ofun__upd(X5,X20,X2,X25,X120),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__upd) ).

fof(fact_fold__Un__disjoint,axiom,
    ! [X1,X113,X21,X5,X20] :
      ( class_Groups_Ocomm__monoid__mult(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X113))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X20,X5,c_Groups_Otimes__class_Otimes(X20)),X1),c_Groups_Oone__class_Oone(X20)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X20,X5,c_Groups_Otimes__class_Otimes(X20)),X1),c_Groups_Oone__class_Oone(X20)),X21)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X20,X5,c_Groups_Otimes__class_Otimes(X20)),X1),c_Groups_Oone__class_Oone(X20)),X113)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__Un__disjoint) ).

fof(fact_uminus__listsum__map,axiom,
    ! [X239,X2,X20,X5] :
      ( class_Groups_Oab__group__add(X5)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X5),hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X20,X5),X2),X239))) = hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X20,X5),hAPP(c_Fun_Ocomp(X5,X5,X20,c_Groups_Ouminus__class_Ouminus(X5)),X2)),X239)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_uminus__listsum__map) ).

fof(fact_neg__map__def,axiom,
    ! [X18,X2,X5,X20] : c_New__Random__Sequence_Oneg__map(X20,X5,X2,X18) = c_New__Random__Sequence_Oneg__bind(X20,X5,X18,hAPP(c_Fun_Ocomp(X5,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X5)))))),X20,c_New__Random__Sequence_Oneg__single(X5)),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__map__def) ).

fof(fact_listsp__lists__eq,axiom,
    ! [X25,X21,X5] :
      ( hBOOL(hAPP(c_List_Olistsp(X5,hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X21)),X25))
    <=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X25),c_List_Olists(X5,X21))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsp__lists__eq) ).

fof(fact_setsum__abs__ge__zero,axiom,
    ! [X21,X2,X20,X5] :
      ( class_Groups_Oordered__ab__group__add__abs(X5)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X20,X5),hAPP(hAPP(c_COMBB(X5,X5,X20),c_Groups_Oabs__class_Oabs(X5)),X2)),X21))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__abs__ge__zero) ).

fof(fact_finite__Collect__subsets,axiom,
    ! [X21,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool))),X21)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Collect__subsets) ).

fof(fact_sum__squares__le__zero__iff,axiom,
    ! [X33,X25,X5] :
      ( class_Rings_Olinordered__ring__strict(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X25),X25)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X33),X33))),c_Groups_Ozero__class_Ozero(X5)))
      <=> ( X25 = c_Groups_Ozero__class_Ozero(X5)
          & X33 = c_Groups_Ozero__class_Ozero(X5) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__squares__le__zero__iff) ).

fof(fact_Min_Oclosed,axiom,
    ! [X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( ! [X3,X177] : hBOOL(hAPP(hAPP(c_member(X5),hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X3),X177)),hAPP(hAPP(c_Set_Oinsert(X5),X3),hAPP(hAPP(c_Set_Oinsert(X5),X177),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))
           => hBOOL(hAPP(hAPP(c_member(X5),c_Big__Operators_Olinorder__class_OMin(X5,X21)),X21)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min_Oclosed) ).

fof(fact_Max_Oclosed,axiom,
    ! [X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( ! [X3,X177] : hBOOL(hAPP(hAPP(c_member(X5),hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X3),X177)),hAPP(hAPP(c_Set_Oinsert(X5),X3),hAPP(hAPP(c_Set_Oinsert(X5),X177),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))
           => hBOOL(hAPP(hAPP(c_member(X5),c_Big__Operators_Olinorder__class_OMax(X5,X21)),X21)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max_Oclosed) ).

fof(fact_Sup__fin_Oclosed,axiom,
    ! [X21,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( ! [X3,X177] : hBOOL(hAPP(hAPP(c_member(X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X3),X177)),hAPP(hAPP(c_Set_Oinsert(X5),X3),hAPP(hAPP(c_Set_Oinsert(X5),X177),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))
           => hBOOL(hAPP(hAPP(c_member(X5),c_Big__Operators_Olattice__class_OSup__fin(X5,X21)),X21)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_Oclosed) ).

fof(fact_Inf__fin_Oclosed,axiom,
    ! [X21,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( ! [X3,X177] : hBOOL(hAPP(hAPP(c_member(X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X3),X177)),hAPP(hAPP(c_Set_Oinsert(X5),X3),hAPP(hAPP(c_Set_Oinsert(X5),X177),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))
           => hBOOL(hAPP(hAPP(c_member(X5),c_Big__Operators_Olattice__class_OInf__fin(X5,X21)),X21)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_Oclosed) ).

fof(fact_folding__image_Oreindex,axiom,
    ! [X1,X122,X21,X205,X120,X2,X20,X5] :
      ( c_Finite__Set_Ofolding__image(X5,X20,X2,X120,X205)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X20),X21))
       => ( c_Fun_Oinj__on(X20,X20,X122,X21)
         => hAPP(hAPP(X205,X1),hAPP(c_Set_Oimage(X20,X20,X122),X21)) = hAPP(hAPP(X205,hAPP(c_Fun_Ocomp(X20,X5,X20,X1),X122)),X21) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image_Oreindex) ).

fof(fact_transpose__column__length,axiom,
    ! [X82,X239,X5] :
      ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X5),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X5))),X239)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X82),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5))),X239)))
       => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5))),hAPP(c_List_Ofilter(tc_List_Olist(X5),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X5)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X82)),c_Nat_Osize__class_Osize(tc_List_Olist(X5)))),c_List_Otranspose(X5,X239))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X5)),X239),X82)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose__column__length) ).

fof(fact_pair__imageI,axiom,
    ! [X2,X116,X21,X24,X6,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X20)),hAPP(hAPP(c_Product__Type_OPair(X5,X20),X6),X24)),X21))
     => hBOOL(hAPP(hAPP(c_member(X116),hAPP(hAPP(X2,X6),X24)),hAPP(c_Set_Oimage(tc_prod(X5,X20),X116,hAPP(c_Product__Type_Oprod_Oprod__case(X5,X20,X116),X2)),X21))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__imageI) ).

fof(fact_length__filter__map,axiom,
    ! [X239,X2,X20,X18,X5] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),hAPP(c_List_Ofilter(X5,X18),hAPP(hAPP(c_List_Omap(X20,X5),X2),X239))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X20)),hAPP(c_List_Ofilter(X20,hAPP(c_Fun_Ocomp(X5,tc_HOL_Obool,X20,X18),X2)),X239)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__filter__map) ).

fof(fact_trancl__subset__Sigma__aux,axiom,
    ! [X21,X171,X24,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X24)),c_Transitive__Closure_Ortrancl(X5,X171)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X171),hAPP(hAPP(c_Product__Type_OSigma(X5,X5),X21),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X5),X21))))
       => ( X6 = X24
          | hBOOL(hAPP(hAPP(c_member(X5),X6),X21)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__subset__Sigma__aux) ).

fof(fact_sum__length__filter__compl,axiom,
    ! [X239,X18,X5] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),hAPP(c_List_Ofilter(X5,X18),X239))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),hAPP(c_List_Ofilter(X5,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),X18)),X239))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__length__filter__compl) ).

fof(fact_rtrancl__trans,axiom,
    ! [X23,X171,X24,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X24)),c_Transitive__Closure_Ortrancl(X5,X171)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X24),X23)),c_Transitive__Closure_Ortrancl(X5,X171)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X23)),c_Transitive__Closure_Ortrancl(X5,X171))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__trans) ).

fof(fact_zdiv__zadd1__eq,axiom,
    ! [X56,X90,X62] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X62),X90)),X56) = 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),X62),X56)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X90),X56))),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,X62,X56)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X90,X56))),X56)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zadd1__eq) ).

fof(fact_div__add1__eq,axiom,
    ! [X56,X90,X62] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X62),X90)),X56) = 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),X62),X56)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X90),X56))),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,X62,X56)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X90,X56))),X56)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__add1__eq) ).

fof(fact_inf2D1,axiom,
    ! [X33,X25,X113,X21,X20,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_fun(X20,tc_HOL_Obool))),X21),X113),X25),X33))
     => hBOOL(hAPP(hAPP(X21,X25),X33)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf2D1) ).

fof(fact_inf2D2,axiom,
    ! [X33,X25,X113,X21,X20,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_fun(X20,tc_HOL_Obool))),X21),X113),X25),X33))
     => hBOOL(hAPP(hAPP(X113,X25),X33)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf2D2) ).

fof(fact_length__takeWhile__less__P__nth,axiom,
    ! [X239,X5,X18,X157] :
      ( ! [X146] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X146),X157))
         => hBOOL(hAPP(X18,hAPP(hAPP(c_List_Onth(X5),X239),X146))) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X157),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X157),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_OtakeWhile(X5,X18,X239)))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__takeWhile__less__P__nth) ).

fof(fact_converse__rtrancl__into__rtrancl,axiom,
    ! [X23,X171,X24,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X24)),X171))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X24),X23)),c_Transitive__Closure_Ortrancl(X5,X171)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X23)),c_Transitive__Closure_Ortrancl(X5,X171))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__rtrancl__into__rtrancl) ).

fof(fact_rtrancl_Ortrancl__into__rtrancl,axiom,
    ! [X23,X171,X24,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X24)),c_Transitive__Closure_Ortrancl(X5,X171)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X24),X23)),X171))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X23)),c_Transitive__Closure_Ortrancl(X5,X171))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl_Ortrancl__into__rtrancl) ).

fof(fact_rtrancl__listrel1__if__listrel,axiom,
    ! [X171,X251,X239,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X239),X251)),c_List_Olistrel(X5,X171)))
     => 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)),X239),X251)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X5),c_List_Olistrel1(X5,X171)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__listrel1__if__listrel) ).

fof(fact_folding_Ocommute__comps_I1_J,axiom,
    ! [X122,X1,X206,X2,X116,X115,X114,X205,X80,X20,X5] :
      ( c_Finite__Set_Ofolding(X5,X20,X80,X205)
     => hAPP(c_Fun_Ocomp(X114,X115,X116,X2),hAPP(c_Fun_Ocomp(X206,X114,X116,X1),X122)) = hAPP(c_Fun_Ocomp(X206,X115,X116,hAPP(c_Fun_Ocomp(X114,X115,X206,X2),X1)),X122) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Ocommute__comps_I1_J) ).

fof(fact_zdiv__mono2__neg__lemma,axiom,
    ! [X141,X142,X143,X134,X140,X90] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X90),X140)),X134) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X143),X142)),X141)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X143),X142)),X141)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X134),X90))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X141))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X143))
             => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X143),X90))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X142),X140)) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__mono2__neg__lemma) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J,axiom,
    ! [X18] : 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)))),X18)) = 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),X18),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J) ).

fof(fact_listrel__reflcl__if__listrel1,axiom,
    ! [X171,X251,X239,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X239),X251)),c_List_Olistrel1(X5,X171)))
     => 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)),X239),X251)),c_List_Olistrel(X5,c_Transitive__Closure_Ortrancl(X5,X171)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__reflcl__if__listrel1) ).

fof(fact_lexord__lex,axiom,
    ! [X171,X33,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X25),X33)),c_List_Olex(X5,X171)))
    <=> ( 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)),X25),X33)),c_List_Olexord(X5,X171)))
        & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X25) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X33) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexord__lex) ).

fof(fact_filter__map,axiom,
    ! [X239,X2,X20,X18,X5] : hAPP(c_List_Ofilter(X5,X18),hAPP(hAPP(c_List_Omap(X20,X5),X2),X239)) = hAPP(hAPP(c_List_Omap(X20,X5),X2),hAPP(c_List_Ofilter(X20,hAPP(c_Fun_Ocomp(X5,tc_HOL_Obool,X20,X18),X2)),X239)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter__map) ).

fof(fact_wfP__SUP,axiom,
    ! [X5,X171,X20] :
      ( ! [X146] : c_Wellfounded_OwfP(X20,hAPP(X171,X146))
     => ( ! [X146,X101] :
            ( hAPP(X171,X146) != hAPP(X171,X101)
           => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20,tc_HOL_Obool)),c_Predicate_ODomainP(X20,X20,hAPP(X171,X146))),c_Predicate_ORangeP(X20,X20,hAPP(X171,X101))) = c_Orderings_Obot__class_Obot(tc_fun(X20,tc_HOL_Obool)) )
       => c_Wellfounded_OwfP(X20,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X20,tc_fun(X20,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),X171)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfP__SUP) ).

fof(fact_partition__filter__conv,axiom,
    ! [X239,X2,X5] : c_List_Opartition(X5,X2,X239) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(c_List_Ofilter(X5,X2),X239)),hAPP(c_List_Ofilter(X5,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,X5,c_fNot),X2)),X239)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_partition__filter__conv) ).

fof(fact_upto_Opinduct,axiom,
    ! [X18,X27,X191] :
      ( 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),X191),X27)))
     => ( ! [X146,X101] :
            ( 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),X146),X101)))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X146),X101))
               => hBOOL(hAPP(hAPP(X18,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X146),c_Groups_Oone__class_Oone(tc_Int_Oint))),X101)) )
             => hBOOL(hAPP(hAPP(X18,X146),X101)) ) )
       => hBOOL(hAPP(hAPP(X18,X191),X27)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_upto_Opinduct) ).

fof(fact_list__all2__map1,axiom,
    ! [X280,X273,X2,X116,X18,X20,X5] :
      ( c_List_Olist__all2(X5,X20,X18,hAPP(hAPP(c_List_Omap(X116,X5),X2),X273),X280)
    <=> c_List_Olist__all2(X116,X20,hAPP(hAPP(c_COMBB(X5,tc_fun(X20,tc_HOL_Obool),X116),X18),X2),X273,X280) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__all2__map1) ).

fof(fact_measures__lesseq,axiom,
    ! [X290,X5,X33,X25,X2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(X2,X25)),hAPP(X2,X33)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X33)),c_List_Omeasures(X5,X290)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X33)),c_List_Omeasures(X5,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X5,tc_Nat_Onat)),X2),X290)))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_measures__lesseq) ).

fof(fact_trans__def,axiom,
    ! [X171,X5] :
      ( c_Relation_Otrans(X5,X171)
    <=> ! [X3,X177] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X177)),X171))
         => ! [X154] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X177),X154)),X171))
             => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X154)),X171)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__def) ).

fof(fact_transD,axiom,
    ! [X23,X24,X6,X171,X5] :
      ( c_Relation_Otrans(X5,X171)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X24)),X171))
       => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X24),X23)),X171))
         => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X23)),X171)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transD) ).

fof(fact_Ints__odd__less__0,axiom,
    ! [X6,X5] :
      ( class_Rings_Olinordered__idom(X5)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X6),c_Int_Oring__1__class_OInts(X5)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),c_Groups_Oone__class_Oone(X5)),X6)),X6)),c_Groups_Ozero__class_Ozero(X5)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),c_Groups_Ozero__class_Ozero(X5))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__odd__less__0) ).

fof(fact_zdiv__zmod__equality2,axiom,
    ! [X96,X90,X62] : 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),X62),X90)),X90)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X62,X90))),X96) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X62),X96),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zmod__equality2) ).

fof(fact_INFI__set__fold,axiom,
    ! [X2,X239,X20,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X20,X5),hAPP(c_List_Oset(X20),X239)),X2) = hAPP(c_List_Ofoldl(X5,X20,hAPP(c_COMBC(X20,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X20),c_Lattices_Osemilattice__inf__class_Oinf(X5)),X2)),c_Orderings_Otop__class_Otop(X5)),X239) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INFI__set__fold) ).

fof(fact_SUPR__set__fold,axiom,
    ! [X2,X239,X20,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,X5),hAPP(c_List_Oset(X20),X239)),X2) = hAPP(c_List_Ofoldl(X5,X20,hAPP(c_COMBC(X20,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X20),c_Lattices_Osemilattice__sup__class_Osup(X5)),X2)),c_Orderings_Obot__class_Obot(X5)),X239) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUPR__set__fold) ).

fof(fact_finite__UN__I,axiom,
    ! [X113,X20,X21,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
     => ( ! [X187] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X187),X21))
           => hBOOL(hAPP(c_Finite__Set_Ofinite(X20),hAPP(X113,X187))) )
       => hBOOL(hAPP(c_Finite__Set_Ofinite(X20),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X20,tc_HOL_Obool)),X21),X113))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UN__I) ).

fof(fact_finite__UN,axiom,
    ! [X113,X20,X21,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X20),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X20,tc_HOL_Obool)),X21),X113)))
      <=> ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X21))
           => hBOOL(hAPP(c_Finite__Set_Ofinite(X20),hAPP(X113,X3))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UN) ).

fof(fact_rel__comp__UNION__distrib,axiom,
    ! [X171,X221,X115,X76,X20,X116,X5] : hAPP(hAPP(c_Relation_Orel__comp(X5,X116,X20),X76),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X115,tc_fun(tc_prod(X116,X20),tc_HOL_Obool)),X221),X171)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X115,tc_fun(tc_prod(X5,X20),tc_HOL_Obool)),X221),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X116,X20),tc_HOL_Obool),tc_fun(tc_prod(X5,X20),tc_HOL_Obool),X115),hAPP(c_Relation_Orel__comp(X5,X116,X20),X76)),X171)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__comp__UNION__distrib) ).

fof(fact_o__assoc,axiom,
    ! [X122,X1,X115,X2,X5,X20,X116] : hAPP(c_Fun_Ocomp(X116,X20,X5,X2),hAPP(c_Fun_Ocomp(X115,X116,X5,X1),X122)) = hAPP(c_Fun_Ocomp(X115,X20,X5,hAPP(c_Fun_Ocomp(X116,X20,X115,X2),X1)),X122),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__assoc) ).

fof(fact_surj__Compl__image__subset,axiom,
    ! [X21,X2,X5,X20] :
      ( hAPP(c_Set_Oimage(X20,X5,X2),c_Orderings_Otop__class_Otop(tc_fun(X20,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Oimage(X20,X5,X2),X21))),hAPP(c_Set_Oimage(X20,X5,X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20,tc_HOL_Obool)),X21)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surj__Compl__image__subset) ).

fof(fact_in__inv__image,axiom,
    ! [X2,X171,X20,X33,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X33)),hAPP(hAPP(c_Relation_Oinv__image(X20,X5),X171),X2)))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(X20,X20)),hAPP(hAPP(c_Product__Type_OPair(X20,X20),hAPP(X2,X25)),hAPP(X2,X33))),X171)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__inv__image) ).

fof(fact_sym__trans__comp__subset,axiom,
    ! [X171,X5] :
      ( c_Relation_Osym(X5,X171)
     => ( c_Relation_Otrans(X5,X171)
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),hAPP(c_Relation_Oconverse(X5,X5),X171)),X171)),X171)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sym__trans__comp__subset) ).

fof(fact_folding_Oremove,axiom,
    ! [X25,X21,X205,X2,X20,X5] :
      ( c_Finite__Set_Ofolding(X5,X20,X2,X205)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => hAPP(X205,X21) = hAPP(c_Fun_Ocomp(X20,X20,X20,hAPP(X205,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))),hAPP(X2,X25)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Oremove) ).

fof(fact_Image__subset,axiom,
    ! [X112,X113,X21,X171,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X20),tc_HOL_Obool)),X171),hAPP(hAPP(c_Product__Type_OSigma(X5,X20),X21),hAPP(c_COMBK(tc_fun(X20,tc_HOL_Obool),X5),X113))))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20,tc_HOL_Obool)),hAPP(c_Relation_OImage(X5,X20,X171),X112)),X113)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__subset) ).

fof(fact_tl__append,axiom,
    ! [X251,X239,X5] : hAPP(c_List_Otl(X5),hAPP(hAPP(c_List_Oappend(X5),X239),X251)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(X5),X5,hAPP(c_List_Otl(X5),X251),hAPP(c_COMBK(tc_fun(tc_List_Olist(X5),tc_List_Olist(X5)),X5),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Oappend(X5)),X251))),X239),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tl__append) ).

fof(fact_pos__map__def,axiom,
    ! [X18,X2,X5,X20] : c_New__Random__Sequence_Opos__map(X20,X5,X2,X18) = c_New__Random__Sequence_Opos__bind(X20,X5,X18,hAPP(c_Fun_Ocomp(X5,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X5))))),X20,c_New__Random__Sequence_Opos__single(X5)),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__map__def) ).

fof(fact_inj__image__Compl__subset,axiom,
    ! [X21,X2,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X20,X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X21))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X20,X2),X21)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__image__Compl__subset) ).

fof(fact_bij__imp__bij__inv,axiom,
    ! [X2,X20,X5] :
      ( c_Fun_Obij__betw(X5,X20,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X20,tc_HOL_Obool)))
     => c_Fun_Obij__betw(X20,X5,c_Hilbert__Choice_Oinv__into(X5,X20,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X2),c_Orderings_Otop__class_Otop(tc_fun(X20,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__imp__bij__inv) ).

fof(fact_folding_Oinsert__remove,axiom,
    ! [X25,X21,X205,X2,X20,X5] :
      ( c_Finite__Set_Ofolding(X5,X20,X2,X205)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => hAPP(X205,hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(c_Fun_Ocomp(X20,X20,X20,hAPP(X205,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))),hAPP(X2,X25)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Oinsert__remove) ).

fof(fact_list__all2__update__cong2,axiom,
    ! [X82,X33,X25,X251,X239,X18,X20,X5] :
      ( c_List_Olist__all2(X5,X20,X18,X239,X251)
     => ( hBOOL(hAPP(hAPP(X18,X25),X33))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X82),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X20)),X251)))
         => c_List_Olist__all2(X5,X20,X18,hAPP(hAPP(c_List_Olist__update(X5,X239),X82),X25),hAPP(hAPP(c_List_Olist__update(X20,X251),X82),X33)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__all2__update__cong2) ).

fof(fact_list__all2__update__cong,axiom,
    ! [X33,X25,X251,X18,X20,X239,X5,X82] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X82),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239)))
     => ( c_List_Olist__all2(X5,X20,X18,X239,X251)
       => ( hBOOL(hAPP(hAPP(X18,X25),X33))
         => c_List_Olist__all2(X5,X20,X18,hAPP(hAPP(c_List_Olist__update(X5,X239),X82),X25),hAPP(hAPP(c_List_Olist__update(X20,X251),X82),X33)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__all2__update__cong) ).

fof(fact_bij__image__Collect__eq,axiom,
    ! [X18,X2,X20,X5] :
      ( c_Fun_Obij__betw(X5,X20,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X20,tc_HOL_Obool)))
     => hAPP(c_Set_Oimage(X5,X20,X2),hAPP(c_Set_OCollect(X5),X18)) = hAPP(c_Set_OCollect(X20),hAPP(hAPP(c_COMBB(X5,tc_HOL_Obool,X20),X18),c_Hilbert__Choice_Oinv__into(X5,X20,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__image__Collect__eq) ).

fof(fact_setprod__nonneg,axiom,
    ! [X2,X21,X5,X20] :
      ( class_Rings_Olinordered__semidom(X20)
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X21))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20),c_Groups_Ozero__class_Ozero(X20)),hAPP(X2,X3))) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20),c_Groups_Ozero__class_Ozero(X20)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X2),X21))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__nonneg) ).

fof(fact_setprod__pos,axiom,
    ! [X2,X21,X5,X20] :
      ( class_Rings_Olinordered__semidom(X20)
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X21))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20),c_Groups_Ozero__class_Ozero(X20)),hAPP(X2,X3))) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20),c_Groups_Ozero__class_Ozero(X20)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X2),X21))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__pos) ).

fof(fact_converse__pred__comp,axiom,
    ! [X76,X171,X116,X5,X20] : c_Predicate_Oconversep(X20,X5,c_Predicate_Opred__comp(X20,X116,X5,X171,X76)) = c_Predicate_Opred__comp(X5,X116,X20,c_Predicate_Oconversep(X116,X5,X76),c_Predicate_Oconversep(X20,X116,X171)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__pred__comp) ).

fof(fact_folding_Ocommute__left__comp_H_H,axiom,
    ! [X1,X116,X113,X21,X205,X2,X20,X5] :
      ( c_Finite__Set_Ofolding(X5,X20,X2,X205)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X113))
         => hAPP(c_Fun_Ocomp(X20,X20,X116,hAPP(X205,X113)),hAPP(c_Fun_Ocomp(X20,X20,X116,hAPP(X205,X21)),X1)) = hAPP(c_Fun_Ocomp(X20,X20,X116,hAPP(X205,X21)),hAPP(c_Fun_Ocomp(X20,X20,X116,hAPP(X205,X113)),X1)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Ocommute__left__comp_H_H) ).

fof(fact_inv__def,axiom,
    ! [X33,X2,X20,X5] : hAPP(c_Hilbert__Choice_Oinv__into(X5,X20,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X2),X33) = c_Hilbert__Choice_OEps(X5,hAPP(hAPP(c_COMBC(X5,X20,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X20,tc_fun(X20,tc_HOL_Obool),X5),c_fequal),X2)),X33)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__def) ).

fof(fact_finite__SigmaI,axiom,
    ! [X113,X20,X21,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
     => ( ! [X187] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X187),X21))
           => hBOOL(hAPP(c_Finite__Set_Ofinite(X20),hAPP(X113,X187))) )
       => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X5,X20)),hAPP(hAPP(c_Product__Type_OSigma(X5,X20),X21),X113))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__SigmaI) ).

fof(fact_convex__bound__le,axiom,
    ! [X136,X55,X65,X62,X66,X58] :
      ( class_Rings_Olinordered__semiring__1(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X66),X62))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X65),X62))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),X55))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),X136))
             => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X55),X136) = c_Groups_Oone__class_Oone(X58)
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X55),X66)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X136),X65))),X62)) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_convex__bound__le) ).

fof(fact_convex__bound__lt,axiom,
    ! [X136,X55,X65,X62,X66,X58] :
      ( class_Rings_Olinordered__semiring__1__strict(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X66),X62))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X65),X62))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),X55))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),X136))
             => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X55),X136) = c_Groups_Oone__class_Oone(X58)
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X55),X66)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X136),X65))),X62)) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_convex__bound__lt) ).

fof(fact_aset_I6_J,axiom,
    ! [X21,X15,X144] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X144))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X15),c_Groups_Oone__class_Oone(tc_Int_Oint))),X21))
       => ! [X3] :
            ( ! [X204] :
                ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X204),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X144)))
               => ! [X228] :
                    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X228),X21))
                   => X3 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X228),X204) ) )
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),X15))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X144)),X15)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_aset_I6_J) ).

fof(fact_lazy__sequence_Orecs_I2_J,axiom,
    ! [X307,X6,X89,X19,X20,X5] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X5,X20,X19,X89,c_Lazy__Sequence_Olazy__sequence_OInsert(X20,X6,X307)) = hAPP(hAPP(hAPP(X89,X6),X307),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X5,X20,X19,X89,X307)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lazy__sequence_Orecs_I2_J) ).

fof(fact_max__extp_Ointros,axiom,
    ! [X32,X196,X194,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X194))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X196))
       => ( X196 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X3),X194))
               => ? [X204] :
                    ( hBOOL(hAPP(hAPP(c_member(X5),X204),X196))
                    & hBOOL(hAPP(hAPP(X32,X3),X204)) ) )
           => c_Wellfounded_Omax__extp(X5,X32,X194,X196) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__extp_Ointros) ).

fof(fact_folding_Ocommute__left__comp_H,axiom,
    ! [X1,X25,X116,X21,X205,X2,X20,X5] :
      ( c_Finite__Set_Ofolding(X5,X20,X2,X205)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => hAPP(c_Fun_Ocomp(X20,X20,X116,hAPP(X2,X25)),hAPP(c_Fun_Ocomp(X20,X20,X116,hAPP(X205,X21)),X1)) = hAPP(c_Fun_Ocomp(X20,X20,X116,hAPP(X205,X21)),hAPP(c_Fun_Ocomp(X20,X20,X116,hAPP(X2,X25)),X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Ocommute__left__comp_H) ).

fof(fact_listrel1I,axiom,
    ! [X251,X258,X259,X239,X171,X33,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X33)),X171))
     => ( X239 = hAPP(hAPP(c_List_Oappend(X5),X259),hAPP(hAPP(c_List_Olist_OCons(X5),X25),X258))
       => ( X251 = hAPP(hAPP(c_List_Oappend(X5),X259),hAPP(hAPP(c_List_Olist_OCons(X5),X33),X258))
         => 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)),X239),X251)),c_List_Olistrel1(X5,X171))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel1I) ).

fof(fact_all__nth__imp__all__set,axiom,
    ! [X25,X18,X239,X5] :
      ( ! [X146] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X146),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239)))
         => hBOOL(hAPP(X18,hAPP(hAPP(c_List_Onth(X5),X239),X146))) )
     => ( hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X239)))
       => hBOOL(hAPP(X18,X25)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_all__nth__imp__all__set) ).

fof(fact_inf__le__fold__inf,axiom,
    ! [X23,X24,X21,X5] :
      ( class_Lattices_Osemilattice__inf(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),X21))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X24),X3)) )
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X24),X23)),hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Lattices_Osemilattice__inf__class_Oinf(X5)),X23),X21))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__le__fold__inf) ).

fof(fact_min__max_Oinf__le__fold__inf,axiom,
    ! [X23,X24,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),X21))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X24),X3)) )
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X24),X23)),hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omin(X5)),X23),X21))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__le__fold__inf) ).

fof(fact_setsum__shift__bounds__nat__ivl,axiom,
    ! [X50,X87,X95,X2,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X95),X87)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X50),X87))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X5,tc_Nat_Onat),X2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X87))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X95),X50)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__shift__bounds__nat__ivl) ).

fof(fact_in__rtrancl__UnI,axiom,
    ! [X192,X32,X25,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X25),c_Transitive__Closure_Ortrancl(X5,X32)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X25),c_Transitive__Closure_Ortrancl(X5,X192))) )
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X25),c_Transitive__Closure_Ortrancl(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X32),X192)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__rtrancl__UnI) ).

fof(fact_folding_Ocommute__left__comp,axiom,
    ! [X1,X25,X33,X116,X205,X2,X20,X5] :
      ( c_Finite__Set_Ofolding(X5,X20,X2,X205)
     => hAPP(c_Fun_Ocomp(X20,X20,X116,hAPP(X2,X33)),hAPP(c_Fun_Ocomp(X20,X20,X116,hAPP(X2,X25)),X1)) = hAPP(c_Fun_Ocomp(X20,X20,X116,hAPP(X2,X25)),hAPP(c_Fun_Ocomp(X20,X20,X116,hAPP(X2,X33)),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Ocommute__left__comp) ).

fof(fact_range__ex1__eq,axiom,
    ! [X24,X2,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => ( hBOOL(hAPP(hAPP(c_member(X20),X24),hAPP(c_Set_Oimage(X5,X20,X2),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))))
      <=> ? [X3] :
            ( X24 = hAPP(X2,X3)
            & ! [X177] :
                ( X24 = hAPP(X2,X177)
               => X177 = X3 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_range__ex1__eq) ).

fof(fact_setsum__Un,axiom,
    ! [X2,X113,X21,X5,X20] :
      ( class_Groups_Oab__group__add(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X113))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X2),X21)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X2),X113))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__Un) ).

fof(fact_rev__update,axiom,
    ! [X65,X242,X58,X96] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X96),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242)))
     => hAPP(c_List_Orev(X58),hAPP(hAPP(c_List_Olist__update(X58,X242),X96),X65)) = hAPP(hAPP(c_List_Olist__update(X58,hAPP(c_List_Orev(X58),X242)),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(X58)),X242)),X96)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X65) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__update) ).

fof(fact_Collect__imp__eq,axiom,
    ! [X16,X18,X5] : hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fimplies),X18)),X16)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_OCollect(X5),X18))),hAPP(c_Set_OCollect(X5),X16)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__imp__eq) ).

fof(fact_single__valued__def,axiom,
    ! [X171,X20,X5] :
      ( c_Relation_Osingle__valued(X5,X20,X171)
    <=> ! [X3,X177] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X20)),hAPP(hAPP(c_Product__Type_OPair(X5,X20),X3),X177)),X171))
         => ! [X154] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X20)),hAPP(hAPP(c_Product__Type_OPair(X5,X20),X3),X154)),X171))
             => X177 = X154 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valued__def) ).

fof(fact_prod__size__simp,axiom,
    ! [X160,X1,X2,X20,X5] : c_Product__Type_Oprod_Oprod__size(X5,X20,X2,X1,X160) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X2,hAPP(c_Product__Type_Ofst(X5,X20),X160))),hAPP(X1,hAPP(c_Product__Type_Osnd(X5,X20),X160)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_prod__size__simp) ).

fof(fact_setsum__shift__bounds__cl__nat__ivl,axiom,
    ! [X50,X87,X95,X2,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X95),X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X50),X87))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X5,tc_Nat_Onat),X2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X87))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X95,X50)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__shift__bounds__cl__nat__ivl) ).

fof(fact_bset_I8_J,axiom,
    ! [X113,X15,X144] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X144))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X15),c_Groups_Oone__class_Oone(tc_Int_Oint))),X113))
       => ! [X3] :
            ( ! [X204] :
                ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X204),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X144)))
               => ! [X228] :
                    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X228),X113))
                   => X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X228),X204) ) )
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X15),X3))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X15),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),X144))) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bset_I8_J) ).

fof(fact_finite__equiv__class,axiom,
    ! [X194,X171,X21,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X171),hAPP(hAPP(c_Product__Type_OSigma(X5,X5),X21),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X5),X21))))
       => ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X194),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X21),X171)))
         => hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X194)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__equiv__class) ).

fof(fact_quotient__eqI,axiom,
    ! [X33,X25,X196,X194,X171,X21,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X21,X171)
     => ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X194),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X21),X171)))
       => ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X196),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X21),X171)))
         => ( hBOOL(hAPP(hAPP(c_member(X5),X25),X194))
           => ( hBOOL(hAPP(hAPP(c_member(X5),X33),X196))
             => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X33)),X171))
               => X194 = X196 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotient__eqI) ).

fof(fact_quotient__eq__iff,axiom,
    ! [X33,X25,X196,X194,X171,X21,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X21,X171)
     => ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X194),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X21),X171)))
       => ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X196),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X21),X171)))
         => ( hBOOL(hAPP(hAPP(c_member(X5),X25),X194))
           => ( hBOOL(hAPP(hAPP(c_member(X5),X33),X196))
             => ( X194 = X196
              <=> hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X33)),X171)) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotient__eq__iff) ).

fof(fact_field__le__mult__one__interval,axiom,
    ! [X65,X66,X58] :
      ( class_Fields_Olinordered__field__inverse__zero(X58)
     => ( ! [X154] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),X154))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X154),c_Groups_Oone__class_Oone(X58)))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X154),X66)),X65)) ) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X66),X65)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_field__le__mult__one__interval) ).

fof(fact_eq__comp__r,axiom,
    ! [X32,X5] : c_Predicate_Opred__comp(X5,X5,X5,c_fequal,c_Predicate_Opred__comp(X5,X5,X5,X32,c_fequal)) = X32,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__comp__r) ).

fof(fact_vimage__eq__UN,axiom,
    ! [X113,X2,X20,X5] : hAPP(c_Set_Ovimage(X5,X20,X2),X113) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,tc_fun(X5,tc_HOL_Obool)),X113),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X20),c_Set_Ovimage(X5,X20,X2)),hAPP(hAPP(c_COMBC(X20,tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),c_Set_Oinsert(X20)),c_Orderings_Obot__class_Obot(tc_fun(X20,tc_HOL_Obool))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__eq__UN) ).

fof(fact_Image__eq__UN,axiom,
    ! [X113,X171,X5,X20] : hAPP(c_Relation_OImage(X20,X5,X171),X113) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,tc_fun(X5,tc_HOL_Obool)),X113),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X20),c_Relation_OImage(X20,X5,X171)),hAPP(hAPP(c_COMBC(X20,tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool)),c_Set_Oinsert(X20)),c_Orderings_Obot__class_Obot(tc_fun(X20,tc_HOL_Obool))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__eq__UN) ).

fof(fact_distrib__inf__le,axiom,
    ! [X94,X65,X66,X58] :
      ( class_Lattices_Olattice(X58)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X66),X65)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X66),X94))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X66),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X65),X94)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distrib__inf__le) ).

fof(fact_min__max_Odistrib__inf__le,axiom,
    ! [X94,X65,X66,X58] :
      ( class_Orderings_Olinorder(X58)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Orderings_Oord__class_Omax(X58),hAPP(hAPP(c_Orderings_Oord__class_Omin(X58),X66),X65)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X58),X66),X94))),hAPP(hAPP(c_Orderings_Oord__class_Omin(X58),X66),hAPP(hAPP(c_Orderings_Oord__class_Omax(X58),X65),X94)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Odistrib__inf__le) ).

fof(fact_bij__betw__inv__into,axiom,
    ! [X113,X21,X2,X20,X5] :
      ( c_Fun_Obij__betw(X5,X20,X2,X21,X113)
     => c_Fun_Obij__betw(X20,X5,c_Hilbert__Choice_Oinv__into(X5,X20,X21,X2),X113,X21) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__betw__inv__into) ).

fof(fact_bij__betw__the__inv__into,axiom,
    ! [X113,X21,X2,X20,X5] :
      ( c_Fun_Obij__betw(X5,X20,X2,X21,X113)
     => c_Fun_Obij__betw(X20,X5,c_Fun_Othe__inv__into(X5,X20,X21,X2),X113,X21) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__betw__the__inv__into) ).

fof(fact_inv__into__inv__into__eq,axiom,
    ! [X6,X202,X21,X2,X20,X5] :
      ( c_Fun_Obij__betw(X5,X20,X2,X21,X202)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X21))
       => hAPP(c_Hilbert__Choice_Oinv__into(X20,X5,X202,c_Hilbert__Choice_Oinv__into(X5,X20,X21,X2)),X6) = hAPP(X2,X6) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__into__inv__into__eq) ).

fof(fact_SUP2__I,axiom,
    ! [X116,X20,X23,X24,X113,X21,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),X21))
     => ( hBOOL(hAPP(hAPP(hAPP(X113,X6),X24),X23))
       => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X20,tc_fun(X116,tc_HOL_Obool))),X21),X113),X24),X23)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUP2__I) ).

fof(fact_splitD_H,axiom,
    ! [X23,X24,X6,X32,X116,X20,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5,X20,tc_fun(X116,tc_HOL_Obool)),X32),hAPP(hAPP(c_Product__Type_OPair(X5,X20),X6),X24)),X23))
     => hBOOL(hAPP(hAPP(hAPP(X32,X6),X24),X23)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_splitD_H) ).

fof(fact_rel__comp__distrib2,axiom,
    ! [X32,X212,X192,X20,X116,X5] : hAPP(hAPP(c_Relation_Orel__comp(X5,X116,X20),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X116),tc_HOL_Obool)),X192),X212)),X32) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X20),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X5,X116,X20),X192),X32)),hAPP(hAPP(c_Relation_Orel__comp(X5,X116,X20),X212),X32)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__comp__distrib2) ).

fof(fact_inf__INFI__fold__inf,axiom,
    ! [X2,X113,X21,X5,X20] :
      ( class_Complete__Lattice_Ocomplete__lattice(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20),X113),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,X20),X21),X2)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X20,hAPP(hAPP(c_COMBB(X20,tc_fun(X20,X20),X5),c_Lattices_Osemilattice__inf__class_Oinf(X20)),X2)),X113),X21) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__INFI__fold__inf) ).

fof(fact_sup__SUPR__fold__sup,axiom,
    ! [X2,X113,X21,X5,X20] :
      ( class_Complete__Lattice_Ocomplete__lattice(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X20),X113),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X20),X21),X2)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X20,hAPP(hAPP(c_COMBB(X20,tc_fun(X20,X20),X5),c_Lattices_Osemilattice__sup__class_Osup(X20)),X2)),X113),X21) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__SUPR__fold__sup) ).

fof(fact_setsum__Un__nat,axiom,
    ! [X2,X113,X21,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X113))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),X2),X21)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),X2),X113))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__Un__nat) ).

fof(fact_finite__Collect__not,axiom,
    ! [X18,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(c_Set_OCollect(X5),X18)))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),X18))))
      <=> hBOOL(hAPP(c_Finite__Set_Ofinite(X5),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Collect__not) ).

fof(fact_zmult2__lemma__aux1,axiom,
    ! [X140,X134,X90,X56] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X56))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X90),X134))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X134),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),X90),X56)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X90),c_Divides_Odiv__class_Omod(tc_Int_Oint,X140,X56))),X134))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult2__lemma__aux1) ).

fof(fact_nat__diff__add__eq2,axiom,
    ! [X57,X72,X55,X97,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X98),X97))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X98),X55)),X72)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X97),X55)),X57)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X72),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),X97),X98)),X55)),X57)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__diff__add__eq2) ).

fof(fact_abs__setsum__abs,axiom,
    ! [X21,X2,X20,X5] :
      ( class_Groups_Oordered__ab__group__add__abs(X5)
     => hAPP(c_Groups_Oabs__class_Oabs(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X20,X5),hAPP(hAPP(c_COMBB(X5,X5,X20),c_Groups_Oabs__class_Oabs(X5)),X2)),X21)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X20,X5),hAPP(hAPP(c_COMBB(X5,X5,X20),c_Groups_Oabs__class_Oabs(X5)),X2)),X21) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__setsum__abs) ).

fof(fact_inj__image__subset__iff,axiom,
    ! [X113,X21,X2,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X20,X2),X21)),hAPP(c_Set_Oimage(X5,X20,X2),X113)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),X113)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__image__subset__iff) ).

fof(fact_gt__half__sum,axiom,
    ! [X90,X62,X58] :
      ( class_Fields_Olinordered__field(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X62),X90))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),X90)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),c_Groups_Oone__class_Oone(X58)),c_Groups_Oone__class_Oone(X58)))),X90)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gt__half__sum) ).

fof(fact_inv__into__injective,axiom,
    ! [X33,X25,X2,X21,X20,X5] :
      ( hAPP(c_Hilbert__Choice_Oinv__into(X5,X20,X21,X2),X25) = hAPP(c_Hilbert__Choice_Oinv__into(X5,X20,X21,X2),X33)
     => ( hBOOL(hAPP(hAPP(c_member(X20),X25),hAPP(c_Set_Oimage(X5,X20,X2),X21)))
       => ( hBOOL(hAPP(hAPP(c_member(X20),X33),hAPP(c_Set_Oimage(X5,X20,X2),X21)))
         => X25 = X33 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__into__injective) ).

fof(fact_list__all2__Cons,axiom,
    ! [X251,X33,X239,X25,X18,X20,X5] :
      ( c_List_Olist__all2(X5,X20,X18,hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239),hAPP(hAPP(c_List_Olist_OCons(X20),X33),X251))
    <=> ( hBOOL(hAPP(hAPP(X18,X25),X33))
        & c_List_Olist__all2(X5,X20,X18,X239,X251) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__all2__Cons) ).

fof(fact_q__neg__lemma,axiom,
    ! [X141,X142,X143] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X143),X142)),X141)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X141))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X143))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X142),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_q__neg__lemma) ).

fof(fact_zip__same,axiom,
    ! [X239,X24,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X24)),hAPP(c_List_Oset(tc_prod(X5,X5)),hAPP(hAPP(c_List_Ozip(X5,X5),X239),X239))))
    <=> ( hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(c_List_Oset(X5),X239)))
        & X6 = X24 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__same) ).

fof(fact_set__zip__leftD,axiom,
    ! [X251,X239,X33,X25,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X20)),hAPP(hAPP(c_Product__Type_OPair(X5,X20),X25),X33)),hAPP(c_List_Oset(tc_prod(X5,X20)),hAPP(hAPP(c_List_Ozip(X5,X20),X239),X251))))
     => hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X239))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__zip__leftD) ).

fof(fact_set__zip__rightD,axiom,
    ! [X251,X239,X33,X25,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X20)),hAPP(hAPP(c_Product__Type_OPair(X5,X20),X25),X33)),hAPP(c_List_Oset(tc_prod(X5,X20)),hAPP(hAPP(c_List_Ozip(X5,X20),X239),X251))))
     => hBOOL(hAPP(hAPP(c_member(X20),X33),hAPP(c_List_Oset(X20),X251))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__zip__rightD) ).

fof(fact_folding_Ounion__inter,axiom,
    ! [X113,X21,X205,X2,X20,X5] :
      ( c_Finite__Set_Ofolding(X5,X20,X2,X205)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X113))
         => hAPP(c_Fun_Ocomp(X20,X20,X20,hAPP(X205,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113))),hAPP(X205,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113))) = hAPP(c_Fun_Ocomp(X20,X20,X20,hAPP(X205,X21)),hAPP(X205,X113)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Ounion__inter) ).

fof(fact_abs__triangle__ineq3,axiom,
    ! [X90,X62,X58] :
      ( class_Groups_Oordered__ab__group__add__abs(X58)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(c_Groups_Oabs__class_Oabs(X58),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X58),hAPP(c_Groups_Oabs__class_Oabs(X58),X62)),hAPP(c_Groups_Oabs__class_Oabs(X58),X90)))),hAPP(c_Groups_Oabs__class_Oabs(X58),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X58),X62),X90)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__triangle__ineq3) ).

fof(fact_odd__less__0,axiom,
    ! [X120] :
      ( 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)),X120)),X120)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X120),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_odd__less__0) ).

fof(fact_INFI__fold__inf,axiom,
    ! [X2,X21,X5,X20] :
      ( class_Complete__Lattice_Ocomplete__lattice(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,X20),X21),X2) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X20,hAPP(hAPP(c_COMBB(X20,tc_fun(X20,X20),X5),c_Lattices_Osemilattice__inf__class_Oinf(X20)),X2)),c_Orderings_Otop__class_Otop(X20)),X21) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INFI__fold__inf) ).

fof(fact_SUPR__fold__sup,axiom,
    ! [X2,X21,X5,X20] :
      ( class_Complete__Lattice_Ocomplete__lattice(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X20),X21),X2) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X20,hAPP(hAPP(c_COMBB(X20,tc_fun(X20,X20),X5),c_Lattices_Osemilattice__sup__class_Osup(X20)),X2)),c_Orderings_Obot__class_Obot(X20)),X21) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUPR__fold__sup) ).

fof(fact_single__valuedD,axiom,
    ! [X120,X33,X25,X171,X20,X5] :
      ( c_Relation_Osingle__valued(X5,X20,X171)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X20)),hAPP(hAPP(c_Product__Type_OPair(X5,X20),X25),X33)),X171))
       => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X20)),hAPP(hAPP(c_Product__Type_OPair(X5,X20),X25),X120)),X171))
         => X33 = X120 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valuedD) ).

fof(fact_Collect__disj__eq,axiom,
    ! [X16,X18,X5] : hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fdisj),X18)),X16)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_OCollect(X5),X18)),hAPP(c_Set_OCollect(X5),X16)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__disj__eq) ).

fof(fact_Collect__conj__eq,axiom,
    ! [X16,X18,X5] : hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),X18)),X16)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_OCollect(X5),X18)),hAPP(c_Set_OCollect(X5),X16)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__conj__eq) ).

fof(fact_list__all2__dropI,axiom,
    ! [X50,X280,X273,X18,X20,X5] :
      ( c_List_Olist__all2(X5,X20,X18,X273,X280)
     => c_List_Olist__all2(X5,X20,X18,hAPP(hAPP(c_List_Odrop(X5),X50),X273),hAPP(hAPP(c_List_Odrop(X20),X50),X280)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__all2__dropI) ).

fof(fact_list__all2__takeI,axiom,
    ! [X50,X251,X239,X18,X20,X5] :
      ( c_List_Olist__all2(X5,X20,X18,X239,X251)
     => c_List_Olist__all2(X5,X20,X18,hAPP(hAPP(c_List_Otake(X5),X50),X239),hAPP(hAPP(c_List_Otake(X20),X50),X251)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__all2__takeI) ).

fof(fact_rtrancl__converseD,axiom,
    ! [X171,X33,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X33)),c_Transitive__Closure_Ortrancl(X5,hAPP(c_Relation_Oconverse(X5,X5),X171))))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X33),X25)),c_Transitive__Closure_Ortrancl(X5,X171))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__converseD) ).

fof(fact_antisymD,axiom,
    ! [X24,X6,X171,X5] :
      ( c_Relation_Oantisym(X5,X171)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X24)),X171))
       => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X24),X6)),X171))
         => X6 = X24 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_antisymD) ).

fof(fact_antisym__def,axiom,
    ! [X171,X5] :
      ( c_Relation_Oantisym(X5,X171)
    <=> ! [X3,X177] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X177)),X171))
         => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X177),X3)),X171))
           => X3 = X177 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_antisym__def) ).

fof(fact_listsum__const__mult,axiom,
    ! [X239,X2,X23,X20,X5] :
      ( class_Rings_Osemiring__0(X5)
     => hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X20,X5),hAPP(hAPP(c_COMBB(X5,X5,X20),hAPP(c_Groups_Otimes__class_Otimes(X5),X23)),X2)),X239)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X23),hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X20,X5),X2),X239))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__const__mult) ).

fof(fact_Image__mono,axiom,
    ! [X21,X202,X171,X203,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X20),tc_HOL_Obool)),X203),X171))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X202),X21))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20,tc_HOL_Obool)),hAPP(c_Relation_OImage(X5,X20,X203),X202)),hAPP(c_Relation_OImage(X5,X20,X171),X21))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__mono) ).

fof(fact_mlex__leq,axiom,
    ! [X32,X5,X33,X25,X2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(X2,X25)),hAPP(X2,X33)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X33)),X32))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X33)),c_Wellfounded_Omlex__prod(X5,X2,X32))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mlex__leq) ).

fof(fact_swap__product,axiom,
    ! [X113,X21,X5,X20] : hAPP(c_Set_Oimage(tc_prod(X20,X5),tc_prod(X5,X20),hAPP(c_Product__Type_Oprod_Oprod__case(X20,X5,tc_prod(X5,X20)),hAPP(c_COMBC(X5,X20,tc_prod(X5,X20)),c_Product__Type_OPair(X5,X20)))),hAPP(hAPP(c_Product__Type_OSigma(X20,X5),X21),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X20),X113))) = hAPP(hAPP(c_Product__Type_OSigma(X5,X20),X113),hAPP(c_COMBK(tc_fun(X20,tc_HOL_Obool),X5),X21)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_swap__product) ).

fof(fact_quotientI,axiom,
    ! [X171,X21,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
     => hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_OImage(X5,X5,X171),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X21),X171))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotientI) ).

fof(fact_Image__singleton__iff,axiom,
    ! [X6,X171,X20,X24,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X24),hAPP(c_Relation_OImage(X20,X5,X171),hAPP(hAPP(c_Set_Oinsert(X20),X6),c_Orderings_Obot__class_Obot(tc_fun(X20,tc_HOL_Obool))))))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(X20,X5)),hAPP(hAPP(c_Product__Type_OPair(X20,X5),X6),X24)),X171)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__singleton__iff) ).

fof(fact_list__all2__rev,axiom,
    ! [X251,X239,X18,X20,X5] :
      ( c_List_Olist__all2(X5,X20,X18,hAPP(c_List_Orev(X5),X239),hAPP(c_List_Orev(X20),X251))
    <=> c_List_Olist__all2(X5,X20,X18,X239,X251) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__all2__rev) ).

fof(fact_norm__frac_Opinduct,axiom,
    ! [X18,X27,X191] :
      ( 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),X191),X27)))
     => ( ! [X187,X188] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X187),X188)))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X188),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
               => hBOOL(hAPP(hAPP(X18,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X187)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X188))) )
             => hBOOL(hAPP(hAPP(X18,X187),X188)) ) )
       => hBOOL(hAPP(hAPP(X18,X191),X27)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__frac_Opinduct) ).

fof(fact_aset_I5_J,axiom,
    ! [X21,X15,X144] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X144))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X15),X21))
       => ! [X3] :
            ( ! [X204] :
                ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X204),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X144)))
               => ! [X228] :
                    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X228),X21))
                   => X3 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X228),X204) ) )
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X15))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X144)),X15)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_aset_I5_J) ).

fof(fact_div__mod__equality2,axiom,
    ! [X56,X62,X90,X58] :
      ( class_Divides_Osemiring__div(X58)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X90),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X58),X62),X90))),c_Divides_Odiv__class_Omod(X58,X62,X90))),X56) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),X56) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mod__equality2) ).

fof(fact_list__all2__rev1,axiom,
    ! [X251,X239,X18,X20,X5] :
      ( c_List_Olist__all2(X5,X20,X18,hAPP(c_List_Orev(X5),X239),X251)
    <=> c_List_Olist__all2(X5,X20,X18,X239,hAPP(c_List_Orev(X20),X251)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__all2__rev1) ).

fof(fact_lexord__Nil__left,axiom,
    ! [X171,X33,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olist_ONil(X5)),X33)),c_List_Olexord(X5,X171)))
    <=> ? [X187,X3] : X33 = hAPP(hAPP(c_List_Olist_OCons(X5),X187),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexord__Nil__left) ).

fof(fact_image__vimage__subset,axiom,
    ! [X21,X2,X20,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Oimage(X20,X5,X2),hAPP(c_Set_Ovimage(X20,X5,X2),X21))),X21)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__vimage__subset) ).

fof(fact_map__sorted__distinct__set__unique,axiom,
    ! [X251,X239,X2,X5,X20] :
      ( class_Orderings_Olinorder(X20)
     => ( c_Fun_Oinj__on(X5,X20,X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),X239)),hAPP(c_List_Oset(X5),X251)))
       => ( c_List_Olinorder__class_Osorted(X20,hAPP(hAPP(c_List_Omap(X5,X20),X2),X239))
         => ( hBOOL(hAPP(c_List_Odistinct(X20),hAPP(hAPP(c_List_Omap(X5,X20),X2),X239)))
           => ( c_List_Olinorder__class_Osorted(X20,hAPP(hAPP(c_List_Omap(X5,X20),X2),X251))
             => ( hBOOL(hAPP(c_List_Odistinct(X20),hAPP(hAPP(c_List_Omap(X5,X20),X2),X251)))
               => ( hAPP(c_List_Oset(X5),X239) = hAPP(c_List_Oset(X5),X251)
                 => X239 = X251 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__sorted__distinct__set__unique) ).

fof(fact_zmult2__lemma__aux3,axiom,
    ! [X140,X90,X134,X56] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X56))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X134))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X134),X90))
         => 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),X90),c_Divides_Odiv__class_Omod(tc_Int_Oint,X140,X56))),X134))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult2__lemma__aux3) ).

fof(fact_finite__quotient,axiom,
    ! [X171,X21,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X171),hAPP(hAPP(c_Product__Type_OSigma(X5,X5),X21),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X5),X21))))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X21),X171))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__quotient) ).

fof(fact_foldl__append,axiom,
    ! [X251,X239,X6,X2,X20,X5] : hAPP(c_List_Ofoldl(X5,X20,X2,X6),hAPP(hAPP(c_List_Oappend(X20),X239),X251)) = hAPP(c_List_Ofoldl(X5,X20,X2,hAPP(c_List_Ofoldl(X5,X20,X2,X6),X239)),X251),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldl__append) ).

fof(fact_rtrancl__converseI,axiom,
    ! [X171,X25,X33,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X33),X25)),c_Transitive__Closure_Ortrancl(X5,X171)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X33)),c_Transitive__Closure_Ortrancl(X5,hAPP(c_Relation_Oconverse(X5,X5),X171)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__converseI) ).

fof(fact_zip__append1,axiom,
    ! [X248,X241,X242,X5,X58] : hAPP(hAPP(c_List_Ozip(X58,X5),hAPP(hAPP(c_List_Oappend(X58),X242),X241)),X248) = hAPP(hAPP(c_List_Oappend(tc_prod(X58,X5)),hAPP(hAPP(c_List_Ozip(X58,X5),X242),hAPP(hAPP(c_List_Otake(X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242)),X248))),hAPP(hAPP(c_List_Ozip(X58,X5),X241),hAPP(hAPP(c_List_Odrop(X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242)),X248))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__append1) ).

fof(fact_Diff__subset__conv,axiom,
    ! [X112,X113,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),X113)),X112))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X113),X112))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__subset__conv) ).

fof(fact_evaln_Oequations_I4_J,axiom,
    ! [X77,X63,X26,X59,X27] :
      ( c_Natural_Oevaln(c_Com_Ocom_OSemi(X27,X59),X26,X63,X77)
    <=> ? [X61] :
          ( c_Natural_Oevaln(X27,X26,X63,X61)
          & c_Natural_Oevaln(X59,X61,X63,X77) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_Oequations_I4_J) ).

fof(fact_image__surj__f__inv__f,axiom,
    ! [X21,X2,X5,X20] :
      ( hAPP(c_Set_Oimage(X20,X5,X2),c_Orderings_Otop__class_Otop(tc_fun(X20,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))
     => hAPP(c_Set_Oimage(X20,X5,X2),hAPP(c_Set_Oimage(X5,X20,c_Hilbert__Choice_Oinv__into(X20,X5,c_Orderings_Otop__class_Otop(tc_fun(X20,tc_HOL_Obool)),X2)),X21)) = X21 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__surj__f__inv__f) ).

fof(fact_bset_I6_J,axiom,
    ! [X15,X113,X144] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X144))
     => ! [X3] :
          ( ! [X204] :
              ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X204),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X144)))
             => ! [X228] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X228),X113))
                 => X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X228),X204) ) )
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),X15))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),X144)),X15)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bset_I6_J) ).

fof(fact_bset_I5_J,axiom,
    ! [X15,X113,X144] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X144))
     => ! [X3] :
          ( ! [X204] :
              ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X204),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X144)))
             => ! [X228] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X228),X113))
                 => X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X228),X204) ) )
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X15))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),X144)),X15)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bset_I5_J) ).

fof(fact_setprod__Un__Int,axiom,
    ! [X1,X113,X21,X5,X20] :
      ( class_Groups_Ocomm__monoid__mult(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X113))
         => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X1),X21)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X1),X113)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__Un__Int) ).

fof(fact_setprod_Ounion__inter,axiom,
    ! [X1,X113,X21,X5,X20] :
      ( class_Groups_Ocomm__monoid__mult(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X113))
         => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X1),X21)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X1),X113)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod_Ounion__inter) ).

fof(fact_setsum__Un__Int,axiom,
    ! [X1,X113,X21,X5,X20] :
      ( class_Groups_Ocomm__monoid__add(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X113))
         => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X1),X21)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X1),X113)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__Un__Int) ).

fof(fact_inf2I,axiom,
    ! [X20,X5,X113,X33,X25,X21] :
      ( hBOOL(hAPP(hAPP(X21,X25),X33))
     => ( hBOOL(hAPP(hAPP(X113,X25),X33))
       => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_fun(X20,tc_HOL_Obool))),X21),X113),X25),X33)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf2I) ).

fof(fact_vimage__subsetD,axiom,
    ! [X21,X113,X2,X5,X20] :
      ( hAPP(c_Set_Oimage(X20,X5,X2),c_Orderings_Otop__class_Otop(tc_fun(X20,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X20,X5,X2),X113)),X21))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X113),hAPP(c_Set_Oimage(X20,X5,X2),X21))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__subsetD) ).

fof(fact_bset_I7_J,axiom,
    ! [X113,X15,X144] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X144))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X15),X113))
       => ! [X3] :
            ( ! [X204] :
                ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X204),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X144)))
               => ! [X228] :
                    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X228),X113))
                   => X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X228),X204) ) )
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X15),X3))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X15),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),X144))) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bset_I7_J) ).

fof(fact_zdiv__mono2__lemma,axiom,
    ! [X141,X142,X143,X134,X140,X90] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X90),X140)),X134) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X143),X142)),X141)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X143),X142)),X141)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X141),X143))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X134))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X143))
             => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X143),X90))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X140),X142)) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__mono2__lemma) ).

fof(fact_converse__INTER,axiom,
    ! [X171,X192,X116,X5,X20] : hAPP(c_Relation_Oconverse(X20,X5),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X116,tc_fun(tc_prod(X20,X5),tc_HOL_Obool)),X192),X171)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X116,tc_fun(tc_prod(X5,X20),tc_HOL_Obool)),X192),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X20,X5),tc_HOL_Obool),tc_fun(tc_prod(X5,X20),tc_HOL_Obool),X116),c_Relation_Oconverse(X20,X5)),X171)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__INTER) ).

fof(fact_converse__UNION,axiom,
    ! [X171,X192,X116,X5,X20] : hAPP(c_Relation_Oconverse(X20,X5),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X116,tc_fun(tc_prod(X20,X5),tc_HOL_Obool)),X192),X171)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X116,tc_fun(tc_prod(X5,X20),tc_HOL_Obool)),X192),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X20,X5),tc_HOL_Obool),tc_fun(tc_prod(X5,X20),tc_HOL_Obool),X116),c_Relation_Oconverse(X20,X5)),X171)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__UNION) ).

fof(fact_eq__Abs__Integ,axiom,
    ! [X120] :
      ~ ! [X3,X177] : X120 != 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),X177)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__Abs__Integ) ).

fof(fact_image__iff,axiom,
    ! [X21,X2,X20,X120,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X120),hAPP(c_Set_Oimage(X20,X5,X2),X21)))
    <=> ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X20),X3),X21))
          & X120 = hAPP(X2,X3) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__iff) ).

fof(fact_eq__equiv__class__iff2,axiom,
    ! [X33,X25,X171,X21,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X21,X171)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X33),X21))
         => ( hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),X171) = hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),hAPP(hAPP(c_Set_Oinsert(X5),X33),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),X171)
          <=> hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X33)),X171)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__equiv__class__iff2) ).

fof(fact_image__inv__into__cancel,axiom,
    ! [X238,X202,X21,X2,X5,X20] :
      ( hAPP(c_Set_Oimage(X20,X5,X2),X21) = X202
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X238),X202))
       => hAPP(c_Set_Oimage(X20,X5,X2),hAPP(c_Set_Oimage(X5,X20,c_Hilbert__Choice_Oinv__into(X20,X5,X21,X2)),X238)) = X238 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__inv__into__cancel) ).

fof(fact_inj__iff,axiom,
    ! [X2,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
    <=> hAPP(c_Fun_Ocomp(X20,X5,X5,c_Hilbert__Choice_Oinv__into(X5,X20,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X2)),X2) = c_Fun_Oid(X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__iff) ).

fof(fact_split__comp,axiom,
    ! [X25,X1,X2,X115,X5,X116,X20] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X20,X116,X5),hAPP(c_Fun_Ocomp(X115,tc_fun(X116,X5),X20,X2),X1)),X25) = hAPP(hAPP(X2,hAPP(X1,hAPP(c_Product__Type_Ofst(X20,X116),X25))),hAPP(c_Product__Type_Osnd(X20,X116),X25)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__comp) ).

fof(fact_inv__inv__eq,axiom,
    ! [X2,X20,X5] :
      ( c_Fun_Obij__betw(X5,X20,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X20,tc_HOL_Obool)))
     => c_Hilbert__Choice_Oinv__into(X20,X5,c_Orderings_Otop__class_Otop(tc_fun(X20,tc_HOL_Obool)),c_Hilbert__Choice_Oinv__into(X5,X20,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X2)) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__inv__eq) ).

fof(fact_transfer__nat__int__set__relations_I5_J,axiom,
    ! [X113,X21] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X21),X113))
    <=> 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)),X21)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X113))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__set__relations_I5_J) ).

fof(fact_transfer__nat__int__set__relations_I4_J,axiom,
    ! [X113,X21] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X21),X113))
    <=> 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)),X21)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X113))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__set__relations_I4_J) ).

fof(fact_min__max_OInf__fin_Ohom__commute,axiom,
    ! [X207,X122,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( ! [X3,X177] : hAPP(X122,hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X3),X177)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),hAPP(X122,X3)),hAPP(X122,X177))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X207))
         => ( X207 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(X122,c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X207)) = c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),hAPP(c_Set_Oimage(X5,X5,X122),X207)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Ohom__commute) ).

fof(fact_min__max_OSup__fin_Ohom__commute,axiom,
    ! [X207,X122,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( ! [X3,X177] : hAPP(X122,hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X3),X177)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),hAPP(X122,X3)),hAPP(X122,X177))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X207))
         => ( X207 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(X122,c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X207)) = c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),hAPP(c_Set_Oimage(X5,X5,X122),X207)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Ohom__commute) ).

fof(fact_list__all2__nthD,axiom,
    ! [X160,X251,X239,X18,X20,X5] :
      ( c_List_Olist__all2(X5,X20,X18,X239,X251)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X160),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239)))
       => hBOOL(hAPP(hAPP(X18,hAPP(hAPP(c_List_Onth(X5),X239),X160)),hAPP(hAPP(c_List_Onth(X20),X251),X160))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__all2__nthD) ).

fof(fact_list__all2__nthD2,axiom,
    ! [X160,X251,X239,X18,X20,X5] :
      ( c_List_Olist__all2(X5,X20,X18,X239,X251)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X160),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X20)),X251)))
       => hBOOL(hAPP(hAPP(X18,hAPP(hAPP(c_List_Onth(X5),X239),X160)),hAPP(hAPP(c_List_Onth(X20),X251),X160))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__all2__nthD2) ).

fof(fact_vimage__subsetI,axiom,
    ! [X21,X113,X2,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20,tc_HOL_Obool)),X113),hAPP(c_Set_Oimage(X5,X20,X2),X21)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X5,X20,X2),X113)),X21)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__subsetI) ).

fof(fact_converse__iff,axiom,
    ! [X171,X24,X6,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X20)),hAPP(hAPP(c_Product__Type_OPair(X5,X20),X6),X24)),hAPP(c_Relation_Oconverse(X20,X5),X171)))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(X20,X5)),hAPP(hAPP(c_Product__Type_OPair(X20,X5),X24),X6)),X171)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__iff) ).

fof(fact_converseD,axiom,
    ! [X171,X24,X6,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X20)),hAPP(hAPP(c_Product__Type_OPair(X5,X20),X6),X24)),hAPP(c_Relation_Oconverse(X20,X5),X171)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X20,X5)),hAPP(hAPP(c_Product__Type_OPair(X20,X5),X24),X6)),X171)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converseD) ).

fof(fact_sup2I1,axiom,
    ! [X113,X20,X5,X33,X25,X21] :
      ( hBOOL(hAPP(hAPP(X21,X25),X33))
     => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_fun(X20,tc_HOL_Obool))),X21),X113),X25),X33)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup2I1) ).

fof(fact_sup2I2,axiom,
    ! [X21,X20,X5,X33,X25,X113] :
      ( hBOOL(hAPP(hAPP(X113,X25),X33))
     => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_fun(X20,tc_HOL_Obool))),X21),X113),X25),X33)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup2I2) ).

fof(fact_Int__mono,axiom,
    ! [X144,X113,X112,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),X112))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X113),X144))
       => 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)),X21),X113)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X112),X144))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__mono) ).

fof(fact_Un__mono,axiom,
    ! [X144,X113,X112,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),X112))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X113),X144))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X112),X144))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__mono) ).

fof(fact_Diff__mono,axiom,
    ! [X113,X144,X112,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),X112))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X144),X113))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),X113)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X112),X144))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__mono) ).

fof(fact_hom__fold1__commute,axiom,
    ! [X207,X122,X5] :
      ( class_Lattices_Oab__semigroup__idem__mult(X5)
     => ( ! [X3,X177] : hAPP(X122,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X3),X177)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(X122,X3)),hAPP(X122,X177))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X207))
         => ( X207 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(X122,hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),X207)) = hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),hAPP(c_Set_Oimage(X5,X5,X122),X207)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hom__fold1__commute) ).

fof(fact_setsum_Oreindex,axiom,
    ! [X1,X122,X21,X5,X20] :
      ( class_Groups_Ocomm__monoid__add(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( c_Fun_Oinj__on(X5,X5,X122,X21)
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X1),hAPP(c_Set_Oimage(X5,X5,X122),X21)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),hAPP(c_Fun_Ocomp(X5,X20,X5,X1),X122)),X21) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum_Oreindex) ).

fof(fact_setprod_Oreindex,axiom,
    ! [X1,X122,X21,X5,X20] :
      ( class_Groups_Ocomm__monoid__mult(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( c_Fun_Oinj__on(X5,X5,X122,X21)
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X1),hAPP(c_Set_Oimage(X5,X5,X122),X21)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),hAPP(c_Fun_Ocomp(X5,X20,X5,X1),X122)),X21) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod_Oreindex) ).

fof(fact_acc_OaccI,axiom,
    ! [X171,X25,X5] :
      ( ! [X177] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X177),X25)),X171))
         => hBOOL(hAPP(hAPP(c_member(X5),X177),c_Wellfounded_Oacc(X5,X171))) )
     => hBOOL(hAPP(hAPP(c_member(X5),X25),c_Wellfounded_Oacc(X5,X171))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc_OaccI) ).

fof(fact_acc_Osimps,axiom,
    ! [X171,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),c_Wellfounded_Oacc(X5,X171)))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X6)),X171))
         => hBOOL(hAPP(hAPP(c_member(X5),X3),c_Wellfounded_Oacc(X5,X171))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc_Osimps) ).

fof(fact_rtrancl__listrel1__eq__len,axiom,
    ! [X171,X33,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X25),X33)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X5),c_List_Olistrel1(X5,X171))))
     => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X25) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X33) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__listrel1__eq__len) ).

fof(fact_list__update_Osimps_I2_J,axiom,
    ! [X123,X82,X239,X25,X5] : hAPP(hAPP(c_List_Olist__update(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239)),X82),X123) = c_Nat_Onat_Onat__case(tc_List_Olist(X5),hAPP(hAPP(c_List_Olist_OCons(X5),X123),X239),hAPP(hAPP(c_COMBB(tc_List_Olist(X5),tc_List_Olist(X5),tc_Nat_Onat),hAPP(c_List_Olist_OCons(X5),X25)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,X5,tc_List_Olist(X5)),c_List_Olist__update(X5,X239)),X123)),X82),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update_Osimps_I2_J) ).

fof(fact_split__eta,axiom,
    ! [X2,X116,X20,X5] : hAPP(c_Product__Type_Oprod_Oprod__case(X5,X20,X116),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_prod(X5,X20)),tc_fun(X20,X116),X5),hAPP(c_COMBB(tc_prod(X5,X20),X116,X20),X2)),c_Product__Type_OPair(X5,X20))) = X2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__eta) ).

fof(fact_aset_I8_J,axiom,
    ! [X15,X21,X144] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X144))
     => ! [X3] :
          ( ! [X204] :
              ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X204),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X144)))
             => ! [X228] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X228),X21))
                 => X3 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X228),X204) ) )
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X15),X3))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X144))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_aset_I8_J) ).

fof(fact_aset_I7_J,axiom,
    ! [X15,X21,X144] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X144))
     => ! [X3] :
          ( ! [X204] :
              ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X204),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X144)))
             => ! [X228] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X228),X21))
                 => X3 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X228),X204) ) )
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X15),X3))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X144))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_aset_I7_J) ).

fof(fact_nth__take__lemma,axiom,
    ! [X241,X242,X58,X96] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X96),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X96),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X241)))
       => ( ! [X146] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X146),X96))
             => hAPP(hAPP(c_List_Onth(X58),X242),X146) = hAPP(hAPP(c_List_Onth(X58),X241),X146) )
         => hAPP(hAPP(c_List_Otake(X58),X96),X242) = hAPP(hAPP(c_List_Otake(X58),X96),X241) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__take__lemma) ).

fof(fact_rel__pow__0__E,axiom,
    ! [X32,X33,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X33)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X32)))
     => X25 = X33 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__pow__0__E) ).

fof(fact_exI__realizer,axiom,
    ! [X5,X20,X25,X33,X18] :
      ( hBOOL(hAPP(hAPP(X18,X33),X25))
     => hBOOL(hAPP(hAPP(X18,hAPP(c_Product__Type_Osnd(X20,X5),hAPP(hAPP(c_Product__Type_OPair(X20,X5),X25),X33))),hAPP(c_Product__Type_Ofst(X20,X5),hAPP(hAPP(c_Product__Type_OPair(X20,X5),X25),X33)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_exI__realizer) ).

fof(fact_comp__inj__on__iff,axiom,
    ! [X119,X116,X21,X2,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,X2,X21)
     => ( c_Fun_Oinj__on(X20,X116,X119,hAPP(c_Set_Oimage(X5,X20,X2),X21))
      <=> c_Fun_Oinj__on(X5,X116,hAPP(c_Fun_Ocomp(X20,X116,X5,X119),X2),X21) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comp__inj__on__iff) ).

fof(fact_comp__surj,axiom,
    ! [X1,X116,X2,X5,X20] :
      ( hAPP(c_Set_Oimage(X20,X5,X2),c_Orderings_Otop__class_Otop(tc_fun(X20,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))
     => ( hAPP(c_Set_Oimage(X5,X116,X1),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X116,tc_HOL_Obool))
       => hAPP(c_Set_Oimage(X20,X116,hAPP(c_Fun_Ocomp(X5,X116,X20,X1),X2)),c_Orderings_Otop__class_Otop(tc_fun(X20,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X116,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comp__surj) ).

fof(fact_zdiv__zmod__equality,axiom,
    ! [X96,X62,X90] : 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),X90),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X62),X90))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X62,X90))),X96) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X62),X96),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zmod__equality) ).

fof(fact_setsum__reindex,axiom,
    ! [X122,X113,X2,X20,X5,X116] :
      ( class_Groups_Ocomm__monoid__add(X116)
     => ( c_Fun_Oinj__on(X5,X20,X2,X113)
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X20,X116),X122),hAPP(c_Set_Oimage(X5,X20,X2),X113)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X116),hAPP(c_Fun_Ocomp(X20,X116,X5,X122),X2)),X113) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__reindex) ).

fof(fact_setprod__reindex,axiom,
    ! [X122,X113,X2,X20,X5,X116] :
      ( class_Groups_Ocomm__monoid__mult(X116)
     => ( c_Fun_Oinj__on(X5,X20,X2,X113)
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X20,X116),X122),hAPP(c_Set_Oimage(X5,X20,X2),X113)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X116),hAPP(c_Fun_Ocomp(X20,X116,X5,X122),X2)),X113) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__reindex) ).

fof(fact_min__max_OSup__fin_Ounion__inter,axiom,
    ! [X113,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X113))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113))),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X21)),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X113)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Ounion__inter) ).

fof(fact_min__max_OInf__fin_Ounion__inter,axiom,
    ! [X113,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X113))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113))),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X21)),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X113)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Ounion__inter) ).

fof(fact_lexn__length,axiom,
    ! [X50,X171,X251,X239,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X239),X251)),hAPP(c_List_Olexn(X5,X171),X50)))
     => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239) = X50
        & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X251) = X50 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexn__length) ).

fof(fact_converseI,axiom,
    ! [X171,X24,X6,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X20)),hAPP(hAPP(c_Product__Type_OPair(X5,X20),X6),X24)),X171))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X20,X5)),hAPP(hAPP(c_Product__Type_OPair(X20,X5),X24),X6)),hAPP(c_Relation_Oconverse(X5,X20),X171))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converseI) ).

fof(fact_rel__comp__distrib,axiom,
    ! [X212,X192,X32,X20,X116,X5] : hAPP(hAPP(c_Relation_Orel__comp(X5,X116,X20),X32),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X116,X20),tc_HOL_Obool)),X192),X212)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X20),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X5,X116,X20),X32),X192)),hAPP(hAPP(c_Relation_Orel__comp(X5,X116,X20),X32),X212)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__comp__distrib) ).

fof(fact_bot__empty__eq2,axiom,
    ! [X33,X25,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_fun(X20,tc_HOL_Obool))),X25),X33))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X20)),hAPP(hAPP(c_Product__Type_OPair(X5,X20),X25),X33)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X20),tc_HOL_Obool)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot__empty__eq2) ).

fof(fact_transpose__transpose,axiom,
    ! [X239,X5] :
      ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X5),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X5))),X239)))
     => c_List_Otranspose(X5,c_List_Otranspose(X5,X239)) = c_List_OtakeWhile(tc_List_Olist(X5),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X5)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_List_Olist(X5),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X5))),X239) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose__transpose) ).

fof(fact_Min_Ohom__commute,axiom,
    ! [X207,X122,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( ! [X3,X177] : hAPP(X122,hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X3),X177)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),hAPP(X122,X3)),hAPP(X122,X177))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X207))
         => ( X207 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(X122,c_Big__Operators_Olinorder__class_OMin(X5,X207)) = c_Big__Operators_Olinorder__class_OMin(X5,hAPP(c_Set_Oimage(X5,X5,X122),X207)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min_Ohom__commute) ).

fof(fact_Max_Ohom__commute,axiom,
    ! [X207,X122,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( ! [X3,X177] : hAPP(X122,hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X3),X177)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),hAPP(X122,X3)),hAPP(X122,X177))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X207))
         => ( X207 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(X122,c_Big__Operators_Olinorder__class_OMax(X5,X207)) = c_Big__Operators_Olinorder__class_OMax(X5,hAPP(c_Set_Oimage(X5,X5,X122),X207)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max_Ohom__commute) ).

fof(fact_Sup__fin_Ohom__commute,axiom,
    ! [X207,X122,X5] :
      ( class_Lattices_Olattice(X5)
     => ( ! [X3,X177] : hAPP(X122,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X3),X177)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),hAPP(X122,X3)),hAPP(X122,X177))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X207))
         => ( X207 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(X122,c_Big__Operators_Olattice__class_OSup__fin(X5,X207)) = c_Big__Operators_Olattice__class_OSup__fin(X5,hAPP(c_Set_Oimage(X5,X5,X122),X207)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_Ohom__commute) ).

fof(fact_Inf__fin_Ohom__commute,axiom,
    ! [X207,X122,X5] :
      ( class_Lattices_Olattice(X5)
     => ( ! [X3,X177] : hAPP(X122,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X3),X177)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),hAPP(X122,X3)),hAPP(X122,X177))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X207))
         => ( X207 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(X122,c_Big__Operators_Olattice__class_OInf__fin(X5,X207)) = c_Big__Operators_Olattice__class_OInf__fin(X5,hAPP(c_Set_Oimage(X5,X5,X122),X207)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_Ohom__commute) ).

fof(fact_periodic__finite__ex,axiom,
    ! [X18,X22] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22))
     => ( ! [X3,X100] :
            ( hBOOL(hAPP(X18,X3))
          <=> hBOOL(hAPP(X18,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X100),X22)))) )
       => ( ? [X138] : hBOOL(hAPP(X18,X138))
        <=> ? [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),X22)))
              & hBOOL(hAPP(X18,X3)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_periodic__finite__ex) ).

fof(fact_listrel__Nil1,axiom,
    ! [X171,X239,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olist_ONil(X5)),X239)),c_List_Olistrel(X5,X171)))
     => X239 = c_List_Olist_ONil(X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__Nil1) ).

fof(fact_the__elem__def,axiom,
    ! [X194,X5] : c_Set_Othe__elem(X5,X194) = c_HOL_OThe(X5,hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool,X5),hAPP(c_fequal,X194)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Set_Oinsert(X5)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__elem__def) ).

fof(fact_transfer__int__nat__set__relations_I5_J,axiom,
    ! [X113,X21] :
      ( c_Nat__Transfer_Onat__set(X21)
     => ( c_Nat__Transfer_Onat__set(X113)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X21),X113))
        <=> 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),X21)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X113))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__set__relations_I5_J) ).

fof(fact_transfer__int__nat__set__relations_I4_J,axiom,
    ! [X113,X21] :
      ( c_Nat__Transfer_Onat__set(X21)
     => ( c_Nat__Transfer_Onat__set(X113)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X21),X113))
        <=> 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),X21)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X113))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__set__relations_I4_J) ).

fof(fact_union__comp__emptyL,axiom,
    ! [X113,X112,X21,X5] :
      ( hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),X21),X112) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X5),tc_HOL_Obool))
     => ( hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),X113),X112) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X5),tc_HOL_Obool))
       => hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X21),X113)),X112) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_union__comp__emptyL) ).

fof(fact_int__def,axiom,
    ! [X95] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X95) = 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),X95),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/sandbox/benchmark/theBenchmark.p',fact_int__def) ).

fof(fact_distrib__sup__le,axiom,
    ! [X94,X65,X66,X58] :
      ( class_Lattices_Olattice(X58)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X66),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X65),X94))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X66),X65)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X66),X94)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distrib__sup__le) ).

fof(fact_min__max_Odistrib__sup__le,axiom,
    ! [X94,X65,X66,X58] :
      ( class_Orderings_Olinorder(X58)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Orderings_Oord__class_Omax(X58),X66),hAPP(hAPP(c_Orderings_Oord__class_Omin(X58),X65),X94))),hAPP(hAPP(c_Orderings_Oord__class_Omin(X58),hAPP(hAPP(c_Orderings_Oord__class_Omax(X58),X66),X65)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X58),X66),X94)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Odistrib__sup__le) ).

fof(fact_fold__inf__le__inf,axiom,
    ! [X24,X6,X21,X5] :
      ( class_Lattices_Osemilattice__inf(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X21))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Lattices_Osemilattice__inf__class_Oinf(X5)),X24),X21)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X6),X24))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__inf__le__inf) ).

fof(fact_min__max_Ofold__inf__le__inf,axiom,
    ! [X24,X6,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X21))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omin(X5)),X24),X21)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X6),X24))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ofold__inf__le__inf) ).

fof(fact_set__update__subsetI,axiom,
    ! [X82,X25,X21,X239,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),X239)),X21))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Olist__update(X5,X239),X82),X25))),X21)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__update__subsetI) ).

fof(fact_setsum__ub__add__nat,axiom,
    ! [X160,X2,X50,X95,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X50),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X95,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X50),X160))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X95,X50))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X50),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X50),X160)))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__ub__add__nat) ).

fof(fact_trans__O__subset,axiom,
    ! [X171,X5] :
      ( c_Relation_Otrans(X5,X171)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),X171),X171)),X171)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__O__subset) ).

fof(fact_Times__Int__distrib1,axiom,
    ! [X112,X113,X21,X20,X5] : hAPP(hAPP(c_Product__Type_OSigma(X5,X20),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113)),hAPP(c_COMBK(tc_fun(X20,tc_HOL_Obool),X5),X112)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X5,X20),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X5,X20),X21),hAPP(c_COMBK(tc_fun(X20,tc_HOL_Obool),X5),X112))),hAPP(hAPP(c_Product__Type_OSigma(X5,X20),X113),hAPP(c_COMBK(tc_fun(X20,tc_HOL_Obool),X5),X112))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Times__Int__distrib1) ).

fof(fact_Times__Un__distrib1,axiom,
    ! [X112,X113,X21,X20,X5] : hAPP(hAPP(c_Product__Type_OSigma(X5,X20),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113)),hAPP(c_COMBK(tc_fun(X20,tc_HOL_Obool),X5),X112)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X20),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X5,X20),X21),hAPP(c_COMBK(tc_fun(X20,tc_HOL_Obool),X5),X112))),hAPP(hAPP(c_Product__Type_OSigma(X5,X20),X113),hAPP(c_COMBK(tc_fun(X20,tc_HOL_Obool),X5),X112))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Times__Un__distrib1) ).

fof(fact_Times__Diff__distrib1,axiom,
    ! [X112,X113,X21,X20,X5] : hAPP(hAPP(c_Product__Type_OSigma(X5,X20),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),X113)),hAPP(c_COMBK(tc_fun(X20,tc_HOL_Obool),X5),X112)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X5,X20),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X5,X20),X21),hAPP(c_COMBK(tc_fun(X20,tc_HOL_Obool),X5),X112))),hAPP(hAPP(c_Product__Type_OSigma(X5,X20),X113),hAPP(c_COMBK(tc_fun(X20,tc_HOL_Obool),X5),X112))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Times__Diff__distrib1) ).

fof(fact_card__inj__on__le,axiom,
    ! [X113,X21,X2,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,X2,X21)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X20,X2),X21)),X113))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X20),X113))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X21)),hAPP(c_Finite__Set_Ocard(X20),X113))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__inj__on__le) ).

fof(fact_fold__image__1,axiom,
    ! [X2,X192,X5,X20] :
      ( class_Groups_Ocomm__monoid__mult(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X192))
       => ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),X192))
             => hAPP(X2,X3) = c_Groups_Oone__class_Oone(X20) )
         => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X20,X5,c_Groups_Otimes__class_Otimes(X20)),X2),c_Groups_Oone__class_Oone(X20)),X192) = c_Groups_Oone__class_Oone(X20) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__image__1) ).

fof(fact_list__ball__nth,axiom,
    ! [X18,X239,X5,X50] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X50),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239)))
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X239)))
           => hBOOL(hAPP(X18,X3)) )
       => hBOOL(hAPP(X18,hAPP(hAPP(c_List_Onth(X5),X239),X50))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__ball__nth) ).

fof(fact_listrel__Nil2,axiom,
    ! [X171,X239,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X239),c_List_Olist_ONil(X5))),c_List_Olistrel(X5,X171)))
     => X239 = c_List_Olist_ONil(X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__Nil2) ).

fof(fact_INF__commute,axiom,
    ! [X2,X113,X116,X21,X20,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X20,X5),X21),hAPP(hAPP(c_COMBB(tc_fun(X116,X5),X5,X20),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X116,X5),X113)),X2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X116,X5),X113),hAPP(hAPP(c_COMBB(tc_fun(X20,X5),X5,X116),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X20,X5),X21)),hAPP(c_COMBC(X20,X116,X5),X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF__commute) ).

fof(fact_SUP__commute,axiom,
    ! [X2,X113,X116,X21,X20,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,X5),X21),hAPP(hAPP(c_COMBB(tc_fun(X116,X5),X5,X20),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X116,X5),X113)),X2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X116,X5),X113),hAPP(hAPP(c_COMBB(tc_fun(X20,X5),X5,X116),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,X5),X21)),hAPP(c_COMBC(X20,X116,X5),X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUP__commute) ).

fof(fact_eq__equiv__class__iff,axiom,
    ! [X33,X25,X171,X21,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X21,X171)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X33),X21))
         => ( hAPP(c_Relation_OImage(X5,X5,X171),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(X5,X5,X171),hAPP(hAPP(c_Set_Oinsert(X5),X33),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))
          <=> hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X33)),X171)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__equiv__class__iff) ).

fof(fact_transfer__int__nat__sum__prod2_I1_J,axiom,
    ! [X2,X21,X5] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),X21))
         => c_Nat__Transfer_Ois__nat(hAPP(X2,X3)) )
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Int_Oint),X2),X21) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X5),c_Int_Onat),X2)),X21)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__sum__prod2_I1_J) ).

fof(fact_transfer__int__nat__sum__prod2_I2_J,axiom,
    ! [X2,X21,X5] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),X21))
         => c_Nat__Transfer_Ois__nat(hAPP(X2,X3)) )
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,tc_Int_Oint),X2),X21) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X5),c_Int_Onat),X2)),X21)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__sum__prod2_I2_J) ).

fof(fact_listrel__eq__len,axiom,
    ! [X171,X251,X239,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X239),X251)),c_List_Olistrel(X5,X171)))
     => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X251) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__eq__len) ).

fof(fact_listrel1__eq__len,axiom,
    ! [X171,X251,X239,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X239),X251)),c_List_Olistrel1(X5,X171)))
     => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X251) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel1__eq__len) ).

fof(fact_symD,axiom,
    ! [X24,X6,X171,X5] :
      ( c_Relation_Osym(X5,X171)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X24)),X171))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X24),X6)),X171)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_symD) ).

fof(fact_sym__def,axiom,
    ! [X171,X5] :
      ( c_Relation_Osym(X5,X171)
    <=> ! [X3,X177] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X177)),X171))
         => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X177),X3)),X171)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sym__def) ).

fof(fact_filter__equals__takeWhile__sorted__rev,axiom,
    ! [X15,X239,X2,X20,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( c_List_Olinorder__class_Osorted(X5,hAPP(c_List_Orev(X5),hAPP(hAPP(c_List_Omap(X20,X5),X2),X239)))
       => hAPP(c_List_Ofilter(X20,hAPP(hAPP(c_COMBB(X5,tc_HOL_Obool,X20),hAPP(c_Orderings_Oord__class_Oless(X5),X15)),X2)),X239) = c_List_OtakeWhile(X20,hAPP(hAPP(c_COMBB(X5,tc_HOL_Obool,X20),hAPP(c_Orderings_Oord__class_Oless(X5),X15)),X2),X239) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter__equals__takeWhile__sorted__rev) ).

fof(fact_Sigma__Union,axiom,
    ! [X113,X194,X20,X5] : hAPP(hAPP(c_Product__Type_OSigma(X5,X20),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X194)),X113) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_prod(X5,X20),tc_HOL_Obool)),X194),hAPP(hAPP(c_COMBC(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_fun(X20,tc_HOL_Obool)),tc_fun(tc_prod(X5,X20),tc_HOL_Obool)),c_Product__Type_OSigma(X5,X20)),X113)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__Union) ).

fof(fact_bset_I4_J,axiom,
    ! [X113,X15,X144] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X144))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X15),X113))
       => ! [X3] :
            ( ! [X204] :
                ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X204),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X144)))
               => ! [X228] :
                    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X228),X113))
                   => X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X228),X204) ) )
           => ( X3 != X15
             => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),X144) != X15 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bset_I4_J) ).

fof(fact_aset_I4_J,axiom,
    ! [X21,X15,X144] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X144))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X15),X21))
       => ! [X3] :
            ( ! [X204] :
                ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X204),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X144)))
               => ! [X228] :
                    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X228),X21))
                   => X3 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X228),X204) ) )
           => ( X3 != X15
             => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X144) != X15 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_aset_I4_J) ).

fof(fact_fold__def,axiom,
    ! [X21,X120,X2,X5,X20] : hAPP(hAPP(c_Finite__Set_Ofold(X20,X5,X2),X120),X21) = c_HOL_OThe(X5,c_Finite__Set_Ofold__graph(X20,X5,X2,X120,X21)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__def) ).

fof(fact_split__paired__All,axiom,
    ! [X20,X5,X18] :
      ( ! [X138] : hBOOL(hAPP(X18,X138))
    <=> ! [X187,X188] : hBOOL(hAPP(X18,hAPP(hAPP(c_Product__Type_OPair(X5,X20),X187),X188))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__paired__All) ).

fof(fact_curryI,axiom,
    ! [X24,X6,X20,X5,X2] :
      ( hBOOL(hAPP(X2,hAPP(hAPP(c_Product__Type_OPair(X5,X20),X6),X24)))
     => hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(X5,X20,tc_HOL_Obool,X2),X6),X24)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_curryI) ).

fof(fact_diff__card__le__card__Diff,axiom,
    ! [X21,X113,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X113))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X21)),hAPP(c_Finite__Set_Ocard(X5),X113))),hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),X113)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__card__le__card__Diff) ).

fof(fact_inj__on__Inter,axiom,
    ! [X2,X20,X5,X192] :
      ( X192 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool))
     => ( ! [X226] :
            ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X226),X192))
           => c_Fun_Oinj__on(X5,X20,X2,X226) )
       => c_Fun_Oinj__on(X5,X20,X2,c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),X192)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__Inter) ).

fof(fact_Bex__set__replicate,axiom,
    ! [X18,X6,X50,X5] :
      ( ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),c_List_Oreplicate(X5,X50,X6))))
          & hBOOL(hAPP(X18,X3)) )
    <=> ( hBOOL(hAPP(X18,X6))
        & X50 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_card__UNIV__bool) ).

fof(fact_Nitpick_Orefl_H__def,axiom,
    ! [X171,X5] :
      ( c_Nitpick_Orefl_H(X5,X171)
    <=> ! [X3] : hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X3)),X171)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Orefl_H__def) ).

fof(fact_decr__mult__lemma,axiom,
    ! [X87,X18,X22] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22))
     => ( ! [X3] :
            ( hBOOL(hAPP(X18,X3))
           => hBOOL(hAPP(X18,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),X22))) )
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X87))
         => ! [X3] :
              ( hBOOL(hAPP(X18,X3))
             => hBOOL(hAPP(X18,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X87),X22)))) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_decr__mult__lemma) ).

fof(fact_incr__mult__lemma,axiom,
    ! [X87,X18,X22] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22))
     => ( ! [X3] :
            ( hBOOL(hAPP(X18,X3))
           => hBOOL(hAPP(X18,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X22))) )
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X87))
         => ! [X3] :
              ( hBOOL(hAPP(X18,X3))
             => hBOOL(hAPP(X18,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X87),X22)))) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_incr__mult__lemma) ).

fof(fact_measures__less,axiom,
    ! [X290,X5,X33,X25,X2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X2,X25)),hAPP(X2,X33)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X33)),c_List_Omeasures(X5,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X5,tc_Nat_Onat)),X2),X290)))) ),
    file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_nat__1__add__1) ).

fof(fact_folding__idem_Oidem__left__comp,axiom,
    ! [X1,X25,X116,X205,X2,X20,X5] :
      ( c_Finite__Set_Ofolding__idem(X5,X20,X2,X205)
     => hAPP(c_Fun_Ocomp(X20,X20,X116,hAPP(X2,X25)),hAPP(c_Fun_Ocomp(X20,X20,X116,hAPP(X2,X25)),X1)) = hAPP(c_Fun_Ocomp(X20,X20,X116,hAPP(X2,X25)),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__idem_Oidem__left__comp) ).

fof(fact_mem__splitI,axiom,
    ! [X116,X20,X24,X6,X23,X120,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X120),hAPP(hAPP(X23,X6),X24)))
     => hBOOL(hAPP(hAPP(c_member(X5),X120),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X20,X116,tc_fun(X5,tc_HOL_Obool)),X23),hAPP(hAPP(c_Product__Type_OPair(X20,X116),X6),X24)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__splitI) ).

fof(fact_Ball__set__replicate,axiom,
    ! [X18,X6,X50,X5] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),c_List_Oreplicate(X5,X50,X6))))
         => hBOOL(hAPP(X18,X3)) )
    <=> ( hBOOL(hAPP(X18,X6))
        | X50 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ball__set__replicate) ).

fof(fact_listrel__Cons,axiom,
    ! [X239,X25,X171,X5] : hAPP(c_Relation_OImage(tc_List_Olist(X5),tc_List_Olist(X5),c_List_Olistrel(X5,X171)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X5)),hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X5),tc_HOL_Obool)))) = c_List_Oset__Cons(X5,hAPP(c_Relation_OImage(X5,X5,X171),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(X5),tc_List_Olist(X5),c_List_Olistrel(X5,X171)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X5)),X239),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X5),tc_HOL_Obool))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__Cons) ).

fof(fact_UN__le__add__shift,axiom,
    ! [X87,X210,X50,X5] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X50)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X5,tc_HOL_Obool),tc_Nat_Onat),X210),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X87))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X87,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X50),X87))),X210),
    file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_semiring__norm_I115_J) ).

fof(fact_lexord__append__rightI,axiom,
    ! [X171,X25,X5,X33] :
      ( ? [X188,X154] : X33 = hAPP(hAPP(c_List_Olist_OCons(X5),X188),X154)
     => 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)),X25),hAPP(hAPP(c_List_Oappend(X5),X25),X33))),c_List_Olexord(X5,X171))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexord__append__rightI) ).

fof(fact_list__eq__iff__zip__eq,axiom,
    ! [X5,X251,X239] :
      ( X239 = X251
    <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X251)
        & ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X3),hAPP(c_List_Oset(tc_prod(X5,X5)),hAPP(hAPP(c_List_Ozip(X5,X5),X239),X251))))
           => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5,X5,tc_HOL_Obool),c_fequal),X3)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__eq__iff__zip__eq) ).

fof(fact_nat__gcd_Opinduct,axiom,
    ! [X18,X27,X191] :
      ( 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),X191),X27)))
     => ( ! [X3,X177] :
            ( 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),X177)))
           => ( ( X177 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
               => hBOOL(hAPP(hAPP(X18,X177),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,X177))) )
             => hBOOL(hAPP(hAPP(X18,X3),X177)) ) )
       => hBOOL(hAPP(hAPP(X18,X191),X27)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__gcd_Opinduct) ).

fof(fact_inj__on__strict__subset,axiom,
    ! [X21,X113,X2,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,X2,X113)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X21),X113))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X20,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X20,X2),X21)),hAPP(c_Set_Oimage(X5,X20,X2),X113))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__strict__subset) ).

fof(fact_evalc_Oequations_I4_J,axiom,
    ! [X59,X26,X60,X27] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(X27,X60)),X26),X59))
    <=> ? [X61] :
          ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X27),X26),X61))
          & hBOOL(hAPP(hAPP(c_Natural_Oevalc(X60),X61),X59)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_Oequations_I4_J) ).

fof(fact_inj__on__image__Int,axiom,
    ! [X113,X21,X112,X2,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,X2,X112)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),X112))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X113),X112))
         => hAPP(c_Set_Oimage(X5,X20,X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X20,X2),X21)),hAPP(c_Set_Oimage(X5,X20,X2),X113)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__image__Int) ).

fof(fact_inj__on__image__set__diff,axiom,
    ! [X113,X21,X112,X2,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,X2,X112)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),X112))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X113),X112))
         => hAPP(c_Set_Oimage(X5,X20,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X20,X2),X21)),hAPP(c_Set_Oimage(X5,X20,X2),X113)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__image__set__diff) ).

fof(fact_filter__in__sublist,axiom,
    ! [X76,X239,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),X239))
     => hAPP(c_List_Ofilter(X5,hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),hAPP(c_List_Oset(X5),c_List_Osublist(X5,X239,X76)))),X239) = c_List_Osublist(X5,X239,X76) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter__in__sublist) ).

fof(fact_surj__iff__all,axiom,
    ! [X2,X5,X20] :
      ( hAPP(c_Set_Oimage(X20,X5,X2),c_Orderings_Otop__class_Otop(tc_fun(X20,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))
    <=> ! [X3] : hAPP(X2,hAPP(c_Hilbert__Choice_Oinv__into(X20,X5,c_Orderings_Otop__class_Otop(tc_fun(X20,tc_HOL_Obool)),X2),X3)) = X3 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surj__iff__all) ).

fof(fact_list__ex1__iff__raw,axiom,
    ! [X239,X18,X5] :
      ( c_List_Olist__ex1(X5,X18,X239)
    <=> ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X239)))
          & hBOOL(hAPP(X18,X3))
          & ! [X177] :
              ( ( hBOOL(hAPP(hAPP(c_member(X5),X177),hAPP(c_List_Oset(X5),X239)))
                & hBOOL(hAPP(X18,X177)) )
             => X177 = X3 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__ex1__iff__raw) ).

fof(fact_list__ex1__iff,axiom,
    ! [X239,X18,X5] :
      ( c_List_Olist__ex1(X5,X18,X239)
    <=> ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X239)))
          & hBOOL(hAPP(X18,X3))
          & ! [X177] :
              ( ( hBOOL(hAPP(hAPP(c_member(X5),X177),hAPP(c_List_Oset(X5),X239)))
                & hBOOL(hAPP(X18,X177)) )
             => X177 = X3 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__ex1__iff) ).

fof(fact_endo__inj__surj,axiom,
    ! [X2,X21,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X5,X2),X21)),X21))
       => ( c_Fun_Oinj__on(X5,X5,X2,X21)
         => hAPP(c_Set_Oimage(X5,X5,X2),X21) = X21 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_endo__inj__surj) ).

fof(fact_insort__insert__key__triv,axiom,
    ! [X239,X20,X25,X2,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_member(X5),hAPP(X2,X25)),hAPP(c_Set_Oimage(X20,X5,X2),hAPP(c_List_Oset(X20),X239))))
       => c_List_Olinorder__class_Oinsort__insert__key(X20,X5,X2,X25,X239) = X239 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insort__insert__key__triv) ).

fof(fact_set__insort__insert,axiom,
    ! [X239,X25,X5] :
      ( class_Orderings_Olinorder(X5)
     => hAPP(c_List_Oset(X5),c_List_Olinorder__class_Oinsort__insert__key(X5,X5,c_COMBI(X5),X25,X239)) = hAPP(hAPP(c_Set_Oinsert(X5),X25),hAPP(c_List_Oset(X5),X239)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__insort__insert) ).

fof(fact_listrel1__subset__listrel,axiom,
    ! [X203,X171,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X171),X203))
     => ( c_Relation_Orefl__on(X5,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X203)
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_HOL_Obool)),c_List_Olistrel1(X5,X171)),c_List_Olistrel(X5,X203))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel1__subset__listrel) ).

fof(fact_folding__image_Oeq__fold,axiom,
    ! [X1,X21,X205,X120,X2,X20,X5] :
      ( c_Finite__Set_Ofolding__image(X5,X20,X2,X120,X205)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X20),X21))
       => hAPP(hAPP(X205,X1),X21) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X5,X20,X2),X1),X120),X21) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image_Oeq__fold) ).

fof(fact_fun__left__comm_Ofold__rec,axiom,
    ! [X120,X25,X21,X2,X20,X5] :
      ( c_Finite__Set_Ofun__left__comm(X5,X20,X2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => hAPP(hAPP(c_Finite__Set_Ofold(X5,X20,X2),X120),X21) = hAPP(hAPP(X2,X25),hAPP(hAPP(c_Finite__Set_Ofold(X5,X20,X2),X120),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__rec) ).

fof(fact_hoare__valids__def,axiom,
    ! [X13,X4,X5] :
      ( c_Hoare__Mirabelle_Ohoare__valids(X5,X4,X13)
    <=> ! [X69] :
          ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X5)),X3),X4))
             => c_Hoare__Mirabelle_Otriple__valid(X5,X69,X3) )
         => ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X5)),X3),X13))
             => c_Hoare__Mirabelle_Otriple__valid(X5,X69,X3) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hoare__valids__def) ).

fof(fact_vimage__compose,axiom,
    ! [X25,X2,X1,X116,X20,X5] : hAPP(c_Set_Ovimage(X5,X20,hAPP(c_Fun_Ocomp(X116,X20,X5,X1),X2)),X25) = hAPP(c_Set_Ovimage(X5,X116,X2),hAPP(c_Set_Ovimage(X116,X20,X1),X25)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__compose) ).

fof(fact_image__compose,axiom,
    ! [X171,X1,X2,X116,X5,X20] : hAPP(c_Set_Oimage(X20,X5,hAPP(c_Fun_Ocomp(X116,X5,X20,X2),X1)),X171) = hAPP(c_Set_Oimage(X116,X5,X2),hAPP(c_Set_Oimage(X20,X116,X1),X171)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__compose) ).

fof(fact_rtrancl__power,axiom,
    ! [X32,X160,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X160),c_Transitive__Closure_Ortrancl(X5,X32)))
    <=> ? [X69] : hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X160),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X69),X32))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__power) ).

fof(fact_scomp__unfold,axiom,
    ! [X25,X1,X2,X5,X115,X116,X20] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(X20,X116,X115,X5),X2),X1),X25) = hAPP(hAPP(X1,hAPP(c_Product__Type_Ofst(X116,X115),hAPP(X2,X25))),hAPP(c_Product__Type_Osnd(X116,X115),hAPP(X2,X25))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_scomp__unfold) ).

fof(fact_equiv__class__eq__iff,axiom,
    ! [X33,X25,X171,X21,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X21,X171)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X33)),X171))
      <=> ( hAPP(c_Relation_OImage(X5,X5,X171),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(X5,X5,X171),hAPP(hAPP(c_Set_Oinsert(X5),X33),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))
          & hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
          & hBOOL(hAPP(hAPP(c_member(X5),X33),X21)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equiv__class__eq__iff) ).

fof(fact_sum__squares__gt__zero__iff,axiom,
    ! [X33,X25,X5] :
      ( class_Rings_Olinordered__ring__strict(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X25),X25)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X33),X33))))
      <=> ( X25 != c_Groups_Ozero__class_Ozero(X5)
          | X33 != c_Groups_Ozero__class_Ozero(X5) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__squares__gt__zero__iff) ).

fof(fact_rtrancl__is__UN__rel__pow,axiom,
    ! [X32,X5] : c_Transitive__Closure_Ortrancl(X5,X32) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool)),X32)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__is__UN__rel__pow) ).

fof(fact_takeWhile__append2,axiom,
    ! [X251,X18,X239,X5] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X239)))
         => hBOOL(hAPP(X18,X3)) )
     => c_List_OtakeWhile(X5,X18,hAPP(hAPP(c_List_Oappend(X5),X239),X251)) = hAPP(hAPP(c_List_Oappend(X5),X239),c_List_OtakeWhile(X5,X18,X251)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_takeWhile__append2) ).

fof(fact_inj__on__imageI,axiom,
    ! [X21,X2,X1,X116,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,hAPP(c_Fun_Ocomp(X116,X20,X5,X1),X2),X21)
     => c_Fun_Oinj__on(X116,X20,X1,hAPP(c_Set_Oimage(X5,X116,X2),X21)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__imageI) ).

fof(fact_setsum__eq__Suc0__iff,axiom,
    ! [X2,X21,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
     => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),X2),X21) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      <=> ? [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X21))
            & hAPP(X2,X3) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
            & ! [X204] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X204),X21))
               => ( X3 != X204
                 => hAPP(X2,X204) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__eq__Suc0__iff) ).

fof(fact_sorted__insort__insert,axiom,
    ! [X25,X239,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( c_List_Olinorder__class_Osorted(X5,X239)
       => c_List_Olinorder__class_Osorted(X5,c_List_Olinorder__class_Oinsort__insert__key(X5,X5,c_COMBI(X5),X25,X239)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__insort__insert) ).

fof(fact_abs__mult__less,axiom,
    ! [X91,X90,X56,X62,X58] :
      ( class_Rings_Olinordered__idom(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(c_Groups_Oabs__class_Oabs(X58),X62)),X56))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(c_Groups_Oabs__class_Oabs(X58),X90)),X91))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),hAPP(c_Groups_Oabs__class_Oabs(X58),X62)),hAPP(c_Groups_Oabs__class_Oabs(X58),X90))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X56),X91))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__mult__less) ).

fof(fact_fun__left__comm_Ofold__insert__remove,axiom,
    ! [X25,X120,X21,X2,X20,X5] :
      ( c_Finite__Set_Ofun__left__comm(X5,X20,X2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => hAPP(hAPP(c_Finite__Set_Ofold(X5,X20,X2),X120),hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(hAPP(X2,X25),hAPP(hAPP(c_Finite__Set_Ofold(X5,X20,X2),X120),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__insert__remove) ).

fof(fact_takeWhile__map,axiom,
    ! [X239,X2,X20,X18,X5] : c_List_OtakeWhile(X5,X18,hAPP(hAPP(c_List_Omap(X20,X5),X2),X239)) = hAPP(hAPP(c_List_Omap(X20,X5),X2),c_List_OtakeWhile(X20,hAPP(c_Fun_Ocomp(X5,tc_HOL_Obool,X20,X18),X2),X239)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_takeWhile__map) ).

fof(fact_fun__upd__def,axiom,
    ! [X24,X2,X20,X5,X6,X25] :
      ( ( X25 = X6
       => hAPP(c_Fun_Ofun__upd(X5,X20,X2,X6,X24),X25) = X24 )
      & ( X25 != X6
       => hAPP(c_Fun_Ofun__upd(X5,X20,X2,X6,X24),X25) = hAPP(X2,X25) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__def) ).

fof(fact_fun__upd__other,axiom,
    ! [X33,X2,X20,X5,X25,X120] :
      ( X120 != X25
     => hAPP(c_Fun_Ofun__upd(X5,X20,X2,X25,X33),X120) = hAPP(X2,X120) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__other) ).

fof(fact_fun__upd__apply,axiom,
    ! [X33,X2,X20,X5,X25,X120] :
      ( ( X120 = X25
       => hAPP(c_Fun_Ofun__upd(X5,X20,X2,X25,X33),X120) = X33 )
      & ( X120 != X25
       => hAPP(c_Fun_Ofun__upd(X5,X20,X2,X25,X33),X120) = hAPP(X2,X120) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__apply) ).

fof(fact_setsum__eq__1__iff,axiom,
    ! [X2,X21,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
     => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),X2),X21) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
      <=> ? [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X21))
            & hAPP(X2,X3) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
            & ! [X204] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X204),X21))
               => ( X3 != X204
                 => hAPP(X2,X204) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__eq__1__iff) ).

fof(fact_refl__on__comp__subset,axiom,
    ! [X171,X21,X5] :
      ( c_Relation_Orefl__on(X5,X21,X171)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X171),hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),hAPP(c_Relation_Oconverse(X5,X5),X171)),X171))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__on__comp__subset) ).

fof(fact_fun__upd__same,axiom,
    ! [X33,X25,X2,X5,X20] : hAPP(c_Fun_Ofun__upd(X20,X5,X2,X25,X33),X25) = X33,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__same) ).

fof(fact_comp__inj__on,axiom,
    ! [X1,X116,X21,X2,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,X2,X21)
     => ( c_Fun_Oinj__on(X20,X116,X1,hAPP(c_Set_Oimage(X5,X20,X2),X21))
       => c_Fun_Oinj__on(X5,X116,hAPP(c_Fun_Ocomp(X20,X116,X5,X1),X2),X21) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comp__inj__on) ).

fof(fact_product_Osimps_I2_J,axiom,
    ! [X251,X239,X25,X20,X5] : c_Enum_Oproduct(X5,X20,hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239),X251) = hAPP(hAPP(c_List_Oappend(tc_prod(X5,X20)),hAPP(hAPP(c_List_Omap(X20,tc_prod(X5,X20)),hAPP(c_Product__Type_OPair(X5,X20),X25)),X251)),c_Enum_Oproduct(X5,X20,X239,X251)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_product_Osimps_I2_J) ).

fof(fact_elem__le__sum,axiom,
    ! [X272,X50] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X50),hAPP(c_List_Oset(tc_Nat_Onat),X272)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X50),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)),X272))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_elem__le__sum) ).

fof(fact_rev__ImageI,axiom,
    ! [X171,X24,X20,X21,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),X21))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X20)),hAPP(hAPP(c_Product__Type_OPair(X5,X20),X6),X24)),X171))
       => hBOOL(hAPP(hAPP(c_member(X20),X24),hAPP(c_Relation_OImage(X5,X20,X171),X21))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__ImageI) ).

fof(fact_map__map,axiom,
    ! [X239,X1,X116,X2,X5,X20] : hAPP(hAPP(c_List_Omap(X20,X5),X2),hAPP(hAPP(c_List_Omap(X116,X20),X1),X239)) = hAPP(hAPP(c_List_Omap(X116,X5),hAPP(c_Fun_Ocomp(X20,X5,X116,X2),X1)),X239),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__map) ).

fof(fact_List_Omap_Ocompositionality,axiom,
    ! [X254,X1,X116,X2,X5,X20] : hAPP(hAPP(c_List_Omap(X20,X5),X2),hAPP(hAPP(c_List_Omap(X116,X20),X1),X254)) = hAPP(hAPP(c_List_Omap(X116,X5),hAPP(c_Fun_Ocomp(X20,X5,X116,X2),X1)),X254),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_List_Omap_Ocompositionality) ).

fof(fact_take__Cons,axiom,
    ! [X239,X25,X50,X5] : hAPP(hAPP(c_List_Otake(X5),X50),hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239)) = c_Nat_Onat_Onat__case(tc_List_Olist(X5),c_List_Olist_ONil(X5),hAPP(hAPP(c_COMBB(tc_List_Olist(X5),tc_List_Olist(X5),tc_Nat_Onat),hAPP(c_List_Olist_OCons(X5),X25)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Otake(X5)),X239)),X50),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__Cons) ).

fof(fact_Un__Image,axiom,
    ! [X21,X192,X32,X5,X20] : hAPP(c_Relation_OImage(X20,X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X20,X5),tc_HOL_Obool)),X32),X192)),X21) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_OImage(X20,X5,X32),X21)),hAPP(c_Relation_OImage(X20,X5,X192),X21)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Image) ).

fof(fact_iterate_Osimps,axiom,
    ! [X25,X2,X5,X20,X87] :
      ( ( X87 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => hAPP(c_Random_Oiterate(X20,X5,X87,X2),X25) = hAPP(c_Product__Type_OPair(X20,X5),X25) )
      & ( X87 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => hAPP(c_Random_Oiterate(X20,X5,X87,X2),X25) = hAPP(hAPP(c_Product__Type_Oscomp(X5,X20,X5,tc_prod(X20,X5)),hAPP(X2,X25)),c_Random_Oiterate(X20,X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X87),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_iterate_Osimps) ).

fof(fact_equiv__class__eq,axiom,
    ! [X24,X6,X171,X21,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X21,X171)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X24)),X171))
       => hAPP(c_Relation_OImage(X5,X5,X171),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(X5,X5,X171),hAPP(hAPP(c_Set_Oinsert(X5),X24),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equiv__class__eq) ).

fof(fact_mem__Sigma__iff,axiom,
    ! [X113,X21,X24,X6,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X20)),hAPP(hAPP(c_Product__Type_OPair(X5,X20),X6),X24)),hAPP(hAPP(c_Product__Type_OSigma(X5,X20),X21),X113)))
    <=> ( hBOOL(hAPP(hAPP(c_member(X5),X6),X21))
        & hBOOL(hAPP(hAPP(c_member(X20),X24),hAPP(X113,X6))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__Sigma__iff) ).

fof(fact_SigmaD2,axiom,
    ! [X113,X21,X24,X6,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X20)),hAPP(hAPP(c_Product__Type_OPair(X5,X20),X6),X24)),hAPP(hAPP(c_Product__Type_OSigma(X5,X20),X21),X113)))
     => hBOOL(hAPP(hAPP(c_member(X20),X24),hAPP(X113,X6))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SigmaD2) ).

fof(fact_listrel__mono,axiom,
    ! [X76,X171,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X171),X76))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_HOL_Obool)),c_List_Olistrel(X5,X171)),c_List_Olistrel(X5,X76))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__mono) ).

fof(fact_listrel1__mono,axiom,
    ! [X76,X171,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X171),X76))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_HOL_Obool)),c_List_Olistrel1(X5,X171)),c_List_Olistrel1(X5,X76))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel1__mono) ).

fof(fact_bij__is__inj,axiom,
    ! [X2,X20,X5] :
      ( c_Fun_Obij__betw(X5,X20,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X20,tc_HOL_Obool)))
     => c_Fun_Oinj__on(X5,X20,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__is__inj) ).

fof(fact_scomp__def,axiom,
    ! [X25,X1,X2,X5,X115,X116,X20] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(X20,X116,X115,X5),X2),X1),X25) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X116,X115,X5),X1),hAPP(X2,X25)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_scomp__def) ).

fof(fact_scomp__apply,axiom,
    ! [X25,X1,X2,X5,X115,X116,X20] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(X20,X116,X115,X5),X2),X1),X25) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X116,X115,X5),X1),hAPP(X2,X25)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_scomp__apply) ).

fof(fact_Un__least,axiom,
    ! [X113,X112,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),X112))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X113),X112))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113)),X112)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__least) ).

fof(fact_folding__one_Ounion__inter,axiom,
    ! [X113,X21,X205,X2,X5] :
      ( c_Finite__Set_Ofolding__one(X5,X2,X205)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X113))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(hAPP(X2,hAPP(X205,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113))),hAPP(X205,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113))) = hAPP(hAPP(X2,hAPP(X205,X21)),hAPP(X205,X113)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one_Ounion__inter) ).

fof(fact_f__the__inv__into__f,axiom,
    ! [X33,X21,X2,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,X2,X21)
     => ( hBOOL(hAPP(hAPP(c_member(X20),X33),hAPP(c_Set_Oimage(X5,X20,X2),X21)))
       => hAPP(X2,hAPP(c_Fun_Othe__inv__into(X5,X20,X21,X2),X33)) = X33 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_f__the__inv__into__f) ).

fof(fact_INT__extend__simps_I8_J,axiom,
    ! [X113,X21,X5,X20] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X20,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_COMBC(tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X20,tc_fun(X5,tc_HOL_Obool))),X113)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X20,tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X20,tc_HOL_Obool),X21)),X113),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__extend__simps_I8_J) ).

fof(fact_UN__extend__simps_I8_J,axiom,
    ! [X113,X21,X5,X20] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X20,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_COMBC(tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,tc_fun(X5,tc_HOL_Obool))),X113)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X20,tc_HOL_Obool),X21)),X113),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__extend__simps_I8_J) ).

fof(fact_INT__simps_I8_J,axiom,
    ! [X113,X21,X5,X20] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X20,tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X20,tc_HOL_Obool),X21)),X113) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X20,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_COMBC(tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X20,tc_fun(X5,tc_HOL_Obool))),X113)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__simps_I8_J) ).

fof(fact_UN__simps_I8_J,axiom,
    ! [X113,X21,X5,X20] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X20,tc_HOL_Obool),X21)),X113) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X20,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_COMBC(tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_fun(X5,tc_HOL_Obool)),tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,tc_fun(X5,tc_HOL_Obool))),X113)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__simps_I8_J) ).

fof(fact_inj__on__def,axiom,
    ! [X21,X2,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,X2,X21)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),X21))
         => ! [X204] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X204),X21))
             => ( hAPP(X2,X3) = hAPP(X2,X204)
               => X3 = X204 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__def) ).

fof(fact_rtrancl__subset,axiom,
    ! [X192,X32,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X32),X192))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X192),c_Transitive__Closure_Ortrancl(X5,X32)))
       => c_Transitive__Closure_Ortrancl(X5,X192) = c_Transitive__Closure_Ortrancl(X5,X32) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__subset) ).

fof(fact_eq__equiv__class,axiom,
    ! [X21,X24,X6,X171,X5] :
      ( hAPP(c_Relation_OImage(X5,X5,X171),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(X5,X5,X171),hAPP(hAPP(c_Set_Oinsert(X5),X24),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))
     => ( c_Equiv__Relations_Oequiv(X5,X21,X171)
       => ( hBOOL(hAPP(hAPP(c_member(X5),X24),X21))
         => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X24)),X171)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__equiv__class) ).

fof(fact_SigmaD1,axiom,
    ! [X113,X21,X24,X6,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X20)),hAPP(hAPP(c_Product__Type_OPair(X5,X20),X6),X24)),hAPP(hAPP(c_Product__Type_OSigma(X5,X20),X21),X113)))
     => hBOOL(hAPP(hAPP(c_member(X5),X6),X21)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SigmaD1) ).

fof(fact_setprod__zero__iff,axiom,
    ! [X2,X21,X5,X20] :
      ( ( class_Rings_Ocomm__semiring__1(X20)
        & class_Rings_Ono__zero__divisors(X20) )
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X2),X21) = c_Groups_Ozero__class_Ozero(X20)
        <=> ? [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),X21))
              & hAPP(X2,X3) = c_Groups_Ozero__class_Ozero(X20) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__zero__iff) ).

fof(fact_card__image__le,axiom,
    ! [X2,X20,X21,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X20),hAPP(c_Set_Oimage(X5,X20,X2),X21))),hAPP(c_Finite__Set_Ocard(X5),X21))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__image__le) ).

fof(fact_INTER__UNIV__conv_I2_J,axiom,
    ! [X113,X21,X5,X20] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X20,tc_fun(X5,tc_HOL_Obool)),X21),X113) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X20),X3),X21))
         => hAPP(X113,X3) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INTER__UNIV__conv_I2_J) ).

fof(fact_UNION__empty__conv_I2_J,axiom,
    ! [X113,X21,X5,X20] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,tc_fun(X5,tc_HOL_Obool)),X21),X113) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X20),X3),X21))
         => hAPP(X113,X3) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNION__empty__conv_I2_J) ).

fof(fact_INTER__UNIV__conv_I1_J,axiom,
    ! [X113,X21,X20,X5] :
      ( c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X20,tc_fun(X5,tc_HOL_Obool)),X21),X113)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X20),X3),X21))
         => hAPP(X113,X3) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INTER__UNIV__conv_I1_J) ).

fof(fact_UNION__empty__conv_I1_J,axiom,
    ! [X113,X21,X20,X5] :
      ( c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,tc_fun(X5,tc_HOL_Obool)),X21),X113)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X20),X3),X21))
         => hAPP(X113,X3) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNION__empty__conv_I1_J) ).

fof(fact_setsum__SucD,axiom,
    ! [X50,X21,X2,X5] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),X2),X21) = hAPP(c_Nat_OSuc,X50)
     => ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),X21))
          & 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/sandbox/benchmark/theBenchmark.p',fact_setsum__SucD) ).

fof(fact_Inf__fin_Ounion__inter,axiom,
    ! [X113,X21,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X113))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),c_Big__Operators_Olattice__class_OInf__fin(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113))),c_Big__Operators_Olattice__class_OInf__fin(X5,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),c_Big__Operators_Olattice__class_OInf__fin(X5,X21)),c_Big__Operators_Olattice__class_OInf__fin(X5,X113)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_Ounion__inter) ).

fof(fact_Sup__fin_Ounion__inter,axiom,
    ! [X113,X21,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X113))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),c_Big__Operators_Olattice__class_OSup__fin(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113))),c_Big__Operators_Olattice__class_OSup__fin(X5,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),c_Big__Operators_Olattice__class_OSup__fin(X5,X21)),c_Big__Operators_Olattice__class_OSup__fin(X5,X113)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_Ounion__inter) ).

fof(fact_Max_Ounion__inter,axiom,
    ! [X113,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X113))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),c_Big__Operators_Olinorder__class_OMax(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113))),c_Big__Operators_Olinorder__class_OMax(X5,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),c_Big__Operators_Olinorder__class_OMax(X5,X21)),c_Big__Operators_Olinorder__class_OMax(X5,X113)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max_Ounion__inter) ).

fof(fact_Min_Ounion__inter,axiom,
    ! [X113,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X113))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),c_Big__Operators_Olinorder__class_OMin(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113))),c_Big__Operators_Olinorder__class_OMin(X5,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),c_Big__Operators_Olinorder__class_OMin(X5,X21)),c_Big__Operators_Olinorder__class_OMin(X5,X113)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min_Ounion__inter) ).

fof(fact_sorted_Osimps,axiom,
    ! [X6,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( c_List_Olinorder__class_Osorted(X5,X6)
      <=> ( X6 = c_List_Olist_ONil(X5)
          | ? [X263,X3] :
              ( X6 = hAPP(hAPP(c_List_Olist_OCons(X5),X3),X263)
              & ! [X204] :
                  ( hBOOL(hAPP(hAPP(c_member(X5),X204),hAPP(c_List_Oset(X5),X263)))
                 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X3),X204)) )
              & c_List_Olinorder__class_Osorted(X5,X263) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted_Osimps) ).

fof(fact_type__definition_OAbs__inject,axiom,
    ! [X33,X25,X21,X232,X233,X20,X5] :
      ( c_Typedef_Otype__definition(X5,X20,X233,X232,X21)
     => ( hBOOL(hAPP(hAPP(c_member(X20),X25),X21))
       => ( hBOOL(hAPP(hAPP(c_member(X20),X33),X21))
         => ( hAPP(X232,X25) = hAPP(X232,X33)
          <=> X25 = X33 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_type__definition_OAbs__inject) ).

fof(fact_acyclicP__converse,axiom,
    ! [X171,X5] :
      ( c_Wellfounded_Oacyclic(X5,hAPP(c_Set_OCollect(tc_prod(X5,X5)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X5,tc_HOL_Obool),c_Predicate_Oconversep(X5,X5,X171))))
    <=> c_Wellfounded_Oacyclic(X5,hAPP(c_Set_OCollect(tc_prod(X5,X5)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X5,tc_HOL_Obool),X171))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acyclicP__converse) ).

fof(fact_Field__insert,axiom,
    ! [X171,X24,X6,X5] : hAPP(c_Relation_OField(X5),hAPP(hAPP(c_Set_Oinsert(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X24)),X171)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X6),hAPP(hAPP(c_Set_Oinsert(X5),X24),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),hAPP(c_Relation_OField(X5),X171)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Field__insert) ).

fof(fact_start__le__sum,axiom,
    ! [X272,X50,X95] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X50))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X50),X272))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_start__le__sum) ).

fof(fact_pair__box_Osize_I1_J,axiom,
    ! [X24,X6,X178,X80,X20,X5] : c_Nitpick_Opair__box_Opair__box__size(X5,X20,X80,X178,c_Nitpick_Opair__box_OPairBox(X5,X20,X6,X24)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X80,X6)),hAPP(X178,X24))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__box_Osize_I1_J) ).

fof(fact_card__partition,axiom,
    ! [X87,X112,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X5,tc_HOL_Obool)),X112))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X112)))
       => ( ! [X283] :
              ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X283),X112))
             => hAPP(c_Finite__Set_Ocard(X5),X283) = X87 )
         => ( ! [X284] :
                ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X284),X112))
               => ! [X285] :
                    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X285),X112))
                   => ( X284 != X285
                     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X284),X285) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ) ) )
           => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X87),hAPP(c_Finite__Set_Ocard(tc_fun(X5,tc_HOL_Obool)),X112)) = hAPP(c_Finite__Set_Ocard(X5),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X112)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__partition) ).

fof(fact_sorted__same,axiom,
    ! [X239,X1,X5] :
      ( class_Orderings_Olinorder(X5)
     => c_List_Olinorder__class_Osorted(X5,hAPP(c_List_Ofilter(X5,hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),hAPP(X1,X239))),X239)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__same) ).

fof(fact_inj__comp,axiom,
    ! [X1,X116,X2,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => ( c_Fun_Oinj__on(X116,X5,X1,c_Orderings_Otop__class_Otop(tc_fun(X116,tc_HOL_Obool)))
       => c_Fun_Oinj__on(X116,X20,hAPP(c_Fun_Ocomp(X5,X20,X116,X2),X1),c_Orderings_Otop__class_Otop(tc_fun(X116,tc_HOL_Obool))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__comp) ).

fof(fact_set__update__subset__insert,axiom,
    ! [X25,X82,X239,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Olist__update(X5,X239),X82),X25))),hAPP(hAPP(c_Set_Oinsert(X5),X25),hAPP(c_List_Oset(X5),X239)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__update__subset__insert) ).

fof(fact_min__max_OInf__fin_Oremove,axiom,
    ! [X25,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X21) = X25 )
            & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X21) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X25),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Oremove) ).

fof(fact_min__max_OSup__fin_Oremove,axiom,
    ! [X25,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X21) = X25 )
            & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X21) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X25),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Oremove) ).

fof(fact_transfer__nat__int__sum__prod2_I1_J,axiom,
    ! [X21,X2,X5] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),X2),X21) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X5),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2)),X21)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__sum__prod2_I1_J) ).

fof(fact_transfer__nat__int__sum__prod2_I2_J,axiom,
    ! [X21,X2,X5] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,tc_Nat_Onat),X2),X21) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X5),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2)),X21)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__sum__prod2_I2_J) ).

fof(fact_vimage__singleton__eq,axiom,
    ! [X24,X2,X20,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(c_Set_Ovimage(X5,X20,X2),hAPP(hAPP(c_Set_Oinsert(X20),X24),c_Orderings_Obot__class_Obot(tc_fun(X20,tc_HOL_Obool))))))
    <=> hAPP(X2,X6) = X24 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__singleton__eq) ).

fof(fact_inj__on__imageI2,axiom,
    ! [X21,X2,X119,X116,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,hAPP(c_Fun_Ocomp(X116,X20,X5,X119),X2),X21)
     => c_Fun_Oinj__on(X5,X116,X2,X21) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__imageI2) ).

fof(fact_finite__Diff__insert,axiom,
    ! [X113,X6,X21,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X6),X113))))
    <=> hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),X113))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Diff__insert) ).

fof(fact_insert__def,axiom,
    ! [X113,X6,X5] : hAPP(hAPP(c_Set_Oinsert(X5),X6),X113) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X6))),X113),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__def) ).

fof(fact_eq__add__iff1,axiom,
    ! [X22,X24,X23,X155,X6,X5] :
      ( class_Rings_Oring(X5)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X155)),X23) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X24),X155)),X22)
      <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X6),X24)),X155)),X23) = X22 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__add__iff1) ).

fof(fact_eq__add__iff2,axiom,
    ! [X22,X24,X23,X155,X6,X5] :
      ( class_Rings_Oring(X5)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X155)),X23) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X24),X155)),X22)
      <=> X23 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X24),X6)),X155)),X22) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__add__iff2) ).

fof(fact_Image__INT__eq,axiom,
    ! [X113,X116,X21,X171,X20,X5] :
      ( c_Relation_Osingle__valued(X5,X20,hAPP(c_Relation_Oconverse(X20,X5),X171))
     => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X116,tc_HOL_Obool))
       => hAPP(c_Relation_OImage(X20,X5,X171),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X116,tc_fun(X20,tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X116,tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X116),c_Relation_OImage(X20,X5,X171)),X113)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__INT__eq) ).

fof(fact_partition__filter2,axiom,
    ! [X239,X18,X5] : hAPP(c_Product__Type_Osnd(tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Opartition(X5,X18,X239)) = hAPP(c_List_Ofilter(X5,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,X5,c_fNot),X18)),X239),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_partition__filter2) ).

fof(fact_inv__into__image__cancel,axiom,
    ! [X192,X21,X2,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,X2,X21)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X192),X21))
       => hAPP(c_Set_Oimage(X20,X5,c_Hilbert__Choice_Oinv__into(X5,X20,X21,X2)),hAPP(c_Set_Oimage(X5,X20,X2),X192)) = X192 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__into__image__cancel) ).

fof(fact_vimage__mono,axiom,
    ! [X2,X20,X113,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),X113))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X20,X5,X2),X21)),hAPP(c_Set_Ovimage(X20,X5,X2),X113))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__mono) ).

fof(fact_image__mono,axiom,
    ! [X2,X20,X113,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),X113))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X20,X2),X21)),hAPP(c_Set_Oimage(X5,X20,X2),X113))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__mono) ).

fof(fact_UN__equiv__class,axiom,
    ! [X6,X2,X20,X171,X21,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X21,X171)
     => ( c_Equiv__Relations_Ocongruent(X5,tc_fun(X20,tc_HOL_Obool),X171,X2)
       => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X21))
         => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X20,tc_HOL_Obool)),hAPP(c_Relation_OImage(X5,X5,X171),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),X2) = hAPP(X2,X6) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__equiv__class) ).

fof(fact_min__max_OInf__fin_Oinsert__remove,axiom,
    ! [X25,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = X25 )
          & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X25),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Oinsert__remove) ).

fof(fact_min__max_OSup__fin_Oinsert__remove,axiom,
    ! [X25,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = X25 )
          & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X25),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Oinsert__remove) ).

fof(fact_comp__cong,axiom,
    ! [X114,X115,X116,X5,X20,X117,X118,X119,X25,X1,X2] :
      ( hAPP(X2,hAPP(X1,X25)) = hAPP(X119,hAPP(X118,X117))
     => hAPP(hAPP(c_Fun_Ocomp(X20,X5,X116,X2),X1),X25) = hAPP(hAPP(c_Fun_Ocomp(X115,X5,X114,X119),X118),X117) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comp__cong) ).

fof(fact_inv__o__cancel,axiom,
    ! [X2,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => hAPP(c_Fun_Ocomp(X20,X5,X5,c_Hilbert__Choice_Oinv__into(X5,X20,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X2)),X2) = c_Fun_Oid(X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__o__cancel) ).

fof(fact_folding__one_Oremove,axiom,
    ! [X25,X21,X205,X2,X5] :
      ( c_Finite__Set_Ofolding__one(X5,X2,X205)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => hAPP(X205,X21) = X25 )
            & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => hAPP(X205,X21) = hAPP(hAPP(X2,X25),hAPP(X205,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one_Oremove) ).

fof(fact_card_Ounion__inter,axiom,
    ! [X113,X21,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X113))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113))),hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X21)),hAPP(c_Finite__Set_Ocard(X5),X113)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card_Ounion__inter) ).

fof(fact_card__Un__Int,axiom,
    ! [X113,X21,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X113))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X21)),hAPP(c_Finite__Set_Ocard(X5),X113)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113))),hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Un__Int) ).

fof(fact_wf__same__fst,axiom,
    ! [X5,X32,X20,X18] :
      ( ! [X3] :
          ( hBOOL(hAPP(X18,X3))
         => c_Wellfounded_Owf(X20,hAPP(X32,X3)) )
     => c_Wellfounded_Owf(tc_prod(X5,X20),c_Recdef_Osame__fst(X5,X20,X18,X32)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__same__fst) ).

fof(fact_in__rel__def,axiom,
    ! [X33,X25,X32,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X5,X20,X32),X25),X33))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X20)),hAPP(hAPP(c_Product__Type_OPair(X5,X20),X25),X33)),X32)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__rel__def) ).

fof(fact_bij__betw__imp__inj__on,axiom,
    ! [X113,X21,X2,X20,X5] :
      ( c_Fun_Obij__betw(X5,X20,X2,X21,X113)
     => c_Fun_Oinj__on(X5,X20,X2,X21) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__betw__imp__inj__on) ).

fof(fact_Image__closed__trancl,axiom,
    ! [X194,X171,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_OImage(X5,X5,X171),X194)),X194))
     => hAPP(c_Relation_OImage(X5,X5,c_Transitive__Closure_Ortrancl(X5,X171)),X194) = X194 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__closed__trancl) ).

fof(fact_acc__downwards__aux,axiom,
    ! [X171,X6,X24,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X24),X6)),c_Transitive__Closure_Ortrancl(X5,X171)))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X6),c_Wellfounded_Oacc(X5,X171)))
       => hBOOL(hAPP(hAPP(c_member(X5),X24),c_Wellfounded_Oacc(X5,X171))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc__downwards__aux) ).

fof(fact_acc__downwards,axiom,
    ! [X24,X171,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),c_Wellfounded_Oacc(X5,X171)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X24),X6)),c_Transitive__Closure_Ortrancl(X5,X171)))
       => hBOOL(hAPP(hAPP(c_member(X5),X24),c_Wellfounded_Oacc(X5,X171))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc__downwards) ).

fof(fact_INT__simps_I2_J,axiom,
    ! [X113,X21,X20,X5,X112] :
      ( ( X112 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X20,tc_HOL_Obool)),X112),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool),X5),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20,tc_HOL_Obool)),X21)),X113)) = c_Orderings_Otop__class_Otop(tc_fun(X20,tc_HOL_Obool)) )
      & ( X112 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X20,tc_HOL_Obool)),X112),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool),X5),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20,tc_HOL_Obool)),X21)),X113)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20,tc_HOL_Obool)),X21),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X20,tc_HOL_Obool)),X112),X113)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__simps_I2_J) ).

fof(fact_INT__simps_I4_J,axiom,
    ! [X113,X21,X20,X5,X112] :
      ( ( X112 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X20,tc_HOL_Obool)),X112),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool),X5),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20,tc_HOL_Obool)),X21)),X113)) = c_Orderings_Otop__class_Otop(tc_fun(X20,tc_HOL_Obool)) )
      & ( X112 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X20,tc_HOL_Obool)),X112),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool),X5),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20,tc_HOL_Obool)),X21)),X113)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20,tc_HOL_Obool)),X21),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X20,tc_HOL_Obool)),X112),X113)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__simps_I4_J) ).

fof(fact_UN__simps_I3_J,axiom,
    ! [X113,X21,X20,X5,X112] :
      ( ( X112 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X20,tc_HOL_Obool)),X112),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool),X5),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20,tc_HOL_Obool)),X21)),X113)) = c_Orderings_Obot__class_Obot(tc_fun(X20,tc_HOL_Obool)) )
      & ( X112 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X20,tc_HOL_Obool)),X112),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool),X5),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20,tc_HOL_Obool)),X21)),X113)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20,tc_HOL_Obool)),X21),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X20,tc_HOL_Obool)),X112),X113)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__simps_I3_J) ).

fof(fact_INT__extend__simps_I2_J,axiom,
    ! [X113,X21,X20,X5,X112] :
      ( ( X112 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20,tc_HOL_Obool)),X21),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X20,tc_HOL_Obool)),X112),X113)) = X21 )
      & ( X112 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20,tc_HOL_Obool)),X21),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X20,tc_HOL_Obool)),X112),X113)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X20,tc_HOL_Obool)),X112),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool),X5),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20,tc_HOL_Obool)),X21)),X113)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__extend__simps_I2_J) ).

fof(fact_UN__extend__simps_I3_J,axiom,
    ! [X113,X21,X20,X5,X112] :
      ( ( X112 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20,tc_HOL_Obool)),X21),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X20,tc_HOL_Obool)),X112),X113)) = X21 )
      & ( X112 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20,tc_HOL_Obool)),X21),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X20,tc_HOL_Obool)),X112),X113)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X20,tc_HOL_Obool)),X112),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool),X5),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20,tc_HOL_Obool)),X21)),X113)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__extend__simps_I3_J) ).

fof(fact_INT__extend__simps_I4_J,axiom,
    ! [X113,X21,X20,X5,X112] :
      ( ( X112 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20,tc_HOL_Obool)),X21),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X20,tc_HOL_Obool)),X112),X113)) = X21 )
      & ( X112 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20,tc_HOL_Obool)),X21),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X20,tc_HOL_Obool)),X112),X113)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X20,tc_HOL_Obool)),X112),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool),X5),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20,tc_HOL_Obool)),X21)),X113)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__extend__simps_I4_J) ).

fof(fact_folding__one_Oinsert__remove,axiom,
    ! [X25,X21,X205,X2,X5] :
      ( c_Finite__Set_Ofolding__one(X5,X2,X205)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(X205,hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = X25 )
          & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(X205,hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(hAPP(X2,X25),hAPP(X205,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one_Oinsert__remove) ).

fof(fact_Min_Oremove,axiom,
    ! [X25,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => c_Big__Operators_Olinorder__class_OMin(X5,X21) = X25 )
            & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => c_Big__Operators_Olinorder__class_OMin(X5,X21) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X25),c_Big__Operators_Olinorder__class_OMin(X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min_Oremove) ).

fof(fact_Max_Oremove,axiom,
    ! [X25,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => c_Big__Operators_Olinorder__class_OMax(X5,X21) = X25 )
            & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => c_Big__Operators_Olinorder__class_OMax(X5,X21) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X25),c_Big__Operators_Olinorder__class_OMax(X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max_Oremove) ).

fof(fact_Sup__fin_Oremove,axiom,
    ! [X25,X21,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => c_Big__Operators_Olattice__class_OSup__fin(X5,X21) = X25 )
            & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => c_Big__Operators_Olattice__class_OSup__fin(X5,X21) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X25),c_Big__Operators_Olattice__class_OSup__fin(X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_Oremove) ).

fof(fact_Inf__fin_Oremove,axiom,
    ! [X25,X21,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => c_Big__Operators_Olattice__class_OInf__fin(X5,X21) = X25 )
            & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => c_Big__Operators_Olattice__class_OInf__fin(X5,X21) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X25),c_Big__Operators_Olattice__class_OInf__fin(X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_Oremove) ).

fof(fact_type__definition_ORep,axiom,
    ! [X25,X21,X232,X233,X20,X5] :
      ( c_Typedef_Otype__definition(X5,X20,X233,X232,X21)
     => hBOOL(hAPP(hAPP(c_member(X20),hAPP(X233,X25)),X21)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_type__definition_ORep) ).

fof(fact_type__definition_OAbs__inverse,axiom,
    ! [X33,X21,X232,X233,X20,X5] :
      ( c_Typedef_Otype__definition(X5,X20,X233,X232,X21)
     => ( hBOOL(hAPP(hAPP(c_member(X20),X33),X21))
       => hAPP(X233,hAPP(X232,X33)) = X33 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_type__definition_OAbs__inverse) ).

fof(fact_sorted__insort__key,axiom,
    ! [X239,X25,X2,X20,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Omap(X20,X5),X2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X20,X5,X2),X25),X239)))
      <=> c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Omap(X20,X5),X2),X239)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__insort__key) ).

fof(fact_mod__induct__0,axiom,
    ! [X82,X18,X160] :
      ( ! [X146] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X146),X160))
         => ( hBOOL(hAPP(X18,X146))
           => hBOOL(hAPP(X18,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X146),X160))) ) )
     => ( hBOOL(hAPP(X18,X82))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X82),X160))
         => hBOOL(hAPP(X18,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__induct__0) ).

fof(fact_zdiv__zmult1__eq,axiom,
    ! [X56,X90,X62] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X62),X90)),X56) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X62),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X90),X56))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X62),c_Divides_Odiv__class_Omod(tc_Int_Oint,X90,X56))),X56)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zmult1__eq) ).

fof(fact_div__mult1__eq,axiom,
    ! [X56,X90,X62] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X62),X90)),X56) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X62),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X90),X56))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X62),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X90,X56))),X56)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult1__eq) ).

fof(fact_nat__eq__add__iff1,axiom,
    ! [X50,X95,X159,X82,X157] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X157),X82))
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X82),X159)),X95) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X157),X159)),X50)
      <=> 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),X82),X157)),X159)),X95) = X50 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__eq__add__iff1) ).

fof(fact_nat__eq__add__iff2,axiom,
    ! [X50,X95,X159,X157,X82] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X82),X157))
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X82),X159)),X95) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X157),X159)),X50)
      <=> X95 = 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),X157),X82)),X159)),X50) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__eq__add__iff2) ).

fof(fact_Un__Int__assoc__eq,axiom,
    ! [X112,X113,X21,X5] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113)),X112) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X113),X112))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X112),X21)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Int__assoc__eq) ).

fof(fact_INT__simps_I7_J,axiom,
    ! [X113,X21,X112,X5,X20] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X20,tc_fun(X5,tc_HOL_Obool)),X112),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X20),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21)),X113)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X20,tc_fun(X5,tc_HOL_Obool)),X112),X113)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__simps_I7_J) ).

fof(fact_UN__simps_I5_J,axiom,
    ! [X113,X21,X112,X5,X20] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,tc_fun(X5,tc_HOL_Obool)),X112),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X20),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21)),X113)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,tc_fun(X5,tc_HOL_Obool)),X112),X113)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__simps_I5_J) ).

fof(fact_UN__simps_I7_J,axiom,
    ! [X113,X21,X112,X5,X20] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,tc_fun(X5,tc_HOL_Obool)),X112),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X20),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21)),X113)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X20,tc_fun(X5,tc_HOL_Obool)),X112),X113)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__simps_I7_J) ).

fof(fact_Int__UN__distrib,axiom,
    ! [X21,X221,X20,X113,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X113),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,tc_fun(X5,tc_HOL_Obool)),X221),X21)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,tc_fun(X5,tc_HOL_Obool)),X221),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X20),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X113)),X21)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__UN__distrib) ).

fof(fact_UN__extend__simps_I5_J,axiom,
    ! [X113,X112,X20,X21,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,tc_fun(X5,tc_HOL_Obool)),X112),X113)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,tc_fun(X5,tc_HOL_Obool)),X112),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X20),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21)),X113)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__extend__simps_I5_J) ).

fof(fact_INT__extend__simps_I7_J,axiom,
    ! [X113,X112,X20,X21,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X20,tc_fun(X5,tc_HOL_Obool)),X112),X113)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X20,tc_fun(X5,tc_HOL_Obool)),X112),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X20),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21)),X113)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__extend__simps_I7_J) ).

fof(fact_Un__INT__distrib,axiom,
    ! [X21,X221,X20,X113,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X113),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X20,tc_fun(X5,tc_HOL_Obool)),X221),X21)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X20,tc_fun(X5,tc_HOL_Obool)),X221),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X20),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X113)),X21)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__INT__distrib) ).

fof(fact_UN__extend__simps_I7_J,axiom,
    ! [X113,X112,X20,X21,X5] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X20,tc_fun(X5,tc_HOL_Obool)),X112),X113)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,tc_fun(X5,tc_HOL_Obool)),X112),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X20),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21)),X113)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__extend__simps_I7_J) ).

fof(fact_union__comp__emptyR,axiom,
    ! [X112,X113,X21,X5] :
      ( hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),X21),X113) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X5),tc_HOL_Obool))
     => ( hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),X21),X112) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X5),tc_HOL_Obool))
       => hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),X21),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X113),X112)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_union__comp__emptyR) ).

fof(fact_BIJ,axiom,
    ! [X113,X20,X21,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X20),X113))
       => ( ? [X227] : c_Fun_Obij__betw(X5,X20,X227,X21,X113)
        <=> hAPP(c_Finite__Set_Ocard(X5),X21) = hAPP(c_Finite__Set_Ocard(X20),X113) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_BIJ) ).

fof(fact_type__definition_ORep__range,axiom,
    ! [X21,X232,X233,X20,X5] :
      ( c_Typedef_Otype__definition(X5,X20,X233,X232,X21)
     => hAPP(c_Set_Oimage(X5,X20,X233),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) = X21 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_type__definition_ORep__range) ).

fof(fact_singleton__quotient,axiom,
    ! [X171,X25,X5] : hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),X171) = hAPP(hAPP(c_Set_Oinsert(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_OImage(X5,X5,X171),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_singleton__quotient) ).

fof(fact_congruentD,axiom,
    ! [X120,X33,X2,X171,X20,X5] :
      ( c_Equiv__Relations_Ocongruent(X5,X20,X171,X2)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X33),X120)),X171))
       => hAPP(X2,X33) = hAPP(X2,X120) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_congruentD) ).

fof(fact_rtrancl__subset__rtrancl,axiom,
    ! [X76,X171,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X171),c_Transitive__Closure_Ortrancl(X5,X76)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X5,X171)),c_Transitive__Closure_Ortrancl(X5,X76))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__subset__rtrancl) ).

fof(fact_rel__pow__imp__rtrancl,axiom,
    ! [X32,X50,X160,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X160),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X50),X32)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X160),c_Transitive__Closure_Ortrancl(X5,X32))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__pow__imp__rtrancl) ).

fof(fact_acc__downward,axiom,
    ! [X6,X171,X24,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X24),c_Wellfounded_Oacc(X5,X171)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X24)),X171))
       => hBOOL(hAPP(hAPP(c_member(X5),X6),c_Wellfounded_Oacc(X5,X171))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc__downward) ).

fof(fact_Min_Oinsert__remove,axiom,
    ! [X25,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => c_Big__Operators_Olinorder__class_OMin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = X25 )
          & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => c_Big__Operators_Olinorder__class_OMin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X25),c_Big__Operators_Olinorder__class_OMin(X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min_Oinsert__remove) ).

fof(fact_Max_Oinsert__remove,axiom,
    ! [X25,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => c_Big__Operators_Olinorder__class_OMax(X5,hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = X25 )
          & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => c_Big__Operators_Olinorder__class_OMax(X5,hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X25),c_Big__Operators_Olinorder__class_OMax(X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max_Oinsert__remove) ).

fof(fact_Sup__fin_Oinsert__remove,axiom,
    ! [X25,X21,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => c_Big__Operators_Olattice__class_OSup__fin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = X25 )
          & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => c_Big__Operators_Olattice__class_OSup__fin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X25),c_Big__Operators_Olattice__class_OSup__fin(X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_Oinsert__remove) ).

fof(fact_Inf__fin_Oinsert__remove,axiom,
    ! [X25,X21,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => c_Big__Operators_Olattice__class_OInf__fin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = X25 )
          & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => c_Big__Operators_Olattice__class_OInf__fin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X25),c_Big__Operators_Olattice__class_OInf__fin(X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_Oinsert__remove) ).

fof(fact_type__definition_OAbs__image,axiom,
    ! [X21,X232,X233,X20,X5] :
      ( c_Typedef_Otype__definition(X5,X20,X233,X232,X21)
     => hAPP(c_Set_Oimage(X20,X5,X232),X21) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_type__definition_OAbs__image) ).

fof(fact_inj__on__mapI,axiom,
    ! [X21,X2,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,X2,c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_List_Olist(X5),tc_fun(X5,tc_HOL_Obool),c_List_Oset(X5)),X21)))
     => c_Fun_Oinj__on(tc_List_Olist(X5),tc_List_Olist(X20),hAPP(c_List_Omap(X5,X20),X2),X21) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__mapI) ).

fof(fact_inv__image__comp,axiom,
    ! [X194,X2,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => hAPP(c_Set_Oimage(X20,X5,c_Hilbert__Choice_Oinv__into(X5,X20,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X2)),hAPP(c_Set_Oimage(X5,X20,X2),X194)) = X194 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__image__comp) ).

fof(fact_image__inv__f__f,axiom,
    ! [X21,X2,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => hAPP(c_Set_Oimage(X20,X5,c_Hilbert__Choice_Oinv__into(X5,X20,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X2)),hAPP(c_Set_Oimage(X5,X20,X2),X21)) = X21 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__inv__f__f) ).

fof(fact_update__zip,axiom,
    ! [X268,X98,X241,X242,X5,X58] : hAPP(hAPP(c_List_Olist__update(tc_prod(X58,X5),hAPP(hAPP(c_List_Ozip(X58,X5),X242),X241)),X98),X268) = hAPP(hAPP(c_List_Ozip(X58,X5),hAPP(hAPP(c_List_Olist__update(X58,X242),X98),hAPP(c_Product__Type_Ofst(X58,X5),X268))),hAPP(hAPP(c_List_Olist__update(X5,X241),X98),hAPP(c_Product__Type_Osnd(X58,X5),X268))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_update__zip) ).

fof(fact_finite__Collect__le__nat,axiom,
    ! [X87] : 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)),X87)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Collect__le__nat) ).

fof(fact_finite__Collect__less__nat,axiom,
    ! [X87] : 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)),X87)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Collect__less__nat) ).

fof(fact_O__assoc,axiom,
    ! [X212,X192,X32,X115,X20,X116,X5] : hAPP(hAPP(c_Relation_Orel__comp(X5,X116,X20),hAPP(hAPP(c_Relation_Orel__comp(X5,X115,X116),X32),X192)),X212) = hAPP(hAPP(c_Relation_Orel__comp(X5,X115,X20),X32),hAPP(hAPP(c_Relation_Orel__comp(X115,X116,X20),X192),X212)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_O__assoc) ).

fof(fact_setsum_Oremove,axiom,
    ! [X1,X25,X21,X5,X20] :
      ( class_Groups_Ocomm__monoid__add(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X1),X21) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20),hAPP(X1,X25)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum_Oremove) ).

fof(fact_setsum__diff1_H,axiom,
    ! [X2,X6,X21,X5,X20] :
      ( class_Groups_Ocomm__monoid__add(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X21))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X2),X21) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20),hAPP(X2,X6)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__diff1_H) ).

fof(fact_setprod_Oremove,axiom,
    ! [X1,X25,X21,X5,X20] :
      ( class_Groups_Ocomm__monoid__mult(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X1),X21) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20),hAPP(X1,X25)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod_Oremove) ).

fof(fact_Pow__INT__eq,axiom,
    ! [X113,X21,X20,X5] : hAPP(c_Set_OPow(X5),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X20,tc_fun(X5,tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X20,tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),X21),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),X20),c_Set_OPow(X5)),X113)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__INT__eq) ).

fof(fact_q__pos__lemma,axiom,
    ! [X141,X142,X143] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X143),X142)),X141)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X141),X143))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X143))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X142)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_q__pos__lemma) ).

fof(fact_bij__betw__empty1,axiom,
    ! [X21,X2,X20,X5] :
      ( c_Fun_Obij__betw(X5,X20,X2,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),X21)
     => X21 = c_Orderings_Obot__class_Obot(tc_fun(X20,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__betw__empty1) ).

fof(fact_bij__betw__empty2,axiom,
    ! [X21,X2,X20,X5] :
      ( c_Fun_Obij__betw(X5,X20,X2,X21,c_Orderings_Obot__class_Obot(tc_fun(X20,tc_HOL_Obool)))
     => X21 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__betw__empty2) ).

fof(fact_UN__le__eq__Un0,axiom,
    ! [X210,X50,X5] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X50)),X210) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X50)),X210)),hAPP(X210,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__le__eq__Un0) ).

fof(fact_card__Diff__subset__Int,axiom,
    ! [X113,X21,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113)))
     => hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X21)),hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113))) ),
    file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_pair__leq__def) ).

fof(fact_INT__Un,axiom,
    ! [X210,X113,X21,X5,X20] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X20,tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20,tc_HOL_Obool)),X21),X113)),X210) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X20,tc_fun(X5,tc_HOL_Obool)),X21),X210)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X20,tc_fun(X5,tc_HOL_Obool)),X113),X210)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__Un) ).

fof(fact_UN__Un,axiom,
    ! [X210,X113,X21,X5,X20] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20,tc_HOL_Obool)),X21),X113)),X210) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,tc_fun(X5,tc_HOL_Obool)),X21),X210)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,tc_fun(X5,tc_HOL_Obool)),X113),X210)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__Un) ).

fof(fact_Compl__subset__Compl__iff,axiom,
    ! [X113,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X21)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X113)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X113),X21)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__subset__Compl__iff) ).

fof(fact_INT__lower,axiom,
    ! [X113,X20,X21,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),X21))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X20,tc_HOL_Obool)),X21),X113)),hAPP(X113,X6))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__lower) ).

fof(fact_rtrancl__mono,axiom,
    ! [X76,X171,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X171),X76))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X5,X171)),c_Transitive__Closure_Ortrancl(X5,X76))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__mono) ).

fof(fact_vimage__INT,axiom,
    ! [X113,X21,X116,X2,X20,X5] : hAPP(c_Set_Ovimage(X5,X20,X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X116,tc_fun(X20,tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X116,tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X116),c_Set_Ovimage(X5,X20,X2)),X113)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__INT) ).

fof(fact_vimage__UN,axiom,
    ! [X113,X21,X116,X2,X20,X5] : hAPP(c_Set_Ovimage(X5,X20,X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X116,tc_fun(X20,tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X116,tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X116),c_Set_Ovimage(X5,X20,X2)),X113)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__UN) ).

fof(fact_Image__UN,axiom,
    ! [X113,X21,X116,X171,X5,X20] : hAPP(c_Relation_OImage(X20,X5,X171),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X116,tc_fun(X20,tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X116,tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X116),c_Relation_OImage(X20,X5,X171)),X113)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__UN) ).

fof(fact_image__UN,axiom,
    ! [X113,X21,X116,X2,X5,X20] : hAPP(c_Set_Oimage(X20,X5,X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X116,tc_fun(X20,tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X116,tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X116),c_Set_Oimage(X20,X5,X2)),X113)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__UN) ).

fof(fact_diff__frac__eq,axiom,
    ! [X128,X66,X94,X65,X58] :
      ( class_Fields_Ofield(X58)
     => ( X65 != c_Groups_Ozero__class_Ozero(X58)
       => ( X94 != c_Groups_Ozero__class_Ozero(X58)
         => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X58),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X66),X65)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X128),X94)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X66),X94)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X128),X65))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X65),X94)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__frac__eq) ).

fof(fact_add__frac__eq,axiom,
    ! [X128,X66,X94,X65,X58] :
      ( class_Fields_Ofield(X58)
     => ( X65 != c_Groups_Ozero__class_Ozero(X58)
       => ( X94 != c_Groups_Ozero__class_Ozero(X58)
         => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X66),X65)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X128),X94)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X66),X94)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X128),X65))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X65),X94)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__frac__eq) ).

fof(fact_Compl__eq,axiom,
    ! [X21,X5] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X21) = hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X21))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__eq) ).

fof(fact_list__all2__lengthD,axiom,
    ! [X251,X239,X18,X20,X5] :
      ( c_List_Olist__all2(X5,X20,X18,X239,X251)
     => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X20)),X251) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__all2__lengthD) ).

fof(fact_Suc__mult__le__cancel1,axiom,
    ! [X50,X95,X87] :
      ( 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,X87)),X95)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X87)),X50)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X50)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mult__le__cancel1) ).

fof(fact_Suc__mult__less__cancel1,axiom,
    ! [X50,X95,X87] :
      ( 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,X87)),X95)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X87)),X50)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),X50)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mult__less__cancel1) ).

fof(fact_split__pos__lemma,axiom,
    ! [X50,X18,X87] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X87))
     => ( hBOOL(hAPP(hAPP(X18,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X50),X87)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X50,X87)))
      <=> ! [X146,X101] :
            ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X101))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X101),X87))
              & X50 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X87),X146)),X101) )
           => hBOOL(hAPP(hAPP(X18,X146),X101)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__pos__lemma) ).

fof(fact_inj__on__inv__into,axiom,
    ! [X21,X2,X20,X113,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X113),hAPP(c_Set_Oimage(X20,X5,X2),X21)))
     => c_Fun_Oinj__on(X5,X20,c_Hilbert__Choice_Oinv__into(X20,X5,X21,X2),X113) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__inv__into) ).

fof(fact_UN__o,axiom,
    ! [X2,X1,X116,X21,X5,X20] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,tc_fun(X5,tc_HOL_Obool)),X21),hAPP(c_Fun_Ocomp(X116,tc_fun(X5,tc_HOL_Obool),X20,X1),X2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X116,tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Oimage(X20,X116,X2),X21)),X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__o) ).

fof(fact_setsum_Oinsert__remove,axiom,
    ! [X25,X1,X21,X5,X20] :
      ( class_Groups_Ocomm__monoid__add(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X1),hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20),hAPP(X1,X25)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum_Oinsert__remove) ).

fof(fact_setprod_Oinsert__remove,axiom,
    ! [X25,X1,X21,X5,X20] :
      ( class_Groups_Ocomm__monoid__mult(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X1),hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20),hAPP(X1,X25)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod_Oinsert__remove) ).

fof(fact_f__inv__into__f,axiom,
    ! [X21,X2,X20,X33,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X33),hAPP(c_Set_Oimage(X20,X5,X2),X21)))
     => hAPP(X2,hAPP(c_Hilbert__Choice_Oinv__into(X20,X5,X21,X2),X33)) = X33 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_f__inv__into__f) ).

fof(fact_split__neg__lemma,axiom,
    ! [X50,X18,X87] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X87),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(X18,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X50),X87)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X50,X87)))
      <=> ! [X146,X101] :
            ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X87),X101))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X101),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & X50 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X87),X146)),X101) )
           => hBOOL(hAPP(hAPP(X18,X146),X101)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__neg__lemma) ).

fof(fact_zip__same__conv__map,axiom,
    ! [X239,X5] : hAPP(hAPP(c_List_Ozip(X5,X5),X239),X239) = hAPP(hAPP(c_List_Omap(X5,tc_prod(X5,X5)),hAPP(hAPP(c_COMBS(X5,X5,tc_prod(X5,X5)),c_Product__Type_OPair(X5,X5)),c_COMBI(X5))),X239),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__same__conv__map) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J,axiom,
    ! [X113,X21] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X21),X113) = 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)),X21)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X113))),
    file('/export/starexec/sandbox/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,
    ! [X113,X21] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X21),X113) = 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)),X21)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X113))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J) ).

fof(fact_surj__iff,axiom,
    ! [X2,X5,X20] :
      ( hAPP(c_Set_Oimage(X20,X5,X2),c_Orderings_Otop__class_Otop(tc_fun(X20,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))
    <=> hAPP(c_Fun_Ocomp(X20,X5,X5,X2),c_Hilbert__Choice_Oinv__into(X20,X5,c_Orderings_Otop__class_Otop(tc_fun(X20,tc_HOL_Obool)),X2)) = c_Fun_Oid(X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surj__iff) ).

fof(fact_power__Suc__less,axiom,
    ! [X57,X62,X58] :
      ( class_Rings_Olinordered__semidom(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),X62))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X62),c_Groups_Oone__class_Oone(X58)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),X57))),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),X57))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__Suc__less) ).

fof(fact_type__definition_ORep__inject,axiom,
    ! [X33,X25,X21,X232,X233,X20,X5] :
      ( c_Typedef_Otype__definition(X5,X20,X233,X232,X21)
     => ( hAPP(X233,X25) = hAPP(X233,X33)
      <=> X25 = X33 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_type__definition_ORep__inject) ).

fof(fact_finite__cartesian__productD2,axiom,
    ! [X113,X21,X20,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X5,X20)),hAPP(hAPP(c_Product__Type_OSigma(X5,X20),X21),hAPP(c_COMBK(tc_fun(X20,tc_HOL_Obool),X5),X113))))
     => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(X20),X113)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__cartesian__productD2) ).

fof(fact_finite__cartesian__productD1,axiom,
    ! [X113,X21,X20,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X5,X20)),hAPP(hAPP(c_Product__Type_OSigma(X5,X20),X21),hAPP(c_COMBK(tc_fun(X20,tc_HOL_Obool),X5),X113))))
     => ( X113 != c_Orderings_Obot__class_Obot(tc_fun(X20,tc_HOL_Obool))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__cartesian__productD1) ).

fof(fact_type__definition_ORep__inverse,axiom,
    ! [X25,X21,X232,X233,X20,X5] :
      ( c_Typedef_Otype__definition(X5,X20,X233,X232,X21)
     => hAPP(X232,hAPP(X233,X25)) = X25 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_type__definition_ORep__inverse) ).

fof(fact_bij__betw__same__card,axiom,
    ! [X113,X21,X2,X20,X5] :
      ( c_Fun_Obij__betw(X5,X20,X2,X21,X113)
     => hAPP(c_Finite__Set_Ocard(X5),X21) = hAPP(c_Finite__Set_Ocard(X20),X113) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__betw__same__card) ).

fof(fact_abs__triangle__ineq2,axiom,
    ! [X90,X62,X58] :
      ( class_Groups_Oordered__ab__group__add__abs(X58)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X58),hAPP(c_Groups_Oabs__class_Oabs(X58),X62)),hAPP(c_Groups_Oabs__class_Oabs(X58),X90))),hAPP(c_Groups_Oabs__class_Oabs(X58),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X58),X62),X90)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__triangle__ineq2) ).

fof(fact_abs__triangle__ineq2__sym,axiom,
    ! [X90,X62,X58] :
      ( class_Groups_Oordered__ab__group__add__abs(X58)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X58),hAPP(c_Groups_Oabs__class_Oabs(X58),X62)),hAPP(c_Groups_Oabs__class_Oabs(X58),X90))),hAPP(c_Groups_Oabs__class_Oabs(X58),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X58),X90),X62)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__triangle__ineq2__sym) ).

fof(fact_vimage__insert,axiom,
    ! [X113,X6,X2,X20,X5] : hAPP(c_Set_Ovimage(X5,X20,X2),hAPP(hAPP(c_Set_Oinsert(X20),X6),X113)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X5,X20,X2),hAPP(hAPP(c_Set_Oinsert(X20),X6),c_Orderings_Obot__class_Obot(tc_fun(X20,tc_HOL_Obool))))),hAPP(c_Set_Ovimage(X5,X20,X2),X113)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__insert) ).

fof(fact_fun__upd__idem__iff,axiom,
    ! [X33,X25,X2,X20,X5] :
      ( c_Fun_Ofun__upd(X5,X20,X2,X25,X33) = X2
    <=> hAPP(X2,X25) = X33 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__idem__iff) ).

fof(fact_list__all2__Nil,axiom,
    ! [X251,X18,X20,X5] :
      ( c_List_Olist__all2(X5,X20,X18,c_List_Olist_ONil(X5),X251)
    <=> X251 = c_List_Olist_ONil(X20) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__all2__Nil) ).

fof(fact_list__all2__Nil2,axiom,
    ! [X239,X18,X20,X5] :
      ( c_List_Olist__all2(X5,X20,X18,X239,c_List_Olist_ONil(X20))
    <=> X239 = c_List_Olist_ONil(X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__all2__Nil2) ).

fof(fact_bij__betw__id__iff,axiom,
    ! [X113,X21,X5] :
      ( c_Fun_Obij__betw(X5,X5,c_Fun_Oid(X5),X21,X113)
    <=> X21 = X113 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__betw__id__iff) ).

fof(fact_DomainI,axiom,
    ! [X171,X24,X6,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X20)),hAPP(hAPP(c_Product__Type_OPair(X5,X20),X6),X24)),X171))
     => hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(c_Relation_ODomain(X5,X20),X171))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DomainI) ).

fof(fact_RangeI,axiom,
    ! [X171,X24,X6,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X20)),hAPP(hAPP(c_Product__Type_OPair(X5,X20),X6),X24)),X171))
     => hBOOL(hAPP(hAPP(c_member(X20),X24),hAPP(c_Relation_ORange(X5,X20),X171))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_RangeI) ).

fof(fact_set__drop__subset__set__drop,axiom,
    ! [X239,X5,X95,X50] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X50),X95))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Odrop(X5),X95),X239))),hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Odrop(X5),X50),X239)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__drop__subset__set__drop) ).

fof(fact_set__take__subset__set__take,axiom,
    ! [X239,X5,X50,X95] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X50))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Otake(X5),X95),X239))),hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Otake(X5),X50),X239)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__take__subset__set__take) ).

fof(fact_list__all2__eq,axiom,
    ! [X5,X251,X239] :
      ( X239 = X251
    <=> c_List_Olist__all2(X5,X5,c_fequal,X239,X251) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__all2__eq) ).

fof(fact_sorted__list__of__set__insert,axiom,
    ! [X25,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => c_List_Olinorder__class_Osorted__list__of__set(X5,hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X5,c_COMBI(X5)),X25),c_List_Olinorder__class_Osorted__list__of__set(X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__list__of__set__insert) ).

fof(fact_power__le__imp__le__base,axiom,
    ! [X90,X57,X62,X58] :
      ( class_Rings_Olinordered__semidom(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),hAPP(c_Nat_OSuc,X57))),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X90),hAPP(c_Nat_OSuc,X57))))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),X90))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X62),X90)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__le__imp__le__base) ).

fof(fact_sup__le__fold__sup,axiom,
    ! [X24,X6,X21,X5] :
      ( class_Lattices_Osemilattice__sup(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X21))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X6),X24)),hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Lattices_Osemilattice__sup__class_Osup(X5)),X24),X21))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__le__fold__sup) ).

fof(fact_min__max_Osup__le__fold__sup,axiom,
    ! [X24,X6,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X21))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X6),X24)),hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omax(X5)),X24),X21))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup__le__fold__sup) ).

fof(fact_Domain__mono,axiom,
    ! [X76,X171,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X20),tc_HOL_Obool)),X171),X76))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X5,X20),X171)),hAPP(c_Relation_ODomain(X5,X20),X76))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__mono) ).

fof(fact_inj__imp__surj__inv,axiom,
    ! [X2,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => hAPP(c_Set_Oimage(X20,X5,c_Hilbert__Choice_Oinv__into(X5,X20,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X2)),c_Orderings_Otop__class_Otop(tc_fun(X20,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__imp__surj__inv) ).

fof(fact_less__half__sum,axiom,
    ! [X90,X62,X58] :
      ( class_Fields_Olinordered__field(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X62),X90))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X62),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),X90)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),c_Groups_Oone__class_Oone(X58)),c_Groups_Oone__class_Oone(X58))))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__half__sum) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J,axiom,
    ! [X113,X21] :
      ( c_Nat__Transfer_Onat__set(X21)
     => ( c_Nat__Transfer_Onat__set(X113)
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X21),X113) = 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),X21)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X113))) ) ),
    file('/export/starexec/sandbox/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,
    ! [X113,X21] :
      ( c_Nat__Transfer_Onat__set(X21)
     => ( c_Nat__Transfer_Onat__set(X113)
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X21),X113) = 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),X21)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X113))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J) ).

fof(fact_combine__common__factor,axiom,
    ! [X56,X90,X133,X62,X58] :
      ( class_Rings_Osemiring(X58)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X133)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X90),X133)),X56)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),X90)),X133)),X56) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_combine__common__factor) ).

fof(fact_Id__on__subset__Times,axiom,
    ! [X21,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Relation_OId__on(X5,X21)),hAPP(hAPP(c_Product__Type_OSigma(X5,X5),X21),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X5),X21)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Id__on__subset__Times) ).

fof(fact_sort__foldl__insort,axiom,
    ! [X239,X5] :
      ( class_Orderings_Olinorder(X5)
     => c_List_Olinorder__class_Osort__key(X5,X5,c_COMBI(X5),X239) = hAPP(c_List_Ofoldl(tc_List_Olist(X5),X5,hAPP(c_COMBC(X5,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olinorder__class_Oinsort__key(X5,X5,c_COMBI(X5))),c_List_Olist_ONil(X5)),X239) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sort__foldl__insort) ).

fof(fact_Range__Collect__split,axiom,
    ! [X18,X5,X20] : hAPP(c_Relation_ORange(X20,X5),hAPP(c_Set_OCollect(tc_prod(X20,X5)),hAPP(c_Product__Type_Oprod_Oprod__case(X20,X5,tc_HOL_Obool),X18))) = hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(X20)),hAPP(c_COMBC(X20,X5,tc_HOL_Obool),X18))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__Collect__split) ).

fof(fact_equiv__type,axiom,
    ! [X171,X21,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X21,X171)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X171),hAPP(hAPP(c_Product__Type_OSigma(X5,X5),X21),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X5),X21)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equiv__type) ).

fof(fact_List_Omap_Ocomp,axiom,
    ! [X1,X2,X5,X20,X116] : hAPP(c_Fun_Ocomp(tc_List_Olist(X116),tc_List_Olist(X20),tc_List_Olist(X5),hAPP(c_List_Omap(X116,X20),X2)),hAPP(c_List_Omap(X5,X116),X1)) = hAPP(c_List_Omap(X5,X20),hAPP(c_Fun_Ocomp(X116,X20,X5,X2),X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_List_Omap_Ocomp) ).

fof(fact_map__comp__map,axiom,
    ! [X1,X2,X5,X20,X116] : hAPP(c_Fun_Ocomp(tc_List_Olist(X116),tc_List_Olist(X20),tc_List_Olist(X5),hAPP(c_List_Omap(X116,X20),X2)),hAPP(c_List_Omap(X5,X116),X1)) = hAPP(c_List_Omap(X5,X20),hAPP(c_Fun_Ocomp(X116,X20,X5,X2),X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__comp__map) ).

fof(fact_refl__onD1,axiom,
    ! [X33,X25,X171,X21,X5] :
      ( c_Relation_Orefl__on(X5,X21,X171)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X33)),X171))
       => hBOOL(hAPP(hAPP(c_member(X5),X25),X21)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__onD1) ).

fof(fact_refl__onD2,axiom,
    ! [X33,X25,X171,X21,X5] :
      ( c_Relation_Orefl__on(X5,X21,X171)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X33)),X171))
       => hBOOL(hAPP(hAPP(c_member(X5),X33),X21)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__onD2) ).

fof(fact_listrel_ONil,axiom,
    ! [X171,X5] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olist_ONil(X5)),c_List_Olist_ONil(X5))),c_List_Olistrel(X5,X171))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel_ONil) ).

fof(fact_Int__Union2,axiom,
    ! [X21,X113,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X113)),X21) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X113),hAPP(hAPP(c_COMBC(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool))),X21)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__Union2) ).

fof(fact_Id__on__iff,axiom,
    ! [X21,X33,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X33)),c_Relation_OId__on(X5,X21)))
    <=> ( X25 = X33
        & hBOOL(hAPP(hAPP(c_member(X5),X25),X21)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Id__on__iff) ).

fof(fact_finite__Plus__iff,axiom,
    ! [X113,X21,X20,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X5,X20)),c_Sum__Type_OPlus(X5,X20,X21,X113)))
    <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(X20),X113)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Plus__iff) ).

fof(fact_finite__PlusD_I1_J,axiom,
    ! [X113,X21,X20,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X5,X20)),c_Sum__Type_OPlus(X5,X20,X21,X113)))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__PlusD_I1_J) ).

fof(fact_finite__PlusD_I2_J,axiom,
    ! [X113,X21,X20,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X5,X20)),c_Sum__Type_OPlus(X5,X20,X21,X113)))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X20),X113)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__PlusD_I2_J) ).

fof(fact_SigmaI,axiom,
    ! [X113,X24,X20,X21,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),X21))
     => ( hBOOL(hAPP(hAPP(c_member(X20),X24),hAPP(X113,X6)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X20)),hAPP(hAPP(c_Product__Type_OPair(X5,X20),X6),X24)),hAPP(hAPP(c_Product__Type_OSigma(X5,X20),X21),X113))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SigmaI) ).

fof(fact_foldl__assoc,axiom,
    ! [X250,X33,X25,X5] :
      ( class_Groups_Osemigroup__add(X5)
     => hAPP(c_List_Ofoldl(X5,X5,c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X25),X33)),X250) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X25),hAPP(c_List_Ofoldl(X5,X5,c_Groups_Oplus__class_Oplus(X5),X33),X250)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldl__assoc) ).

fof(fact_rel__pow__0__I,axiom,
    ! [X32,X25,X5] : hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X25)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X32))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__pow__0__I) ).

fof(fact_quotient__disj,axiom,
    ! [X196,X194,X171,X21,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X21,X171)
     => ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X194),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X21),X171)))
       => ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X196),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X21),X171)))
         => ( X194 = X196
            | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X194),X196) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotient__disj) ).

fof(fact_pick__same,axiom,
    ! [X239,X5,X156] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X156),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239)))
     => hAPP(c_Random_Opick(X5,hAPP(hAPP(c_List_Omap(X5,tc_prod(tc_Code__Numeral_Ocode__numeral,X5)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X5),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),X239)),hAPP(c_Code__Numeral_Oof__nat,X156)) = hAPP(hAPP(c_List_Onth(X5),X239),X156) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pick__same) ).

fof(fact_subset__card__intvl__is__intvl,axiom,
    ! [X87,X21] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X21),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X87),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X21)))))
     => X21 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X87),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X21))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__card__intvl__is__intvl) ).

fof(fact_ord_OatLeastAtMost__iff,axiom,
    ! [X159,X156,X208,X82,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X82),c_SetInterval_Oord_OatLeastAtMost(X5,X208,X156,X159)))
    <=> ( hBOOL(hAPP(hAPP(X208,X156),X82))
        & hBOOL(hAPP(hAPP(X208,X82),X159)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord_OatLeastAtMost__iff) ).

fof(fact_ord_OgreaterThanLessThan__iff,axiom,
    ! [X159,X156,X209,X82,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X82),c_SetInterval_Oord_OgreaterThanLessThan(X5,X209,X156,X159)))
    <=> ( hBOOL(hAPP(hAPP(X209,X156),X82))
        & hBOOL(hAPP(hAPP(X209,X82),X159)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord_OgreaterThanLessThan__iff) ).

fof(fact_set__Cons__sing__Nil,axiom,
    ! [X21,X5] : c_List_Oset__Cons(X5,X21,hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X5)),c_List_Olist_ONil(X5)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X5),tc_HOL_Obool)))) = hAPP(c_Set_Oimage(X5,tc_List_Olist(X5),hAPP(hAPP(c_COMBC(X5,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olist_OCons(X5)),c_List_Olist_ONil(X5))),X21),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__Cons__sing__Nil) ).

fof(fact_INT__insert__distrib,axiom,
    ! [X113,X6,X20,X21,X159,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X159),X21))
     => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X20,tc_HOL_Obool)),X21),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool),X5),hAPP(c_Set_Oinsert(X20),X6)),X113)) = hAPP(hAPP(c_Set_Oinsert(X20),X6),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X20,tc_HOL_Obool)),X21),X113)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__insert__distrib) ).

fof(fact_UN__insert__distrib,axiom,
    ! [X113,X6,X20,X21,X159,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X159),X21))
     => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X20,tc_HOL_Obool)),X21),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool),X5),hAPP(c_Set_Oinsert(X20),X6)),X113)) = hAPP(hAPP(c_Set_Oinsert(X20),X6),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X20,tc_HOL_Obool)),X21),X113)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__insert__distrib) ).

fof(fact_finite__conv__nat__seg__image,axiom,
    ! [X21,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
    <=> ? [X69,X227] : X21 = hAPP(c_Set_Oimage(tc_Nat_Onat,X5,X227),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)),X69))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__conv__nat__seg__image) ).

fof(fact_nat__seg__image__imp__finite,axiom,
    ! [X50,X2,X5,X21] :
      ( X21 = hAPP(c_Set_Oimage(tc_Nat_Onat,X5,X2),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X50)))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__seg__image__imp__finite) ).

fof(fact_take__hd__drop,axiom,
    ! [X242,X58,X57] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X57),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242)))
     => hAPP(hAPP(c_List_Oappend(X58),hAPP(hAPP(c_List_Otake(X58),X57),X242)),hAPP(hAPP(c_List_Olist_OCons(X58),hAPP(c_List_Ohd(X58),hAPP(hAPP(c_List_Odrop(X58),X57),X242))),c_List_Olist_ONil(X58))) = hAPP(hAPP(c_List_Otake(X58),hAPP(c_Nat_OSuc,X57)),X242) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__hd__drop) ).

fof(fact_Diff__insert2,axiom,
    ! [X113,X6,X21,X5] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X6),X113)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),X113),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__insert2) ).

fof(fact_listrel__rtrancl__refl,axiom,
    ! [X171,X239,X5] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X239),X239)),c_List_Olistrel(X5,c_Transitive__Closure_Ortrancl(X5,X171)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__rtrancl__refl) ).

fof(fact_Inter__subset,axiom,
    ! [X113,X21,X5] :
      ( ! [X291] :
          ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X291),X21))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X291),X113)) )
     => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),X21)),X113)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__subset) ).

fof(fact_zmod__zmult2__eq,axiom,
    ! [X90,X62,X56] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X56))
     => c_Divides_Odiv__class_Omod(tc_Int_Oint,X62,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X90),X56)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X90),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X62),X90),X56))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X62,X90)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zmult2__eq) ).

fof(fact_Int__greatest,axiom,
    ! [X113,X21,X112,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X112),X21))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X112),X113))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X112),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__greatest) ).

fof(fact_max__Suc2,axiom,
    ! [X50,X95] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X95),hAPP(c_Nat_OSuc,X50)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,X50),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)),X50)),X95),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__Suc2) ).

fof(fact_rel__pow__add,axiom,
    ! [X32,X50,X95,X5] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X95),X50)),X32) = hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X95),X32)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X50),X32)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__pow__add) ).

fof(fact_Inter__anti__mono,axiom,
    ! [X21,X113,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),X113),X21))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),X21)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),X113))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__anti__mono) ).

fof(fact_Union__mono,axiom,
    ! [X113,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),X21),X113))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X21)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X113))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__mono) ).

fof(fact_abs__triangle__ineq4,axiom,
    ! [X90,X62,X58] :
      ( class_Groups_Oordered__ab__group__add__abs(X58)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(c_Groups_Oabs__class_Oabs(X58),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X58),X62),X90))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(c_Groups_Oabs__class_Oabs(X58),X62)),hAPP(c_Groups_Oabs__class_Oabs(X58),X90)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__triangle__ineq4) ).

fof(fact_abs__triangle__ineq,axiom,
    ! [X90,X62,X58] :
      ( class_Groups_Oordered__ab__group__add__abs(X58)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(c_Groups_Oabs__class_Oabs(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),X90))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(c_Groups_Oabs__class_Oabs(X58),X62)),hAPP(c_Groups_Oabs__class_Oabs(X58),X90)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__triangle__ineq) ).

fof(fact_min__Suc2,axiom,
    ! [X50,X95] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X95),hAPP(c_Nat_OSuc,X50)) = 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)),X50)),X95),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__Suc2) ).

fof(fact_card_Oremove,axiom,
    ! [X25,X21,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
       => hAPP(c_Finite__Set_Ocard(X5),X21) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card_Oremove) ).

fof(fact_zip__update,axiom,
    ! [X65,X241,X66,X98,X242,X5,X58] : hAPP(hAPP(c_List_Ozip(X58,X5),hAPP(hAPP(c_List_Olist__update(X58,X242),X98),X66)),hAPP(hAPP(c_List_Olist__update(X5,X241),X98),X65)) = hAPP(hAPP(c_List_Olist__update(tc_prod(X58,X5),hAPP(hAPP(c_List_Ozip(X58,X5),X242),X241)),X98),hAPP(hAPP(c_Product__Type_OPair(X58,X5),X66),X65)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__update) ).

fof(fact_image__Int,axiom,
    ! [X113,X21,X2,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => hAPP(c_Set_Oimage(X5,X20,X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X20,X2),X21)),hAPP(c_Set_Oimage(X5,X20,X2),X113)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__Int) ).

fof(fact_image__set__diff,axiom,
    ! [X113,X21,X2,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => hAPP(c_Set_Oimage(X5,X20,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X20,X2),X21)),hAPP(c_Set_Oimage(X5,X20,X2),X113)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__set__diff) ).

fof(fact_the__inv__into__onto,axiom,
    ! [X21,X2,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,X2,X21)
     => hAPP(c_Set_Oimage(X20,X5,c_Fun_Othe__inv__into(X5,X20,X21,X2)),hAPP(c_Set_Oimage(X5,X20,X2),X21)) = X21 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__inv__into__onto) ).

fof(fact_pair__box_Osimps_I2_J,axiom,
    ! [X24,X6,X19,X5,X116,X20] : c_Nitpick_Opair__box_Opair__box__case(X20,X116,X5,X19,c_Nitpick_Opair__box_OPairBox(X20,X116,X6,X24)) = hAPP(hAPP(X19,X6),X24),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__box_Osimps_I2_J) ).

fof(fact_pair__box_Orecs,axiom,
    ! [X24,X6,X19,X5,X116,X20] : c_Nitpick_Opair__box_Opair__box__rec(X20,X116,X5,X19,c_Nitpick_Opair__box_OPairBox(X20,X116,X6,X24)) = hAPP(hAPP(X19,X6),X24),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__box_Orecs) ).

fof(fact_zip__takeWhile__fst,axiom,
    ! [X251,X239,X18,X20,X5] : hAPP(hAPP(c_List_Ozip(X5,X20),c_List_OtakeWhile(X5,X18,X239)),X251) = c_List_OtakeWhile(tc_prod(X5,X20),hAPP(c_Fun_Ocomp(X5,tc_HOL_Obool,tc_prod(X5,X20),X18),c_Product__Type_Ofst(X5,X20)),hAPP(hAPP(c_List_Ozip(X5,X20),X239),X251)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__takeWhile__fst) ).

fof(fact_zmult__zless__mono2__lemma,axiom,
    ! [X96,X97,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X98),X97))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X96))
       => 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),X96)),X98)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X96)),X97))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__zless__mono2__lemma) ).

fof(fact_Diff__Int2,axiom,
    ! [X113,X112,X21,X5] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X112)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X113),X112)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X112)),X113),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__Int2) ).

fof(fact_Int__Un__distrib2,axiom,
    ! [X21,X112,X113,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X113),X112)),X21) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X113),X21)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X112),X21)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__Un__distrib2) ).

fof(fact_Diff__Int__distrib2,axiom,
    ! [X112,X113,X21,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),X113)),X112) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X112)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X113),X112)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__Int__distrib2) ).

fof(fact_Un__Int__distrib2,axiom,
    ! [X21,X112,X113,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X113),X112)),X21) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X113),X21)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X112),X21)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Int__distrib2) ).

fof(fact_Un__Diff,axiom,
    ! [X112,X113,X21,X5] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113)),X112) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),X112)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X113),X112)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Diff) ).

fof(fact_bset_I3_J,axiom,
    ! [X113,X15,X144] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X144))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X15),c_Groups_Oone__class_Oone(tc_Int_Oint))),X113))
       => ( ! [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),X144)))
             => ! [X204] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X204),X113))
                 => X15 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X204),X3) ) )
         => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X15),X144) = X15 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bset_I3_J) ).

fof(fact_aset_I3_J,axiom,
    ! [X21,X15,X144] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X144))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X15),c_Groups_Oone__class_Oone(tc_Int_Oint))),X21))
       => ( ! [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),X144)))
             => ! [X204] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X204),X21))
                 => X15 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X204),X3) ) )
         => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X15),X144) = X15 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_aset_I3_J) ).

fof(fact_take__add,axiom,
    ! [X242,X58,X97,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),X97)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242)))
     => hAPP(hAPP(c_List_Otake(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),X97)),X242) = hAPP(hAPP(c_List_Oappend(X58),hAPP(hAPP(c_List_Otake(X58),X98),X242)),hAPP(hAPP(c_List_Otake(X58),X97),hAPP(hAPP(c_List_Odrop(X58),X98),X242))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__add) ).

fof(fact_card_Ounion__inter__neutral,axiom,
    ! [X113,X21,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X113))
       => ( ( ? [X3] : hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113)))
           => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
         => hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X21)),hAPP(c_Finite__Set_Ocard(X5),X113)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card_Ounion__inter__neutral) ).

fof(fact_card__Suc__Diff1,axiom,
    ! [X25,X21,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
       => hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(X5),X21) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Suc__Diff1) ).

fof(fact_folding_Ocommute__comp_H_H,axiom,
    ! [X113,X21,X205,X2,X20,X5] :
      ( c_Finite__Set_Ofolding(X5,X20,X2,X205)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X113))
         => hAPP(c_Fun_Ocomp(X20,X20,X20,hAPP(X205,X113)),hAPP(X205,X21)) = hAPP(c_Fun_Ocomp(X20,X20,X20,hAPP(X205,X21)),hAPP(X205,X113)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Ocommute__comp_H_H) ).

fof(fact_takeWhile__not__last,axiom,
    ! [X5,X239] :
      ( X239 != c_List_Olist_ONil(X5)
     => ( hBOOL(hAPP(c_List_Odistinct(X5),X239))
       => c_List_OtakeWhile(X5,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),c_List_Olast(X5,X239))),X239) = c_List_Obutlast(X5,X239) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_takeWhile__not__last) ).

fof(fact_Compl__INT,axiom,
    ! [X113,X21,X20,X5] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X20,tc_fun(X5,tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X20),c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool))),X113)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__INT) ).

fof(fact_Compl__UN,axiom,
    ! [X113,X21,X20,X5] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,tc_fun(X5,tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X20,tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X20),c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool))),X113)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__UN) ).

fof(fact_fold1Set__sing,axiom,
    ! [X24,X6,X2,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(X5,X2,hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),X24))
    <=> X6 = X24 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1Set__sing) ).

fof(fact_folding_Ounion,axiom,
    ! [X113,X21,X205,X2,X20,X5] :
      ( c_Finite__Set_Ofolding(X5,X20,X2,X205)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X113))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(X205,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113)) = hAPP(c_Fun_Ocomp(X20,X20,X20,hAPP(X205,X21)),hAPP(X205,X113)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Ounion) ).

fof(fact_split__div_H,axiom,
    ! [X50,X95,X18] :
      ( hBOOL(hAPP(X18,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X95),X50)))
    <=> ( ( X50 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & hBOOL(hAPP(X18,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
        | ? [X151] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X50),X151)),X95))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X50),hAPP(c_Nat_OSuc,X151))))
            & hBOOL(hAPP(X18,X151)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__div_H) ).

fof(fact_card_Oinsert__remove,axiom,
    ! [X25,X21,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
     => hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card_Oinsert__remove) ).

fof(fact_o__eq__elim,axiom,
    ! [X22,X23,X115,X24,X6,X5,X20,X116] :
      ( hAPP(c_Fun_Ocomp(X116,X20,X5,X6),X24) = hAPP(c_Fun_Ocomp(X115,X20,X5,X23),X22)
     => ! [X124] : hAPP(X6,hAPP(X24,X124)) = hAPP(X23,hAPP(X22,X124)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__eq__elim) ).

fof(fact_o__eq__dest,axiom,
    ! [X123,X22,X23,X115,X24,X6,X5,X20,X116] :
      ( hAPP(c_Fun_Ocomp(X116,X20,X5,X6),X24) = hAPP(c_Fun_Ocomp(X115,X20,X5,X23),X22)
     => hAPP(X6,hAPP(X24,X123)) = hAPP(X23,hAPP(X22,X123)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__eq__dest) ).

fof(fact_insort__left__comm,axiom,
    ! [X239,X33,X25,X5] :
      ( class_Orderings_Olinorder(X5)
     => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X5,c_COMBI(X5)),X25),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X5,c_COMBI(X5)),X33),X239)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X5,c_COMBI(X5)),X33),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X5,c_COMBI(X5)),X25),X239)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insort__left__comm) ).

fof(fact_o__eq__id__dest,axiom,
    ! [X123,X23,X24,X6,X5,X20,X116] :
      ( hAPP(c_Fun_Ocomp(X116,X20,X5,X6),X24) = hAPP(c_Fun_Ocomp(X20,X20,X5,c_Fun_Oid(X20)),X23)
     => hAPP(X6,hAPP(X24,X123)) = hAPP(X23,X123) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__eq__id__dest) ).

fof(fact_distinct__sort,axiom,
    ! [X239,X2,X5,X20] :
      ( class_Orderings_Olinorder(X20)
     => ( hBOOL(hAPP(c_List_Odistinct(X5),c_List_Olinorder__class_Osort__key(X5,X20,X2,X239)))
      <=> hBOOL(hAPP(c_List_Odistinct(X5),X239)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__sort) ).

fof(fact_equiv__class__self,axiom,
    ! [X6,X171,X21,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X21,X171)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X21))
       => hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(c_Relation_OImage(X5,X5,X171),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equiv__class__self) ).

fof(fact_inj__image__mem__iff,axiom,
    ! [X21,X6,X2,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => ( hBOOL(hAPP(hAPP(c_member(X20),hAPP(X2,X6)),hAPP(c_Set_Oimage(X5,X20,X2),X21)))
      <=> hBOOL(hAPP(hAPP(c_member(X5),X6),X21)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__image__mem__iff) ).

fof(fact_INF__subset,axiom,
    ! [X2,X113,X21,X5,X20] :
      ( class_Complete__Lattice_Ocomplete__lattice(X20)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),X113))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,X20),X113),X2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,X20),X21),X2))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF__subset) ).

fof(fact_SUP__subset,axiom,
    ! [X2,X113,X21,X5,X20] :
      ( class_Complete__Lattice_Ocomplete__lattice(X20)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),X113))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X20),X21),X2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X20),X113),X2))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUP__subset) ).

fof(fact_UN__simps_I1_J,axiom,
    ! [X113,X6,X20,X5,X112] :
      ( ( X112 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X20,tc_HOL_Obool)),X112),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool),X5),hAPP(c_Set_Oinsert(X20),X6)),X113)) = c_Orderings_Obot__class_Obot(tc_fun(X20,tc_HOL_Obool)) )
      & ( X112 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X20,tc_HOL_Obool)),X112),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool),X5),hAPP(c_Set_Oinsert(X20),X6)),X113)) = hAPP(hAPP(c_Set_Oinsert(X20),X6),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X20,tc_HOL_Obool)),X112),X113)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__simps_I1_J) ).

fof(fact_UN__extend__simps_I1_J,axiom,
    ! [X113,X6,X20,X5,X112] :
      ( ( X112 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Set_Oinsert(X20),X6),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X20,tc_HOL_Obool)),X112),X113)) = hAPP(hAPP(c_Set_Oinsert(X20),X6),c_Orderings_Obot__class_Obot(tc_fun(X20,tc_HOL_Obool))) )
      & ( X112 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Set_Oinsert(X20),X6),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X20,tc_HOL_Obool)),X112),X113)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X20,tc_HOL_Obool)),X112),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_fun(X20,tc_HOL_Obool),X5),hAPP(c_Set_Oinsert(X20),X6)),X113)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__extend__simps_I1_J) ).

fof(fact_setsum__right__distrib,axiom,
    ! [X21,X2,X20,X171,X5] :
      ( class_Rings_Osemiring__0(X5)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X171),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X20,X5),X2),X21)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X20,X5),hAPP(hAPP(c_COMBB(X5,X5,X20),hAPP(c_Groups_Otimes__class_Otimes(X5),X171)),X2)),X21) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__right__distrib) ).

fof(fact_mlex__less,axiom,
    ! [X32,X5,X33,X25,X2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X2,X25)),hAPP(X2,X33)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X33)),c_Wellfounded_Omlex__prod(X5,X2,X32))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mlex__less) ).

fof(fact_range__composition,axiom,
    ! [X1,X2,X116,X5,X20] : hAPP(c_Set_Oimage(X20,X5,hAPP(hAPP(c_COMBB(X116,X5,X20),X2),X1)),c_Orderings_Otop__class_Otop(tc_fun(X20,tc_HOL_Obool))) = hAPP(c_Set_Oimage(X116,X5,X2),hAPP(c_Set_Oimage(X20,X116,X1),c_Orderings_Otop__class_Otop(tc_fun(X20,tc_HOL_Obool)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_range__composition) ).

fof(fact_sorted__nth__monoI,axiom,
    ! [X242,X58] :
      ( class_Orderings_Olinorder(X58)
     => ( ! [X146,X101] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X146),X101))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X101),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242)))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_List_Onth(X58),X242),X146)),hAPP(hAPP(c_List_Onth(X58),X242),X101))) ) )
       => c_List_Olinorder__class_Osorted(X58,X242) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__nth__monoI) ).

fof(fact_sorted__equals__nth__mono,axiom,
    ! [X239,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( c_List_Olinorder__class_Osorted(X5,X239)
      <=> ! [X101] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X101),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239)))
           => ! [X146] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X146),X101))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_List_Onth(X5),X239),X146)),hAPP(hAPP(c_List_Onth(X5),X239),X101))) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__equals__nth__mono) ).

fof(fact_INT__D,axiom,
    ! [X6,X113,X21,X20,X24,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X24),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X20,tc_fun(X5,tc_HOL_Obool)),X21),X113)))
     => ( hBOOL(hAPP(hAPP(c_member(X20),X6),X21))
       => hBOOL(hAPP(hAPP(c_member(X5),X24),hAPP(X113,X6))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__D) ).

fof(fact_foldl__absorb0,axiom,
    ! [X250,X25,X5] :
      ( class_Groups_Omonoid__add(X5)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X25),hAPP(c_List_Ofoldl(X5,X5,c_Groups_Oplus__class_Oplus(X5),c_Groups_Ozero__class_Ozero(X5)),X250)) = hAPP(c_List_Ofoldl(X5,X5,c_Groups_Oplus__class_Oplus(X5),X25),X250) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldl__absorb0) ).

fof(fact_list__update__swap,axiom,
    ! [X269,X66,X242,X58,X270,X98] :
      ( X98 != X270
     => hAPP(hAPP(c_List_Olist__update(X58,hAPP(hAPP(c_List_Olist__update(X58,X242),X98),X66)),X270),X269) = hAPP(hAPP(c_List_Olist__update(X58,hAPP(hAPP(c_List_Olist__update(X58,X242),X270),X269)),X98),X66) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update__swap) ).

fof(fact_rel__pow__commute,axiom,
    ! [X50,X32,X5] : hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),X32),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X50),X32)) = hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X50),X32)),X32),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__pow__commute) ).

fof(fact_card__insert,axiom,
    ! [X25,X21,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
     => hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__insert) ).

fof(fact_divide__left__mono,axiom,
    ! [X56,X62,X90,X58] :
      ( class_Fields_Olinordered__field(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X90),X62))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),X56))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X90)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X56),X62)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X56),X90))) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__left__mono) ).

fof(fact_divide__strict__left__mono,axiom,
    ! [X56,X62,X90,X58] :
      ( class_Fields_Olinordered__field(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X90),X62))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),X56))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X90)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X56),X62)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X56),X90))) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__strict__left__mono) ).

fof(fact_mono__Field,axiom,
    ! [X76,X171,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X171),X76))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_OField(X5),X171)),hAPP(c_Relation_OField(X5),X76))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mono__Field) ).

fof(fact_folding_Ocommute__comp_H,axiom,
    ! [X25,X21,X205,X2,X20,X5] :
      ( c_Finite__Set_Ofolding(X5,X20,X2,X205)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => hAPP(c_Fun_Ocomp(X20,X20,X20,hAPP(X2,X25)),hAPP(X205,X21)) = hAPP(c_Fun_Ocomp(X20,X20,X20,hAPP(X205,X21)),hAPP(X2,X25)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Ocommute__comp_H) ).

fof(fact_INT__simps_I5_J,axiom,
    ! [X113,X6,X112,X5,X20] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X20,tc_fun(X5,tc_HOL_Obool)),X112),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X20),hAPP(c_Set_Oinsert(X5),X6)),X113)) = hAPP(hAPP(c_Set_Oinsert(X5),X6),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X20,tc_fun(X5,tc_HOL_Obool)),X112),X113)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__simps_I5_J) ).

fof(fact_INT__extend__simps_I5_J,axiom,
    ! [X113,X112,X20,X6,X5] : hAPP(hAPP(c_Set_Oinsert(X5),X6),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X20,tc_fun(X5,tc_HOL_Obool)),X112),X113)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X20,tc_fun(X5,tc_HOL_Obool)),X112),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),X20),hAPP(c_Set_Oinsert(X5),X6)),X113)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__extend__simps_I5_J) ).

fof(fact_left__add__mult__distrib,axiom,
    ! [X96,X97,X55,X98] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X98),X55)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X97),X55)),X96)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),X97)),X55)),X96),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_left__add__mult__distrib) ).

fof(fact_zip__takeWhile__snd,axiom,
    ! [X251,X18,X239,X20,X5] : hAPP(hAPP(c_List_Ozip(X5,X20),X239),c_List_OtakeWhile(X20,X18,X251)) = c_List_OtakeWhile(tc_prod(X5,X20),hAPP(c_Fun_Ocomp(X20,tc_HOL_Obool,tc_prod(X5,X20),X18),c_Product__Type_Osnd(X5,X20)),hAPP(hAPP(c_List_Ozip(X5,X20),X239),X251)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__takeWhile__snd) ).

fof(fact_New__DSequence_Oneg__decr__bind__def,axiom,
    ! [X2,X25,X5,X20,X82] :
      ( ( X82 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => hAPP(c_New__DSequence_Oneg__decr__bind(X20,X5,X25,X2),X82) = c_Lazy__Sequence_Ohit__bound(X5) )
      & ( X82 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => hAPP(c_New__DSequence_Oneg__decr__bind(X20,X5,X25,X2),X82) = c_Lazy__Sequence_Ohb__bind(X20,X5,hAPP(X25,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X82),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(X20,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X5))),X2),X82)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_New__DSequence_Oneg__decr__bind__def) ).

fof(fact_inj__fun,axiom,
    ! [X116,X2,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => c_Fun_Oinj__on(X5,tc_fun(X116,X20),hAPP(hAPP(c_COMBB(X20,tc_fun(X116,X20),X5),c_COMBK(X20,X116)),X2),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__fun) ).

fof(fact_Int__eq__Inter,axiom,
    ! [X113,X21,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113) = c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(tc_fun(X5,tc_HOL_Obool)),X113),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__eq__Inter) ).

fof(fact_Un__eq__Union,axiom,
    ! [X113,X21,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113) = c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(tc_fun(X5,tc_HOL_Obool)),X113),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__eq__Union) ).

fof(fact_divide__left__mono__neg,axiom,
    ! [X56,X90,X62,X58] :
      ( class_Fields_Olinordered__field__inverse__zero(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X62),X90))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X56),c_Groups_Ozero__class_Ozero(X58)))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X90)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X56),X62)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X56),X90))) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__left__mono__neg) ).

fof(fact_divide__strict__left__mono__neg,axiom,
    ! [X56,X90,X62,X58] :
      ( class_Fields_Olinordered__field(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X62),X90))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X56),c_Groups_Ozero__class_Ozero(X58)))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X90)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X56),X62)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X56),X90))) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__strict__left__mono__neg) ).

fof(fact_New__DSequence_Opos__decr__bind__def,axiom,
    ! [X2,X25,X5,X20,X82] :
      ( ( X82 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => hAPP(c_New__DSequence_Opos__decr__bind(X20,X5,X25,X2),X82) = c_Lazy__Sequence_Oempty(X5) )
      & ( X82 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => hAPP(c_New__DSequence_Opos__decr__bind(X20,X5,X25,X2),X82) = hAPP(c_Lazy__Sequence_Obind(X20,X5,hAPP(X25,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X82),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBC(X20,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X5)),X2),X82)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_New__DSequence_Opos__decr__bind__def) ).

fof(fact_nth__zip,axiom,
    ! [X241,X5,X242,X58,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X241)))
       => hAPP(hAPP(c_List_Onth(tc_prod(X58,X5)),hAPP(hAPP(c_List_Ozip(X58,X5),X242),X241)),X98) = hAPP(hAPP(c_Product__Type_OPair(X58,X5),hAPP(hAPP(c_List_Onth(X58),X242),X98)),hAPP(hAPP(c_List_Onth(X5),X241),X98)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__zip) ).

fof(fact_mod__mult2__eq,axiom,
    ! [X56,X90,X62] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X62,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X90),X56)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X90),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X62),X90),X56))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X62,X90)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult2__eq) ).

fof(fact_list__update__length,axiom,
    ! [X65,X241,X66,X242,X58] : hAPP(hAPP(c_List_Olist__update(X58,hAPP(hAPP(c_List_Oappend(X58),X242),hAPP(hAPP(c_List_Olist_OCons(X58),X66),X241))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242)),X65) = hAPP(hAPP(c_List_Oappend(X58),X242),hAPP(hAPP(c_List_Olist_OCons(X58),X65),X241)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update__length) ).

fof(fact_listrel1__rtrancl__subset__rtrancl__listrel1,axiom,
    ! [X171,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_HOL_Obool)),c_List_Olistrel1(X5,c_Transitive__Closure_Ortrancl(X5,X171))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X5),c_List_Olistrel1(X5,X171)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel1__rtrancl__subset__rtrancl__listrel1) ).

fof(fact_rtrancl__Un__rtrancl,axiom,
    ! [X192,X32,X5] : c_Transitive__Closure_Ortrancl(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X5,X32)),c_Transitive__Closure_Ortrancl(X5,X192))) = c_Transitive__Closure_Ortrancl(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X32),X192)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__Un__rtrancl) ).

fof(fact_zip__map__fst__snd,axiom,
    ! [X250,X20,X5] : hAPP(hAPP(c_List_Ozip(X5,X20),hAPP(hAPP(c_List_Omap(tc_prod(X5,X20),X5),c_Product__Type_Ofst(X5,X20)),X250)),hAPP(hAPP(c_List_Omap(tc_prod(X5,X20),X20),c_Product__Type_Osnd(X5,X20)),X250)) = X250,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__map__fst__snd) ).

fof(fact_setprod__reindex__cong,axiom,
    ! [X122,X1,X113,X21,X2,X20,X5,X116] :
      ( class_Groups_Ocomm__monoid__mult(X116)
     => ( c_Fun_Oinj__on(X5,X20,X2,X21)
       => ( X113 = hAPP(c_Set_Oimage(X5,X20,X2),X21)
         => ( X1 = hAPP(c_Fun_Ocomp(X20,X116,X5,X122),X2)
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X20,X116),X122),X113) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X116),X1),X21) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__reindex__cong) ).

fof(fact_sum__squares__ge__zero,axiom,
    ! [X65,X66,X58] :
      ( class_Rings_Olinordered__ring(X58)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X66),X66)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X65),X65)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__squares__ge__zero) ).

fof(fact_pred__nat__trancl__eq__le,axiom,
    ! [X50,X95] :
      ( 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),X95),X50)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X50)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__nat__trancl__eq__le) ).

fof(fact_folding_Ocommute__comp,axiom,
    ! [X25,X33,X205,X2,X20,X5] :
      ( c_Finite__Set_Ofolding(X5,X20,X2,X205)
     => hAPP(c_Fun_Ocomp(X20,X20,X20,hAPP(X2,X33)),hAPP(X2,X25)) = hAPP(c_Fun_Ocomp(X20,X20,X20,hAPP(X2,X25)),hAPP(X2,X33)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Ocommute__comp) ).

fof(fact_Sigma__Int__distrib1,axiom,
    ! [X112,X222,X221,X20,X5] : hAPP(hAPP(c_Product__Type_OSigma(X5,X20),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X221),X222)),X112) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X5,X20),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X5,X20),X221),X112)),hAPP(hAPP(c_Product__Type_OSigma(X5,X20),X222),X112)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__Int__distrib1) ).

fof(fact_Sigma__Un__distrib1,axiom,
    ! [X112,X222,X221,X20,X5] : hAPP(hAPP(c_Product__Type_OSigma(X5,X20),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X221),X222)),X112) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X20),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X5,X20),X221),X112)),hAPP(hAPP(c_Product__Type_OSigma(X5,X20),X222),X112)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__Un__distrib1) ).

fof(fact_Sigma__Diff__distrib1,axiom,
    ! [X112,X222,X221,X20,X5] : hAPP(hAPP(c_Product__Type_OSigma(X5,X20),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X221),X222)),X112) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X5,X20),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X5,X20),X221),X112)),hAPP(hAPP(c_Product__Type_OSigma(X5,X20),X222),X112)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__Diff__distrib1) ).

fof(fact_in__set__butlast__appendI,axiom,
    ! [X251,X239,X25,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),c_List_Obutlast(X5,X239))))
        | hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),c_List_Obutlast(X5,X251)))) )
     => hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),c_List_Obutlast(X5,hAPP(hAPP(c_List_Oappend(X5),X239),X251))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__set__butlast__appendI) ).

fof(fact_acc__subset,axiom,
    ! [X189,X190,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X190),X189))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),c_Wellfounded_Oacc(X5,X189)),c_Wellfounded_Oacc(X5,X190))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc__subset) ).

fof(fact_insort__key__left__comm,axiom,
    ! [X239,X20,X33,X25,X2,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hAPP(X2,X25) != hAPP(X2,X33)
       => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X20,X5,X2),X33),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X20,X5,X2),X25),X239)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X20,X5,X2),X25),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X20,X5,X2),X33),X239)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insort__key__left__comm) ).

fof(fact_surj__f__inv__f,axiom,
    ! [X33,X2,X5,X20] :
      ( hAPP(c_Set_Oimage(X20,X5,X2),c_Orderings_Otop__class_Otop(tc_fun(X20,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))
     => hAPP(X2,hAPP(c_Hilbert__Choice_Oinv__into(X20,X5,c_Orderings_Otop__class_Otop(tc_fun(X20,tc_HOL_Obool)),X2),X33)) = X33 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surj__f__inv__f) ).

fof(fact_divmod__int__rel__div__mod,axiom,
    ! [X62,X90] :
      ( X90 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
     => hBOOL(hAPP(c_Divides_Odivmod__int__rel(X62,X90),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X62),X90)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X62,X90)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__int__rel__div__mod) ).

fof(fact_INT__extend__simps_I10_J,axiom,
    ! [X2,X113,X116,X21,X5,X20] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X20,tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_COMBB(X116,tc_fun(X5,tc_HOL_Obool),X20),X113),X2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X116,tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Oimage(X20,X116,X2),X21)),X113),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__extend__simps_I10_J) ).

fof(fact_UN__extend__simps_I10_J,axiom,
    ! [X2,X113,X116,X21,X5,X20] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_COMBB(X116,tc_fun(X5,tc_HOL_Obool),X20),X113),X2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X116,tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Oimage(X20,X116,X2),X21)),X113),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__extend__simps_I10_J) ).

fof(fact_INT__simps_I10_J,axiom,
    ! [X113,X21,X2,X116,X5,X20] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X20,tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Oimage(X116,X20,X2),X21)),X113) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X116,tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_COMBB(X20,tc_fun(X5,tc_HOL_Obool),X116),X113),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__simps_I10_J) ).

fof(fact_UN__simps_I10_J,axiom,
    ! [X113,X21,X2,X116,X5,X20] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Oimage(X116,X20,X2),X21)),X113) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X116,tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_COMBB(X20,tc_fun(X5,tc_HOL_Obool),X116),X113),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__simps_I10_J) ).

fof(fact_divmod__nat__rel,axiom,
    ! [X57,X72] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X72,X57),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X72),X57)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X72,X57)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__rel) ).

fof(fact_Compl__anti__mono,axiom,
    ! [X113,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),X113))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X113)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X21))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__anti__mono) ).

fof(fact_finite__surj__inj,axiom,
    ! [X2,X21,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(c_Set_Oimage(X5,X5,X2),X21)))
       => c_Fun_Oinj__on(X5,X5,X2,X21) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__surj__inj) ).

fof(fact_Compl__Times__UNIV1,axiom,
    ! [X21,X20,X5] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(X5,X20),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X5,X20),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X20,tc_HOL_Obool),X5),X21))) = hAPP(hAPP(c_Product__Type_OSigma(X5,X20),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X20,tc_HOL_Obool),X5),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20,tc_HOL_Obool)),X21))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__Times__UNIV1) ).

fof(fact_Compl__Times__UNIV2,axiom,
    ! [X21,X20,X5] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(X5,X20),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X5,X20),X21),hAPP(c_COMBK(tc_fun(X20,tc_HOL_Obool),X5),c_Orderings_Otop__class_Otop(tc_fun(X20,tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(X5,X20),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X21)),hAPP(c_COMBK(tc_fun(X20,tc_HOL_Obool),X5),c_Orderings_Otop__class_Otop(tc_fun(X20,tc_HOL_Obool)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__Times__UNIV2) ).

fof(fact_Cons__acc__listrel1I,axiom,
    ! [X239,X171,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X25),c_Wellfounded_Oacc(X5,X171)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X239),c_Wellfounded_Oacc(tc_List_Olist(X5),c_List_Olistrel1(X5,X171))))
       => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239)),c_Wellfounded_Oacc(tc_List_Olist(X5),c_List_Olistrel1(X5,X171)))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Cons__acc__listrel1I) ).

fof(fact_neg__divide__le__eq,axiom,
    ! [X6,X24,X23,X5] :
      ( class_Fields_Olinordered__field(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X24),X23)),X6))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X23)),X24)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__divide__le__eq) ).

fof(fact_neg__divide__less__eq,axiom,
    ! [X6,X24,X23,X5] :
      ( class_Fields_Olinordered__field(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X24),X23)),X6))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X23)),X24)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__divide__less__eq) ).

fof(fact_accp__subset,axiom,
    ! [X189,X190,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_fun(X5,tc_HOL_Obool))),X190),X189))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),c_Wellfounded_Oaccp(X5,X189)),c_Wellfounded_Oaccp(X5,X190))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_accp__subset) ).

fof(fact_folding__idem_Osubset__comp__idem,axiom,
    ! [X113,X21,X205,X2,X20,X5] :
      ( c_Finite__Set_Ofolding__idem(X5,X20,X2,X205)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X113),X21))
         => hAPP(c_Fun_Ocomp(X20,X20,X20,hAPP(X205,X21)),hAPP(X205,X113)) = hAPP(X205,X21) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__idem_Osubset__comp__idem) ).

fof(fact_insort__insert__triv,axiom,
    ! [X239,X25,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X239)))
       => c_List_Olinorder__class_Oinsort__insert__key(X5,X5,c_COMBI(X5),X25,X239) = X239 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insort__insert__triv) ).

fof(fact_split__div__lemma,axiom,
    ! [X95,X153,X50] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X50))
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X50),X153)),X95))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X50),hAPP(c_Nat_OSuc,X153)))) )
      <=> X153 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X95),X50) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__div__lemma) ).

fof(fact_setsum__diff,axiom,
    ! [X2,X113,X21,X5,X20] :
      ( class_Groups_Oab__group__add(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X113),X21))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X2),X21)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X2),X113)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__diff) ).

fof(fact_id__take__nth__drop,axiom,
    ! [X242,X58,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242)))
     => X242 = hAPP(hAPP(c_List_Oappend(X58),hAPP(hAPP(c_List_Otake(X58),X98),X242)),hAPP(hAPP(c_List_Olist_OCons(X58),hAPP(hAPP(c_List_Onth(X58),X242),X98)),hAPP(hAPP(c_List_Odrop(X58),hAPP(c_Nat_OSuc,X98)),X242))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_id__take__nth__drop) ).

fof(fact_less__than__iff,axiom,
    ! [X33,X25] :
      ( 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),X25),X33)),c_Wellfounded_Oless__than))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),X33)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__than__iff) ).

fof(fact_image__image,axiom,
    ! [X21,X1,X116,X2,X5,X20] : hAPP(c_Set_Oimage(X20,X5,X2),hAPP(c_Set_Oimage(X116,X20,X1),X21)) = hAPP(c_Set_Oimage(X116,X5,hAPP(hAPP(c_COMBB(X20,X5,X116),X2),X1)),X21),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__image) ).

fof(fact_map__inj__on,axiom,
    ! [X251,X239,X2,X5,X20] :
      ( hAPP(hAPP(c_List_Omap(X20,X5),X2),X239) = hAPP(hAPP(c_List_Omap(X20,X5),X2),X251)
     => ( c_Fun_Oinj__on(X20,X5,X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20,tc_HOL_Obool)),hAPP(c_List_Oset(X20),X239)),hAPP(c_List_Oset(X20),X251)))
       => X239 = X251 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__inj__on) ).

fof(fact_inj__on__map__eq__map,axiom,
    ! [X251,X239,X2,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),X239)),hAPP(c_List_Oset(X5),X251)))
     => ( hAPP(hAPP(c_List_Omap(X5,X20),X2),X239) = hAPP(hAPP(c_List_Omap(X5,X20),X2),X251)
      <=> X239 = X251 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__map__eq__map) ).

fof(fact_zdiff__int__split,axiom,
    ! [X33,X25,X18] :
      ( hBOOL(hAPP(X18,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25),X33))))
    <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33),X25))
         => hBOOL(hAPP(X18,hAPP(hAPP(c_Groups_Ominus__class_Ominus(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),X33)))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),X33))
         => hBOOL(hAPP(X18,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiff__int__split) ).

fof(fact_listsp__infI,axiom,
    ! [X113,X156,X21,X5] :
      ( hBOOL(hAPP(c_List_Olistsp(X5,X21),X156))
     => ( hBOOL(hAPP(c_List_Olistsp(X5,X113),X156))
       => hBOOL(hAPP(c_List_Olistsp(X5,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113)),X156)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsp__infI) ).

fof(fact_Image__Int__eq,axiom,
    ! [X113,X21,X32,X20,X5] :
      ( c_Relation_Osingle__valued(X5,X20,hAPP(c_Relation_Oconverse(X20,X5),X32))
     => hAPP(c_Relation_OImage(X20,X5,X32),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20,tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_OImage(X20,X5,X32),X21)),hAPP(c_Relation_OImage(X20,X5,X32),X113)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__Int__eq) ).

fof(fact_frac__le,axiom,
    ! [X94,X128,X65,X66,X58] :
      ( class_Fields_Olinordered__field(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),X66))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X66),X65))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),X128))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X128),X94))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X66),X94)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X65),X128))) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_frac__le) ).

fof(fact_mult__mono_H,axiom,
    ! [X91,X56,X90,X62,X58] :
      ( class_Rings_Oordered__semiring(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X62),X90))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X56),X91))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),X62))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),X56))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X56)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X90),X91))) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__mono_H) ).

fof(fact_mult__mono,axiom,
    ! [X91,X56,X90,X62,X58] :
      ( class_Rings_Oordered__semiring(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X62),X90))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X56),X91))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),X90))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),X56))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X56)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X90),X91))) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__mono) ).

fof(fact_frac__less,axiom,
    ! [X94,X128,X65,X66,X58] :
      ( class_Fields_Olinordered__field(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),X66))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X66),X65))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),X128))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X128),X94))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X66),X94)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X65),X128))) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_frac__less) ).

fof(fact_frac__less2,axiom,
    ! [X94,X128,X65,X66,X58] :
      ( class_Fields_Olinordered__field(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),X66))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X66),X65))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),X128))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X128),X94))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X66),X94)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X65),X128))) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_frac__less2) ).

fof(fact_mult__less__le__imp__less,axiom,
    ! [X91,X56,X90,X62,X58] :
      ( class_Rings_Olinordered__semiring__strict(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X62),X90))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X56),X91))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),X62))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),X56))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X56)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X90),X91))) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__le__imp__less) ).

fof(fact_mult__le__less__imp__less,axiom,
    ! [X91,X56,X90,X62,X58] :
      ( class_Rings_Olinordered__semiring__strict(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X62),X90))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X56),X91))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),X62))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),X56))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X56)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X90),X91))) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__less__imp__less) ).

fof(fact_mult__strict__mono_H,axiom,
    ! [X91,X56,X90,X62,X58] :
      ( class_Rings_Olinordered__semiring__strict(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X62),X90))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X56),X91))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),X62))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),X56))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X56)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X90),X91))) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__mono_H) ).

fof(fact_mult__strict__mono,axiom,
    ! [X91,X56,X90,X62,X58] :
      ( class_Rings_Olinordered__semiring__strict(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X62),X90))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X56),X91))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),X90))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),X56))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X56)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X90),X91))) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__mono) ).

fof(fact_setsum__diff1__ring,axiom,
    ! [X2,X6,X21,X5,X20] :
      ( class_Rings_Oring(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X21))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X2),X21)),hAPP(X2,X6)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__diff1__ring) ).

fof(fact_geometric__sum,axiom,
    ! [X50,X25,X5] :
      ( class_Fields_Ofield(X5)
     => ( X25 != c_Groups_Oone__class_Oone(X5)
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),hAPP(c_Power_Opower__class_Opower(X5),X25)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X50)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X25),X50)),c_Groups_Oone__class_Oone(X5))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X25),c_Groups_Oone__class_Oone(X5))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_geometric__sum) ).

fof(fact_listsum__abs,axiom,
    ! [X239,X5] :
      ( class_Groups_Oordered__ab__group__add__abs(X5)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Groups_Oabs__class_Oabs(X5),hAPP(c_List_Omonoid__add__class_Olistsum(X5),X239))),hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X5,X5),c_Groups_Oabs__class_Oabs(X5)),X239)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__abs) ).

fof(fact_image__add__atLeastLessThan,axiom,
    ! [X157,X82,X87] : 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)),X87)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X82),X157)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X82),X87)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X157),X87)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__add__atLeastLessThan) ).

fof(fact_setsum__diff__nat__ivl,axiom,
    ! [X2,X160,X50,X95,X5] :
      ( class_Groups_Oab__group__add(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X50))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X50),X160))
         => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X95),X160))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X95),X50))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X50),X160)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__diff__nat__ivl) ).

fof(fact_setsum__add__nat__ivl,axiom,
    ! [X2,X160,X50,X95,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X50))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X50),X160))
         => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X95),X50))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X50),X160))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X95),X160)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__add__nat__ivl) ).

fof(fact_mult__right__le__imp__le,axiom,
    ! [X90,X56,X62,X58] :
      ( class_Rings_Olinordered__semiring__strict(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X56)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X90),X56)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),X56))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X62),X90)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right__le__imp__le) ).

fof(fact_mult__left__le__imp__le,axiom,
    ! [X90,X62,X56,X58] :
      ( class_Rings_Olinordered__semiring__strict(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X56),X62)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X56),X90)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),X56))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X62),X90)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left__le__imp__le) ).

fof(fact_mult__le__cancel__left__pos,axiom,
    ! [X24,X6,X23,X5] :
      ( class_Rings_Olinordered__ring__strict(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X23),X6)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X23),X24)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),X24)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__cancel__left__pos) ).

fof(fact_mult__right__less__imp__less,axiom,
    ! [X90,X56,X62,X58] :
      ( class_Rings_Olinordered__semiring(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X56)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X90),X56)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),X56))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X62),X90)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right__less__imp__less) ).

fof(fact_mult__less__imp__less__right,axiom,
    ! [X90,X56,X62,X58] :
      ( class_Rings_Olinordered__semiring__strict(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X56)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X90),X56)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),X56))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X62),X90)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__imp__less__right) ).

fof(fact_power__less__imp__less__base,axiom,
    ! [X90,X57,X62,X58] :
      ( class_Rings_Olinordered__semidom(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),X57)),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X90),X57)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),X90))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X62),X90)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__less__imp__less__base) ).

fof(fact_mult__left__less__imp__less,axiom,
    ! [X90,X62,X56,X58] :
      ( class_Rings_Olinordered__semiring(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X56),X62)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X56),X90)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),X56))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X62),X90)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left__less__imp__less) ).

fof(fact_mult__less__imp__less__left,axiom,
    ! [X90,X62,X56,X58] :
      ( class_Rings_Olinordered__semiring__strict(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X56),X62)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X56),X90)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),X56))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X62),X90)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__imp__less__left) ).

fof(fact_mult__less__cancel__left__pos,axiom,
    ! [X24,X6,X23,X5] :
      ( class_Rings_Olinordered__ring__strict(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X23),X6)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X23),X24)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),X24)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel__left__pos) ).

fof(fact_setsum__diff__nat,axiom,
    ! [X2,X21,X113,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X113))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X113),X21))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),X2),X21)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),X2),X113)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__diff__nat) ).

fof(fact_fold1__strict__below__iff,axiom,
    ! [X25,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Finite__Set_Ofold1(X5,c_Orderings_Oord__class_Omin(X5)),X21)),X25))
          <=> ? [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X3),X21))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X3),X25)) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__strict__below__iff) ).

fof(fact_fold1__below__iff,axiom,
    ! [X25,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Finite__Set_Ofold1(X5,c_Orderings_Oord__class_Omin(X5)),X21)),X25))
          <=> ? [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X3),X21))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X3),X25)) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__below__iff) ).

fof(fact_INF1__D,axiom,
    ! [X6,X24,X113,X21,X20,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X20,tc_HOL_Obool)),X21),X113),X24))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X21))
       => hBOOL(hAPP(hAPP(X113,X6),X24)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF1__D) ).

fof(fact_power__le__imp__le__exp,axiom,
    ! [X57,X72,X62,X58] :
      ( class_Rings_Olinordered__semidom(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Oone__class_Oone(X58)),X62))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),X72)),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),X57)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X72),X57)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__le__imp__le__exp) ).

fof(fact_power__increasing__iff,axiom,
    ! [X33,X25,X24,X5] :
      ( class_Rings_Olinordered__semidom(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Oone__class_Oone(X5)),X24))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X24),X25)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X24),X33)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25),X33)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__increasing__iff) ).

fof(fact_power__strict__increasing__iff,axiom,
    ! [X33,X25,X24,X5] :
      ( class_Rings_Olinordered__semidom(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Oone__class_Oone(X5)),X24))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X24),X25)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X24),X33)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),X33)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__strict__increasing__iff) ).

fof(fact_power__less__imp__less__exp,axiom,
    ! [X57,X72,X62,X58] :
      ( class_Rings_Olinordered__semidom(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Oone__class_Oone(X58)),X62))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),X72)),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),X57)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X72),X57)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__less__imp__less__exp) ).

fof(fact_select,axiom,
    ! [X76,X5,X239] :
      ( X239 != c_List_Olist_ONil(X5)
     => hBOOL(hAPP(hAPP(c_member(X5),hAPP(c_Product__Type_Ofst(X5,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect(X5,X239),X76))),hAPP(c_List_Oset(X5),X239))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_select) ).

fof(fact_card__cartesian__product__singleton,axiom,
    ! [X21,X25,X20,X5] : hAPP(c_Finite__Set_Ocard(tc_prod(X5,X20)),hAPP(hAPP(c_Product__Type_OSigma(X5,X20),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),hAPP(c_COMBK(tc_fun(X20,tc_HOL_Obool),X5),X21))) = hAPP(c_Finite__Set_Ocard(X20),X21),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__cartesian__product__singleton) ).

fof(fact_evalc_Oequations_I9_J,axiom,
    ! [X63,X26,X27] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X27)),X26),X63))
    <=> hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X27))),X26),X63)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_Oequations_I9_J) ).

fof(fact_evalc_OBody,axiom,
    ! [X45,X46,X47] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X47))),X46),X45))
     => hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X47)),X46),X45)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_OBody) ).

fof(fact_splitD,axiom,
    ! [X24,X6,X2,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5,X20,tc_HOL_Obool),X2),hAPP(hAPP(c_Product__Type_OPair(X5,X20),X6),X24)))
     => hBOOL(hAPP(hAPP(X2,X6),X24)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_splitD) ).

fof(fact_swap__inj__on,axiom,
    ! [X21,X20,X5] : c_Fun_Oinj__on(tc_prod(X5,X20),tc_prod(X20,X5),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X20,tc_prod(X20,X5)),hAPP(c_COMBC(X20,X5,tc_prod(X20,X5)),c_Product__Type_OPair(X20,X5))),X21),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_swap__inj__on) ).

fof(fact_setprod__pos__nat,axiom,
    ! [X2,X192,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X192))
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X192))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X2,X3))) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,tc_Nat_Onat),X2),X192))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__pos__nat) ).

fof(fact_setprod__pos__nat__iff,axiom,
    ! [X2,X192,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X192))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,tc_Nat_Onat),X2),X192)))
      <=> ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X192))
           => 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/sandbox/benchmark/theBenchmark.p',fact_setprod__pos__nat__iff) ).

fof(fact_setsum__shift__bounds__cl__Suc__ivl,axiom,
    ! [X50,X95,X2,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X95),hAPP(c_Nat_OSuc,X50))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X5,tc_Nat_Onat),X2),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X95,X50)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__shift__bounds__cl__Suc__ivl) ).

fof(fact_mult__le__cancel__left__neg,axiom,
    ! [X24,X6,X23,X5] :
      ( class_Rings_Olinordered__ring__strict(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X23),X6)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X23),X24)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X24),X6)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__cancel__left__neg) ).

fof(fact_mult__less__cancel__left__neg,axiom,
    ! [X24,X6,X23,X5] :
      ( class_Rings_Olinordered__ring__strict(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X23),X6)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X23),X24)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X24),X6)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel__left__neg) ).

fof(fact_Int__lower1,axiom,
    ! [X113,X21,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)),X21),X113)),X21)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__lower1) ).

fof(fact_Int__lower2,axiom,
    ! [X113,X21,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)),X21),X113)),X113)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__lower2) ).

fof(fact_Diff__subset,axiom,
    ! [X113,X21,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),X113)),X21)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__subset) ).

fof(fact_listsum__map__remove1,axiom,
    ! [X2,X239,X25,X5,X20] :
      ( class_Groups_Ocomm__monoid__add(X20)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X239)))
       => hAPP(c_List_Omonoid__add__class_Olistsum(X20),hAPP(hAPP(c_List_Omap(X5,X20),X2),X239)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20),hAPP(X2,X25)),hAPP(c_List_Omonoid__add__class_Olistsum(X20),hAPP(hAPP(c_List_Omap(X5,X20),X2),c_List_Oremove1(X5,X25,X239)))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__map__remove1) ).

fof(fact_Int__Un__distrib,axiom,
    ! [X112,X113,X21,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X113),X112)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X112)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__Un__distrib) ).

fof(fact_Diff__Int__distrib,axiom,
    ! [X113,X21,X112,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X112),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X112),X21)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X112),X113)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__Int__distrib) ).

fof(fact_Un__Int__distrib,axiom,
    ! [X112,X113,X21,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X113),X112)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X112)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Int__distrib) ).

fof(fact_Diff__Int,axiom,
    ! [X112,X113,X21,X5] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X113),X112)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),X113)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),X112)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__Int) ).

fof(fact_Diff__Un,axiom,
    ! [X112,X113,X21,X5] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X113),X112)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),X113)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),X112)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__Un) ).

fof(fact_prod_Orecs,axiom,
    ! [X24,X6,X19,X5,X116,X20] : c_Product__Type_Oprod_Oprod__rec(X20,X116,X5,X19,hAPP(hAPP(c_Product__Type_OPair(X20,X116),X6),X24)) = hAPP(hAPP(X19,X6),X24),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_prod_Orecs) ).

fof(fact_New__DSequence_Oneg__bind__def,axiom,
    ! [X82,X2,X25,X5,X20] : hAPP(c_New__DSequence_Oneg__bind(X20,X5,X25,X2),X82) = c_Lazy__Sequence_Ohb__bind(X20,X5,hAPP(X25,X82),hAPP(hAPP(c_COMBC(X20,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X5))),X2),X82)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_New__DSequence_Oneg__bind__def) ).

fof(fact_setsum__shift__bounds__Suc__ivl,axiom,
    ! [X50,X95,X2,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X95)),hAPP(c_Nat_OSuc,X50))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X5,tc_Nat_Onat),X2),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X95),X50)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__shift__bounds__Suc__ivl) ).

fof(fact_image__add__atLeastAtMost,axiom,
    ! [X157,X82,X87] : 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)),X87)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X82,X157)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X82),X87),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X157),X87)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__add__atLeastAtMost) ).

fof(fact_Int__Collect,axiom,
    ! [X18,X21,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(c_Set_OCollect(X5),X18))))
    <=> ( hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
        & hBOOL(hAPP(X18,X25)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__Collect) ).

fof(fact_atLeastLessThan__subset__iff,axiom,
    ! [X22,X23,X24,X6,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X6),X24)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X23),X22)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X24),X6))
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X23),X6))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X24),X22)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__subset__iff) ).

fof(fact_folding__idem_Ounion__idem,axiom,
    ! [X113,X21,X205,X2,X20,X5] :
      ( c_Finite__Set_Ofolding__idem(X5,X20,X2,X205)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X113))
         => hAPP(X205,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113)) = hAPP(c_Fun_Ocomp(X20,X20,X20,hAPP(X205,X21)),hAPP(X205,X113)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__idem_Ounion__idem) ).

fof(fact_wf__Un,axiom,
    ! [X76,X171,X5] :
      ( c_Wellfounded_Owf(X5,X171)
     => ( c_Wellfounded_Owf(X5,X76)
       => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X5,X5),X171)),hAPP(c_Relation_ORange(X5,X5),X76)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => c_Wellfounded_Owf(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X171),X76)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__Un) ).

fof(fact_fun__left__comm_Ofold__set__remdups,axiom,
    ! [X239,X33,X2,X20,X5] :
      ( c_Finite__Set_Ofun__left__comm(X5,X20,X2)
     => hAPP(hAPP(c_Finite__Set_Ofold(X5,X20,X2),X33),hAPP(c_List_Oset(X5),X239)) = hAPP(c_List_Ofoldl(X20,X5,hAPP(c_COMBC(X5,X20,X20),X2),X33),c_List_Oremdups(X5,X239)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__set__remdups) ).

fof(fact_converse__meet,axiom,
    ! [X76,X171,X5,X20] : c_Predicate_Oconversep(X20,X5,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20,tc_fun(X5,tc_HOL_Obool))),X171),X76)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_fun(X20,tc_HOL_Obool))),c_Predicate_Oconversep(X20,X5,X171)),c_Predicate_Oconversep(X20,X5,X76)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__meet) ).

fof(fact_converse__join,axiom,
    ! [X76,X171,X5,X20] : c_Predicate_Oconversep(X20,X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20,tc_fun(X5,tc_HOL_Obool))),X171),X76)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_fun(X20,tc_HOL_Obool))),c_Predicate_Oconversep(X20,X5,X171)),c_Predicate_Oconversep(X20,X5,X76)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__join) ).

fof(fact_le__diff__iff,axiom,
    ! [X50,X95,X87] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X87),X95))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X87),X50))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X95),X87)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X50),X87)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X50)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__diff__iff) ).

fof(fact_less__diff__iff,axiom,
    ! [X50,X95,X87] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X87),X95))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X87),X50))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X95),X87)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X50),X87)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),X50)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__diff__iff) ).

fof(fact_mult__less__cancel__left__disj,axiom,
    ! [X24,X6,X23,X5] :
      ( class_Rings_Olinordered__ring__strict(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X23),X6)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X23),X24)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),X24)) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X24),X6)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel__left__disj) ).

fof(fact_mult__less__cancel__right__disj,axiom,
    ! [X24,X23,X6,X5] :
      ( class_Rings_Olinordered__ring__strict(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X23)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X24),X23)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),X24)) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X24),X6)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel__right__disj) ).

fof(fact_insert__subset,axiom,
    ! [X113,X21,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)),X113))
    <=> ( hBOOL(hAPP(hAPP(c_member(X5),X25),X113))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),X113)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__subset) ).

fof(fact_transfer__int__nat__sum__prod_I1_J,axiom,
    ! [X2,X21,X5] :
      ( ( class_Groups_Ocomm__monoid__add(X5)
        & class_Groups_Ocomm__monoid__mult(X5) )
     => ( c_Nat__Transfer_Onat__set(X21)
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X5),X2),X21) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),hAPP(hAPP(c_COMBB(tc_Int_Oint,X5,tc_Nat_Onat),X2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X21)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__sum__prod_I1_J) ).

fof(fact_transfer__int__nat__sum__prod_I2_J,axiom,
    ! [X2,X21,X5] :
      ( ( class_Groups_Ocomm__monoid__add(X5)
        & class_Groups_Ocomm__monoid__mult(X5) )
     => ( c_Nat__Transfer_Onat__set(X21)
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X5),X2),X21) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,X5),hAPP(hAPP(c_COMBB(tc_Int_Oint,X5,tc_Nat_Onat),X2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X21)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__sum__prod_I2_J) ).

fof(fact_setsum__Un__disjoint,axiom,
    ! [X1,X113,X21,X5,X20] :
      ( class_Groups_Ocomm__monoid__add(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X113))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X1),X21)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X1),X113)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__Un__disjoint) ).

fof(fact_setprod_Ounion__disjoint,axiom,
    ! [X1,X113,X21,X5,X20] :
      ( class_Groups_Ocomm__monoid__mult(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X113))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X1),X21)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X1),X113)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod_Ounion__disjoint) ).

fof(fact_setprod__Un__disjoint,axiom,
    ! [X1,X113,X21,X5,X20] :
      ( class_Groups_Ocomm__monoid__mult(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X113))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X1),X21)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X1),X113)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__Un__disjoint) ).

fof(fact_transfer__nat__int__sum__prod_I1_J,axiom,
    ! [X21,X2,X5] :
      ( ( class_Groups_Ocomm__monoid__add(X5)
        & class_Groups_Ocomm__monoid__mult(X5) )
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),X21) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X5),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X5,tc_Int_Oint),X2),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X21)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__sum__prod_I1_J) ).

fof(fact_transfer__nat__int__sum__prod_I2_J,axiom,
    ! [X21,X2,X5] :
      ( ( class_Groups_Ocomm__monoid__add(X5)
        & class_Groups_Ocomm__monoid__mult(X5) )
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,X5),X2),X21) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X5),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X5,tc_Int_Oint),X2),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X21)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__sum__prod_I2_J) ).

fof(fact_listrel__subset__rtrancl__listrel1,axiom,
    ! [X171,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_HOL_Obool)),c_List_Olistrel(X5,X171)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X5),c_List_Olistrel1(X5,X171)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__subset__rtrancl__listrel1) ).

fof(fact_image__add__int__atLeastLessThan,axiom,
    ! [X159,X156] : 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)),X156)),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),X159),X156))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X156),X159),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__add__int__atLeastLessThan) ).

fof(fact_drop__append,axiom,
    ! [X241,X242,X57,X58] : hAPP(hAPP(c_List_Odrop(X58),X57),hAPP(hAPP(c_List_Oappend(X58),X242),X241)) = hAPP(hAPP(c_List_Oappend(X58),hAPP(hAPP(c_List_Odrop(X58),X57),X242)),hAPP(hAPP(c_List_Odrop(X58),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X57),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242))),X241)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__append) ).

fof(fact_take__append,axiom,
    ! [X241,X242,X57,X58] : hAPP(hAPP(c_List_Otake(X58),X57),hAPP(hAPP(c_List_Oappend(X58),X242),X241)) = hAPP(hAPP(c_List_Oappend(X58),hAPP(hAPP(c_List_Otake(X58),X57),X242)),hAPP(hAPP(c_List_Otake(X58),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X57),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242))),X241)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__append) ).

fof(fact_set__remove1__subset,axiom,
    ! [X239,X25,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),c_List_Oremove1(X5,X25,X239))),hAPP(c_List_Oset(X5),X239))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__remove1__subset) ).

fof(fact_set__sublist__subset,axiom,
    ! [X221,X239,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),c_List_Osublist(X5,X239,X221))),hAPP(c_List_Oset(X5),X239))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__sublist__subset) ).

fof(fact_inj__on__the__inv__into,axiom,
    ! [X21,X2,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,X2,X21)
     => c_Fun_Oinj__on(X20,X5,c_Fun_Othe__inv__into(X5,X20,X21,X2),hAPP(c_Set_Oimage(X5,X20,X2),X21)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__the__inv__into) ).

fof(fact_Domain__Collect__split,axiom,
    ! [X18,X20,X5] : hAPP(c_Relation_ODomain(X5,X20),hAPP(c_Set_OCollect(tc_prod(X5,X20)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X20,tc_HOL_Obool),X18))) = hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_fun(X20,tc_HOL_Obool),tc_HOL_Obool,X5),c_HOL_OEx(X20)),X18)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__Collect__split) ).

fof(fact_fun__left__comm__idem_Ofold__set,axiom,
    ! [X239,X33,X2,X20,X5] :
      ( c_Finite__Set_Ofun__left__comm__idem(X5,X20,X2)
     => hAPP(hAPP(c_Finite__Set_Ofold(X5,X20,X2),X33),hAPP(c_List_Oset(X5),X239)) = hAPP(c_List_Ofoldl(X20,X5,hAPP(c_COMBC(X5,X20,X20),X2),X33),X239) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__idem_Ofold__set) ).

fof(fact_setsum__negf,axiom,
    ! [X21,X2,X20,X5] :
      ( class_Groups_Oab__group__add(X5)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X20,X5),hAPP(hAPP(c_COMBB(X5,X5,X20),c_Groups_Ouminus__class_Ouminus(X5)),X2)),X21) = hAPP(c_Groups_Ouminus__class_Ouminus(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X20,X5),X2),X21)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__negf) ).

fof(fact_abs__setprod,axiom,
    ! [X21,X2,X20,X5] :
      ( class_Fields_Olinordered__field(X5)
     => hAPP(c_Groups_Oabs__class_Oabs(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X20,X5),X2),X21)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X20,X5),hAPP(hAPP(c_COMBB(X5,X5,X20),c_Groups_Oabs__class_Oabs(X5)),X2)),X21) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__setprod) ).

fof(fact_all__set__conv__all__nth,axiom,
    ! [X18,X239,X5] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X239)))
         => hBOOL(hAPP(X18,X3)) )
    <=> ! [X146] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X146),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239)))
         => hBOOL(hAPP(X18,hAPP(hAPP(c_List_Onth(X5),X239),X146))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_all__set__conv__all__nth) ).

fof(fact_insert__mono,axiom,
    ! [X6,X144,X112,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X112),X144))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X6),X112)),hAPP(hAPP(c_Set_Oinsert(X5),X6),X144))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__mono) ).

fof(fact_sorted__append,axiom,
    ! [X251,X239,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Oappend(X5),X239),X251))
      <=> ( c_List_Olinorder__class_Osorted(X5,X239)
          & c_List_Olinorder__class_Osorted(X5,X251)
          & ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X239)))
             => ! [X204] :
                  ( hBOOL(hAPP(hAPP(c_member(X5),X204),hAPP(c_List_Oset(X5),X251)))
                 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X3),X204)) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__append) ).

fof(fact_power__less__power__Suc,axiom,
    ! [X57,X62,X58] :
      ( class_Rings_Olinordered__semidom(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Oone__class_Oone(X58)),X62))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),X57)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),X57)))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__less__power__Suc) ).

fof(fact_double__diff,axiom,
    ! [X112,X113,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),X113))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X113),X112))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X113),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X112),X21)) = X21 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__diff) ).

fof(fact_Pow__mono,axiom,
    ! [X113,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),X113))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X5),X21)),hAPP(c_Set_OPow(X5),X113))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__mono) ).

fof(fact_K__record__comp,axiom,
    ! [X25,X2,X23,X116,X5,X20] : hAPP(hAPP(c_Fun_Ocomp(X20,X5,X116,hAPP(c_COMBK(X5,X20),X23)),X2),X25) = X23,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_K__record__comp) ).

fof(fact_Body__triple__valid__Suc,axiom,
    ! [X16,X17,X18,X50,X5] :
      ( c_Hoare__Mirabelle_Otriple__valid(X5,X50,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),X18),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X17))),X16))
    <=> c_Hoare__Mirabelle_Otriple__valid(X5,hAPP(c_Nat_OSuc,X50),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),X18),hAPP(c_Com_Ocom_OBODY,X17)),X16)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Body__triple__valid__Suc) ).

fof(fact_set__drop__subset,axiom,
    ! [X239,X50,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Odrop(X5),X50),X239))),hAPP(c_List_Oset(X5),X239))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__drop__subset) ).

fof(fact_set__take__subset,axiom,
    ! [X239,X50,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Otake(X5),X50),X239))),hAPP(c_List_Oset(X5),X239))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__take__subset) ).

fof(fact_pos__le__divide__eq,axiom,
    ! [X24,X6,X23,X5] :
      ( class_Fields_Olinordered__field(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X24),X23)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X23)),X24)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__le__divide__eq) ).

fof(fact_pos__divide__le__eq,axiom,
    ! [X6,X24,X23,X5] :
      ( class_Fields_Olinordered__field(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X24),X23)),X6))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X23))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__divide__le__eq) ).

fof(fact_mult__imp__le__div__pos,axiom,
    ! [X66,X94,X65,X58] :
      ( class_Fields_Olinordered__field(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),X65))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X94),X65)),X66))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X94),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X66),X65))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__imp__le__div__pos) ).

fof(fact_pos__less__divide__eq,axiom,
    ! [X24,X6,X23,X5] :
      ( class_Fields_Olinordered__field(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X24),X23)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X23)),X24)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__less__divide__eq) ).

fof(fact_pos__divide__less__eq,axiom,
    ! [X6,X24,X23,X5] :
      ( class_Fields_Olinordered__field(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X24),X23)),X6))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X23))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__divide__less__eq) ).

fof(fact_mult__imp__less__div__pos,axiom,
    ! [X66,X94,X65,X58] :
      ( class_Fields_Olinordered__field(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),X65))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X94),X65)),X66))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X94),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X66),X65))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__imp__less__div__pos) ).

fof(fact_takeWhile__nth,axiom,
    ! [X239,X18,X5,X157] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X157),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_OtakeWhile(X5,X18,X239))))
     => hAPP(hAPP(c_List_Onth(X5),c_List_OtakeWhile(X5,X18,X239)),X157) = hAPP(hAPP(c_List_Onth(X5),X239),X157) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_takeWhile__nth) ).

fof(fact_of__int__setprod,axiom,
    ! [X21,X2,X20,X5] :
      ( ( class_Groups_Ocomm__monoid__mult(X5)
        & class_Rings_Oring__1(X5) )
     => hAPP(c_Int_Oring__1__class_Oof__int(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X20,tc_Int_Oint),X2),X21)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X20,X5),hAPP(hAPP(c_COMBB(tc_Int_Oint,X5,X20),c_Int_Oring__1__class_Oof__int(X5)),X2)),X21) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__setprod) ).

fof(fact_of__nat__setprod,axiom,
    ! [X21,X2,X20,X5] :
      ( ( class_Groups_Ocomm__monoid__mult(X5)
        & class_Rings_Osemiring__1(X5) )
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X20,tc_Nat_Onat),X2),X21)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X20,X5),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X5,X20),c_Nat_Osemiring__1__class_Oof__nat(X5)),X2)),X21) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__setprod) ).

fof(fact_converse__Int,axiom,
    ! [X76,X171,X5,X20] : hAPP(c_Relation_Oconverse(X20,X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X20,X5),tc_HOL_Obool)),X171),X76)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X5,X20),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X20,X5),X171)),hAPP(c_Relation_Oconverse(X20,X5),X76)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__Int) ).

fof(fact_converse__Un,axiom,
    ! [X76,X171,X5,X20] : hAPP(c_Relation_Oconverse(X20,X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X20,X5),tc_HOL_Obool)),X171),X76)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X20),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X20,X5),X171)),hAPP(c_Relation_Oconverse(X20,X5),X76)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__Un) ).

fof(fact_length__takeWhile__le,axiom,
    ! [X239,X18,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_OtakeWhile(X5,X18,X239))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__takeWhile__le) ).

fof(fact_funpow__add,axiom,
    ! [X2,X50,X95,X5] : hAPP(hAPP(c_Nat_Ocompow(X5,X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X95),X50)),X2) = hAPP(c_Fun_Ocomp(X5,X5,X5,hAPP(hAPP(c_Nat_Ocompow(X5,X5),X95),X2)),hAPP(hAPP(c_Nat_Ocompow(X5,X5),X50),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funpow__add) ).

fof(fact_of__int__setsum,axiom,
    ! [X21,X2,X20,X5] :
      ( class_Rings_Oring__1(X5)
     => hAPP(c_Int_Oring__1__class_Oof__int(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X20,tc_Int_Oint),X2),X21)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X20,X5),hAPP(hAPP(c_COMBB(tc_Int_Oint,X5,X20),c_Int_Oring__1__class_Oof__int(X5)),X2)),X21) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__setsum) ).

fof(fact_of__nat__setsum,axiom,
    ! [X21,X2,X20,X5] :
      ( class_Rings_Osemiring__1(X5)
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X20,tc_Nat_Onat),X2),X21)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X20,X5),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X5,X20),c_Nat_Osemiring__1__class_Oof__nat(X5)),X2)),X21) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__setsum) ).

fof(fact_inj__singleton,axiom,
    ! [X5] : c_Fun_Oinj__on(X5,tc_fun(X5,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Set_Oinsert(X5)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__singleton) ).

fof(fact_finite__cartesian__product,axiom,
    ! [X113,X20,X21,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X20),X113))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X5,X20)),hAPP(hAPP(c_Product__Type_OSigma(X5,X20),X21),hAPP(c_COMBK(tc_fun(X20,tc_HOL_Obool),X5),X113)))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__cartesian__product) ).

fof(fact_card__psubset,axiom,
    ! [X21,X113,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X113))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),X113))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X21)),hAPP(c_Finite__Set_Ocard(X5),X113)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X21),X113)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__psubset) ).

fof(fact_finite__surj,axiom,
    ! [X2,X113,X20,X21,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20,tc_HOL_Obool)),X113),hAPP(c_Set_Oimage(X5,X20,X2),X21)))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(X20),X113)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__surj) ).

fof(fact_bij__id,axiom,
    ! [X5] : c_Fun_Obij__betw(X5,X5,c_Fun_Oid(X5),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__id) ).

fof(fact_inj__on__Int,axiom,
    ! [X113,X21,X2,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,X2,X21)
     => ( c_Fun_Oinj__on(X5,X20,X2,X113)
       => c_Fun_Oinj__on(X5,X20,X2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__Int) ).

fof(fact_nth__drop,axiom,
    ! [X242,X58,X98,X57] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X57),X98)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242)))
     => hAPP(hAPP(c_List_Onth(X58),hAPP(hAPP(c_List_Odrop(X58),X57),X242)),X98) = hAPP(hAPP(c_List_Onth(X58),X242),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X57),X98)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__drop) ).

fof(fact_sorted__rev__nth__mono,axiom,
    ! [X97,X98,X242,X58] :
      ( class_Orderings_Olinorder(X58)
     => ( c_List_Olinorder__class_Osorted(X58,hAPP(c_List_Orev(X58),X242))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X98),X97))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X97),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_List_Onth(X58),X242),X97)),hAPP(hAPP(c_List_Onth(X58),X242),X98))) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__rev__nth__mono) ).

fof(fact_zip__append,axiom,
    ! [X271,X241,X247,X5,X242,X58] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X247)
     => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X241) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X271)
       => hAPP(hAPP(c_List_Ozip(X58,X5),hAPP(hAPP(c_List_Oappend(X58),X242),X241)),hAPP(hAPP(c_List_Oappend(X5),X247),X271)) = hAPP(hAPP(c_List_Oappend(tc_prod(X58,X5)),hAPP(hAPP(c_List_Ozip(X58,X5),X242),X247)),hAPP(hAPP(c_List_Ozip(X58,X5),X241),X271)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__append) ).

fof(fact_list__size__map,axiom,
    ! [X239,X1,X20,X2,X5] : c_List_Olist_Olist__size(X5,X2,hAPP(hAPP(c_List_Omap(X20,X5),X1),X239)) = c_List_Olist_Olist__size(X20,hAPP(c_Fun_Ocomp(X5,tc_Nat_Onat,X20,X2),X1),X239),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__size__map) ).

fof(fact_refl__onD,axiom,
    ! [X6,X171,X21,X5] :
      ( c_Relation_Orefl__on(X5,X21,X171)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X21))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X6)),X171)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__onD) ).

fof(fact_UN__upper,axiom,
    ! [X113,X20,X21,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),X21))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20,tc_HOL_Obool)),hAPP(X113,X6)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X20,tc_HOL_Obool)),X21),X113))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__upper) ).

fof(fact_take__Cons__number__of,axiom,
    ! [X242,X66,X58,X136] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Otake(X58),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)),hAPP(hAPP(c_List_Olist_OCons(X58),X66),X242)) = c_List_Olist_ONil(X58) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Otake(X58),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)),hAPP(hAPP(c_List_Olist_OCons(X58),X66),X242)) = hAPP(hAPP(c_List_Olist_OCons(X58),X66),hAPP(hAPP(c_List_Otake(X58),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X242)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__Cons__number__of) ).

fof(fact_evalc_Oequations_I7_J,axiom,
    ! [X26,X63,X27] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X27,X63)),X26),X26))
    <=> ( hBOOL(hAPP(X27,X26))
       => ? [X61] :
            ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X63),X26),X61))
            & hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X27,X63)),X61),X26)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_Oequations_I7_J) ).

fof(fact_predicate2D,axiom,
    ! [X33,X25,X16,X18,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_fun(X20,tc_HOL_Obool))),X18),X16))
     => ( hBOOL(hAPP(hAPP(X18,X25),X33))
       => hBOOL(hAPP(hAPP(X16,X25),X33)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_predicate2D) ).

fof(fact_rev__predicate2D,axiom,
    ! [X16,X20,X5,X33,X25,X18] :
      ( hBOOL(hAPP(hAPP(X18,X25),X33))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_fun(X20,tc_HOL_Obool))),X18),X16))
       => hBOOL(hAPP(hAPP(X16,X25),X33)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__predicate2D) ).

fof(fact_fold1__antimono,axiom,
    ! [X113,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),X113))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X113))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Finite__Set_Ofold1(X5,c_Orderings_Oord__class_Omin(X5)),X113)),hAPP(c_Finite__Set_Ofold1(X5,c_Orderings_Oord__class_Omin(X5)),X21))) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__antimono) ).

fof(fact_Un__iff,axiom,
    ! [X113,X21,X23,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X23),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113)))
    <=> ( hBOOL(hAPP(hAPP(c_member(X5),X23),X21))
        | hBOOL(hAPP(hAPP(c_member(X5),X23),X113)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__iff) ).

fof(fact_field__le__epsilon,axiom,
    ! [X65,X66,X58] :
      ( class_Fields_Olinordered__field(X58)
     => ( ! [X161] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),X161))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X66),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X65),X161))) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X66),X65)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_field__le__epsilon) ).

fof(fact_foldl__Cons,axiom,
    ! [X239,X25,X6,X2,X20,X5] : hAPP(c_List_Ofoldl(X5,X20,X2,X6),hAPP(hAPP(c_List_Olist_OCons(X20),X25),X239)) = hAPP(c_List_Ofoldl(X5,X20,X2,hAPP(hAPP(X2,X6),X25)),X239),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldl__Cons) ).

fof(fact_length__transpose__sorted,axiom,
    ! [X239,X5] :
      ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X5),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X5))),X239)))
     => ( ( X239 = c_List_Olist_ONil(tc_List_Olist(X5))
         => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5))),c_List_Otranspose(X5,X239)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        & ( X239 != c_List_Olist_ONil(tc_List_Olist(X5))
         => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X5))),c_List_Otranspose(X5,X239)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X5)),X239),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__transpose__sorted) ).

fof(fact_power__strict__mono,axiom,
    ! [X57,X90,X62,X58] :
      ( class_Rings_Olinordered__semidom(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X62),X90))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),X62))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X57))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),X57)),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X90),X57))) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__strict__mono) ).

fof(fact_power__decreasing,axiom,
    ! [X62,X163,X57,X58] :
      ( class_Rings_Olinordered__semidom(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X57),X163))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),X62))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X62),c_Groups_Oone__class_Oone(X58)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),X163)),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),X57))) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__decreasing) ).

fof(fact_power__strict__decreasing,axiom,
    ! [X62,X163,X57,X58] :
      ( class_Rings_Olinordered__semidom(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X57),X163))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),X62))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X62),c_Groups_Oone__class_Oone(X58)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),X163)),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),X57))) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__strict__decreasing) ).

fof(fact_vimage__Int,axiom,
    ! [X113,X21,X2,X20,X5] : hAPP(c_Set_Ovimage(X5,X20,X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20,tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X5,X20,X2),X21)),hAPP(c_Set_Ovimage(X5,X20,X2),X113)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__Int) ).

fof(fact_vimage__Un,axiom,
    ! [X113,X21,X2,X20,X5] : hAPP(c_Set_Ovimage(X5,X20,X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20,tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X5,X20,X2),X21)),hAPP(c_Set_Ovimage(X5,X20,X2),X113)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__Un) ).

fof(fact_vimage__Diff,axiom,
    ! [X113,X21,X2,X20,X5] : hAPP(c_Set_Ovimage(X5,X20,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20,tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X5,X20,X2),X21)),hAPP(c_Set_Ovimage(X5,X20,X2),X113)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__Diff) ).

fof(fact_Image__Un,axiom,
    ! [X113,X21,X32,X5,X20] : hAPP(c_Relation_OImage(X20,X5,X32),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20,tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_OImage(X20,X5,X32),X21)),hAPP(c_Relation_OImage(X20,X5,X32),X113)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__Un) ).

fof(fact_image__Un,axiom,
    ! [X113,X21,X2,X5,X20] : hAPP(c_Set_Oimage(X20,X5,X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20,tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Oimage(X20,X5,X2),X21)),hAPP(c_Set_Oimage(X20,X5,X2),X113)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__Un) ).

fof(fact_append__in__lists__conv,axiom,
    ! [X21,X251,X239,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),hAPP(hAPP(c_List_Oappend(X5),X239),X251)),c_List_Olists(X5,X21)))
    <=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X239),c_List_Olists(X5,X21)))
        & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X251),c_List_Olists(X5,X21))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__in__lists__conv) ).

fof(fact_Powp__mono,axiom,
    ! [X113,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),X113))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(X5,X21)),c_Predicate_OPowp(X5,X113))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Powp__mono) ).

fof(fact_distinct__product,axiom,
    ! [X241,X5,X242,X58] :
      ( hBOOL(hAPP(c_List_Odistinct(X58),X242))
     => ( hBOOL(hAPP(c_List_Odistinct(X5),X241))
       => hBOOL(hAPP(c_List_Odistinct(tc_prod(X58,X5)),c_Enum_Oproduct(X58,X5,X242,X241))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__product) ).

fof(fact_finite__Plus,axiom,
    ! [X113,X20,X21,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X20),X113))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X5,X20)),c_Sum__Type_OPlus(X5,X20,X21,X113))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Plus) ).

fof(fact_Id__on__eqI,axiom,
    ! [X21,X5,X24,X6] :
      ( X6 = X24
     => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X21))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X24)),c_Relation_OId__on(X5,X21))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Id__on__eqI) ).

fof(fact_Rep__Integ__induct,axiom,
    ! [X18,X33] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X33),c_Int_OInteg))
     => ( ! [X3] : hBOOL(hAPP(X18,hAPP(c_Int_ORep__Integ,X3)))
       => hBOOL(hAPP(X18,X33)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Rep__Integ__induct) ).

fof(fact_list__update__append1,axiom,
    ! [X66,X241,X242,X58,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242)))
     => hAPP(hAPP(c_List_Olist__update(X58,hAPP(hAPP(c_List_Oappend(X58),X242),X241)),X98),X66) = hAPP(hAPP(c_List_Oappend(X58),hAPP(hAPP(c_List_Olist__update(X58,X242),X98),X66)),X241) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update__append1) ).

fof(fact_mult__le__cancel2,axiom,
    ! [X50,X87,X95] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X95),X87)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X50),X87)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X87))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X50)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__cancel2) ).

fof(fact_mult__le__cancel1,axiom,
    ! [X50,X95,X87] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X87),X95)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X87),X50)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X87))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X50)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__cancel1) ).

fof(fact_nat__mult__le__cancel1,axiom,
    ! [X50,X95,X87] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X87))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X87),X95)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X87),X50)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X50)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__le__cancel1) ).

fof(fact_nat__power__less__imp__less,axiom,
    ! [X57,X72,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X98))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X98),X72)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X98),X57)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X72),X57)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__power__less__imp__less) ).

fof(fact_nat__mult__less__cancel1,axiom,
    ! [X50,X95,X87] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X87))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X87),X95)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X87),X50)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),X50)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__less__cancel1) ).

fof(fact_wfE__pf,axiom,
    ! [X21,X32,X5] :
      ( c_Wellfounded_Owf(X5,X32)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(c_Relation_OImage(X5,X5,X32),X21)))
       => X21 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfE__pf) ).

fof(fact_int__setsum,axiom,
    ! [X21,X2,X5] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),X2),X21)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X5),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2)),X21),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__setsum) ).

fof(fact_int__setprod,axiom,
    ! [X21,X2,X5] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,tc_Nat_Onat),X2),X21)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X5),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2)),X21),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__setprod) ).

fof(fact_fun__left__comm_Ofun__comp__comm,axiom,
    ! [X33,X25,X2,X20,X5] :
      ( c_Finite__Set_Ofun__left__comm(X5,X20,X2)
     => hAPP(c_Fun_Ocomp(X20,X20,X20,hAPP(X2,X25)),hAPP(X2,X33)) = hAPP(c_Fun_Ocomp(X20,X20,X20,hAPP(X2,X33)),hAPP(X2,X25)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofun__comp__comm) ).

fof(fact_hoare__derivs_Oequations_I7_J,axiom,
    ! [X26,X27,X5] : c_Hoare__Mirabelle_Ohoare__derivs(X5,X27,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X5)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),X26),c_Com_Ocom_OSKIP),X26)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hoare__derivs_Oequations_I7_J) ).

fof(fact_hoare__derivs_OSkip,axiom,
    ! [X18,X4,X5] : c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X5)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),X18),c_Com_Ocom_OSKIP),X18)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hoare__derivs_OSkip) ).

fof(fact_set__update__memI,axiom,
    ! [X25,X239,X5,X50] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X50),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239)))
     => hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Olist__update(X5,X239),X50),X25)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__update__memI) ).

fof(fact_UN__I,axiom,
    ! [X113,X24,X20,X21,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),X21))
     => ( hBOOL(hAPP(hAPP(c_member(X20),X24),hAPP(X113,X6)))
       => hBOOL(hAPP(hAPP(c_member(X20),X24),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X20,tc_HOL_Obool)),X21),X113))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__I) ).

fof(fact_unique__quotient,axiom,
    ! [X141,X142,X134,X140,X90,X62] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X62,X90),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X140),X134)))
     => ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X62,X90),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X142),X141)))
       => ( X90 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => X140 = X142 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_unique__quotient) ).

fof(fact_unique__remainder,axiom,
    ! [X141,X142,X134,X140,X90,X62] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X62,X90),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X140),X134)))
     => ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X62,X90),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X142),X141)))
       => ( X90 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => X134 = X141 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_unique__remainder) ).

fof(fact_finite__imageD,axiom,
    ! [X21,X2,X20,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(c_Set_Oimage(X20,X5,X2),X21)))
     => ( c_Fun_Oinj__on(X20,X5,X2,X21)
       => hBOOL(hAPP(c_Finite__Set_Ofinite(X20),X21)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__imageD) ).

fof(fact_single__valued__subset,axiom,
    ! [X76,X171,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X20),tc_HOL_Obool)),X171),X76))
     => ( c_Relation_Osingle__valued(X5,X20,X76)
       => c_Relation_Osingle__valued(X5,X20,X171) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valued__subset) ).

fof(fact_add__le__imp__le__right,axiom,
    ! [X90,X56,X62,X58] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),X56)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X90),X56)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X62),X90)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__imp__le__right) ).

fof(fact_add__le__cancel__right,axiom,
    ! [X24,X23,X6,X5] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),X23)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X24),X23)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),X24)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__cancel__right) ).

fof(fact_add__le__imp__le__left,axiom,
    ! [X90,X62,X56,X58] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X56),X62)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X56),X90)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X62),X90)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__imp__le__left) ).

fof(fact_add__le__cancel__left,axiom,
    ! [X24,X6,X23,X5] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X23),X6)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X23),X24)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),X24)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__cancel__left) ).

fof(fact_add__less__cancel__right,axiom,
    ! [X24,X23,X6,X5] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),X23)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X24),X23)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),X24)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__cancel__right) ).

fof(fact_add__less__imp__less__right,axiom,
    ! [X90,X56,X62,X58] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),X56)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X90),X56)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X62),X90)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__imp__less__right) ).

fof(fact_add__less__cancel__left,axiom,
    ! [X24,X6,X23,X5] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X23),X6)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X23),X24)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),X24)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__cancel__left) ).

fof(fact_add__less__imp__less__left,axiom,
    ! [X90,X62,X56,X58] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X56),X62)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X56),X90)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X62),X90)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__imp__less__left) ).

fof(fact_evaln_Oequations_I7_J,axiom,
    ! [X60,X26,X63,X27] :
      ( c_Natural_Oevaln(c_Com_Ocom_OWhile(X27,X63),X26,X60,X26)
    <=> ( hBOOL(hAPP(X27,X26))
       => ? [X61] :
            ( c_Natural_Oevaln(X63,X26,X60,X61)
            & c_Natural_Oevaln(c_Com_Ocom_OWhile(X27,X63),X61,X60,X26) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_Oequations_I7_J) ).

fof(fact_sorted__nth__mono,axiom,
    ! [X97,X98,X242,X58] :
      ( class_Orderings_Olinorder(X58)
     => ( c_List_Olinorder__class_Osorted(X58,X242)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X98),X97))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X97),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_List_Onth(X58),X242),X98)),hAPP(hAPP(c_List_Onth(X58),X242),X97))) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__nth__mono) ).

fof(fact_relpow_Osimps_I2_J,axiom,
    ! [X32,X50,X5] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),hAPP(c_Nat_OSuc,X50)),X32) = hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X50),X32)),X32),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_relpow_Osimps_I2_J) ).

fof(fact_diff__divide__eq__iff,axiom,
    ! [X65,X66,X94,X58] :
      ( class_Fields_Ofield(X58)
     => ( X94 != c_Groups_Ozero__class_Ozero(X58)
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X58),X66),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X65),X94)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X94),X66)),X65)),X94) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__divide__eq__iff) ).

fof(fact_add__divide__eq__iff,axiom,
    ! [X65,X66,X94,X58] :
      ( class_Fields_Ofield(X58)
     => ( X94 != c_Groups_Ozero__class_Ozero(X58)
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X66),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X65),X94)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X94),X66)),X65)),X94) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__divide__eq__iff) ).

fof(fact_filter__insort,axiom,
    ! [X25,X18,X239,X2,X20,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Omap(X20,X5),X2),X239))
       => ( hBOOL(hAPP(X18,X25))
         => hAPP(c_List_Ofilter(X20,X18),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X20,X5,X2),X25),X239)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X20,X5,X2),X25),hAPP(c_List_Ofilter(X20,X18),X239)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter__insort) ).

fof(fact_subset__singletonD,axiom,
    ! [X25,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))
     => ( X21 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
        | X21 = hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__singletonD) ).

fof(fact_DiffE,axiom,
    ! [X113,X21,X23,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X23),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),X113)))
     => ~ ( hBOOL(hAPP(hAPP(c_member(X5),X23),X21))
         => hBOOL(hAPP(hAPP(c_member(X5),X23),X113)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DiffE) ).

fof(fact_fun__upd__triv,axiom,
    ! [X25,X2,X20,X5] : c_Fun_Ofun__upd(X5,X20,X2,X25,hAPP(X2,X25)) = X2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__triv) ).

fof(fact_fun__upd__idem,axiom,
    ! [X5,X20,X33,X25,X2] :
      ( hAPP(X2,X25) = X33
     => c_Fun_Ofun__upd(X20,X5,X2,X25,X33) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__idem) ).

fof(fact_folding__idem_Oin__comp__idem,axiom,
    ! [X25,X21,X205,X2,X20,X5] :
      ( c_Finite__Set_Ofolding__idem(X5,X20,X2,X205)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => hAPP(c_Fun_Ocomp(X20,X20,X20,hAPP(X205,X21)),hAPP(X2,X25)) = hAPP(X205,X21) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__idem_Oin__comp__idem) ).

fof(fact_take__Suc__conv__app__nth,axiom,
    ! [X242,X58,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242)))
     => hAPP(hAPP(c_List_Otake(X58),hAPP(c_Nat_OSuc,X98)),X242) = hAPP(hAPP(c_List_Oappend(X58),hAPP(hAPP(c_List_Otake(X58),X98),X242)),hAPP(hAPP(c_List_Olist_OCons(X58),hAPP(hAPP(c_List_Onth(X58),X242),X98)),c_List_Olist_ONil(X58))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__Suc__conv__app__nth) ).

fof(fact_min__max_OInf__fin_Ounion__disjoint,axiom,
    ! [X113,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X113))
           => ( X113 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
               => c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X21)),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X113)) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Ounion__disjoint) ).

fof(fact_min__max_OSup__fin_Ounion__disjoint,axiom,
    ! [X113,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X113))
           => ( X113 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
               => c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X21)),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X113)) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Ounion__disjoint) ).

fof(fact_comp__funpow,axiom,
    ! [X2,X50,X20,X5] : hAPP(hAPP(c_Nat_Ocompow(tc_fun(X5,X20),tc_fun(X5,X20)),X50),c_Fun_Ocomp(X20,X20,X5,X2)) = c_Fun_Ocomp(X20,X20,X5,hAPP(hAPP(c_Nat_Ocompow(X20,X20),X50),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comp__funpow) ).

fof(fact_New__DSequence_Opos__bind__def,axiom,
    ! [X82,X2,X25,X5,X20] : hAPP(c_New__DSequence_Opos__bind(X20,X5,X25,X2),X82) = hAPP(c_Lazy__Sequence_Obind(X20,X5,hAPP(X25,X82)),hAPP(hAPP(c_COMBC(X20,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X5)),X2),X82)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_New__DSequence_Opos__bind__def) ).

fof(fact_curry__def,axiom,
    ! [X33,X25,X23,X5,X116,X20] : hAPP(hAPP(c_Product__Type_Ocurry(X20,X116,X5,X23),X25),X33) = hAPP(X23,hAPP(hAPP(c_Product__Type_OPair(X20,X116),X25),X33)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_curry__def) ).

fof(fact_inj__on__Un__image__eq__iff,axiom,
    ! [X113,X21,X2,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113))
     => ( hAPP(c_Set_Oimage(X5,X20,X2),X21) = hAPP(c_Set_Oimage(X5,X20,X2),X113)
      <=> X21 = X113 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__Un__image__eq__iff) ).

fof(fact_mult__imp__div__pos__le,axiom,
    ! [X94,X66,X65,X58] :
      ( class_Fields_Olinordered__field(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),X65))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X66),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X94),X65)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X66),X65)),X94)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__imp__div__pos__le) ).

fof(fact_mult__imp__div__pos__less,axiom,
    ! [X94,X66,X65,X58] :
      ( class_Fields_Olinordered__field(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),X65))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X66),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X94),X65)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X66),X65)),X94)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__imp__div__pos__less) ).

fof(fact_refl__on__Int,axiom,
    ! [X76,X113,X171,X21,X5] :
      ( c_Relation_Orefl__on(X5,X21,X171)
     => ( c_Relation_Orefl__on(X5,X113,X76)
       => c_Relation_Orefl__on(X5,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X171),X76)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__on__Int) ).

fof(fact_refl__on__Un,axiom,
    ! [X76,X113,X171,X21,X5] :
      ( c_Relation_Orefl__on(X5,X21,X171)
     => ( c_Relation_Orefl__on(X5,X113,X76)
       => c_Relation_Orefl__on(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X171),X76)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__on__Un) ).

fof(fact_lazy__sequence_Orecs_I1_J,axiom,
    ! [X89,X19,X20,X5] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X5,X20,X19,X89,c_Lazy__Sequence_Olazy__sequence_OEmpty(X20)) = X19,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lazy__sequence_Orecs_I1_J) ).

fof(fact_surj__imp__inj__inv,axiom,
    ! [X2,X5,X20] :
      ( hAPP(c_Set_Oimage(X20,X5,X2),c_Orderings_Otop__class_Otop(tc_fun(X20,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))
     => c_Fun_Oinj__on(X5,X20,c_Hilbert__Choice_Oinv__into(X20,X5,c_Orderings_Otop__class_Otop(tc_fun(X20,tc_HOL_Obool)),X2),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surj__imp__inj__inv) ).

fof(fact_bij__betw__id,axiom,
    ! [X21,X5] : c_Fun_Obij__betw(X5,X5,c_Fun_Oid(X5),X21,X21),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bij__betw__id) ).

fof(fact_Domain__insert,axiom,
    ! [X171,X24,X6,X20,X5] : hAPP(c_Relation_ODomain(X5,X20),hAPP(hAPP(c_Set_Oinsert(tc_prod(X5,X20)),hAPP(hAPP(c_Product__Type_OPair(X5,X20),X6),X24)),X171)) = hAPP(hAPP(c_Set_Oinsert(X5),X6),hAPP(c_Relation_ODomain(X5,X20),X171)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__insert) ).

fof(fact_Range__insert,axiom,
    ! [X171,X24,X6,X5,X20] : hAPP(c_Relation_ORange(X20,X5),hAPP(hAPP(c_Set_Oinsert(tc_prod(X20,X5)),hAPP(hAPP(c_Product__Type_OPair(X20,X5),X6),X24)),X171)) = hAPP(hAPP(c_Set_Oinsert(X5),X24),hAPP(c_Relation_ORange(X20,X5),X171)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__insert) ).

fof(fact_subset__trans,axiom,
    ! [X112,X113,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),X113))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X113),X112))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),X112)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__trans) ).

fof(fact_psubset__subset__trans,axiom,
    ! [X112,X113,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X21),X113))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X113),X112))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X21),X112)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__subset__trans) ).

fof(fact_subset__psubset__trans,axiom,
    ! [X112,X113,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),X113))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X113),X112))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X21),X112)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__psubset__trans) ).

fof(fact_psubset__trans,axiom,
    ! [X112,X113,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X21),X113))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X113),X112))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X21),X112)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__trans) ).

fof(fact_transfer__nat__int__set__relations_I2_J,axiom,
    ! [X21,X25] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X25),X21))
    <=> hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X21))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__set__relations_I2_J) ).

fof(fact_Pair__scomp,axiom,
    ! [X2,X25,X20,X116,X5] : hAPP(hAPP(c_Product__Type_Oscomp(X5,X116,X5,X20),hAPP(c_Product__Type_OPair(X116,X5),X25)),X2) = hAPP(X2,X25),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pair__scomp) ).

fof(fact_mod__div__equality,axiom,
    ! [X90,X62,X58] :
      ( class_Divides_Osemiring__div(X58)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X58),X62),X90)),X90)),c_Divides_Odiv__class_Omod(X58,X62,X90)) = X62 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__div__equality) ).

fof(fact_mod__div__decomp,axiom,
    ! [X90,X62,X58] :
      ( class_Divides_Osemiring__div(X58)
     => X62 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X58),X62),X90)),X90)),c_Divides_Odiv__class_Omod(X58,X62,X90)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__div__decomp) ).

fof(fact_sorted__sort__key,axiom,
    ! [X239,X2,X20,X5] :
      ( class_Orderings_Olinorder(X5)
     => c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Omap(X20,X5),X2),c_List_Olinorder__class_Osort__key(X20,X5,X2,X239))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__sort__key) ).

fof(fact_evalc__elim__cases_I6_J,axiom,
    ! [X45,X48,X49] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X49)),X48),X45))
     => hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X49))),X48),X45)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc__elim__cases_I6_J) ).

fof(fact_UN__singleton,axiom,
    ! [X21,X5] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),c_Set_Oinsert(X5)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = X21,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__singleton) ).

fof(fact_upd__conv__take__nth__drop,axiom,
    ! [X62,X242,X58,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242)))
     => hAPP(hAPP(c_List_Olist__update(X58,X242),X98),X62) = hAPP(hAPP(c_List_Oappend(X58),hAPP(hAPP(c_List_Otake(X58),X98),X242)),hAPP(hAPP(c_List_Olist_OCons(X58),X62),hAPP(hAPP(c_List_Odrop(X58),hAPP(c_Nat_OSuc,X98)),X242))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_upd__conv__take__nth__drop) ).

fof(fact_distinct__set__sublists,axiom,
    ! [X239,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),X239))
     => hBOOL(hAPP(c_List_Odistinct(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_List_Omap(tc_List_Olist(X5),tc_fun(X5,tc_HOL_Obool)),c_List_Oset(X5)),c_Enum_Osublists(X5,X239)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__set__sublists) ).

fof(fact_Pow__insert,axiom,
    ! [X21,X6,X5] : hAPP(c_Set_OPow(X5),hAPP(hAPP(c_Set_Oinsert(X5),X6),X21)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X5),X21)),hAPP(c_Set_Oimage(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),hAPP(c_Set_Oinsert(X5),X6)),hAPP(c_Set_OPow(X5),X21))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__insert) ).

fof(fact_evalc_OIfTrue,axiom,
    ! [X105,X104,X103,X76,X24] :
      ( hBOOL(hAPP(X24,X76))
     => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X103),X76),X104))
       => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X24,X103,X105)),X76),X104)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_OIfTrue) ).

fof(fact_finite__vimageD,axiom,
    ! [X205,X122,X20,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(c_Set_Ovimage(X5,X20,X122),X205)))
     => ( hAPP(c_Set_Oimage(X5,X20,X122),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X20,tc_HOL_Obool))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(X20),X205)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__vimageD) ).

fof(fact_Cons__in__lists__iff,axiom,
    ! [X21,X239,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239)),c_List_Olists(X5,X21)))
    <=> ( hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
        & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X239),c_List_Olists(X5,X21))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Cons__in__lists__iff) ).

fof(fact_range,axiom,
    ! [X48,X96] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),X96))
     => 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(X96),X48))),X96)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_range) ).

fof(fact_Int__iff,axiom,
    ! [X113,X21,X23,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X23),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113)))
    <=> ( hBOOL(hAPP(hAPP(c_member(X5),X23),X21))
        & hBOOL(hAPP(hAPP(c_member(X5),X23),X113)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__iff) ).

fof(fact_IntD1,axiom,
    ! [X113,X21,X23,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X23),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113)))
     => hBOOL(hAPP(hAPP(c_member(X5),X23),X21)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_IntD1) ).

fof(fact_DiffD1,axiom,
    ! [X113,X21,X23,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X23),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),X113)))
     => hBOOL(hAPP(hAPP(c_member(X5),X23),X21)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DiffD1) ).

fof(fact_IntD2,axiom,
    ! [X113,X21,X23,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X23),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113)))
     => hBOOL(hAPP(hAPP(c_member(X5),X23),X113)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_IntD2) ).

fof(fact_Diff__insert,axiom,
    ! [X113,X6,X21,X5] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X6),X113)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),X113)),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__insert) ).

fof(fact_fold1__Un,axiom,
    ! [X113,X21,X5] :
      ( class_Groups_Oab__semigroup__mult(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X113))
           => ( X113 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
               => hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),X21)),hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),X113)) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__Un) ).

fof(fact_folding__idem_Oinsert__idem,axiom,
    ! [X25,X21,X205,X2,X20,X5] :
      ( c_Finite__Set_Ofolding__idem(X5,X20,X2,X205)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => hAPP(X205,hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(c_Fun_Ocomp(X20,X20,X20,hAPP(X205,X21)),hAPP(X2,X25)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__idem_Oinsert__idem) ).

fof(fact_scomp__Pair,axiom,
    ! [X25,X116,X20,X5] : hAPP(hAPP(c_Product__Type_Oscomp(X5,X20,X116,tc_prod(X20,X116)),X25),c_Product__Type_OPair(X20,X116)) = X25,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_scomp__Pair) ).

fof(fact_Pow__def,axiom,
    ! [X21,X5] : hAPP(c_Set_OPow(X5),X21) = hAPP(c_Set_OCollect(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool))),X21)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__def) ).

fof(fact_rev__foldl__cons,axiom,
    ! [X239,X5] : hAPP(c_List_Orev(X5),X239) = hAPP(c_List_Ofoldl(tc_List_Olist(X5),X5,hAPP(c_COMBC(X5,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olist_OCons(X5)),c_List_Olist_ONil(X5)),X239),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__foldl__cons) ).

fof(fact_gauss__sum,axiom,
    ! [X50,X5] :
      ( class_Rings_Ocomm__semiring__1(X5)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),c_Groups_Oone__class_Oone(X5)),c_Groups_Oone__class_Oone(X5))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),c_Nat_Osemiring__1__class_Oof__nat(X5)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X50))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X50)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X50)),c_Groups_Oone__class_Oone(X5))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gauss__sum) ).

fof(fact_length__n__lists__elem,axiom,
    ! [X239,X50,X251,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X251),hAPP(c_List_Oset(tc_List_Olist(X5)),c_Enum_On__lists(X5,X50,X239))))
     => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X251) = X50 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__n__lists__elem) ).

fof(fact_antisym__subset,axiom,
    ! [X76,X171,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X171),X76))
     => ( c_Relation_Oantisym(X5,X76)
       => c_Relation_Oantisym(X5,X171) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_antisym__subset) ).

fof(fact_acyclic__subset,axiom,
    ! [X171,X76,X5] :
      ( c_Wellfounded_Oacyclic(X5,X76)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X171),X76))
       => c_Wellfounded_Oacyclic(X5,X171) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acyclic__subset) ).

fof(fact_wf__subset,axiom,
    ! [X160,X171,X5] :
      ( c_Wellfounded_Owf(X5,X171)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X160),X171))
       => c_Wellfounded_Owf(X5,X160) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__subset) ).

fof(fact_in__set__remove1,axiom,
    ! [X239,X5,X24,X6] :
      ( X6 != X24
     => ( hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(c_List_Oset(X5),c_List_Oremove1(X5,X24,X239))))
      <=> hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(c_List_Oset(X5),X239))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__set__remove1) ).

fof(fact_Int__assoc,axiom,
    ! [X112,X113,X21,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113)),X112) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X113),X112)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__assoc) ).

fof(fact_Un__assoc,axiom,
    ! [X112,X113,X21,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113)),X112) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X113),X112)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__assoc) ).

fof(fact_Int__Diff,axiom,
    ! [X112,X113,X21,X5] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113)),X112) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X113),X112)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__Diff) ).

fof(fact_le__add__diff,axiom,
    ! [X72,X57,X96] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X96),X57))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X72),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X57),X72)),X96))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add__diff) ).

fof(fact_set__takeWhileD,axiom,
    ! [X239,X18,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),c_List_OtakeWhile(X5,X18,X239))))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X239)))
        & hBOOL(hAPP(X18,X25)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__takeWhileD) ).

fof(fact_in__set__sublistD,axiom,
    ! [X221,X239,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),c_List_Osublist(X5,X239,X221))))
     => hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X239))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__set__sublistD) ).

fof(fact_evaln_OWhileTrue,axiom,
    ! [X110,X104,X50,X23,X111,X24] :
      ( hBOOL(hAPP(X24,X111))
     => ( c_Natural_Oevaln(X23,X111,X50,X104)
       => ( c_Natural_Oevaln(c_Com_Ocom_OWhile(X24,X23),X104,X50,X110)
         => c_Natural_Oevaln(c_Com_Ocom_OWhile(X24,X23),X111,X50,X110) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_OWhileTrue) ).

fof(fact_filter__is__subset,axiom,
    ! [X239,X18,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),hAPP(c_List_Ofilter(X5,X18),X239))),hAPP(c_List_Oset(X5),X239))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter__is__subset) ).

fof(fact_crossproduct__noteq,axiom,
    ! [X22,X23,X24,X6,X5] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5)
     => ( ( X6 != X24
          & X23 != X22 )
      <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X23)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X24),X22)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X22)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X24),X23)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_crossproduct__noteq) ).

fof(fact_crossproduct__eq,axiom,
    ! [X120,X25,X33,X121,X5] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X121),X33)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X25),X120)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X121),X120)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X25),X33))
      <=> ( X121 = X25
          | X33 = X120 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_crossproduct__eq) ).

fof(fact_reflp__def,axiom,
    ! [X171,X5] :
      ( c_Predicate_Oreflp(X5,X171)
    <=> c_Relation_Orefl__on(X5,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(X5,X5)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X5,tc_HOL_Obool),X171))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_reflp__def) ).

fof(fact_le__diff__conv2,axiom,
    ! [X82,X157,X87] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X87),X157))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X82),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X157),X87)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X82),X87)),X157)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__diff__conv2) ).

fof(fact_THE__default__def,axiom,
    ! [X22,X5,X18] :
      ( ( ? [X3] :
            ( hBOOL(hAPP(X18,X3))
            & ! [X177] :
                ( hBOOL(hAPP(X18,X177))
               => X177 = X3 ) )
       => c_FunDef_OTHE__default(X5,X22,X18) = c_HOL_OThe(X5,X18) )
      & ( ~ ? [X3] :
              ( hBOOL(hAPP(X18,X3))
              & ! [X177] :
                  ( hBOOL(hAPP(X18,X177))
                 => X177 = X3 ) )
       => c_FunDef_OTHE__default(X5,X22,X18) = X22 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_THE__default__def) ).

fof(fact_vimage__eq,axiom,
    ! [X113,X2,X20,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(c_Set_Ovimage(X5,X20,X2),X113)))
    <=> hBOOL(hAPP(hAPP(c_member(X20),hAPP(X2,X6)),X113)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__eq) ).

fof(fact_vimageD,axiom,
    ! [X21,X2,X20,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(c_Set_Ovimage(X5,X20,X2),X21)))
     => hBOOL(hAPP(hAPP(c_member(X20),hAPP(X2,X6)),X21)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimageD) ).

fof(fact_drop__Cons,axiom,
    ! [X239,X25,X50,X5] : hAPP(hAPP(c_List_Odrop(X5),X50),hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239)) = c_Nat_Onat_Onat__case(tc_List_Olist(X5),hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Odrop(X5)),X239),X50),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__Cons) ).

fof(fact_mult__right__le__one__le,axiom,
    ! [X65,X66,X58] :
      ( class_Rings_Olinordered__idom(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),X66))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),X65))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X65),c_Groups_Oone__class_Oone(X58)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X66),X65)),X66)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right__le__one__le) ).

fof(fact_mult__left__le__one__le,axiom,
    ! [X65,X66,X58] :
      ( class_Rings_Olinordered__idom(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),X66))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),X65))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X65),c_Groups_Oone__class_Oone(X58)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X65),X66)),X66)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left__le__one__le) ).

fof(fact_Union__disjoint,axiom,
    ! [X21,X112,X5] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X112)),X21) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X3),X112))
         => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X3),X21) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__disjoint) ).

fof(fact_zdiv__mono2,axiom,
    ! [X90,X143,X62] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X62))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X143))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X143),X90))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X62),X90)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X62),X143))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__mono2) ).

fof(fact_Domain__Un__eq,axiom,
    ! [X113,X21,X20,X5] : hAPP(c_Relation_ODomain(X5,X20),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X20),tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X5,X20),X21)),hAPP(c_Relation_ODomain(X5,X20),X113)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__Un__eq) ).

fof(fact_Range__Un__eq,axiom,
    ! [X113,X21,X5,X20] : hAPP(c_Relation_ORange(X20,X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X20,X5),tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_ORange(X20,X5),X21)),hAPP(c_Relation_ORange(X20,X5),X113)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__Un__eq) ).

fof(fact_map__update,axiom,
    ! [X33,X87,X239,X2,X5,X20] : hAPP(hAPP(c_List_Omap(X20,X5),X2),hAPP(hAPP(c_List_Olist__update(X20,X239),X87),X33)) = hAPP(hAPP(c_List_Olist__update(X5,hAPP(hAPP(c_List_Omap(X20,X5),X2),X239)),X87),hAPP(X2,X33)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__update) ).

fof(fact_set__ConsD,axiom,
    ! [X239,X25,X33,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X33),hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239))))
     => ( X33 = X25
        | hBOOL(hAPP(hAPP(c_member(X5),X33),hAPP(c_List_Oset(X5),X239))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__ConsD) ).

fof(fact_code__numeral__decr,axiom,
    ! [X96] :
      ( X96 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X96)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Code__Numeral_Onat__of,X96))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_code__numeral__decr) ).

fof(fact_in__set__dropD,axiom,
    ! [X239,X50,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Odrop(X5),X50),X239))))
     => hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X239))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__set__dropD) ).

fof(fact_in__set__takeD,axiom,
    ! [X239,X50,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Otake(X5),X50),X239))))
     => hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X239))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__set__takeD) ).

fof(fact_power__Suc__less__one,axiom,
    ! [X57,X62,X58] :
      ( class_Rings_Olinordered__semidom(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),X62))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X62),c_Groups_Oone__class_Oone(X58)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),hAPP(c_Nat_OSuc,X57))),c_Groups_Oone__class_Oone(X58))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__Suc__less__one) ).

fof(fact_zdiv__mono2__neg,axiom,
    ! [X90,X143,X62] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X62),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X143))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X143),X90))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X62),X143)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X62),X90))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__mono2__neg) ).

fof(fact_Id__onE,axiom,
    ! [X21,X23,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X23),c_Relation_OId__on(X5,X21)))
     => ~ ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X21))
           => X23 != hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X3) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Id__onE) ).

fof(fact_inv__f__f,axiom,
    ! [X25,X2,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => hAPP(c_Hilbert__Choice_Oinv__into(X5,X20,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X2),hAPP(X2,X25)) = X25 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__f__f) ).

fof(fact_the__inv__f__f,axiom,
    ! [X25,X2,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => hAPP(c_Fun_Othe__inv__into(X5,X20,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X2),hAPP(X2,X25)) = X25 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__inv__f__f) ).

fof(fact_fun__left__comm_Ofold__fun__comm,axiom,
    ! [X120,X25,X21,X2,X20,X5] :
      ( c_Finite__Set_Ofun__left__comm(X5,X20,X2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => hAPP(hAPP(X2,X25),hAPP(hAPP(c_Finite__Set_Ofold(X5,X20,X2),X120),X21)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X20,X2),hAPP(hAPP(X2,X25),X120)),X21) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__fun__comm) ).

fof(fact_inv__f__eq,axiom,
    ! [X33,X25,X2,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => ( hAPP(X2,X25) = X33
       => hAPP(c_Hilbert__Choice_Oinv__into(X5,X20,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X2),X33) = X25 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__f__eq) ).

fof(fact_wfP__subset,axiom,
    ! [X160,X171,X5] :
      ( c_Wellfounded_OwfP(X5,X171)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_fun(X5,tc_HOL_Obool))),X160),X171))
       => c_Wellfounded_OwfP(X5,X160) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfP__subset) ).

fof(fact_pred__equals__eq,axiom,
    ! [X192,X32,X5] :
      ( hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X32) = hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X192)
    <=> X32 = X192 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__equals__eq) ).

fof(fact_mult__less__cancel1,axiom,
    ! [X50,X95,X87] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X87),X95)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X87),X50)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X87))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),X50)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel1) ).

fof(fact_mult__less__cancel2,axiom,
    ! [X50,X87,X95] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X95),X87)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X50),X87)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X87))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),X50)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel2) ).

fof(fact_sort__key__simps_I2_J,axiom,
    ! [X239,X25,X2,X5,X20] :
      ( class_Orderings_Olinorder(X20)
     => c_List_Olinorder__class_Osort__key(X5,X20,X2,hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X20,X2),X25),c_List_Olinorder__class_Osort__key(X5,X20,X2,X239)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sort__key__simps_I2_J) ).

fof(fact_divide__right__mono,axiom,
    ! [X56,X90,X62,X58] :
      ( class_Fields_Olinordered__field__inverse__zero(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X62),X90))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),X56))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X62),X56)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X90),X56))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__right__mono) ).

fof(fact_power__mono,axiom,
    ! [X57,X90,X62,X58] :
      ( class_Rings_Olinordered__semidom(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X62),X90))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),X62))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),X57)),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X90),X57))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__mono) ).

fof(fact_mult__right__mono,axiom,
    ! [X56,X90,X62,X58] :
      ( class_Rings_Oordered__semiring(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X62),X90))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),X56))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X56)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X90),X56))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right__mono) ).

fof(fact_comm__mult__left__mono,axiom,
    ! [X56,X90,X62,X58] :
      ( class_Rings_Oordered__comm__semiring(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X62),X90))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),X56))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X56),X62)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X56),X90))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__mult__left__mono) ).

fof(fact_mult__left__mono,axiom,
    ! [X56,X90,X62,X58] :
      ( class_Rings_Oordered__semiring(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X62),X90))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),X56))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X56),X62)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X56),X90))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left__mono) ).

fof(fact_divide__strict__right__mono,axiom,
    ! [X56,X90,X62,X58] :
      ( class_Fields_Olinordered__field(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X62),X90))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),X56))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X62),X56)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X90),X56))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__strict__right__mono) ).

fof(fact_mult__strict__right__mono,axiom,
    ! [X56,X90,X62,X58] :
      ( class_Rings_Olinordered__semiring__strict(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X62),X90))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),X56))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X56)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X90),X56))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__right__mono) ).

fof(fact_comm__mult__strict__left__mono,axiom,
    ! [X56,X90,X62,X58] :
      ( class_Rings_Olinordered__comm__semiring__strict(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X62),X90))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),X56))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X56),X62)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X56),X90))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__mult__strict__left__mono) ).

fof(fact_mult__strict__left__mono,axiom,
    ! [X56,X90,X62,X58] :
      ( class_Rings_Olinordered__semiring__strict(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X62),X90))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),X56))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X56),X62)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X56),X90))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__left__mono) ).

fof(fact_zip__Cons__Cons,axiom,
    ! [X241,X65,X242,X66,X5,X58] : hAPP(hAPP(c_List_Ozip(X58,X5),hAPP(hAPP(c_List_Olist_OCons(X58),X66),X242)),hAPP(hAPP(c_List_Olist_OCons(X5),X65),X241)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(X58,X5)),hAPP(hAPP(c_Product__Type_OPair(X58,X5),X66),X65)),hAPP(hAPP(c_List_Ozip(X58,X5),X242),X241)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__Cons__Cons) ).

fof(fact_divide__le__0__iff,axiom,
    ! [X24,X6,X5] :
      ( class_Fields_Olinordered__field__inverse__zero(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X6),X24)),c_Groups_Ozero__class_Ozero(X5)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),X6))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X24),c_Groups_Ozero__class_Ozero(X5))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),c_Groups_Ozero__class_Ozero(X5)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),X24)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__le__0__iff) ).

fof(fact_mult__le__0__iff,axiom,
    ! [X24,X6,X5] :
      ( class_Rings_Olinordered__ring__strict(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X24)),c_Groups_Ozero__class_Ozero(X5)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),X6))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X24),c_Groups_Ozero__class_Ozero(X5))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),c_Groups_Ozero__class_Ozero(X5)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),X24)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__0__iff) ).

fof(fact_divide__less__0__iff,axiom,
    ! [X24,X6,X5] :
      ( class_Fields_Olinordered__field__inverse__zero(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X6),X24)),c_Groups_Ozero__class_Ozero(X5)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X6))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X24),c_Groups_Ozero__class_Ozero(X5))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),c_Groups_Ozero__class_Ozero(X5)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X24)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__less__0__iff) ).

fof(fact_transfer__int__nat__set__relations_I2_J,axiom,
    ! [X21,X25] :
      ( c_Nat__Transfer_Ois__nat(X25)
     => ( c_Nat__Transfer_Onat__set(X21)
       => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X25),X21))
        <=> hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,X25)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X21))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__set__relations_I2_J) ).

fof(fact_Max__eqI,axiom,
    ! [X25,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( ! [X177] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X177),X21))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X177),X25)) )
         => ( hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
           => c_Big__Operators_Olinorder__class_OMax(X5,X21) = X25 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max__eqI) ).

fof(fact_list__all__length,axiom,
    ! [X239,X18,X5] :
      ( c_List_Olist__all(X5,X18,X239)
    <=> ! [X69] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X69),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239)))
         => hBOOL(hAPP(X18,hAPP(hAPP(c_List_Onth(X5),X239),X69))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__all__length) ).

fof(fact_mod__pos__neg__1__number__of,axiom,
    ! [X128] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)),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),X128)) = 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),X128))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__pos__neg__1__number__of) ).

fof(fact_subset__inj__on,axiom,
    ! [X21,X113,X2,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,X2,X113)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),X113))
       => c_Fun_Oinj__on(X5,X20,X2,X21) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__inj__on) ).

fof(fact_length__filter__le,axiom,
    ! [X239,X18,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),hAPP(c_List_Ofilter(X5,X18),X239))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__filter__le) ).

fof(fact_rtrancl_Ortrancl__refl,axiom,
    ! [X171,X6,X5] : hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X6)),c_Transitive__Closure_Ortrancl(X5,X171))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl_Ortrancl__refl) ).

fof(fact_nat__add__left__cancel__le,axiom,
    ! [X50,X95,X87] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X87),X95)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X87),X50)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X50)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel__le) ).

fof(fact_nat__add__left__cancel__less,axiom,
    ! [X50,X95,X87] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X87),X95)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X87),X50)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),X50)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel__less) ).

fof(fact_inv__into__f__f,axiom,
    ! [X25,X21,X2,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,X2,X21)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
       => hAPP(c_Hilbert__Choice_Oinv__into(X5,X20,X21,X2),hAPP(X2,X25)) = X25 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__into__f__f) ).

fof(fact_the__inv__into__f__f,axiom,
    ! [X25,X21,X2,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,X2,X21)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
       => hAPP(c_Fun_Othe__inv__into(X5,X20,X21,X2),hAPP(X2,X25)) = X25 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__inv__into__f__f) ).

fof(fact_div__pos__neg__1__number__of,axiom,
    ! [X128] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)),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),X128)) = 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),X128))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__pos__neg__1__number__of) ).

fof(fact_inv__into__f__eq,axiom,
    ! [X33,X25,X21,X2,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,X2,X21)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
       => ( hAPP(X2,X25) = X33
         => hAPP(c_Hilbert__Choice_Oinv__into(X5,X20,X21,X2),X33) = X25 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__into__f__eq) ).

fof(fact_the__inv__into__f__eq,axiom,
    ! [X33,X25,X21,X2,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,X2,X21)
     => ( hAPP(X2,X25) = X33
       => ( hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => hAPP(c_Fun_Othe__inv__into(X5,X20,X21,X2),X33) = X25 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__inv__into__f__eq) ).

fof(fact_finite__INT,axiom,
    ! [X21,X20,X221,X5] :
      ( ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),X221))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(X20),hAPP(X21,X3))) )
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X20),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X20,tc_HOL_Obool)),X221),X21))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__INT) ).

fof(fact_power__increasing,axiom,
    ! [X62,X163,X57,X58] :
      ( class_Rings_Olinordered__semidom(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X57),X163))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Oone__class_Oone(X58)),X62))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),X57)),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),X163))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__increasing) ).

fof(fact_power__strict__increasing,axiom,
    ! [X62,X163,X57,X58] :
      ( class_Rings_Olinordered__semidom(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X57),X163))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Oone__class_Oone(X58)),X62))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),X57)),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),X163))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__strict__increasing) ).

fof(fact_divide__right__mono__neg,axiom,
    ! [X56,X90,X62,X58] :
      ( class_Fields_Olinordered__field__inverse__zero(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X62),X90))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X56),c_Groups_Ozero__class_Ozero(X58)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X90),X56)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X62),X56))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__right__mono__neg) ).

fof(fact_mult__right__mono__neg,axiom,
    ! [X56,X62,X90,X58] :
      ( class_Rings_Oordered__ring(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X90),X62))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X56),c_Groups_Ozero__class_Ozero(X58)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X56)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X90),X56))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right__mono__neg) ).

fof(fact_mult__left__mono__neg,axiom,
    ! [X56,X62,X90,X58] :
      ( class_Rings_Oordered__ring(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X90),X62))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X56),c_Groups_Ozero__class_Ozero(X58)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X56),X62)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X56),X90))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left__mono__neg) ).

fof(fact_divide__strict__right__mono__neg,axiom,
    ! [X56,X62,X90,X58] :
      ( class_Fields_Olinordered__field(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X90),X62))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X56),c_Groups_Ozero__class_Ozero(X58)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X62),X56)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X90),X56))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__strict__right__mono__neg) ).

fof(fact_mult__strict__right__mono__neg,axiom,
    ! [X56,X62,X90,X58] :
      ( class_Rings_Olinordered__ring__strict(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X90),X62))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X56),c_Groups_Ozero__class_Ozero(X58)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X56)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X90),X56))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__right__mono__neg) ).

fof(fact_mult__strict__left__mono__neg,axiom,
    ! [X56,X62,X90,X58] :
      ( class_Rings_Olinordered__ring__strict(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X90),X62))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X56),c_Groups_Ozero__class_Ozero(X58)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X56),X62)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X56),X90))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__left__mono__neg) ).

fof(fact_card__Diff__singleton,axiom,
    ! [X25,X21,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
       => hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X21)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Diff__singleton) ).

fof(fact_finite__Diff2,axiom,
    ! [X21,X113,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X113))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),X113)))
      <=> hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Diff2) ).

fof(fact_listsum__update__nat,axiom,
    ! [X57,X275,X96] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X96),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),X275)))
     => hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat,X275),X96),X57)) = 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),X275)),X57)),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),X275),X96)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__update__nat) ).

fof(fact_o__def,axiom,
    ! [X25,X1,X2,X116,X5,X20] : hAPP(hAPP(c_Fun_Ocomp(X20,X5,X116,X2),X1),X25) = hAPP(X2,hAPP(X1,X25)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__def) ).

fof(fact_o__apply,axiom,
    ! [X25,X1,X2,X116,X5,X20] : hAPP(hAPP(c_Fun_Ocomp(X20,X5,X116,X2),X1),X25) = hAPP(X2,hAPP(X1,X25)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__apply) ).

fof(fact_inf__mono,axiom,
    ! [X91,X90,X56,X62,X58] :
      ( class_Lattices_Osemilattice__inf(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X62),X56))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X90),X91))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X62),X90)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X56),X91))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__mono) ).

fof(fact_sup__mono,axiom,
    ! [X91,X90,X56,X62,X58] :
      ( class_Lattices_Osemilattice__sup(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X62),X56))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X90),X91))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X62),X90)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X56),X91))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__mono) ).

fof(fact_min__max_Osup__mono,axiom,
    ! [X91,X90,X56,X62,X58] :
      ( class_Orderings_Olinorder(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X62),X56))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X90),X91))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Orderings_Oord__class_Omax(X58),X62),X90)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X58),X56),X91))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup__mono) ).

fof(fact_min__max_Oinf__mono,axiom,
    ! [X91,X90,X56,X62,X58] :
      ( class_Orderings_Olinorder(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X62),X56))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X90),X91))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Orderings_Oord__class_Omin(X58),X62),X90)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X58),X56),X91))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__mono) ).

fof(fact_add__mono,axiom,
    ! [X91,X56,X90,X62,X58] :
      ( class_Groups_Oordered__ab__semigroup__add(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X62),X90))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X56),X91))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),X56)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X90),X91))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__mono) ).

fof(fact_add__less__le__mono,axiom,
    ! [X91,X56,X90,X62,X58] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X62),X90))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X56),X91))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),X56)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X90),X91))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__le__mono) ).

fof(fact_add__le__less__mono,axiom,
    ! [X91,X56,X90,X62,X58] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X62),X90))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X56),X91))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),X56)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X90),X91))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__less__mono) ).

fof(fact_add__strict__mono,axiom,
    ! [X91,X56,X90,X62,X58] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X62),X90))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X56),X91))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),X56)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X90),X91))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__mono) ).

fof(fact_right__diff__distrib__number__of,axiom,
    ! [X56,X90,X136,X5] :
      ( ( class_Int_Onumber(X5)
        & class_Rings_Oring(X5) )
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X136)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X90),X56)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X136)),X90)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X136)),X56)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_right__diff__distrib__number__of) ).

fof(fact_right__distrib__number__of,axiom,
    ! [X56,X90,X136,X5] :
      ( ( class_Int_Onumber(X5)
        & class_Rings_Osemiring(X5) )
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X136)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X90),X56)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X136)),X90)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X136)),X56)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_right__distrib__number__of) ).

fof(fact_fold__inf__insert,axiom,
    ! [X6,X24,X21,X5] :
      ( class_Lattices_Osemilattice__inf(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Lattices_Osemilattice__inf__class_Oinf(X5)),X24),hAPP(hAPP(c_Set_Oinsert(X5),X6),X21)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X6),hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Lattices_Osemilattice__inf__class_Oinf(X5)),X24),X21)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__inf__insert) ).

fof(fact_fold__sup__insert,axiom,
    ! [X6,X24,X21,X5] :
      ( class_Lattices_Osemilattice__sup(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Lattices_Osemilattice__sup__class_Osup(X5)),X24),hAPP(hAPP(c_Set_Oinsert(X5),X6),X21)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X6),hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Lattices_Osemilattice__sup__class_Osup(X5)),X24),X21)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__sup__insert) ).

fof(fact_min__max_Ofold__sup__insert,axiom,
    ! [X6,X24,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omax(X5)),X24),hAPP(hAPP(c_Set_Oinsert(X5),X6),X21)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X6),hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omax(X5)),X24),X21)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ofold__sup__insert) ).

fof(fact_min__max_Ofold__inf__insert,axiom,
    ! [X6,X24,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omin(X5)),X24),hAPP(hAPP(c_Set_Oinsert(X5),X6),X21)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X6),hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omin(X5)),X24),X21)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ofold__inf__insert) ).

fof(fact_finite__vimageI,axiom,
    ! [X122,X20,X205,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X205))
     => ( c_Fun_Oinj__on(X20,X5,X122,c_Orderings_Otop__class_Otop(tc_fun(X20,tc_HOL_Obool)))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(X20),hAPP(c_Set_Ovimage(X20,X5,X122),X205))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__vimageI) ).

fof(fact_INF__leI,axiom,
    ! [X210,X21,X82,X5,X20] :
      ( class_Complete__Lattice_Ocomplete__lattice(X20)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X82),X21))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,X20),X21),X210)),hAPP(X210,X82))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF__leI) ).

fof(fact_add__number__of__diff2,axiom,
    ! [X128,X56,X136,X58] :
      ( class_Int_Onumber__ring(X58)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(c_Int_Onumber__class_Onumber__of(X58),X136)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X58),X56),hAPP(c_Int_Onumber__class_Onumber__of(X58),X128))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(c_Int_Onumber__class_Onumber__of(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X136),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X128)))),X56) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__number__of__diff2) ).

fof(fact_less__eq__nat_Osimps_I2_J,axiom,
    ! [X50,X95] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X95)),X50))
    <=> hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X50)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I2_J) ).

fof(fact_SUP1__I,axiom,
    ! [X20,X24,X113,X21,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),X21))
     => ( hBOOL(hAPP(hAPP(X113,X6),X24))
       => hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X20,tc_HOL_Obool)),X21),X113),X24)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUP1__I) ).

fof(fact_Sup__le__iff,axiom,
    ! [X24,X21,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Complete__Lattice_OSup__class_OSup(X5,X21)),X24))
      <=> ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X21))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X3),X24)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__le__iff) ).

fof(fact_fun__left__comm__idem_Ofold__insert__idem,axiom,
    ! [X25,X120,X21,X2,X20,X5] :
      ( c_Finite__Set_Ofun__left__comm__idem(X5,X20,X2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => hAPP(hAPP(c_Finite__Set_Ofold(X5,X20,X2),X120),hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(hAPP(X2,X25),hAPP(hAPP(c_Finite__Set_Ofold(X5,X20,X2),X120),X21)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__idem_Ofold__insert__idem) ).

fof(fact_sum__eq__0__conv,axiom,
    ! [X272,X95] :
      ( hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X95),X272) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> ( X95 = 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),X272)))
           => X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__eq__0__conv) ).

fof(fact_evaln_OSemi,axiom,
    ! [X51,X52,X45,X57,X46,X53] :
      ( c_Natural_Oevaln(X53,X46,X57,X45)
     => ( c_Natural_Oevaln(X52,X45,X57,X51)
       => c_Natural_Oevaln(c_Com_Ocom_OSemi(X53,X52),X46,X57,X51) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_OSemi) ).

fof(fact_one__le__mult__iff,axiom,
    ! [X50,X95] :
      ( 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),X95),X50)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X95))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X50)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__le__mult__iff) ).

fof(fact_one__less__mult,axiom,
    ! [X72,X57] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X57))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X72))
       => 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),X72),X57))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__less__mult) ).

fof(fact_mod__mult__self4,axiom,
    ! [X72,X57,X96] : 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),X96),X57)),X72)),X57) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X72),X57),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__self4) ).

fof(fact_Inter__Un__distrib,axiom,
    ! [X113,X21,X5] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),X21)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),X113)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__Un__distrib) ).

fof(fact_Union__Un__distrib,axiom,
    ! [X113,X21,X5] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X21)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X113)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__Un__distrib) ).

fof(fact_split__mod,axiom,
    ! [X87,X50,X18] :
      ( hBOOL(hAPP(X18,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X50,X87)))
    <=> ( ( X87 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => hBOOL(hAPP(X18,X50)) )
        & ( X87 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => ! [X146,X101] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X101),X87))
             => ( X50 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X87),X146)),X101)
               => hBOOL(hAPP(X18,X101)) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__mod) ).

fof(fact_in__lists__conv__set,axiom,
    ! [X21,X239,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X239),c_List_Olists(X5,X21)))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X239)))
         => hBOOL(hAPP(hAPP(c_member(X5),X3),X21)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__lists__conv__set) ).

fof(fact_list_Osize_I2_J,axiom,
    ! [X254,X6,X80,X5] : c_List_Olist_Olist__size(X5,X80,hAPP(hAPP(c_List_Olist_OCons(X5),X6),X254)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X80,X6)),c_List_Olist_Olist__size(X5,X80,X254))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list_Osize_I2_J) ).

fof(fact_select__weight__cons__zero,axiom,
    ! [X239,X25,X5] : c_Random_Oselect__weight(X5,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X5)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X5),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),X25)),X239)) = c_Random_Oselect__weight(X5,X239),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_select__weight__cons__zero) ).

fof(fact_transpose_Opsimps_I2_J,axiom,
    ! [X286,X5] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(X5)),c_List_Otranspose__rel(X5)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X5)),c_List_Olist_ONil(X5)),X286)))
     => c_List_Otranspose(X5,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X5)),c_List_Olist_ONil(X5)),X286)) = c_List_Otranspose(X5,X286) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose_Opsimps_I2_J) ).

fof(fact_disjoint__eq__subset__Compl,axiom,
    ! [X113,X21,X5] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X113))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_disjoint__eq__subset__Compl) ).

fof(fact_card__seteq,axiom,
    ! [X21,X113,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X113))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),X113))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X113)),hAPP(c_Finite__Set_Ocard(X5),X21)))
         => X21 = X113 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__seteq) ).

fof(fact_Inter__lower,axiom,
    ! [X21,X113,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X113),X21))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),X21)),X113)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__lower) ).

fof(fact_converse__rel__comp,axiom,
    ! [X76,X171,X116,X5,X20] : hAPP(c_Relation_Oconverse(X20,X5),hAPP(hAPP(c_Relation_Orel__comp(X20,X116,X5),X171),X76)) = hAPP(hAPP(c_Relation_Orel__comp(X5,X116,X20),hAPP(c_Relation_Oconverse(X116,X5),X76)),hAPP(c_Relation_Oconverse(X20,X116),X171)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__rel__comp) ).

fof(fact_min__le__iff__disj,axiom,
    ! [X120,X33,X25,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X25),X33)),X120))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X25),X120))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X33),X120)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__le__iff__disj) ).

fof(fact_min__less__iff__disj,axiom,
    ! [X120,X33,X25,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X25),X33)),X120))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X25),X120))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X33),X120)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__less__iff__disj) ).

fof(fact_split__div,axiom,
    ! [X87,X50,X18] :
      ( hBOOL(hAPP(X18,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X50),X87)))
    <=> ( ( X87 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => hBOOL(hAPP(X18,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
        & ( X87 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => ! [X146,X101] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X101),X87))
             => ( X50 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X87),X146)),X101)
               => hBOOL(hAPP(X18,X146)) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__div) ).

fof(fact_min__max_OSup__fin_Osubset__idem,axiom,
    ! [X113,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( X113 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X113),X21))
           => hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X113)),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X21)) = c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X21) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Osubset__idem) ).

fof(fact_min__max_OInf__fin_Osubset__idem,axiom,
    ! [X113,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( X113 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X113),X21))
           => hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X113)),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X21)) = c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X21) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Osubset__idem) ).

fof(fact_evalc_OWhileTrue,axiom,
    ! [X110,X104,X23,X111,X24] :
      ( hBOOL(hAPP(X24,X111))
     => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X23),X111),X104))
       => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X24,X23)),X104),X110))
         => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X24,X23)),X111),X110)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_OWhileTrue) ).

fof(fact_subset__Pow__Union,axiom,
    ! [X21,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),X21),hAPP(c_Set_OPow(X5),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X21)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__Pow__Union) ).

fof(fact_IntI,axiom,
    ! [X113,X21,X23,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X23),X21))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X23),X113))
       => hBOOL(hAPP(hAPP(c_member(X5),X23),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_IntI) ).

fof(fact_conjI__realizer,axiom,
    ! [X20,X5,X153,X16,X160,X18] :
      ( hBOOL(hAPP(X18,X160))
     => ( hBOOL(hAPP(X16,X153))
       => ( hBOOL(hAPP(X18,hAPP(c_Product__Type_Ofst(X5,X20),hAPP(hAPP(c_Product__Type_OPair(X5,X20),X160),X153))))
          & hBOOL(hAPP(X16,hAPP(c_Product__Type_Osnd(X5,X20),hAPP(hAPP(c_Product__Type_OPair(X5,X20),X160),X153)))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_conjI__realizer) ).

fof(fact_INFI__apply,axiom,
    ! [X25,X2,X21,X116,X20,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X20,tc_fun(X116,X5)),X21),X2),X25) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X20,X5),X21),hAPP(hAPP(c_COMBC(X20,X116,X5),X2),X25)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INFI__apply) ).

fof(fact_SUPR__apply,axiom,
    ! [X25,X2,X21,X116,X20,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,tc_fun(X116,X5)),X21),X2),X25) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,X5),X21),hAPP(hAPP(c_COMBC(X20,X116,X5),X2),X25)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUPR__apply) ).

fof(fact_finite__Un,axiom,
    ! [X4,X205,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X205),X4)))
    <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X205))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Un) ).

fof(fact_Un__Diff__Int,axiom,
    ! [X113,X21,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),X113)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113)) = X21,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Diff__Int) ).

fof(fact_listsp__mono,axiom,
    ! [X113,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),X113))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),c_List_Olistsp(X5,X21)),c_List_Olistsp(X5,X113))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsp__mono) ).

fof(fact_lists__mono,axiom,
    ! [X113,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),X113))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),c_List_Olists(X5,X21)),c_List_Olists(X5,X113))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lists__mono) ).

fof(fact_neg__le__divide__eq,axiom,
    ! [X24,X6,X23,X5] :
      ( class_Fields_Olinordered__field(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X24),X23)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X23))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__le__divide__eq) ).

fof(fact_neg__less__divide__eq,axiom,
    ! [X24,X6,X23,X5] :
      ( class_Fields_Olinordered__field(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X24),X23)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X23))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__less__divide__eq) ).

fof(fact_symp__def,axiom,
    ! [X171,X5] :
      ( c_Predicate_Osymp(X5,X171)
    <=> c_Relation_Osym(X5,hAPP(c_Set_OCollect(tc_prod(X5,X5)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X5,tc_HOL_Obool),X171))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_symp__def) ).

fof(fact_transp__def,axiom,
    ! [X171,X5] :
      ( c_Predicate_Otransp(X5,X171)
    <=> c_Relation_Otrans(X5,hAPP(c_Set_OCollect(tc_prod(X5,X5)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X5,tc_HOL_Obool),X171))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transp__def) ).

fof(fact_wfP__def,axiom,
    ! [X171,X5] :
      ( c_Wellfounded_OwfP(X5,X171)
    <=> c_Wellfounded_Owf(X5,hAPP(c_Set_OCollect(tc_prod(X5,X5)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X5,tc_HOL_Obool),X171))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfP__def) ).

fof(fact_pos__imp__zdiv__neg__iff,axiom,
    ! [X6,X24] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X6),X24)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X6),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__imp__zdiv__neg__iff) ).

fof(fact_Times__eq__cancel2,axiom,
    ! [X113,X21,X20,X112,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X25),X112))
     => ( hAPP(hAPP(c_Product__Type_OSigma(X20,X5),X21),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X20),X112)) = hAPP(hAPP(c_Product__Type_OSigma(X20,X5),X113),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X20),X112))
      <=> X21 = X113 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Times__eq__cancel2) ).

fof(fact_mod__pos__neg__trivial,axiom,
    ! [X90,X62] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X62))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X62),X90)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,X62,X90) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X62),X90) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__pos__neg__trivial) ).

fof(fact_wfI__pf,axiom,
    ! [X32,X5] :
      ( ! [X226] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X226),hAPP(c_Relation_OImage(X5,X5,X32),X226)))
         => X226 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) )
     => c_Wellfounded_Owf(X5,X32) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfI__pf) ).

fof(fact_splitI,axiom,
    ! [X20,X5,X24,X6,X2] :
      ( hBOOL(hAPP(hAPP(X2,X6),X24))
     => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5,X20,tc_HOL_Obool),X2),hAPP(hAPP(c_Product__Type_OPair(X5,X20),X6),X24))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_splitI) ).

fof(fact_prod__caseI,axiom,
    ! [X20,X5,X24,X6,X19] :
      ( hBOOL(hAPP(hAPP(X19,X6),X24))
     => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5,X20,tc_HOL_Obool),X19),hAPP(hAPP(c_Product__Type_OPair(X5,X20),X6),X24))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_prod__caseI) ).

fof(fact_neg__imp__zdiv__neg__iff,axiom,
    ! [X6,X24] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X6),X24)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__imp__zdiv__neg__iff) ).

fof(fact_le__diff__conv,axiom,
    ! [X82,X87,X157] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X157),X87)),X82))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X157),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X82),X87))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__diff__conv) ).

fof(fact_less__diff__conv,axiom,
    ! [X87,X157,X82] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X82),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X157),X87)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X82),X87)),X157)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__diff__conv) ).

fof(fact_card__Diff__subset,axiom,
    ! [X21,X113,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X113))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X113),X21))
       => hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X21)),hAPP(c_Finite__Set_Ocard(X5),X113)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Diff__subset) ).

fof(fact_folding__idem_Oidem__comp,axiom,
    ! [X25,X205,X2,X20,X5] :
      ( c_Finite__Set_Ofolding__idem(X5,X20,X2,X205)
     => hAPP(c_Fun_Ocomp(X20,X20,X20,hAPP(X2,X25)),hAPP(X2,X25)) = hAPP(X2,X25) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__idem_Oidem__comp) ).

fof(fact_Field__Un,axiom,
    ! [X76,X171,X5] : hAPP(c_Relation_OField(X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X171),X76)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_OField(X5),X171)),hAPP(c_Relation_OField(X5),X76)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Field__Un) ).

fof(fact_product__list__set,axiom,
    ! [X251,X239,X20,X5] : hAPP(c_List_Oset(tc_prod(X5,X20)),c_Enum_Oproduct(X5,X20,X239,X251)) = hAPP(hAPP(c_Product__Type_OSigma(X5,X20),hAPP(c_List_Oset(X5),X239)),hAPP(c_COMBK(tc_fun(X20,tc_HOL_Obool),X5),hAPP(c_List_Oset(X20),X251))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_product__list__set) ).

fof(fact_zip__eq__conv,axiom,
    ! [X250,X251,X20,X239,X5] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X20)),X251)
     => ( hAPP(hAPP(c_List_Ozip(X5,X20),X239),X251) = X250
      <=> ( hAPP(hAPP(c_List_Omap(tc_prod(X5,X20),X5),c_Product__Type_Ofst(X5,X20)),X250) = X239
          & hAPP(hAPP(c_List_Omap(tc_prod(X5,X20),X20),c_Product__Type_Osnd(X5,X20)),X250) = X251 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__eq__conv) ).

fof(fact_inf1D1,axiom,
    ! [X25,X113,X21,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113),X25))
     => hBOOL(hAPP(X21,X25)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf1D1) ).

fof(fact_inf1D2,axiom,
    ! [X25,X113,X21,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113),X25))
     => hBOOL(hAPP(X113,X25)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf1D2) ).

fof(fact_listrelp_Oequations_I2_J,axiom,
    ! [X60,X26,X63,X27,X171,X5] :
      ( c_List_Olistrelp(X5,X171,hAPP(hAPP(c_List_Olist_OCons(X5),X27),X63),hAPP(hAPP(c_List_Olist_OCons(X5),X26),X60))
    <=> ( hBOOL(hAPP(hAPP(X171,X27),X26))
        & c_List_Olistrelp(X5,X171,X63,X60) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrelp_Oequations_I2_J) ).

fof(fact_listrelp_OCons,axiom,
    ! [X251,X239,X5,X33,X25,X171] :
      ( hBOOL(hAPP(hAPP(X171,X25),X33))
     => ( c_List_Olistrelp(X5,X171,X239,X251)
       => c_List_Olistrelp(X5,X171,hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239),hAPP(hAPP(c_List_Olist_OCons(X5),X33),X251)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrelp_OCons) ).

fof(fact_Rep__Integ__cases,axiom,
    ! [X33] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X33),c_Int_OInteg))
     => ~ ! [X3] : X33 != hAPP(c_Int_ORep__Integ,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Rep__Integ__cases) ).

fof(fact_InterI,axiom,
    ! [X21,X112,X5] :
      ( ! [X291] :
          ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X291),X112))
         => hBOOL(hAPP(hAPP(c_member(X5),X21),X291)) )
     => hBOOL(hAPP(hAPP(c_member(X5),X21),c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),X112))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_InterI) ).

fof(fact_lists_Osimps,axiom,
    ! [X21,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X6),c_List_Olists(X5,X21)))
    <=> ( X6 = c_List_Olist_ONil(X5)
        | ? [X187,X274] :
            ( X6 = hAPP(hAPP(c_List_Olist_OCons(X5),X187),X274)
            & hBOOL(hAPP(hAPP(c_member(X5),X187),X21))
            & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X274),c_List_Olists(X5,X21))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lists_Osimps) ).

fof(fact_in__set__replicate,axiom,
    ! [X33,X50,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),c_List_Oreplicate(X5,X50,X33))))
    <=> ( X25 = X33
        & X50 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__set__replicate) ).

fof(fact_folding__one_Ounion__disjoint,axiom,
    ! [X113,X21,X205,X2,X5] :
      ( c_Finite__Set_Ofolding__one(X5,X2,X205)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X113))
           => ( X113 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
               => hAPP(X205,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(X2,hAPP(X205,X21)),hAPP(X205,X113)) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one_Ounion__disjoint) ).

fof(fact_mod__diff__eq,axiom,
    ! [X56,X90,X62,X58] :
      ( class_Divides_Oring__div(X58)
     => c_Divides_Odiv__class_Omod(X58,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X58),X62),X90),X56) = c_Divides_Odiv__class_Omod(X58,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X58),c_Divides_Odiv__class_Omod(X58,X62,X56)),c_Divides_Odiv__class_Omod(X58,X90,X56)),X56) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__diff__eq) ).

fof(fact_mod__mult__eq,axiom,
    ! [X56,X90,X62,X58] :
      ( class_Divides_Osemiring__div(X58)
     => c_Divides_Odiv__class_Omod(X58,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X90),X56) = c_Divides_Odiv__class_Omod(X58,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),c_Divides_Odiv__class_Omod(X58,X62,X56)),c_Divides_Odiv__class_Omod(X58,X90,X56)),X56) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__eq) ).

fof(fact_mod__add__eq,axiom,
    ! [X56,X90,X62,X58] :
      ( class_Divides_Osemiring__div(X58)
     => c_Divides_Odiv__class_Omod(X58,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),X90),X56) = c_Divides_Odiv__class_Omod(X58,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),c_Divides_Odiv__class_Omod(X58,X62,X56)),c_Divides_Odiv__class_Omod(X58,X90,X56)),X56) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__add__eq) ).

fof(fact_power__gt1__lemma,axiom,
    ! [X57,X62,X58] :
      ( class_Rings_Olinordered__semidom(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Oone__class_Oone(X58)),X62))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Oone__class_Oone(X58)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),X57)))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__gt1__lemma) ).

fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
    ! [X6,X5] :
      ( class_Groups_Olinordered__ab__group__add(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),X6)),c_Groups_Ozero__class_Ozero(X5)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),c_Groups_Ozero__class_Ozero(X5))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__add__le__zero__iff__single__add__le__zero) ).

fof(fact_even__less__0__iff,axiom,
    ! [X6,X5] :
      ( class_Rings_Olinordered__idom(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),X6)),c_Groups_Ozero__class_Ozero(X5)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),c_Groups_Ozero__class_Ozero(X5))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_even__less__0__iff) ).

fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
    ! [X6,X5] :
      ( class_Groups_Olinordered__ab__group__add(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),X6)),c_Groups_Ozero__class_Ozero(X5)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),c_Groups_Ozero__class_Ozero(X5))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__add__less__zero__iff__single__add__less__zero) ).

fof(fact_inj__on__diff__nat,axiom,
    ! [X87,X207] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),X207))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X87),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)),X87),X207) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__diff__nat) ).

fof(fact_InterE,axiom,
    ! [X194,X112,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X21),c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),X112)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X194),X112))
       => hBOOL(hAPP(hAPP(c_member(X5),X21),X194)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_InterE) ).

fof(fact_InterD,axiom,
    ! [X194,X112,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X21),c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),X112)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X194),X112))
       => hBOOL(hAPP(hAPP(c_member(X5),X21),X194)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_InterD) ).

fof(fact_div__pos__neg__trivial,axiom,
    ! [X90,X62] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X62))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X62),X90)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X62),X90) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__pos__neg__trivial) ).

fof(fact_finite__fun__UNIVD1,axiom,
    ! [X20,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X5,X20)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X5,X20),tc_HOL_Obool))))
     => ( hAPP(c_Finite__Set_Ocard(X20),c_Orderings_Otop__class_Otop(tc_fun(X20,tc_HOL_Obool))) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(X5),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__fun__UNIVD1) ).

fof(fact_min__max_OInf__fin_Ounion__idem,axiom,
    ! [X113,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X113))
           => ( X113 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X21)),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X113)) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Ounion__idem) ).

fof(fact_min__max_OSup__fin_Ounion__idem,axiom,
    ! [X113,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X113))
           => ( X113 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X21)),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X113)) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Ounion__idem) ).

fof(fact_zdiv__mono1,axiom,
    ! [X90,X150,X62] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X62),X150))
     => ( 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),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X62),X90)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X150),X90))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__mono1) ).

fof(fact_div__le__mono2,axiom,
    ! [X96,X57,X72] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X72))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X72),X57))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X96),X57)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X96),X72))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__le__mono2) ).

fof(fact_zmult__zless__mono2,axiom,
    ! [X96,X97,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X98),X97))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X96))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X96),X98)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X96),X97))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__zless__mono2) ).

fof(fact_mult__less__mono1,axiom,
    ! [X96,X97,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),X97))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X96))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X98),X96)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X97),X96))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__mono1) ).

fof(fact_mult__less__mono2,axiom,
    ! [X96,X97,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),X97))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X96))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X96),X98)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X96),X97))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__mono2) ).

fof(fact_inj__mapD,axiom,
    ! [X2,X20,X5] :
      ( c_Fun_Oinj__on(tc_List_Olist(X5),tc_List_Olist(X20),hAPP(c_List_Omap(X5,X20),X2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X5),tc_HOL_Obool)))
     => c_Fun_Oinj__on(X5,X20,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__mapD) ).

fof(fact_inj__map,axiom,
    ! [X2,X20,X5] :
      ( c_Fun_Oinj__on(tc_List_Olist(X5),tc_List_Olist(X20),hAPP(c_List_Omap(X5,X20),X2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X5),tc_HOL_Obool)))
    <=> c_Fun_Oinj__on(X5,X20,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__map) ).

fof(fact_subset__insertI2,axiom,
    ! [X24,X113,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),X113))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X24),X113))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__insertI2) ).

fof(fact_replicate__app__Cons__same,axiom,
    ! [X242,X66,X57,X58] : hAPP(hAPP(c_List_Oappend(X58),c_List_Oreplicate(X58,X57,X66)),hAPP(hAPP(c_List_Olist_OCons(X58),X66),X242)) = hAPP(hAPP(c_List_Olist_OCons(X58),X66),hAPP(hAPP(c_List_Oappend(X58),c_List_Oreplicate(X58,X57,X66)),X242)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_replicate__app__Cons__same) ).

fof(fact_INT__insert,axiom,
    ! [X113,X21,X6,X5,X20] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X20,tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X20),X6),X21)),X113) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(X113,X6)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X20,tc_fun(X5,tc_HOL_Obool)),X21),X113)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__insert) ).

fof(fact_UN__insert,axiom,
    ! [X113,X21,X6,X5,X20] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X20),X6),X21)),X113) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(X113,X6)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,tc_fun(X5,tc_HOL_Obool)),X21),X113)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__insert) ).

fof(fact_strict__below__fold1__iff,axiom,
    ! [X25,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X25),hAPP(c_Finite__Set_Ofold1(X5,c_Orderings_Oord__class_Omin(X5)),X21)))
          <=> ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X3),X21))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X25),X3)) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_strict__below__fold1__iff) ).

fof(fact_min__max_Obelow__fold1__iff,axiom,
    ! [X25,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X25),hAPP(c_Finite__Set_Ofold1(X5,c_Orderings_Oord__class_Omin(X5)),X21)))
          <=> ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X3),X21))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X25),X3)) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Obelow__fold1__iff) ).

fof(fact_below__fold1__iff,axiom,
    ! [X25,X21,X5] :
      ( class_Lattices_Osemilattice__inf(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X25),hAPP(c_Finite__Set_Ofold1(X5,c_Lattices_Osemilattice__inf__class_Oinf(X5)),X21)))
          <=> ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X5),X3),X21))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X25),X3)) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_below__fold1__iff) ).

fof(fact_maps__simps_I1_J,axiom,
    ! [X239,X25,X2,X5,X20] : c_List_Omaps(X20,X5,X2,hAPP(hAPP(c_List_Olist_OCons(X20),X25),X239)) = hAPP(hAPP(c_List_Oappend(X5),hAPP(X2,X25)),c_List_Omaps(X20,X5,X2,X239)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_maps__simps_I1_J) ).

fof(fact_le__iff__diff__le__0,axiom,
    ! [X24,X6,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),X24))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X6),X24)),c_Groups_Ozero__class_Ozero(X5))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__iff__diff__le__0) ).

fof(fact_less__iff__diff__less__0,axiom,
    ! [X24,X6,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),X24))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X6),X24)),c_Groups_Ozero__class_Ozero(X5))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__iff__diff__less__0) ).

fof(fact_zdiv__mono1__neg,axiom,
    ! [X90,X150,X62] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X62),X150))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X90),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),X150),X90)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X62),X90))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__mono1__neg) ).

fof(fact_nth__mem,axiom,
    ! [X239,X5,X50] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X50),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239)))
     => hBOOL(hAPP(hAPP(c_member(X5),hAPP(hAPP(c_List_Onth(X5),X239),X50)),hAPP(c_List_Oset(X5),X239))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__mem) ).

fof(fact_n__less__n__mult__m,axiom,
    ! [X72,X57] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X57))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X72))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X57),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X57),X72))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__less__n__mult__m) ).

fof(fact_n__less__m__mult__n,axiom,
    ! [X72,X57] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X57))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X72))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X57),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X72),X57))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__less__m__mult__n) ).

fof(fact_card_Oeq__fold__g,axiom,
    ! [X21,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
     => hAPP(c_Finite__Set_Ocard(X5),X21) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,X5,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,X5),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X21) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card_Oeq__fold__g) ).

fof(fact_divide__diff__eq__iff,axiom,
    ! [X65,X66,X94,X58] :
      ( class_Fields_Ofield(X58)
     => ( X94 != c_Groups_Ozero__class_Ozero(X58)
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X58),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X66),X94)),X65) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X58),X66),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X94),X65))),X94) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__diff__eq__iff) ).

fof(fact_divide__add__eq__iff,axiom,
    ! [X65,X66,X94,X58] :
      ( class_Fields_Ofield(X58)
     => ( X94 != c_Groups_Ozero__class_Ozero(X58)
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X66),X94)),X65) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X66),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X94),X65))),X94) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__add__eq__iff) ).

fof(fact_add__frac__num,axiom,
    ! [X94,X66,X65,X58] :
      ( class_Fields_Ofield__inverse__zero(X58)
     => ( X65 != c_Groups_Ozero__class_Ozero(X58)
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X66),X65)),X94) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X66),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X94),X65))),X65) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__frac__num) ).

fof(fact_in__set__conv__nth,axiom,
    ! [X239,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X239)))
    <=> ? [X146] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X146),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239)))
          & hAPP(hAPP(c_List_Onth(X5),X239),X146) = X25 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__set__conv__nth) ).

fof(fact_mult__le__mono,axiom,
    ! [X99,X96,X97,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X98),X97))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X96),X99))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X98),X96)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X97),X99))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__mono) ).

fof(fact_add__le__mono,axiom,
    ! [X99,X96,X97,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X98),X97))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X96),X99))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),X96)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X97),X99))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__mono) ).

fof(fact_zadd__zless__mono,axiom,
    ! [X94,X135,X128,X139] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X139),X128))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X135),X94))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X139),X135)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X128),X94))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__zless__mono) ).

fof(fact_diff__less__mono,axiom,
    ! [X56,X90,X62] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X62),X90))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X56),X62))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X62),X56)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X90),X56))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__less__mono) ).

fof(fact_diff__less__mono2,axiom,
    ! [X99,X57,X72] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X72),X57))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X72),X99))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X99),X57)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X99),X72))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__less__mono2) ).

fof(fact_add__less__mono,axiom,
    ! [X99,X96,X97,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),X97))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X96),X99))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),X96)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X97),X99))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__mono) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
    ! [X129,X130,X131,X132,X58] :
      ( class_Rings_Ocomm__semiring__1(X58)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X132),X131)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X130),X129)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X130),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X132),X131)),X129)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).

fof(fact_atMost__subset__iff,axiom,
    ! [X33,X25,X5] :
      ( class_Orderings_Oorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X5),X25)),hAPP(c_SetInterval_Oord__class_OatMost(X5),X33)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X25),X33)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atMost__subset__iff) ).

fof(fact_lessThan__subset__iff,axiom,
    ! [X33,X25,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X5),X25)),hAPP(c_SetInterval_Oord__class_OlessThan(X5),X33)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X25),X33)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lessThan__subset__iff) ).

fof(fact_atLeast__subset__iff,axiom,
    ! [X33,X25,X5] :
      ( class_Orderings_Oorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X5),X25)),hAPP(c_SetInterval_Oord__class_OatLeast(X5),X33)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X33),X25)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeast__subset__iff) ).

fof(fact_greaterThan__subset__iff,axiom,
    ! [X33,X25,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X5),X25)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X5),X33)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X33),X25)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThan__subset__iff) ).

fof(fact_lessThan__strict__subset__iff,axiom,
    ! [X50,X95,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X5),X95)),hAPP(c_SetInterval_Oord__class_OlessThan(X5),X50)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X95),X50)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lessThan__strict__subset__iff) ).

fof(fact_divide__nonpos__pos,axiom,
    ! [X65,X66,X58] :
      ( class_Fields_Olinordered__field(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X66),c_Groups_Ozero__class_Ozero(X58)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),X65))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X66),X65)),c_Groups_Ozero__class_Ozero(X58))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__nonpos__pos) ).

fof(fact_divide__nonneg__neg,axiom,
    ! [X65,X66,X58] :
      ( class_Fields_Olinordered__field(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),X66))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X65),c_Groups_Ozero__class_Ozero(X58)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X66),X65)),c_Groups_Ozero__class_Ozero(X58))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__nonneg__neg) ).

fof(fact_split__mult__neg__le,axiom,
    ! [X90,X62,X58] :
      ( class_Rings_Oordered__cancel__semiring(X58)
     => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),X62))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X90),c_Groups_Ozero__class_Ozero(X58))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X62),c_Groups_Ozero__class_Ozero(X58)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),X90)) ) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X90)),c_Groups_Ozero__class_Ozero(X58))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__mult__neg__le) ).

fof(fact_mult__nonpos__nonneg,axiom,
    ! [X90,X62,X58] :
      ( class_Rings_Oordered__cancel__semiring(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X62),c_Groups_Ozero__class_Ozero(X58)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),X90))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X90)),c_Groups_Ozero__class_Ozero(X58))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__nonpos__nonneg) ).

fof(fact_mult__nonneg__nonpos,axiom,
    ! [X90,X62,X58] :
      ( class_Rings_Oordered__cancel__semiring(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),X62))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X90),c_Groups_Ozero__class_Ozero(X58)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X90)),c_Groups_Ozero__class_Ozero(X58))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__nonneg__nonpos) ).

fof(fact_mult__nonneg__nonpos2,axiom,
    ! [X90,X62,X58] :
      ( class_Rings_Oordered__cancel__semiring(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),X62))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X90),c_Groups_Ozero__class_Ozero(X58)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X90),X62)),c_Groups_Ozero__class_Ozero(X58))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__nonneg__nonpos2) ).

fof(fact_divide__neg__pos,axiom,
    ! [X65,X66,X58] :
      ( class_Fields_Olinordered__field(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X66),c_Groups_Ozero__class_Ozero(X58)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),X65))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X66),X65)),c_Groups_Ozero__class_Ozero(X58))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__neg__pos) ).

fof(fact_divide__pos__neg,axiom,
    ! [X65,X66,X58] :
      ( class_Fields_Olinordered__field(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),X66))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X65),c_Groups_Ozero__class_Ozero(X58)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X66),X65)),c_Groups_Ozero__class_Ozero(X58))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__pos__neg) ).

fof(fact_mult__neg__pos,axiom,
    ! [X90,X62,X58] :
      ( class_Rings_Olinordered__semiring__strict(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X62),c_Groups_Ozero__class_Ozero(X58)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),X90))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X90)),c_Groups_Ozero__class_Ozero(X58))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__neg__pos) ).

fof(fact_mult__pos__neg,axiom,
    ! [X90,X62,X58] :
      ( class_Rings_Olinordered__semiring__strict(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),X62))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X90),c_Groups_Ozero__class_Ozero(X58)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X90)),c_Groups_Ozero__class_Ozero(X58))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__pos__neg) ).

fof(fact_mult__pos__neg2,axiom,
    ! [X90,X62,X58] :
      ( class_Rings_Olinordered__semiring__strict(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),X62))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X90),c_Groups_Ozero__class_Ozero(X58)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X90),X62)),c_Groups_Ozero__class_Ozero(X58))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__pos__neg2) ).

fof(fact_set__subset__Cons,axiom,
    ! [X25,X239,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),X239)),hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__subset__Cons) ).

fof(fact_transpose__map__map,axiom,
    ! [X239,X2,X20,X5] : c_List_Otranspose(X5,hAPP(hAPP(c_List_Omap(tc_List_Olist(X20),tc_List_Olist(X5)),hAPP(c_List_Omap(X20,X5),X2)),X239)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(X20),tc_List_Olist(X5)),hAPP(c_List_Omap(X20,X5),X2)),c_List_Otranspose(X20,X239)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose__map__map) ).

fof(fact_le__sup__iff,axiom,
    ! [X120,X33,X25,X5] :
      ( class_Lattices_Osemilattice__sup(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X25),X33)),X120))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X25),X120))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X33),X120)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__sup__iff) ).

fof(fact_min__max_Ole__sup__iff,axiom,
    ! [X120,X33,X25,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X25),X33)),X120))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X25),X120))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X33),X120)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ole__sup__iff) ).

fof(fact_max__less__iff__conj,axiom,
    ! [X120,X33,X25,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X25),X33)),X120))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X25),X120))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X33),X120)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__less__iff__conj) ).

fof(fact_nth__eq__iff__index__eq,axiom,
    ! [X157,X82,X239,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),X239))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X82),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X157),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239)))
         => ( hAPP(hAPP(c_List_Onth(X5),X239),X82) = hAPP(hAPP(c_List_Onth(X5),X239),X157)
          <=> X82 = X157 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__eq__iff__index__eq) ).

fof(fact_distinct__conv__nth,axiom,
    ! [X239,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),X239))
    <=> ! [X146] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X146),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239)))
         => ! [X101] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X101),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239)))
             => ( X146 != X101
               => hAPP(hAPP(c_List_Onth(X5),X239),X146) != hAPP(hAPP(c_List_Onth(X5),X239),X101) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__conv__nth) ).

fof(fact_distinct__map,axiom,
    ! [X239,X2,X20,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),hAPP(hAPP(c_List_Omap(X20,X5),X2),X239)))
    <=> ( hBOOL(hAPP(c_List_Odistinct(X20),X239))
        & c_Fun_Oinj__on(X20,X5,X2,hAPP(c_List_Oset(X20),X239)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__map) ).

fof(fact_min__max_OInf__le__Sup,axiom,
    ! [X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X21)),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X21))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__le__Sup) ).

fof(fact_inj__on__diff,axiom,
    ! [X113,X21,X2,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,X2,X21)
     => c_Fun_Oinj__on(X5,X20,X2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),X113)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__diff) ).

fof(fact_lazy__sequence_Osize_I2_J,axiom,
    ! [X307,X6,X80,X5] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X5,X80),c_Lazy__Sequence_Olazy__sequence_OInsert(X5,X6,X307)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X80,X6)),hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X5,X80),X307))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lazy__sequence_Osize_I2_J) ).

fof(fact_fun__left__comm__idem_Ofold__insert__idem2,axiom,
    ! [X25,X120,X21,X2,X20,X5] :
      ( c_Finite__Set_Ofun__left__comm__idem(X5,X20,X2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => hAPP(hAPP(c_Finite__Set_Ofold(X5,X20,X2),X120),hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X20,X2),hAPP(hAPP(X2,X25),X120)),X21) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__idem_Ofold__insert__idem2) ).

fof(fact_insert__Diff,axiom,
    ! [X21,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),X21))
     => hAPP(hAPP(c_Set_Oinsert(X5),X6),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))) = X21 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__Diff) ).

fof(fact_finite__Plus__UNIV__iff,axiom,
    ! [X20,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X5,X20)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X5,X20),tc_HOL_Obool))))
    <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(X20),c_Orderings_Otop__class_Otop(tc_fun(X20,tc_HOL_Obool)))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Plus__UNIV__iff) ).

fof(fact_finite__Prod__UNIV,axiom,
    ! [X20,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X20),c_Orderings_Otop__class_Otop(tc_fun(X20,tc_HOL_Obool))))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X5,X20)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X5,X20),tc_HOL_Obool)))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Prod__UNIV) ).

fof(fact_setsum__head__Suc,axiom,
    ! [X2,X50,X95,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X50))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X95,X50)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(X2,X95)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X95),X50))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__head__Suc) ).

fof(fact_vimageI2,axiom,
    ! [X20,X21,X6,X2,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),hAPP(X2,X6)),X21))
     => hBOOL(hAPP(hAPP(c_member(X20),X6),hAPP(c_Set_Ovimage(X20,X5,X2),X21))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimageI2) ).

fof(fact_sorted__insort,axiom,
    ! [X239,X25,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X5,c_COMBI(X5)),X25),X239))
      <=> c_List_Olinorder__class_Osorted(X5,X239) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__insort) ).

fof(fact_setsum__head__upt__Suc,axiom,
    ! [X2,X50,X95,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),X50))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X95),X50)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(X2,X95)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X95)),X50))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__head__upt__Suc) ).

fof(fact_set__eq__subset,axiom,
    ! [X5,X113,X21] :
      ( X21 = X113
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),X113))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X113),X21)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__eq__subset) ).

fof(fact_equalityI,axiom,
    ! [X113,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),X113))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X113),X21))
       => X21 = X113 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityI) ).

fof(fact_rev__nth,axiom,
    ! [X242,X58,X57] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X57),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242)))
     => hAPP(hAPP(c_List_Onth(X58),hAPP(c_List_Orev(X58),X242)),X57) = hAPP(hAPP(c_List_Onth(X58),X242),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242)),hAPP(c_Nat_OSuc,X57))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__nth) ).

fof(fact_INT__absorb,axiom,
    ! [X21,X20,X221,X87,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X87),X221))
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20,tc_HOL_Obool)),hAPP(X21,X87)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X20,tc_HOL_Obool)),X221),X21)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X20,tc_HOL_Obool)),X221),X21) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__absorb) ).

fof(fact_UN__absorb,axiom,
    ! [X21,X20,X221,X87,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X87),X221))
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20,tc_HOL_Obool)),hAPP(X21,X87)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X20,tc_HOL_Obool)),X221),X21)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X20,tc_HOL_Obool)),X221),X21) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__absorb) ).

fof(fact_list__update__overwrite,axiom,
    ! [X65,X66,X98,X242,X58] : hAPP(hAPP(c_List_Olist__update(X58,hAPP(hAPP(c_List_Olist__update(X58,X242),X98),X66)),X98),X65) = hAPP(hAPP(c_List_Olist__update(X58,X242),X98),X65),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update__overwrite) ).

fof(fact_negative__zless,axiom,
    ! [X72,X57] : 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,X57)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X72))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negative__zless) ).

fof(fact_Ints__diff,axiom,
    ! [X24,X6,X5] :
      ( class_Rings_Oring__1(X5)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X6),c_Int_Oring__1__class_OInts(X5)))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X24),c_Int_Oring__1__class_OInts(X5)))
         => hBOOL(hAPP(hAPP(c_member(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X6),X24)),c_Int_Oring__1__class_OInts(X5))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__diff) ).

fof(fact_Nats__mult,axiom,
    ! [X24,X6,X5] :
      ( class_Rings_Osemiring__1(X5)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X6),c_Nat_Osemiring__1__class_ONats(X5)))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X24),c_Nat_Osemiring__1__class_ONats(X5)))
         => hBOOL(hAPP(hAPP(c_member(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X24)),c_Nat_Osemiring__1__class_ONats(X5))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nats__mult) ).

fof(fact_Ints__mult,axiom,
    ! [X24,X6,X5] :
      ( class_Rings_Oring__1(X5)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X6),c_Int_Oring__1__class_OInts(X5)))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X24),c_Int_Oring__1__class_OInts(X5)))
         => hBOOL(hAPP(hAPP(c_member(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X24)),c_Int_Oring__1__class_OInts(X5))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__mult) ).

fof(fact_Nats__add,axiom,
    ! [X24,X6,X5] :
      ( class_Rings_Osemiring__1(X5)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X6),c_Nat_Osemiring__1__class_ONats(X5)))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X24),c_Nat_Osemiring__1__class_ONats(X5)))
         => hBOOL(hAPP(hAPP(c_member(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),X24)),c_Nat_Osemiring__1__class_ONats(X5))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nats__add) ).

fof(fact_Ints__add,axiom,
    ! [X24,X6,X5] :
      ( class_Rings_Oring__1(X5)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X6),c_Int_Oring__1__class_OInts(X5)))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X24),c_Int_Oring__1__class_OInts(X5)))
         => hBOOL(hAPP(hAPP(c_member(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),X24)),c_Int_Oring__1__class_OInts(X5))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__add) ).

fof(fact_add__nonpos__nonpos,axiom,
    ! [X90,X62,X58] :
      ( class_Groups_Oordered__comm__monoid__add(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X62),c_Groups_Ozero__class_Ozero(X58)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X90),c_Groups_Ozero__class_Ozero(X58)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),X90)),c_Groups_Ozero__class_Ozero(X58))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonpos__nonpos) ).

fof(fact_add__neg__nonpos,axiom,
    ! [X90,X62,X58] :
      ( class_Groups_Oordered__comm__monoid__add(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X62),c_Groups_Ozero__class_Ozero(X58)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X90),c_Groups_Ozero__class_Ozero(X58)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),X90)),c_Groups_Ozero__class_Ozero(X58))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__neg__nonpos) ).

fof(fact_add__nonpos__neg,axiom,
    ! [X90,X62,X58] :
      ( class_Groups_Oordered__comm__monoid__add(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X62),c_Groups_Ozero__class_Ozero(X58)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X90),c_Groups_Ozero__class_Ozero(X58)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),X90)),c_Groups_Ozero__class_Ozero(X58))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonpos__neg) ).

fof(fact_add__neg__neg,axiom,
    ! [X90,X62,X58] :
      ( class_Groups_Oordered__comm__monoid__add(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X62),c_Groups_Ozero__class_Ozero(X58)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X90),c_Groups_Ozero__class_Ozero(X58)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),X90)),c_Groups_Ozero__class_Ozero(X58))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__neg__neg) ).

fof(fact_list__size__conv__listsum,axiom,
    ! [X239,X2,X5] : c_List_Olist_Olist__size(X5,X2,X239) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(X5,tc_Nat_Onat),X2),X239))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__size__conv__listsum) ).

fof(fact_finite__UNIV__inj__surj,axiom,
    ! [X2,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))))
     => ( c_Fun_Oinj__on(X5,X5,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
       => hAPP(c_Set_Oimage(X5,X5,X2),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UNIV__inj__surj) ).

fof(fact_listsum__triv,axiom,
    ! [X239,X171,X20,X5] :
      ( class_Rings_Osemiring__1(X5)
     => hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X20,X5),hAPP(c_COMBK(X5,X20),X171)),X239)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X20)),X239))),X171) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__triv) ).

fof(fact_power__minus,axiom,
    ! [X57,X62,X58] :
      ( class_Rings_Oring__1(X58)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X58),hAPP(c_Groups_Ouminus__class_Ouminus(X58),X62)),X57) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),hAPP(hAPP(c_Power_Opower__class_Opower(X58),hAPP(c_Groups_Ouminus__class_Ouminus(X58),c_Groups_Oone__class_Oone(X58))),X57)),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),X57)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__minus) ).

fof(fact_rangeI,axiom,
    ! [X20,X25,X2,X5] : hBOOL(hAPP(hAPP(c_member(X5),hAPP(X2,X25)),hAPP(c_Set_Oimage(X20,X5,X2),c_Orderings_Otop__class_Otop(tc_fun(X20,tc_HOL_Obool))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rangeI) ).

fof(fact_left__diff__distrib__number__of,axiom,
    ! [X136,X90,X62,X5] :
      ( ( class_Int_Onumber(X5)
        & class_Rings_Oring(X5) )
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X62),X90)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X136)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X62),hAPP(c_Int_Onumber__class_Onumber__of(X5),X136))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X90),hAPP(c_Int_Onumber__class_Onumber__of(X5),X136))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_left__diff__distrib__number__of) ).

fof(fact_left__distrib__number__of,axiom,
    ! [X136,X90,X62,X5] :
      ( ( class_Int_Onumber(X5)
        & class_Rings_Osemiring(X5) )
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X62),X90)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X136)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X62),hAPP(c_Int_Onumber__class_Onumber__of(X5),X136))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X90),hAPP(c_Int_Onumber__class_Onumber__of(X5),X136))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_left__distrib__number__of) ).

fof(fact_Min_Ounion__disjoint,axiom,
    ! [X113,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X113))
           => ( X113 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
               => c_Big__Operators_Olinorder__class_OMin(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),c_Big__Operators_Olinorder__class_OMin(X5,X21)),c_Big__Operators_Olinorder__class_OMin(X5,X113)) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min_Ounion__disjoint) ).

fof(fact_Max_Ounion__disjoint,axiom,
    ! [X113,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X113))
           => ( X113 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
               => c_Big__Operators_Olinorder__class_OMax(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),c_Big__Operators_Olinorder__class_OMax(X5,X21)),c_Big__Operators_Olinorder__class_OMax(X5,X113)) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max_Ounion__disjoint) ).

fof(fact_Sup__fin_Ounion__disjoint,axiom,
    ! [X113,X21,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X113))
           => ( X113 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
               => c_Big__Operators_Olattice__class_OSup__fin(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),c_Big__Operators_Olattice__class_OSup__fin(X5,X21)),c_Big__Operators_Olattice__class_OSup__fin(X5,X113)) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_Ounion__disjoint) ).

fof(fact_Inf__fin_Ounion__disjoint,axiom,
    ! [X113,X21,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X113))
           => ( X113 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
               => c_Big__Operators_Olattice__class_OInf__fin(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),c_Big__Operators_Olattice__class_OInf__fin(X5,X21)),c_Big__Operators_Olattice__class_OInf__fin(X5,X113)) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_Ounion__disjoint) ).

fof(fact_add__right__mono,axiom,
    ! [X56,X90,X62,X58] :
      ( class_Groups_Oordered__ab__semigroup__add(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X62),X90))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),X56)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X90),X56))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__right__mono) ).

fof(fact_add__left__mono,axiom,
    ! [X56,X90,X62,X58] :
      ( class_Groups_Oordered__ab__semigroup__add(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X62),X90))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X56),X62)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X56),X90))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__mono) ).

fof(fact_add__strict__right__mono,axiom,
    ! [X56,X90,X62,X58] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X62),X90))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),X56)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X90),X56))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__right__mono) ).

fof(fact_add__strict__left__mono,axiom,
    ! [X56,X90,X62,X58] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X62),X90))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X56),X62)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X56),X90))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__left__mono) ).

fof(fact_fold1__Un2,axiom,
    ! [X113,X21,X5] :
      ( class_Lattices_Oab__semigroup__idem__mult(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X113))
           => ( X113 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),X21)),hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),X113)) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__Un2) ).

fof(fact_rev__drop,axiom,
    ! [X242,X98,X58] : hAPP(c_List_Orev(X58),hAPP(hAPP(c_List_Odrop(X58),X98),X242)) = hAPP(hAPP(c_List_Otake(X58),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242)),X98)),hAPP(c_List_Orev(X58),X242)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__drop) ).

fof(fact_rev__take,axiom,
    ! [X242,X98,X58] : hAPP(c_List_Orev(X58),hAPP(hAPP(c_List_Otake(X58),X98),X242)) = hAPP(hAPP(c_List_Odrop(X58),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242)),X98)),hAPP(c_List_Orev(X58),X242)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__take) ).

fof(fact_ivl__disj__un_I5_J,axiom,
    ! [X159,X156,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X156),X159))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X156),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X156,X159)) = c_SetInterval_Oord__class_OatLeastAtMost(X5,X156,X159) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I5_J) ).

fof(fact_subset__Compl__self__eq,axiom,
    ! [X21,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X21)))
    <=> X21 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__Compl__self__eq) ).

fof(fact_pdivmod__def,axiom,
    ! [X99,X96] : c_Divides_Opdivmod(X96,X99) = 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),X96)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X99))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X96),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X99))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pdivmod__def) ).

fof(fact_Union__upper,axiom,
    ! [X21,X113,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X113),X21))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X113),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X21))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__upper) ).

fof(fact_fold__image__def,axiom,
    ! [X1,X2,X20,X5] : hAPP(c_Finite__Set_Ofold__image(X5,X20,X2),X1) = c_Finite__Set_Ofold(X20,X5,hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X20),X2),X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__image__def) ).

fof(fact_max__Suc1,axiom,
    ! [X95,X50] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X50)),X95) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,X50),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),X50)),X95),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__Suc1) ).

fof(fact_Field__Union,axiom,
    ! [X32,X5] : hAPP(c_Relation_OField(X5),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),X32)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),c_Relation_OField(X5)),X32)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Field__Union) ).

fof(fact_Diff__partition,axiom,
    ! [X113,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),X113))
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X113),X21)) = X113 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__partition) ).

fof(fact_inj__mapI,axiom,
    ! [X2,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => c_Fun_Oinj__on(tc_List_Olist(X5),tc_List_Olist(X20),hAPP(c_List_Omap(X5,X20),X2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X5),tc_HOL_Obool))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__mapI) ).

fof(fact_Compl__Int,axiom,
    ! [X113,X21,X5] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X21)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X113)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__Int) ).

fof(fact_Compl__Un,axiom,
    ! [X113,X21,X5] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X21)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X113)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__Un) ).

fof(fact_peek__and__def,axiom,
    ! [X76,X165,X160,X18,X5] :
      ( hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(X5,X18,X160),X165),X76))
    <=> ( hBOOL(hAPP(hAPP(X18,X165),X76))
        & hBOOL(hAPP(X160,X76)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_peek__and__def) ).

fof(fact_conversepD,axiom,
    ! [X24,X6,X171,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X5,X20,X171),X6),X24))
     => hBOOL(hAPP(hAPP(X171,X24),X6)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_conversepD) ).

fof(fact_conversep_Oequations,axiom,
    ! [X27,X26,X171,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X5,X20,X171),X26),X27))
    <=> hBOOL(hAPP(hAPP(X171,X27),X26)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_conversep_Oequations) ).

fof(fact_conversep__iff,axiom,
    ! [X24,X6,X171,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X5,X20,X171),X6),X24))
    <=> hBOOL(hAPP(hAPP(X171,X24),X6)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_conversep__iff) ).

fof(fact_vimage__code,axiom,
    ! [X25,X21,X2,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_Set_Ovimage(X5,X20,X2),X21),X25))
    <=> hBOOL(hAPP(X21,hAPP(X2,X25))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__code) ).

fof(fact_triples__valid__Suc,axiom,
    ! [X50,X13,X5] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X5)),X3),X13))
         => c_Hoare__Mirabelle_Otriple__valid(X5,hAPP(c_Nat_OSuc,X50),X3) )
     => ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X5)),X3),X13))
         => c_Hoare__Mirabelle_Otriple__valid(X5,X50,X3) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_triples__valid__Suc) ).

fof(fact_Inf__less__iff,axiom,
    ! [X6,X192,X5] :
      ( ( class_Complete__Lattice_Ocomplete__lattice(X5)
        & class_Orderings_Olinorder(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Complete__Lattice_OInf__class_OInf(X5,X192)),X6))
      <=> ? [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X192))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X3),X6)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__less__iff) ).

fof(fact_mult__number__of__left,axiom,
    ! [X94,X128,X136,X58] :
      ( class_Int_Onumber__ring(X58)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),hAPP(c_Int_Onumber__class_Onumber__of(X58),X136)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),hAPP(c_Int_Onumber__class_Onumber__of(X58),X128)),X94)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),hAPP(c_Int_Onumber__class_Onumber__of(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X136),X128))),X94) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__number__of__left) ).

fof(fact_add__number__of__diff1,axiom,
    ! [X56,X128,X136,X58] :
      ( class_Int_Onumber__ring(X58)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(c_Int_Onumber__class_Onumber__of(X58),X136)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X58),hAPP(c_Int_Onumber__class_Onumber__of(X58),X128)),X56)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X58),hAPP(c_Int_Onumber__class_Onumber__of(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X136),X128))),X56) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__number__of__diff1) ).

fof(fact_add__number__of__left,axiom,
    ! [X94,X128,X136,X58] :
      ( class_Int_Onumber__ring(X58)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(c_Int_Onumber__class_Onumber__of(X58),X136)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(c_Int_Onumber__class_Onumber__of(X58),X128)),X94)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(c_Int_Onumber__class_Onumber__of(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X136),X128))),X94) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__number__of__left) ).

fof(fact_ivl__disj__un_I3_J,axiom,
    ! [X159,X156,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X156),X159))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X156),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X156,X159)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X156),X159) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I3_J) ).

fof(fact_nth__map,axiom,
    ! [X2,X20,X239,X5,X50] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X50),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239)))
     => hAPP(hAPP(c_List_Onth(X20),hAPP(hAPP(c_List_Omap(X5,X20),X2),X239)),X50) = hAPP(X2,hAPP(hAPP(c_List_Onth(X5),X239),X50)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__map) ).

fof(fact_nat__gcd_Opsimps,axiom,
    ! [X33,X25] :
      ( 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),X25),X33)))
     => ( ( X33 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => c_Nitpick_Onat__gcd(X25,X33) = X25 )
        & ( X33 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => c_Nitpick_Onat__gcd(X25,X33) = c_Nitpick_Onat__gcd(X33,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X25,X33)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__gcd_Opsimps) ).

fof(fact_UnionI,axiom,
    ! [X21,X112,X194,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X194),X112))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X21),X194))
       => hBOOL(hAPP(hAPP(c_member(X5),X21),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X112))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UnionI) ).

fof(fact_zero__less__mult__pos2,axiom,
    ! [X62,X90,X58] :
      ( class_Rings_Olinordered__semiring__strict(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X90),X62)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),X62))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),X90)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__mult__pos2) ).

fof(fact_zero__less__mult__pos,axiom,
    ! [X90,X62,X58] :
      ( class_Rings_Olinordered__semiring__strict(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X90)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),X62))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),X90)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__mult__pos) ).

fof(fact_in__set__conv__decomp,axiom,
    ! [X239,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X239)))
    <=> ? [X262,X289] : X239 = hAPP(hAPP(c_List_Oappend(X5),X262),hAPP(hAPP(c_List_Olist_OCons(X5),X25),X289)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__set__conv__decomp) ).

fof(fact_sym__Int__converse,axiom,
    ! [X171,X5] : c_Relation_Osym(X5,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X171),hAPP(c_Relation_Oconverse(X5,X5),X171))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sym__Int__converse) ).

fof(fact_sym__Un__converse,axiom,
    ! [X171,X5] : c_Relation_Osym(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X171),hAPP(c_Relation_Oconverse(X5,X5),X171))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sym__Un__converse) ).

fof(fact_card__Un__disjoint,axiom,
    ! [X113,X21,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X113))
       => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X21)),hAPP(c_Finite__Set_Ocard(X5),X113)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Un__disjoint) ).

fof(fact_min__Suc1,axiom,
    ! [X95,X50] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X50)),X95) = 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),X50)),X95),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__Suc1) ).

fof(fact_sorted__list__of__set__remove,axiom,
    ! [X25,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => c_List_Olinorder__class_Osorted__list__of__set(X5,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))) = c_List_Oremove1(X5,X25,c_List_Olinorder__class_Osorted__list__of__set(X5,X21)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__list__of__set__remove) ).

fof(fact_finite__fun__UNIVD2,axiom,
    ! [X20,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X5,X20)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X5,X20),tc_HOL_Obool))))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X20),c_Orderings_Otop__class_Otop(tc_fun(X20,tc_HOL_Obool)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__fun__UNIVD2) ).

fof(fact_filter__sort,axiom,
    ! [X239,X2,X18,X5,X20] :
      ( class_Orderings_Olinorder(X20)
     => hAPP(c_List_Ofilter(X5,X18),c_List_Olinorder__class_Osort__key(X5,X20,X2,X239)) = c_List_Olinorder__class_Osort__key(X5,X20,X2,hAPP(c_List_Ofilter(X5,X18),X239)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter__sort) ).

fof(fact_PowD,axiom,
    ! [X113,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(c_Set_OPow(X5),X113)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),X113)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_PowD) ).

fof(fact_Pow__iff,axiom,
    ! [X113,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(c_Set_OPow(X5),X113)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),X113)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__iff) ).

fof(fact_zero__less__zpower__abs__iff,axiom,
    ! [X50,X25] :
      ( 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),X25)),X50)))
    <=> ( X25 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | X50 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__zpower__abs__iff) ).

fof(fact_ivl__disj__un_I22_J,axiom,
    ! [X159,X95,X156,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X156),X95))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X95),X159))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X156,X95)),c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X95,X159)) = c_SetInterval_Oord__class_OatLeastAtMost(X5,X156,X159) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I22_J) ).

fof(fact_ivl__disj__un_I20_J,axiom,
    ! [X159,X95,X156,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X156),X95))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X95),X159))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X156,X95)),c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X95,X159)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X156,X159) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I20_J) ).

fof(fact_ivl__disj__un_I16_J,axiom,
    ! [X159,X95,X156,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X156),X95))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X95),X159))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X156,X95)),c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X95,X159)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X156,X159) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I16_J) ).

fof(fact_ivl__disj__un_I19_J,axiom,
    ! [X159,X95,X156,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X156),X95))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X95),X159))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X156,X95)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X95,X159)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X156,X159) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I19_J) ).

fof(fact_Un__upper1,axiom,
    ! [X113,X21,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__upper1) ).

fof(fact_Un__upper2,axiom,
    ! [X21,X113,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X113),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__upper2) ).

fof(fact_r__into__rtrancl,axiom,
    ! [X171,X160,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X160),X171))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),X160),c_Transitive__Closure_Ortrancl(X5,X171))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_r__into__rtrancl) ).

fof(fact_card__Plus,axiom,
    ! [X113,X20,X21,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X20),X113))
       => hAPP(c_Finite__Set_Ocard(tc_sum(X5,X20)),c_Sum__Type_OPlus(X5,X20,X21,X113)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X21)),hAPP(c_Finite__Set_Ocard(X20),X113)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Plus) ).

fof(fact_card__Plus__conv__if,axiom,
    ! [X113,X20,X21,X5] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(X20),X113)) )
       => hAPP(c_Finite__Set_Ocard(tc_sum(X5,X20)),c_Sum__Type_OPlus(X5,X20,X21,X113)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X21)),hAPP(c_Finite__Set_Ocard(X20),X113)) )
      & ( ~ ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
            & hBOOL(hAPP(c_Finite__Set_Ofinite(X20),X113)) )
       => hAPP(c_Finite__Set_Ocard(tc_sum(X5,X20)),c_Sum__Type_OPlus(X5,X20,X21,X113)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Plus__conv__if) ).

fof(fact_sup__least,axiom,
    ! [X94,X66,X65,X58] :
      ( class_Lattices_Osemilattice__sup(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X65),X66))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X94),X66))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X65),X94)),X66)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__least) ).

fof(fact_le__supI,axiom,
    ! [X90,X66,X62,X58] :
      ( class_Lattices_Osemilattice__sup(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X62),X66))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X90),X66))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X62),X90)),X66)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__supI) ).

fof(fact_min__max_Osup__least,axiom,
    ! [X94,X66,X65,X58] :
      ( class_Orderings_Olinorder(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X65),X66))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X94),X66))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Orderings_Oord__class_Omax(X58),X65),X94)),X66)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup__least) ).

fof(fact_min__max_Ole__supI,axiom,
    ! [X90,X66,X62,X58] :
      ( class_Orderings_Olinorder(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X62),X66))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X90),X66))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Orderings_Oord__class_Omax(X58),X62),X90)),X66)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ole__supI) ).

fof(fact_Int__left__commute,axiom,
    ! [X112,X113,X21,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X113),X112)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X113),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X112)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__left__commute) ).

fof(fact_Un__left__commute,axiom,
    ! [X112,X113,X21,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X113),X112)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X113),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X112)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__left__commute) ).

fof(fact_Un__Diff__cancel2,axiom,
    ! [X21,X113,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X113),X21)),X21) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X113),X21),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Diff__cancel2) ).

fof(fact_Diff__idemp,axiom,
    ! [X113,X21,X5] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),X113)),X113) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),X113),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__idemp) ).

fof(fact_imageI,axiom,
    ! [X2,X20,X21,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
     => hBOOL(hAPP(hAPP(c_member(X20),hAPP(X2,X25)),hAPP(c_Set_Oimage(X5,X20,X2),X21))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_imageI) ).

fof(fact_hoare__derivs_Oinsert,axiom,
    ! [X13,X15,X4,X5] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X5)),X15),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool))))
     => ( c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,X13)
       => c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X5)),X15),X13)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hoare__derivs_Oinsert) ).

fof(fact_fun__left__comm_Ofun__left__comm__apply,axiom,
    ! [X1,X116,X2,X20,X5] :
      ( c_Finite__Set_Ofun__left__comm(X5,X20,X2)
     => c_Finite__Set_Ofun__left__comm(X116,X20,hAPP(hAPP(c_COMBB(X5,tc_fun(X20,X20),X116),X2),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofun__left__comm__apply) ).

fof(fact_fun__left__comm__idem_Ofun__left__comm__idem__apply,axiom,
    ! [X1,X116,X2,X20,X5] :
      ( c_Finite__Set_Ofun__left__comm__idem(X5,X20,X2)
     => c_Finite__Set_Ofun__left__comm__idem(X116,X20,hAPP(hAPP(c_COMBB(X5,tc_fun(X20,X20),X116),X2),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__idem_Ofun__left__comm__idem__apply) ).

fof(fact_Int__insert__left__if1,axiom,
    ! [X113,X112,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),X112))
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X6),X113)),X112) = hAPP(hAPP(c_Set_Oinsert(X5),X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X113),X112)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__insert__left__if1) ).

fof(fact_inj__image__eq__iff,axiom,
    ! [X113,X21,X2,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => ( hAPP(c_Set_Oimage(X5,X20,X2),X21) = hAPP(c_Set_Oimage(X5,X20,X2),X113)
      <=> X21 = X113 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__image__eq__iff) ).

fof(fact_o__eq__dest__lhs,axiom,
    ! [X123,X23,X24,X6,X5,X20,X116] :
      ( hAPP(c_Fun_Ocomp(X116,X20,X5,X6),X24) = X23
     => hAPP(X6,hAPP(X24,X123)) = hAPP(X23,X123) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__eq__dest__lhs) ).

fof(fact_negative__zless__0,axiom,
    ! [X57] : 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,X57)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negative__zless__0) ).

fof(fact_nth__drop_H,axiom,
    ! [X242,X58,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242)))
     => hAPP(hAPP(c_List_Olist_OCons(X58),hAPP(hAPP(c_List_Onth(X58),X242),X98)),hAPP(hAPP(c_List_Odrop(X58),hAPP(c_Nat_OSuc,X98)),X242)) = hAPP(hAPP(c_List_Odrop(X58),X98),X242) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__drop_H) ).

fof(fact_image__vimage__eq,axiom,
    ! [X21,X2,X5,X20] : hAPP(c_Set_Oimage(X20,X5,X2),hAPP(c_Set_Ovimage(X20,X5,X2),X21)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(c_Set_Oimage(X20,X5,X2),c_Orderings_Otop__class_Otop(tc_fun(X20,tc_HOL_Obool)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__vimage__eq) ).

fof(fact_add1__zle__eq,axiom,
    ! [X120,X121] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X121),c_Groups_Oone__class_Oone(tc_Int_Oint))),X120))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X121),X120)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add1__zle__eq) ).

fof(fact_ivl__disj__un_I18_J,axiom,
    ! [X159,X95,X156,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X156),X95))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X95),X159))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X156,X95)),c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X95,X159)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X156),X159) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I18_J) ).

fof(fact_transfer__nat__int__set__relations_I1_J,axiom,
    ! [X21] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X21))
    <=> 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)),X21))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__set__relations_I1_J) ).

fof(fact_card__mono,axiom,
    ! [X21,X113,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X113))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),X113))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X21)),hAPP(c_Finite__Set_Ocard(X5),X113))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__mono) ).

fof(fact_psubset__card__mono,axiom,
    ! [X21,X113,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X113))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X21),X113))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X21)),hAPP(c_Finite__Set_Ocard(X5),X113))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__card__mono) ).

fof(fact_UnI1,axiom,
    ! [X113,X21,X23,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X23),X21))
     => hBOOL(hAPP(hAPP(c_member(X5),X23),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UnI1) ).

fof(fact_UnI2,axiom,
    ! [X21,X113,X23,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X23),X113))
     => hBOOL(hAPP(hAPP(c_member(X5),X23),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UnI2) ).

fof(fact_finite__UNIV__surj__inj,axiom,
    ! [X2,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))))
     => ( hAPP(c_Set_Oimage(X5,X5,X2),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))
       => c_Fun_Oinj__on(X5,X5,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UNIV__surj__inj) ).

fof(fact_abs__leI,axiom,
    ! [X90,X62,X58] :
      ( class_Groups_Oordered__ab__group__add__abs(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X62),X90))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(c_Groups_Ouminus__class_Ouminus(X58),X62)),X90))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(c_Groups_Oabs__class_Oabs(X58),X62)),X90)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__leI) ).

fof(fact_abs__le__iff,axiom,
    ! [X24,X6,X5] :
      ( class_Groups_Oordered__ab__group__add__abs(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Groups_Oabs__class_Oabs(X5),X6)),X24))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),X24))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X6)),X24)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__le__iff) ).

fof(fact_abs__less__iff,axiom,
    ! [X24,X6,X5] :
      ( class_Rings_Olinordered__idom(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Groups_Oabs__class_Oabs(X5),X6)),X24))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),X24))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X6)),X24)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__less__iff) ).

fof(fact_lists__accI,axiom,
    ! [X171,X239,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X239),c_Wellfounded_Oacc(tc_List_Olist(X5),c_List_Olistrel1(X5,X171))))
     => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X239),c_List_Olists(X5,c_Wellfounded_Oacc(X5,X171)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lists__accI) ).

fof(fact_inj__vimage__image__eq,axiom,
    ! [X21,X2,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => hAPP(c_Set_Ovimage(X5,X20,X2),hAPP(c_Set_Oimage(X5,X20,X2),X21)) = X21 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__vimage__image__eq) ).

fof(fact_ivl__disj__un_I15_J,axiom,
    ! [X159,X95,X156,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X156),X95))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X95),X159))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X156,X95)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X95),X159)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X156,X159) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I15_J) ).

fof(fact_div__mult__self2,axiom,
    ! [X56,X62,X90,X58] :
      ( class_Divides_Osemiring__div(X58)
     => ( X90 != c_Groups_Ozero__class_Ozero(X58)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X90),X56))),X90) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X56),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X58),X62),X90)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__self2) ).

fof(fact_div__mult__self1,axiom,
    ! [X56,X62,X90,X58] :
      ( class_Divides_Osemiring__div(X58)
     => ( X90 != c_Groups_Ozero__class_Ozero(X58)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X56),X90))),X90) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X56),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X58),X62),X90)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__self1) ).

fof(fact_add__num__frac,axiom,
    ! [X66,X94,X65,X58] :
      ( class_Fields_Ofield__inverse__zero(X58)
     => ( X65 != c_Groups_Ozero__class_Ozero(X58)
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X94),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X66),X65)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X66),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X94),X65))),X65) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__num__frac) ).

fof(fact_setsum__reindex__id,axiom,
    ! [X113,X2,X5,X20] :
      ( class_Groups_Ocomm__monoid__add(X20)
     => ( c_Fun_Oinj__on(X5,X20,X2,X113)
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X2),X113) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X20,X20),c_Fun_Oid(X20)),hAPP(c_Set_Oimage(X5,X20,X2),X113)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__reindex__id) ).

fof(fact_setprod__reindex__id,axiom,
    ! [X113,X2,X5,X20] :
      ( class_Groups_Ocomm__monoid__mult(X20)
     => ( c_Fun_Oinj__on(X5,X20,X2,X113)
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X2),X113) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X20,X20),c_Fun_Oid(X20)),hAPP(c_Set_Oimage(X5,X20,X2),X113)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__reindex__id) ).

fof(fact_wf__comp__self,axiom,
    ! [X32,X5] :
      ( c_Wellfounded_Owf(X5,X32)
    <=> c_Wellfounded_Owf(X5,hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),X32),X32)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__comp__self) ).

fof(fact_less__by__empty,axiom,
    ! [X113,X5,X21] :
      ( X21 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X5),tc_HOL_Obool))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X21),X113)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__by__empty) ).

fof(fact_distinct__append,axiom,
    ! [X251,X239,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),hAPP(hAPP(c_List_Oappend(X5),X239),X251)))
    <=> ( hBOOL(hAPP(c_List_Odistinct(X5),X239))
        & hBOOL(hAPP(c_List_Odistinct(X5),X251))
        & hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),X239)),hAPP(c_List_Oset(X5),X251)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__append) ).

fof(fact_min__max_OInf__fin__set__fold,axiom,
    ! [X239,X25,X5] :
      ( class_Orderings_Olinorder(X5)
     => c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239))) = hAPP(c_List_Ofoldl(X5,X5,c_Orderings_Oord__class_Omin(X5),X25),X239) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__fin__set__fold) ).

fof(fact_min__max_OSup__fin__set__fold,axiom,
    ! [X239,X25,X5] :
      ( class_Orderings_Olinorder(X5)
     => c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239))) = hAPP(c_List_Ofoldl(X5,X5,c_Orderings_Oord__class_Omax(X5),X25),X239) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OSup__fin__set__fold) ).

fof(fact_setsum__head,axiom,
    ! [X18,X50,X95,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X50))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X18),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X95,X50)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(X18,X95)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X18),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X95,X50))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__head) ).

fof(fact_funpow_Osimps_I2_J,axiom,
    ! [X2,X50,X5] : hAPP(hAPP(c_Nat_Ocompow(X5,X5),hAPP(c_Nat_OSuc,X50)),X2) = hAPP(c_Fun_Ocomp(X5,X5,X5,X2),hAPP(hAPP(c_Nat_Ocompow(X5,X5),X50),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funpow_Osimps_I2_J) ).

fof(fact_list__size__estimation_H,axiom,
    ! [X2,X33,X239,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X239)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33),hAPP(X2,X25)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33),c_List_Olist_Olist__size(X5,X2,X239))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__size__estimation_H) ).

fof(fact_list__size__estimation,axiom,
    ! [X2,X33,X239,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X239)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33),hAPP(X2,X25)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33),c_List_Olist_Olist__size(X5,X2,X239))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__size__estimation) ).

fof(fact_elem__le__listsum__nat,axiom,
    ! [X275,X96] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X96),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),X275)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),X275),X96)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X275))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_elem__le__listsum__nat) ).

fof(fact_le__div__geq,axiom,
    ! [X72,X57] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X57))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X57),X72))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X72),X57) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X72),X57)),X57)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__div__geq) ).

fof(fact_lists__accD,axiom,
    ! [X171,X239,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X239),c_List_Olists(X5,c_Wellfounded_Oacc(X5,X171))))
     => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X239),c_Wellfounded_Oacc(tc_List_Olist(X5),c_List_Olistrel1(X5,X171)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lists__accD) ).

fof(fact_semiring__1__class_Oof__nat__code,axiom,
    ! [X50,X5] :
      ( class_Rings_Osemiring__1(X5)
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X50) = c_Nat_Osemiring__1__class_Oof__nat__aux(X5,hAPP(hAPP(c_COMBC(X5,X5,X5),c_Groups_Oplus__class_Oplus(X5)),c_Groups_Oone__class_Oone(X5)),X50,c_Groups_Ozero__class_Ozero(X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_semiring__1__class_Oof__nat__code) ).

fof(fact_impossible__Cons,axiom,
    ! [X66,X241,X242,X58] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X241)))
     => X242 != hAPP(hAPP(c_List_Olist_OCons(X58),X66),X241) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_impossible__Cons) ).

fof(fact_PowI,axiom,
    ! [X113,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),X113))
     => hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(c_Set_OPow(X5),X113))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_PowI) ).

fof(fact_power_Opower_Opower__Suc,axiom,
    ! [X50,X6,X166,X167,X5] : hAPP(hAPP(c_Power_Opower_Opower(X5,X167,X166),X6),hAPP(c_Nat_OSuc,X50)) = hAPP(hAPP(X166,X6),hAPP(hAPP(c_Power_Opower_Opower(X5,X167,X166),X6),X50)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power_Opower_Opower__Suc) ).

fof(fact_Min__antimono,axiom,
    ! [X207,X210,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X210),X207))
       => ( X210 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X207))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Big__Operators_Olinorder__class_OMin(X5,X207)),c_Big__Operators_Olinorder__class_OMin(X5,X210))) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min__antimono) ).

fof(fact_Max__mono,axiom,
    ! [X207,X210,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X210),X207))
       => ( X210 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X207))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Big__Operators_Olinorder__class_OMax(X5,X210)),c_Big__Operators_Olinorder__class_OMax(X5,X207))) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max__mono) ).

fof(fact_less__bin__lemma,axiom,
    ! [X156,X87] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X87),X156))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X87),X156)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__bin__lemma) ).

fof(fact_singletonE,axiom,
    ! [X6,X24,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X24),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))
     => X24 = X6 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_singletonE) ).

fof(fact_singleton__iff,axiom,
    ! [X6,X24,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X24),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))
    <=> X24 = X6 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_singleton__iff) ).

fof(fact_range__eqI,axiom,
    ! [X20,X5,X25,X2,X24] :
      ( X24 = hAPP(X2,X25)
     => hBOOL(hAPP(hAPP(c_member(X5),X24),hAPP(c_Set_Oimage(X20,X5,X2),c_Orderings_Otop__class_Otop(tc_fun(X20,tc_HOL_Obool))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_range__eqI) ).

fof(fact_snd__image__times,axiom,
    ! [X113,X20,X5,X21] :
      ( ( X21 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(c_Set_Oimage(tc_prod(X5,X20),X20,c_Product__Type_Osnd(X5,X20)),hAPP(hAPP(c_Product__Type_OSigma(X5,X20),X21),hAPP(c_COMBK(tc_fun(X20,tc_HOL_Obool),X5),X113))) = c_Orderings_Obot__class_Obot(tc_fun(X20,tc_HOL_Obool)) )
      & ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(c_Set_Oimage(tc_prod(X5,X20),X20,c_Product__Type_Osnd(X5,X20)),hAPP(hAPP(c_Product__Type_OSigma(X5,X20),X21),hAPP(c_COMBK(tc_fun(X20,tc_HOL_Obool),X5),X113))) = X113 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_snd__image__times) ).

fof(fact_fst__image__times,axiom,
    ! [X21,X20,X5,X113] :
      ( ( X113 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(c_Set_Oimage(tc_prod(X20,X5),X20,c_Product__Type_Ofst(X20,X5)),hAPP(hAPP(c_Product__Type_OSigma(X20,X5),X21),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X20),X113))) = c_Orderings_Obot__class_Obot(tc_fun(X20,tc_HOL_Obool)) )
      & ( X113 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(c_Set_Oimage(tc_prod(X20,X5),X20,c_Product__Type_Ofst(X20,X5)),hAPP(hAPP(c_Product__Type_OSigma(X20,X5),X21),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X20),X113))) = X21 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fst__image__times) ).

fof(fact_doubleton__eq__iff,axiom,
    ! [X22,X23,X24,X6,X5] :
      ( hAPP(hAPP(c_Set_Oinsert(X5),X6),hAPP(hAPP(c_Set_Oinsert(X5),X24),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(X5),X23),hAPP(hAPP(c_Set_Oinsert(X5),X22),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))
    <=> ( ( X6 = X23
          & X24 = X22 )
        | ( X6 = X22
          & X24 = X23 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_doubleton__eq__iff) ).

fof(fact_nth__list__update,axiom,
    ! [X66,X97,X242,X58,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242)))
     => ( ( X98 = X97
         => hAPP(hAPP(c_List_Onth(X58),hAPP(hAPP(c_List_Olist__update(X58,X242),X98),X66)),X97) = X66 )
        & ( X98 != X97
         => hAPP(hAPP(c_List_Onth(X58),hAPP(hAPP(c_List_Olist__update(X58,X242),X98),X66)),X97) = hAPP(hAPP(c_List_Onth(X58),X242),X97) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__list__update) ).

fof(fact_add__leD1,axiom,
    ! [X57,X96,X72] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X72),X96)),X57))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X72),X57)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leD1) ).

fof(fact_add__leD2,axiom,
    ! [X57,X96,X72] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X72),X96)),X57))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X96),X57)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leD2) ).

fof(fact_add__lessD1,axiom,
    ! [X96,X97,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),X97)),X96))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),X96)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__lessD1) ).

fof(fact_diff__Suc__less,axiom,
    ! [X98,X57] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X57))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X57),hAPP(c_Nat_OSuc,X98))),X57)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__less) ).

fof(fact_evaln_Oequations_I9_J,axiom,
    ! [X60,X63,X26,X27] :
      ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X27),X26,hAPP(c_Nat_OSuc,X63),X60)
    <=> c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X27)),X26,X63,X60) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_Oequations_I9_J) ).

fof(fact_evaln_OBody,axiom,
    ! [X45,X57,X46,X47] :
      ( c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X47)),X46,X57,X45)
     => c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X47),X46,hAPP(c_Nat_OSuc,X57),X45) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_OBody) ).

fof(fact_ivl__disj__un_I21_J,axiom,
    ! [X159,X95,X156,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X156),X95))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X95),X159))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X156),X95)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X95,X159)) = c_SetInterval_Oord__class_OatLeastAtMost(X5,X156,X159) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I21_J) ).

fof(fact_atLeastLessThan__add__Un,axiom,
    ! [X87,X157,X82] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X82),X157))
     => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X82),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X157),X87)) = 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,X82),X157)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X157),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X157),X87))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__add__Un) ).

fof(fact_insert__Diff__single,axiom,
    ! [X21,X6,X5] : hAPP(hAPP(c_Set_Oinsert(X5),X6),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(X5),X6),X21),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__Diff__single) ).

fof(fact_card__insert__le,axiom,
    ! [X25,X21,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X21)),hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__insert__le) ).

fof(fact_zadd__int__left,axiom,
    ! [X94,X57,X72] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X72)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X57)),X94)) = 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),X72),X57))),X94),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__int__left) ).

fof(fact_less__Sup__iff,axiom,
    ! [X192,X6,X5] :
      ( ( class_Complete__Lattice_Ocomplete__lattice(X5)
        & class_Orderings_Olinorder(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),c_Complete__Lattice_OSup__class_OSup(X5,X192)))
      <=> ? [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X192))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),X3)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Sup__iff) ).

fof(fact_transfer__int__nat__set__relations_I1_J,axiom,
    ! [X21] :
      ( c_Nat__Transfer_Onat__set(X21)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),X21))
      <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X21))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__set__relations_I1_J) ).

fof(fact_transfer__nat__int__relations_I3_J,axiom,
    ! [X33,X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X33))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X25)),hAPP(c_Int_Onat,X33)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25),X33)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__relations_I3_J) ).

fof(fact_transfer__nat__int__relations_I2_J,axiom,
    ! [X33,X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X33))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X25)),hAPP(c_Int_Onat,X33)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25),X33)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__relations_I2_J) ).

fof(fact_ivl__disj__un_I4_J,axiom,
    ! [X159,X156,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X156),X159))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X156,X159)),hAPP(hAPP(c_Set_Oinsert(X5),X159),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X156,X159) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I4_J) ).

fof(fact_evaln_OIfTrue,axiom,
    ! [X105,X104,X50,X103,X76,X24] :
      ( hBOOL(hAPP(X24,X76))
     => ( c_Natural_Oevaln(X103,X76,X50,X104)
       => c_Natural_Oevaln(c_Com_Ocom_OCond(X24,X103,X105),X76,X50,X104) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_OIfTrue) ).

fof(fact_Min__eqI,axiom,
    ! [X25,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( ! [X177] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X177),X21))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X25),X177)) )
         => ( hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
           => c_Big__Operators_Olinorder__class_OMin(X5,X21) = X25 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min__eqI) ).

fof(fact_map__append,axiom,
    ! [X251,X239,X2,X5,X20] : hAPP(hAPP(c_List_Omap(X20,X5),X2),hAPP(hAPP(c_List_Oappend(X20),X239),X251)) = hAPP(hAPP(c_List_Oappend(X5),hAPP(hAPP(c_List_Omap(X20,X5),X2),X239)),hAPP(hAPP(c_List_Omap(X20,X5),X2),X251)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__append) ).

fof(fact_finite__Union,axiom,
    ! [X21,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X5,tc_HOL_Obool)),X21))
     => ( ! [X282] :
            ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X282),X21))
           => hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X282)) )
       => hBOOL(hAPP(c_Finite__Set_Ofinite(X5),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X21))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Union) ).

fof(fact_int__div__less__self,axiom,
    ! [X96,X66] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X66))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X96))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X66),X96)),X66)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__div__less__self) ).

fof(fact_diff__less,axiom,
    ! [X72,X57] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X57))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X72))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X72),X57)),X72)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__less) ).

fof(fact_div__less__dividend,axiom,
    ! [X72,X57] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X57))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X72))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X72),X57)),X72)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__less__dividend) ).

fof(fact_insert__inter__insert,axiom,
    ! [X113,X21,X6,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X6),X21)),hAPP(hAPP(c_Set_Oinsert(X5),X6),X113)) = hAPP(hAPP(c_Set_Oinsert(X5),X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__inter__insert) ).

fof(fact_div__nonpos__pos__le0,axiom,
    ! [X90,X62] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X62),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X90))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X62),X90)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__nonpos__pos__le0) ).

fof(fact_div__nonneg__neg__le0,axiom,
    ! [X90,X62] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X62))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X90),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),X62),X90)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__nonneg__neg__le0) ).

fof(fact_div__neg__pos__less0,axiom,
    ! [X90,X62] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X62),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X90))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X62),X90)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__neg__pos__less0) ).

fof(fact_evaln__nonstrict,axiom,
    ! [X72,X54,X57,X48,X56] :
      ( c_Natural_Oevaln(X56,X48,X57,X54)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X57),X72))
       => c_Natural_Oevaln(X56,X48,X72,X54) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln__nonstrict) ).

fof(fact_semiring__div__class_Omod__div__equality_H,axiom,
    ! [X90,X62,X58] :
      ( class_Divides_Osemiring__div(X58)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),c_Divides_Odiv__class_Omod(X58,X62,X90)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X58),X62),X90)),X90)) = X62 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_semiring__div__class_Omod__div__equality_H) ).

fof(fact_zero__le__divide__iff,axiom,
    ! [X24,X6,X5] :
      ( class_Fields_Olinordered__field__inverse__zero(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X6),X24)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),X6))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),X24)) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),c_Groups_Ozero__class_Ozero(X5)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X24),c_Groups_Ozero__class_Ozero(X5))) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__divide__iff) ).

fof(fact_zero__le__mult__iff,axiom,
    ! [X24,X6,X5] :
      ( class_Rings_Olinordered__ring__strict(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X24)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),X6))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),X24)) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),c_Groups_Ozero__class_Ozero(X5)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X24),c_Groups_Ozero__class_Ozero(X5))) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__mult__iff) ).

fof(fact_zero__less__divide__iff,axiom,
    ! [X24,X6,X5] :
      ( class_Fields_Olinordered__field__inverse__zero(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X6),X24)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X6))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X24)) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),c_Groups_Ozero__class_Ozero(X5)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X24),c_Groups_Ozero__class_Ozero(X5))) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__divide__iff) ).

fof(fact_all__interval__int__def,axiom,
    ! [X157,X82,X18] :
      ( c_List_Oall__interval__int(X18,X82,X157)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X3),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X82,X157)))
         => hBOOL(hAPP(X18,X3)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_all__interval__int__def) ).

fof(fact_zadd__left__mono,axiom,
    ! [X96,X97,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X98),X97))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X96),X98)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X96),X97))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__left__mono) ).

fof(fact_diff__le__mono,axiom,
    ! [X99,X57,X72] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X72),X57))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X72),X99)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X57),X99))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__le__mono) ).

fof(fact_diff__le__mono2,axiom,
    ! [X99,X57,X72] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X72),X57))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X99),X57)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X99),X72))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__le__mono2) ).

fof(fact_div__le__mono,axiom,
    ! [X96,X57,X72] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X72),X57))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X72),X96)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X57),X96))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__le__mono) ).

fof(fact_mult__le__mono1,axiom,
    ! [X96,X97,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X98),X97))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X98),X96)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X97),X96))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__mono1) ).

fof(fact_mult__le__mono2,axiom,
    ! [X96,X97,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X98),X97))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X96),X98)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X96),X97))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__mono2) ).

fof(fact_add__le__mono1,axiom,
    ! [X96,X97,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X98),X97))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),X96)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X97),X96))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__mono1) ).

fof(fact_zadd__strict__right__mono,axiom,
    ! [X96,X97,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X98),X97))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X98),X96)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X97),X96))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__strict__right__mono) ).

fof(fact_add__less__mono1,axiom,
    ! [X96,X97,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),X97))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),X96)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X97),X96))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__mono1) ).

fof(fact_Min__fin__set__fold,axiom,
    ! [X239,X25,X5] :
      ( class_Orderings_Olinorder(X5)
     => c_Big__Operators_Olinorder__class_OMin(X5,hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239))) = hAPP(c_List_Ofoldl(X5,X5,c_Orderings_Oord__class_Omin(X5),X25),X239) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min__fin__set__fold) ).

fof(fact_Max__fin__set__fold,axiom,
    ! [X239,X25,X5] :
      ( class_Orderings_Olinorder(X5)
     => c_Big__Operators_Olinorder__class_OMax(X5,hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239))) = hAPP(c_List_Ofoldl(X5,X5,c_Orderings_Oord__class_Omax(X5),X25),X239) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max__fin__set__fold) ).

fof(fact_Sup__fin__set__fold,axiom,
    ! [X239,X25,X5] :
      ( class_Lattices_Olattice(X5)
     => c_Big__Operators_Olattice__class_OSup__fin(X5,hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239))) = hAPP(c_List_Ofoldl(X5,X5,c_Lattices_Osemilattice__sup__class_Osup(X5),X25),X239) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin__set__fold) ).

fof(fact_Inf__fin__set__fold,axiom,
    ! [X239,X25,X5] :
      ( class_Lattices_Olattice(X5)
     => c_Big__Operators_Olattice__class_OInf__fin(X5,hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239))) = hAPP(c_List_Ofoldl(X5,X5,c_Lattices_Osemilattice__inf__class_Oinf(X5),X25),X239) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin__set__fold) ).

fof(fact_diff__Suc__diff__eq2,axiom,
    ! [X72,X97,X96] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X96),X97))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X97),X96))),X72) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X97)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X96),X72)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__diff__eq2) ).

fof(fact_mod__div__equality2,axiom,
    ! [X62,X90,X58] :
      ( class_Divides_Osemiring__div(X58)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X90),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X58),X62),X90))),c_Divides_Odiv__class_Omod(X58,X62,X90)) = X62 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__div__equality2) ).

fof(fact_list__update__code_I3_J,axiom,
    ! [X65,X98,X242,X66,X58] : hAPP(hAPP(c_List_Olist__update(X58,hAPP(hAPP(c_List_Olist_OCons(X58),X66),X242)),hAPP(c_Nat_OSuc,X98)),X65) = hAPP(hAPP(c_List_Olist_OCons(X58),X66),hAPP(hAPP(c_List_Olist__update(X58,X242),X98),X65)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update__code_I3_J) ).

fof(fact_pair__box_Oinject,axiom,
    ! [X179,X180,X24,X6,X20,X5] :
      ( c_Nitpick_Opair__box_OPairBox(X5,X20,X6,X24) = c_Nitpick_Opair__box_OPairBox(X5,X20,X180,X179)
    <=> ( X6 = X180
        & X24 = X179 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__box_Oinject) ).

fof(fact_vimageI,axiom,
    ! [X20,X113,X5,X24,X6,X2] :
      ( hAPP(X2,X6) = X24
     => ( hBOOL(hAPP(hAPP(c_member(X5),X24),X113))
       => hBOOL(hAPP(hAPP(c_member(X20),X6),hAPP(c_Set_Ovimage(X20,X5,X2),X113))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimageI) ).

fof(fact_image__eqI,axiom,
    ! [X5,X21,X20,X25,X2,X24] :
      ( X24 = hAPP(X2,X25)
     => ( hBOOL(hAPP(hAPP(c_member(X20),X25),X21))
       => hBOOL(hAPP(hAPP(c_member(X5),X24),hAPP(c_Set_Oimage(X20,X5,X2),X21))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__eqI) ).

fof(fact_rev__image__eqI,axiom,
    ! [X20,X2,X24,X21,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
     => ( X24 = hAPP(X2,X25)
       => hBOOL(hAPP(hAPP(c_member(X20),X24),hAPP(c_Set_Oimage(X5,X20,X2),X21))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__image__eqI) ).

fof(fact_inj__on__iff,axiom,
    ! [X33,X25,X21,X2,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,X2,X21)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X33),X21))
         => ( hAPP(X2,X25) = hAPP(X2,X33)
          <=> X25 = X33 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__iff) ).

fof(fact_inj__on__contraD,axiom,
    ! [X33,X25,X21,X2,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,X2,X21)
     => ( X25 != X33
       => ( hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => ( hBOOL(hAPP(hAPP(c_member(X5),X33),X21))
           => hAPP(X2,X25) != hAPP(X2,X33) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__contraD) ).

fof(fact_inj__onD,axiom,
    ! [X33,X25,X21,X2,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,X2,X21)
     => ( hAPP(X2,X25) = hAPP(X2,X33)
       => ( hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => ( hBOOL(hAPP(hAPP(c_member(X5),X33),X21))
           => X25 = X33 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__onD) ).

fof(fact_nonneg1__imp__zdiv__pos__iff,axiom,
    ! [X24,X6] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X6),X24)))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24),X6))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonneg1__imp__zdiv__pos__iff) ).

fof(fact_list__ex__length,axiom,
    ! [X239,X18,X5] :
      ( c_List_Olist__ex(X5,X18,X239)
    <=> ? [X69] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X69),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239)))
          & hBOOL(hAPP(X18,hAPP(hAPP(c_List_Onth(X5),X239),X69))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__ex__length) ).

fof(fact_folding__one__idem_Osubset__idem,axiom,
    ! [X113,X21,X205,X2,X5] :
      ( c_Finite__Set_Ofolding__one__idem(X5,X2,X205)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( X113 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X113),X21))
           => hAPP(hAPP(X2,hAPP(X205,X113)),hAPP(X205,X21)) = hAPP(X205,X21) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Osubset__idem) ).

fof(fact_part__equivp__def,axiom,
    ! [X32,X5] :
      ( c_Equiv__Relations_Opart__equivp(X5,X32)
    <=> ( ? [X3] : hBOOL(hAPP(hAPP(X32,X3),X3))
        & ! [X3,X177] :
            ( hBOOL(hAPP(hAPP(X32,X3),X177))
          <=> ( hBOOL(hAPP(hAPP(X32,X3),X3))
              & hBOOL(hAPP(hAPP(X32,X177),X177))
              & hAPP(X32,X3) = hAPP(X32,X177) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_part__equivp__def) ).

fof(fact_comp__equivI,axiom,
    ! [X21,X171,X5] :
      ( hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),hAPP(c_Relation_Oconverse(X5,X5),X171)),X171) = X171
     => ( hAPP(c_Relation_ODomain(X5,X5),X171) = X21
       => c_Equiv__Relations_Oequiv(X5,X21,X171) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comp__equivI) ).

fof(fact_zip__replicate,axiom,
    ! [X65,X97,X66,X98,X5,X58] : hAPP(hAPP(c_List_Ozip(X58,X5),c_List_Oreplicate(X58,X98,X66)),c_List_Oreplicate(X5,X97,X65)) = c_List_Oreplicate(tc_prod(X58,X5),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X98),X97),hAPP(hAPP(c_Product__Type_OPair(X58,X5),X66),X65)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__replicate) ).

fof(fact_com_Osize_I13_J,axiom,
    ! [X41,X42,X84] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCond(X84,X42,X41)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X42)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X41))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osize_I13_J) ).

fof(fact_le__funE,axiom,
    ! [X25,X1,X2,X5,X20] :
      ( class_Orderings_Oord(X20)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X20)),X2),X1))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20),hAPP(X2,X25)),hAPP(X1,X25))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__funE) ).

fof(fact_le__funD,axiom,
    ! [X25,X1,X2,X5,X20] :
      ( class_Orderings_Oord(X20)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X20)),X2),X1))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20),hAPP(X2,X25)),hAPP(X1,X25))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__funD) ).

fof(fact_inj__map__eq__map,axiom,
    ! [X251,X239,X2,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => ( hAPP(hAPP(c_List_Omap(X5,X20),X2),X239) = hAPP(hAPP(c_List_Omap(X5,X20),X2),X251)
      <=> X239 = X251 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__map__eq__map) ).

fof(fact_map__injective,axiom,
    ! [X251,X239,X2,X5,X20] :
      ( hAPP(hAPP(c_List_Omap(X20,X5),X2),X239) = hAPP(hAPP(c_List_Omap(X20,X5),X2),X251)
     => ( c_Fun_Oinj__on(X20,X5,X2,c_Orderings_Otop__class_Otop(tc_fun(X20,tc_HOL_Obool)))
       => X239 = X251 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__injective) ).

fof(fact_nth__list__update__eq,axiom,
    ! [X66,X242,X58,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242)))
     => hAPP(hAPP(c_List_Onth(X58),hAPP(hAPP(c_List_Olist__update(X58,X242),X98),X66)),X98) = X66 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__list__update__eq) ).

fof(fact_setsum__atMost__Suc,axiom,
    ! [X50,X2,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,X50))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X50))),hAPP(X2,hAPP(c_Nat_OSuc,X50))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__atMost__Suc) ).

fof(fact_sym__Int,axiom,
    ! [X76,X171,X5] :
      ( c_Relation_Osym(X5,X171)
     => ( c_Relation_Osym(X5,X76)
       => c_Relation_Osym(X5,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X171),X76)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sym__Int) ).

fof(fact_sym__Un,axiom,
    ! [X76,X171,X5] :
      ( c_Relation_Osym(X5,X171)
     => ( c_Relation_Osym(X5,X76)
       => c_Relation_Osym(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X171),X76)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sym__Un) ).

fof(fact_trans__Int,axiom,
    ! [X76,X171,X5] :
      ( c_Relation_Otrans(X5,X171)
     => ( c_Relation_Otrans(X5,X76)
       => c_Relation_Otrans(X5,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X171),X76)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__Int) ).

fof(fact_ivl__disj__un_I17_J,axiom,
    ! [X159,X95,X156,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X156),X95))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X95),X159))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X156),X95)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X95),X159)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X156),X159) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I17_J) ).

fof(fact_butlast__conv__take,axiom,
    ! [X242,X58] : c_List_Obutlast(X58,X242) = hAPP(hAPP(c_List_Otake(X58),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X242),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_butlast__conv__take) ).

fof(fact_fold1__belowI,axiom,
    ! [X6,X21,X5] :
      ( class_Lattices_Osemilattice__inf(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X21))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Finite__Set_Ofold1(X5,c_Lattices_Osemilattice__inf__class_Oinf(X5)),X21)),X6)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__belowI) ).

fof(fact_min__max_Ofold1__belowI,axiom,
    ! [X6,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X21))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Finite__Set_Ofold1(X5,c_Orderings_Oord__class_Omin(X5)),X21)),X6)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ofold1__belowI) ).

fof(fact_sorted_OCons,axiom,
    ! [X25,X239,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X239)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X25),X3)) )
       => ( c_List_Olinorder__class_Osorted(X5,X239)
         => c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted_OCons) ).

fof(fact_sorted_Oequations_I2_J,axiom,
    ! [X27,X26,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X26),X27))
      <=> ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X27)))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X26),X3)) )
          & c_List_Olinorder__class_Osorted(X5,X27) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted_Oequations_I2_J) ).

fof(fact_sorted__Cons,axiom,
    ! [X239,X25,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239))
      <=> ( c_List_Olinorder__class_Osorted(X5,X239)
          & ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X239)))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X25),X3)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__Cons) ).

fof(fact_evalc_Oequations_I2_J,axiom,
    ! [X63,X26,X27] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(X27,X26)),X63),hAPP(hAPP(hAPP(c_Natural_Oupdate,X63),X27),hAPP(X26,X63)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_Oequations_I2_J) ).

fof(fact_evalc_OAssign,axiom,
    ! [X76,X6,X194] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(X194,X6)),X76),hAPP(hAPP(hAPP(c_Natural_Oupdate,X76),X194),hAPP(X6,X76)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_OAssign) ).

fof(fact_int__power__div__base,axiom,
    ! [X96,X72] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X72))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X96))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X96),X72)),X96) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X96),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X72),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__power__div__base) ).

fof(fact_divide__nonneg__pos,axiom,
    ! [X65,X66,X58] :
      ( class_Fields_Olinordered__field(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),X66))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),X65))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X66),X65))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__nonneg__pos) ).

fof(fact_split__mult__pos__le,axiom,
    ! [X90,X62,X58] :
      ( class_Rings_Oordered__ring(X58)
     => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),X62))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),X90)) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X62),c_Groups_Ozero__class_Ozero(X58)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X90),c_Groups_Ozero__class_Ozero(X58))) ) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X90))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__mult__pos__le) ).

fof(fact_mult__nonneg__nonneg,axiom,
    ! [X90,X62,X58] :
      ( class_Rings_Oordered__cancel__semiring(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),X62))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),X90))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X90))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__nonneg__nonneg) ).

fof(fact_add__nonneg__nonneg,axiom,
    ! [X90,X62,X58] :
      ( class_Groups_Oordered__comm__monoid__add(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),X62))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),X90))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),X90))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonneg__nonneg) ).

fof(fact_less__1__mult,axiom,
    ! [X57,X72,X58] :
      ( class_Rings_Olinordered__semidom(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Oone__class_Oone(X58)),X72))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Oone__class_Oone(X58)),X57))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Oone__class_Oone(X58)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X72),X57))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__1__mult) ).

fof(fact_divide__pos__pos,axiom,
    ! [X65,X66,X58] :
      ( class_Fields_Olinordered__field(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),X66))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),X65))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X66),X65))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__pos__pos) ).

fof(fact_mult__pos__pos,axiom,
    ! [X90,X62,X58] :
      ( class_Rings_Olinordered__semiring__strict(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),X62))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),X90))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X90))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__pos__pos) ).

fof(fact_add__pos__nonneg,axiom,
    ! [X90,X62,X58] :
      ( class_Groups_Oordered__comm__monoid__add(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),X62))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),X90))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),X90))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__pos__nonneg) ).

fof(fact_add__nonneg__pos,axiom,
    ! [X90,X62,X58] :
      ( class_Groups_Oordered__comm__monoid__add(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),X62))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),X90))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),X90))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonneg__pos) ).

fof(fact_add__pos__pos,axiom,
    ! [X90,X62,X58] :
      ( class_Groups_Oordered__comm__monoid__add(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),X62))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),X90))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),X90))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__pos__pos) ).

fof(fact_eq__card__imp__inj__on,axiom,
    ! [X2,X20,X21,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
     => ( hAPP(c_Finite__Set_Ocard(X20),hAPP(c_Set_Oimage(X5,X20,X2),X21)) = hAPP(c_Finite__Set_Ocard(X5),X21)
       => c_Fun_Oinj__on(X5,X20,X2,X21) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__card__imp__inj__on) ).

fof(fact_inj__on__iff__eq__card,axiom,
    ! [X2,X20,X21,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
     => ( c_Fun_Oinj__on(X5,X20,X2,X21)
      <=> hAPP(c_Finite__Set_Ocard(X20),hAPP(c_Set_Oimage(X5,X20,X2),X21)) = hAPP(c_Finite__Set_Ocard(X5),X21) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__iff__eq__card) ).

fof(fact_Compl__Diff__eq,axiom,
    ! [X113,X21,X5] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X21)),X113),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__Diff__eq) ).

fof(fact_power__eq__imp__eq__base,axiom,
    ! [X90,X57,X62,X58] :
      ( class_Rings_Olinordered__semidom(X58)
     => ( hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),X57) = hAPP(hAPP(c_Power_Opower__class_Opower(X58),X90),X57)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),X62))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),X90))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X57))
             => X62 = X90 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__eq__imp__eq__base) ).

fof(fact_card__cartesian__product,axiom,
    ! [X113,X21,X20,X5] : hAPP(c_Finite__Set_Ocard(tc_prod(X5,X20)),hAPP(hAPP(c_Product__Type_OSigma(X5,X20),X21),hAPP(c_COMBK(tc_fun(X20,tc_HOL_Obool),X5),X113))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X21)),hAPP(c_Finite__Set_Ocard(X20),X113)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__cartesian__product) ).

fof(fact_Int__insert__right__if1,axiom,
    ! [X113,X21,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),X21))
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X6),X113)) = hAPP(hAPP(c_Set_Oinsert(X5),X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__insert__right__if1) ).

fof(fact_list__eq__iff__nth__eq,axiom,
    ! [X5,X251,X239] :
      ( X239 = X251
    <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X251)
        & ! [X146] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X146),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239)))
           => hAPP(hAPP(c_List_Onth(X5),X239),X146) = hAPP(hAPP(c_List_Onth(X5),X251),X146) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__eq__iff__nth__eq) ).

fof(fact_folding_Oeq__fold,axiom,
    ! [X76,X21,X205,X2,X20,X5] :
      ( c_Finite__Set_Ofolding(X5,X20,X2,X205)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => hAPP(hAPP(X205,X21),X76) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X20,X2),X76),X21) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Oeq__fold) ).

fof(fact_weaken,axiom,
    ! [X13,X145,X4,X5] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,X145)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool)),X13),X145))
       => c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,X13) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_weaken) ).

fof(fact_thin,axiom,
    ! [X4,X13,X14,X5] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(X5,X14,X13)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool)),X14),X4))
       => c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,X13) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_thin) ).

fof(fact_le__SUPI,axiom,
    ! [X210,X21,X82,X5,X20] :
      ( class_Complete__Lattice_Ocomplete__lattice(X20)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X82),X21))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20),hAPP(X210,X82)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X20),X21),X210))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__SUPI) ).

fof(fact_zmod__simps_I4_J,axiom,
    ! [X90,X56,X62,X58] :
      ( class_Divides_Osemiring__div(X58)
     => c_Divides_Odiv__class_Omod(X58,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),c_Divides_Odiv__class_Omod(X58,X62,X56)),X90),X56) = c_Divides_Odiv__class_Omod(X58,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X90),X56) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__simps_I4_J) ).

fof(fact_zmod__simps_I1_J,axiom,
    ! [X90,X56,X62,X58] :
      ( class_Divides_Osemiring__div(X58)
     => c_Divides_Odiv__class_Omod(X58,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),c_Divides_Odiv__class_Omod(X58,X62,X56)),X90),X56) = c_Divides_Odiv__class_Omod(X58,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),X90),X56) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__simps_I1_J) ).

fof(fact_mod__diff__left__eq,axiom,
    ! [X56,X90,X62,X58] :
      ( class_Divides_Oring__div(X58)
     => c_Divides_Odiv__class_Omod(X58,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X58),X62),X90),X56) = c_Divides_Odiv__class_Omod(X58,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X58),c_Divides_Odiv__class_Omod(X58,X62,X56)),X90),X56) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__diff__left__eq) ).

fof(fact_mod__mult__left__eq,axiom,
    ! [X56,X90,X62,X58] :
      ( class_Divides_Osemiring__div(X58)
     => c_Divides_Odiv__class_Omod(X58,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X90),X56) = c_Divides_Odiv__class_Omod(X58,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),c_Divides_Odiv__class_Omod(X58,X62,X56)),X90),X56) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__left__eq) ).

fof(fact_mod__add__left__eq,axiom,
    ! [X56,X90,X62,X58] :
      ( class_Divides_Osemiring__div(X58)
     => c_Divides_Odiv__class_Omod(X58,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),X90),X56) = c_Divides_Odiv__class_Omod(X58,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),c_Divides_Odiv__class_Omod(X58,X62,X56)),X90),X56) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__add__left__eq) ).

fof(fact_psubset__eq,axiom,
    ! [X113,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X21),X113))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),X113))
        & X21 != X113 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__eq) ).

fof(fact_subset__iff__psubset__eq,axiom,
    ! [X113,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),X113))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X21),X113))
        | X21 = X113 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__iff__psubset__eq) ).

fof(fact_finite__UnI,axiom,
    ! [X4,X205,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X205))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X205),X4))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UnI) ).

fof(fact_Pow__Int__eq,axiom,
    ! [X113,X21,X5] : hAPP(c_Set_OPow(X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X5),X21)),hAPP(c_Set_OPow(X5),X113)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__Int__eq) ).

fof(fact_finite__maxlen,axiom,
    ! [X210,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X5)),X210))
     => ? [X69] :
        ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X3),X210))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X3)),X69)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__maxlen) ).

fof(fact_setsum_Oeq__fold,axiom,
    ! [X1,X21,X5,X20] :
      ( class_Groups_Ocomm__monoid__add(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X1),X21) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X20,X5,c_Groups_Oplus__class_Oplus(X20)),X1),c_Groups_Ozero__class_Ozero(X20)),X21) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum_Oeq__fold) ).

fof(fact_setprod_Oeq__fold,axiom,
    ! [X1,X21,X5,X20] :
      ( class_Groups_Ocomm__monoid__mult(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X1),X21) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X20,X5,c_Groups_Otimes__class_Otimes(X20)),X1),c_Groups_Oone__class_Oone(X20)),X21) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod_Oeq__fold) ).

fof(fact_psubset__imp__subset,axiom,
    ! [X113,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X21),X113))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),X113)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__imp__subset) ).

fof(fact_append__replicate__commute,axiom,
    ! [X96,X66,X57,X58] : hAPP(hAPP(c_List_Oappend(X58),c_List_Oreplicate(X58,X57,X66)),c_List_Oreplicate(X58,X96,X66)) = hAPP(hAPP(c_List_Oappend(X58),c_List_Oreplicate(X58,X96,X66)),c_List_Oreplicate(X58,X57,X66)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__replicate__commute) ).

fof(fact_mod__pos__neg,axiom,
    ! [X90,X62] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X62))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X90),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,X62,X90) = 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),X62),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X90)))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__pos__neg) ).

fof(fact_ex__nat__less,axiom,
    ! [X18,X50] :
      ( ? [X86] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X86),X50))
          & hBOOL(hAPP(X18,X86)) )
    <=> ? [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),X50)))
          & hBOOL(hAPP(X18,X3)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ex__nat__less) ).

fof(fact_drop__Cons__number__of,axiom,
    ! [X242,X66,X58,X136] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Odrop(X58),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)),hAPP(hAPP(c_List_Olist_OCons(X58),X66),X242)) = hAPP(hAPP(c_List_Olist_OCons(X58),X66),X242) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Odrop(X58),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)),hAPP(hAPP(c_List_Olist_OCons(X58),X66),X242)) = hAPP(hAPP(c_List_Odrop(X58),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X242) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__Cons__number__of) ).

fof(fact_Abs__Integ__induct,axiom,
    ! [X25,X18] :
      ( ! [X177] :
          ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X177),c_Int_OInteg))
         => hBOOL(hAPP(X18,hAPP(c_Int_OAbs__Integ,X177))) )
     => hBOOL(hAPP(X18,X25)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Abs__Integ__induct) ).

fof(fact_wf__Int1,axiom,
    ! [X203,X171,X5] :
      ( c_Wellfounded_Owf(X5,X171)
     => c_Wellfounded_Owf(X5,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X171),X203)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__Int1) ).

fof(fact_wf__Int2,axiom,
    ! [X203,X171,X5] :
      ( c_Wellfounded_Owf(X5,X171)
     => c_Wellfounded_Owf(X5,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),X203),X171)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__Int2) ).

fof(fact_div__pos__neg,axiom,
    ! [X90,X62] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X62))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X90),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X62),X90) = 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),X62),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X90)))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__pos__neg) ).

fof(fact_fold1__set,axiom,
    ! [X239,X5] :
      ( class_Lattices_Oab__semigroup__idem__mult(X5)
     => ( X239 != c_List_Olist_ONil(X5)
       => hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),hAPP(c_List_Oset(X5),X239)) = hAPP(c_List_Ofoldl(X5,X5,c_Groups_Otimes__class_Otimes(X5),hAPP(c_List_Ohd(X5),X239)),hAPP(c_List_Otl(X5),X239)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__set) ).

fof(fact_drop__zip,axiom,
    ! [X241,X242,X57,X5,X58] : hAPP(hAPP(c_List_Odrop(tc_prod(X58,X5)),X57),hAPP(hAPP(c_List_Ozip(X58,X5),X242),X241)) = hAPP(hAPP(c_List_Ozip(X58,X5),hAPP(hAPP(c_List_Odrop(X58),X57),X242)),hAPP(hAPP(c_List_Odrop(X5),X57),X241)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__zip) ).

fof(fact_take__zip,axiom,
    ! [X241,X242,X57,X5,X58] : hAPP(hAPP(c_List_Otake(tc_prod(X58,X5)),X57),hAPP(hAPP(c_List_Ozip(X58,X5),X242),X241)) = hAPP(hAPP(c_List_Ozip(X58,X5),hAPP(hAPP(c_List_Otake(X58),X57),X242)),hAPP(hAPP(c_List_Otake(X5),X57),X241)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__zip) ).

fof(fact_ivl__disj__un_I6_J,axiom,
    ! [X159,X156,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X156),X159))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X156),X159)),hAPP(hAPP(c_Set_Oinsert(X5),X159),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(X5,X156,X159) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I6_J) ).

fof(fact_mod__neg__neg,axiom,
    ! [X90,X62] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X62),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X90),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,X62,X90) = 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),X62),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X90)))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__neg__neg) ).

fof(fact_single__valued__rel__comp,axiom,
    ! [X76,X116,X171,X20,X5] :
      ( c_Relation_Osingle__valued(X5,X20,X171)
     => ( c_Relation_Osingle__valued(X20,X116,X76)
       => c_Relation_Osingle__valued(X5,X116,hAPP(hAPP(c_Relation_Orel__comp(X5,X20,X116),X171),X76)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valued__rel__comp) ).

fof(fact_sorted__transpose,axiom,
    ! [X239,X5] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X5),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X5))),c_List_Otranspose(X5,X239)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__transpose) ).

fof(fact_Int__atLeastLessThan,axiom,
    ! [X22,X23,X24,X6,X5] :
      ( class_Orderings_Olinorder(X5)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X6),X24)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X23),X22)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X6),X23)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X24),X22)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__atLeastLessThan) ).

fof(fact_Int__atLeastAtMost,axiom,
    ! [X22,X23,X24,X6,X5] :
      ( class_Orderings_Olinorder(X5)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,X24)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X23,X22)) = c_SetInterval_Oord__class_OatLeastAtMost(X5,hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X6),X23),hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X24),X22)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__atLeastAtMost) ).

fof(fact_Int__greaterThanAtMost,axiom,
    ! [X22,X23,X24,X6,X5] :
      ( class_Orderings_Olinorder(X5)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X6,X24)),c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X23,X22)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X5,hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X6),X23),hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X24),X22)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__greaterThanAtMost) ).

fof(fact_Int__greaterThanLessThan,axiom,
    ! [X22,X23,X24,X6,X5] :
      ( class_Orderings_Olinorder(X5)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X6,X24)),c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X23,X22)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X5,hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X6),X23),hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X24),X22)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__greaterThanLessThan) ).

fof(fact_set__rev__mp,axiom,
    ! [X113,X21,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),X113))
       => hBOOL(hAPP(hAPP(c_member(X5),X25),X113)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__rev__mp) ).

fof(fact_set__mp,axiom,
    ! [X25,X113,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),X113))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
       => hBOOL(hAPP(hAPP(c_member(X5),X25),X113)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__mp) ).

fof(fact_in__mono,axiom,
    ! [X25,X113,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),X113))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
       => hBOOL(hAPP(hAPP(c_member(X5),X25),X113)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__mono) ).

fof(fact_subsetD,axiom,
    ! [X23,X113,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),X113))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X23),X21))
       => hBOOL(hAPP(hAPP(c_member(X5),X23),X113)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subsetD) ).

fof(fact_psubsetD,axiom,
    ! [X23,X113,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X21),X113))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X23),X21))
       => hBOOL(hAPP(hAPP(c_member(X5),X23),X113)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubsetD) ).

fof(fact_nth__append__length,axiom,
    ! [X241,X66,X242,X58] : hAPP(hAPP(c_List_Onth(X58),hAPP(hAPP(c_List_Oappend(X58),X242),hAPP(hAPP(c_List_Olist_OCons(X58),X66),X241))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242)) = X66,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__append__length) ).

fof(fact_div__neg__neg,axiom,
    ! [X90,X62] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X62),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X90),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X62),X90) = 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),X62),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X90)))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__neg__neg) ).

fof(fact_inj__on__add__nat,axiom,
    ! [X207,X87] : 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)),X87),X207),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__add__nat) ).

fof(fact_pos__imp__zdiv__nonneg__iff,axiom,
    ! [X6,X24] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X6),X24)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__imp__zdiv__nonneg__iff) ).

fof(fact_times__divide__times__eq,axiom,
    ! [X128,X94,X65,X66,X58] :
      ( class_Fields_Ofield__inverse__zero(X58)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X66),X65)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X94),X128)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X66),X94)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X65),X128)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_times__divide__times__eq) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
    ! [X129,X130,X131,X132,X58] :
      ( class_Rings_Ocomm__semiring__1(X58)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X132),X131)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X130),X129)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X132),X130)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X131),X129)) ),
    file('/export/starexec/sandbox/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,
    ! [X91,X56,X90,X62,X58] :
      ( class_Rings_Ocomm__semiring__1(X58)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),X90)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X56),X91)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),X56)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X90),X91)) ),
    file('/export/starexec/sandbox/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,
    ! [X129,X130,X131,X132,X58] :
      ( class_Rings_Ocomm__semiring__1(X58)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X132),X131)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X130),X129)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X132),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X131),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X130),X129))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).

fof(fact_sorted__map__remove1,axiom,
    ! [X25,X239,X2,X20,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Omap(X20,X5),X2),X239))
       => c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Omap(X20,X5),X2),c_List_Oremove1(X20,X25,X239))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__map__remove1) ).

fof(fact_Domain__Union,axiom,
    ! [X192,X20,X5] : hAPP(c_Relation_ODomain(X5,X20),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X5,X20),tc_HOL_Obool),X192)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(X5,X20),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X192),c_Relation_ODomain(X5,X20)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__Union) ).

fof(fact_Range__Union,axiom,
    ! [X192,X5,X20] : hAPP(c_Relation_ORange(X20,X5),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X20,X5),tc_HOL_Obool),X192)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(X20,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X192),c_Relation_ORange(X20,X5)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__Union) ).

fof(fact_all__nat__less,axiom,
    ! [X18,X50] :
      ( ! [X86] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X86),X50))
         => hBOOL(hAPP(X18,X86)) )
    <=> ! [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),X50)))
         => hBOOL(hAPP(X18,X3)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_all__nat__less) ).

fof(fact_Ints__power,axiom,
    ! [X50,X6,X5] :
      ( class_Rings_Oring__1(X5)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X6),c_Int_Oring__1__class_OInts(X5)))
       => hBOOL(hAPP(hAPP(c_member(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X50)),c_Int_Oring__1__class_OInts(X5))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__power) ).

fof(fact_Collect__mem__eq,axiom,
    ! [X21,X5] : hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X21)) = X21,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__mem__eq) ).

fof(fact_nat__one__le__power,axiom,
    ! [X57,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X98))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X98),X57))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__one__le__power) ).

fof(fact_one__less__power,axiom,
    ! [X57,X62,X58] :
      ( class_Rings_Olinordered__semidom(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Oone__class_Oone(X58)),X62))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X57))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Oone__class_Oone(X58)),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),X57))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__less__power) ).

fof(fact_divide__nonpos__neg,axiom,
    ! [X65,X66,X58] :
      ( class_Fields_Olinordered__field(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X66),c_Groups_Ozero__class_Ozero(X58)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X65),c_Groups_Ozero__class_Ozero(X58)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X66),X65))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__nonpos__neg) ).

fof(fact_mult__nonpos__nonpos,axiom,
    ! [X90,X62,X58] :
      ( class_Rings_Oordered__ring(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X62),c_Groups_Ozero__class_Ozero(X58)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X90),c_Groups_Ozero__class_Ozero(X58)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X90))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__nonpos__nonpos) ).

fof(fact_divide__neg__neg,axiom,
    ! [X65,X66,X58] :
      ( class_Fields_Olinordered__field(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X66),c_Groups_Ozero__class_Ozero(X58)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X65),c_Groups_Ozero__class_Ozero(X58)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X66),X65))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__neg__neg) ).

fof(fact_mult__neg__neg,axiom,
    ! [X90,X62,X58] :
      ( class_Rings_Olinordered__ring__strict(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X62),c_Groups_Ozero__class_Ozero(X58)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X90),c_Groups_Ozero__class_Ozero(X58)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X90))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__neg__neg) ).

fof(fact_setsum__lessThan__Suc,axiom,
    ! [X50,X2,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X50))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X50))),hAPP(X2,X50)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__lessThan__Suc) ).

fof(fact_posDivAlg__div__mod,axiom,
    ! [X99,X96] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X96))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X99))
       => c_Divides_OposDivAlg(X96,X99) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X96),X99)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X96,X99)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_posDivAlg__div__mod) ).

fof(fact_pos__imp__zdiv__pos__iff,axiom,
    ! [X82,X87] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X87))
     => ( 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),X82),X87)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X87),X82)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__imp__zdiv__pos__iff) ).

fof(fact_lex__def,axiom,
    ! [X171,X5] : c_List_Olex(X5,X171) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(X5,X171)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lex__def) ).

fof(fact_le__max__iff__disj,axiom,
    ! [X33,X25,X120,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X120),hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X25),X33)))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X120),X25))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X120),X33)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__max__iff__disj) ).

fof(fact_less__max__iff__disj,axiom,
    ! [X33,X25,X120,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X120),hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X25),X33)))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X120),X25))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X120),X33)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__max__iff__disj) ).

fof(fact_neg__imp__zdiv__nonneg__iff,axiom,
    ! [X6,X24] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X6),X24)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X6),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__imp__zdiv__nonneg__iff) ).

fof(fact_select__weigth__select,axiom,
    ! [X5,X239] :
      ( X239 != c_List_Olist_ONil(X5)
     => c_Random_Oselect__weight(X5,hAPP(hAPP(c_List_Omap(X5,tc_prod(tc_Code__Numeral_Ocode__numeral,X5)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X5),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),X239)) = c_Random_Oselect(X5,X239) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_select__weigth__select) ).

fof(fact_finite__Inter,axiom,
    ! [X210,X5] :
      ( ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X3),X210))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X3)) )
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X5),c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),X210))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Inter) ).

fof(fact_abs__eq__mult,axiom,
    ! [X90,X62,X58] :
      ( class_Rings_Oordered__ring__abs(X58)
     => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),X62))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X62),c_Groups_Ozero__class_Ozero(X58))) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),X90))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X90),c_Groups_Ozero__class_Ozero(X58))) ) )
       => hAPP(c_Groups_Oabs__class_Oabs(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X90)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),hAPP(c_Groups_Oabs__class_Oabs(X58),X62)),hAPP(c_Groups_Oabs__class_Oabs(X58),X90)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__eq__mult) ).

fof(fact_butlast__take,axiom,
    ! [X242,X58,X57] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X57),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242)))
     => c_List_Obutlast(X58,hAPP(hAPP(c_List_Otake(X58),X57),X242)) = hAPP(hAPP(c_List_Otake(X58),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X57),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X242) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_butlast__take) ).

fof(fact_single__Diff__lessThan,axiom,
    ! [X87,X5] :
      ( class_Orderings_Oorder(X5)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X87),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(X5),X87)) = hAPP(hAPP(c_Set_Oinsert(X5),X87),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__Diff__lessThan) ).

fof(fact_disjoint__iff__not__equal,axiom,
    ! [X113,X21,X5] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),X21))
         => ! [X204] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X204),X113))
             => X3 != X204 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_disjoint__iff__not__equal) ).

fof(fact_insort__remove1,axiom,
    ! [X239,X6,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(c_List_Oset(X5),X239)))
       => ( c_List_Olinorder__class_Osorted(X5,X239)
         => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X5,c_COMBI(X5)),X6),c_List_Oremove1(X5,X6,X239)) = X239 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insort__remove1) ).

fof(fact_negDivAlg__div__mod,axiom,
    ! [X99,X96] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X96),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)),X99))
       => c_Divides_OnegDivAlg(X96,X99) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X96),X99)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X96,X99)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negDivAlg__div__mod) ).

fof(fact_Inf__fin_Osubset__idem,axiom,
    ! [X113,X21,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( X113 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X113),X21))
           => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),c_Big__Operators_Olattice__class_OInf__fin(X5,X113)),c_Big__Operators_Olattice__class_OInf__fin(X5,X21)) = c_Big__Operators_Olattice__class_OInf__fin(X5,X21) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_Osubset__idem) ).

fof(fact_Sup__fin_Osubset__idem,axiom,
    ! [X113,X21,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( X113 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X113),X21))
           => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),c_Big__Operators_Olattice__class_OSup__fin(X5,X113)),c_Big__Operators_Olattice__class_OSup__fin(X5,X21)) = c_Big__Operators_Olattice__class_OSup__fin(X5,X21) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_Osubset__idem) ).

fof(fact_Max_Osubset__idem,axiom,
    ! [X113,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( X113 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X113),X21))
           => hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),c_Big__Operators_Olinorder__class_OMax(X5,X113)),c_Big__Operators_Olinorder__class_OMax(X5,X21)) = c_Big__Operators_Olinorder__class_OMax(X5,X21) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max_Osubset__idem) ).

fof(fact_Min_Osubset__idem,axiom,
    ! [X113,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( X113 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X113),X21))
           => hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),c_Big__Operators_Olinorder__class_OMin(X5,X113)),c_Big__Operators_Olinorder__class_OMin(X5,X21)) = c_Big__Operators_Olinorder__class_OMin(X5,X21) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min_Osubset__idem) ).

fof(fact_zpower__zmod,axiom,
    ! [X65,X72,X66] : 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,X66,X72)),X65),X72) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X66),X65),X72),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zpower__zmod) ).

fof(fact_zdiff__zmod__left,axiom,
    ! [X65,X72,X66] : 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,X66,X72)),X65),X72) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X66),X65),X72),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiff__zmod__left) ).

fof(fact_le__Inf__iff,axiom,
    ! [X21,X24,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X24),c_Complete__Lattice_OInf__class_OInf(X5,X21)))
      <=> ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X21))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X24),X3)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__Inf__iff) ).

fof(fact_take__Cons_H,axiom,
    ! [X242,X66,X58,X57] :
      ( ( X57 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Otake(X58),X57),hAPP(hAPP(c_List_Olist_OCons(X58),X66),X242)) = c_List_Olist_ONil(X58) )
      & ( X57 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Otake(X58),X57),hAPP(hAPP(c_List_Olist_OCons(X58),X66),X242)) = hAPP(hAPP(c_List_Olist_OCons(X58),X66),hAPP(hAPP(c_List_Otake(X58),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X57),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X242)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__Cons_H) ).

fof(fact_inf1I,axiom,
    ! [X5,X113,X25,X21] :
      ( hBOOL(hAPP(X21,X25))
     => ( hBOOL(hAPP(X113,X25))
       => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113),X25)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf1I) ).

fof(fact_list__ex__iff__raw,axiom,
    ! [X239,X18,X5] :
      ( c_List_Olist__ex(X5,X18,X239)
    <=> ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X239)))
          & hBOOL(hAPP(X18,X3)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__ex__iff__raw) ).

fof(fact_Bex__set__list__ex,axiom,
    ! [X18,X239,X5] :
      ( ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X239)))
          & hBOOL(hAPP(X18,X3)) )
    <=> c_List_Olist__ex(X5,X18,X239) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bex__set__list__ex) ).

fof(fact_list__ex__iff,axiom,
    ! [X239,X18,X5] :
      ( c_List_Olist__ex(X5,X18,X239)
    <=> ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X239)))
          & hBOOL(hAPP(X18,X3)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__ex__iff) ).

fof(fact_Rep__Integ,axiom,
    ! [X25] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,X25)),c_Int_OInteg)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Rep__Integ) ).

fof(fact_folding__one__idem_Ounion__idem,axiom,
    ! [X113,X21,X205,X2,X5] :
      ( c_Finite__Set_Ofolding__one__idem(X5,X2,X205)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X113))
           => ( X113 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => hAPP(X205,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(X2,hAPP(X205,X21)),hAPP(X205,X113)) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Ounion__idem) ).

fof(fact_in__listsp__conv__set,axiom,
    ! [X239,X21,X5] :
      ( hBOOL(hAPP(c_List_Olistsp(X5,X21),X239))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X239)))
         => hBOOL(hAPP(X21,X3)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__listsp__conv__set) ).

fof(fact_add__increasing,axiom,
    ! [X56,X90,X62,X58] :
      ( class_Groups_Oordered__comm__monoid__add(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),X62))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X90),X56))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X90),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),X56))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__increasing) ).

fof(fact_add__increasing2,axiom,
    ! [X62,X90,X56,X58] :
      ( class_Groups_Oordered__comm__monoid__add(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),X56))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X90),X62))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X90),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),X56))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__increasing2) ).

fof(fact_pos__add__strict,axiom,
    ! [X56,X90,X62,X58] :
      ( class_Rings_Olinordered__semidom(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),X62))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X90),X56))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X90),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),X56))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__add__strict) ).

fof(fact_add__strict__increasing,axiom,
    ! [X56,X90,X62,X58] :
      ( class_Groups_Oordered__comm__monoid__add(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),X62))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X90),X56))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X90),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),X56))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__increasing) ).

fof(fact_add__strict__increasing2,axiom,
    ! [X56,X90,X62,X58] :
      ( class_Groups_Oordered__comm__monoid__add(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),X62))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X90),X56))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X90),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),X56))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__increasing2) ).

fof(fact_zmod__zdiv__equality,axiom,
    ! [X90,X62] : X62 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X90),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X62),X90))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X62,X90)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zdiv__equality) ).

fof(fact_le__infI1,axiom,
    ! [X90,X66,X62,X58] :
      ( class_Lattices_Osemilattice__inf(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X62),X66))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X62),X90)),X66)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__infI1) ).

fof(fact_le__infI2,axiom,
    ! [X62,X66,X90,X58] :
      ( class_Lattices_Osemilattice__inf(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X90),X66))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X62),X90)),X66)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__infI2) ).

fof(fact_min__max_Ole__infI1,axiom,
    ! [X90,X66,X62,X58] :
      ( class_Orderings_Olinorder(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X62),X66))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Orderings_Oord__class_Omin(X58),X62),X90)),X66)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ole__infI1) ).

fof(fact_min__max_Ole__infI2,axiom,
    ! [X62,X66,X90,X58] :
      ( class_Orderings_Olinorder(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X90),X66))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Orderings_Oord__class_Omin(X58),X62),X90)),X66)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ole__infI2) ).

fof(fact_less__infI1,axiom,
    ! [X90,X66,X62,X58] :
      ( class_Lattices_Osemilattice__inf(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X62),X66))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X62),X90)),X66)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__infI1) ).

fof(fact_less__infI2,axiom,
    ! [X62,X66,X90,X58] :
      ( class_Lattices_Osemilattice__inf(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X90),X66))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X62),X90)),X66)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__infI2) ).

fof(fact_min__max_Oless__infI1,axiom,
    ! [X90,X66,X62,X58] :
      ( class_Orderings_Olinorder(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X62),X66))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(hAPP(c_Orderings_Oord__class_Omin(X58),X62),X90)),X66)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oless__infI1) ).

fof(fact_min__max_Oless__infI2,axiom,
    ! [X62,X66,X90,X58] :
      ( class_Orderings_Olinorder(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X90),X66))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(hAPP(c_Orderings_Oord__class_Omin(X58),X62),X90)),X66)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oless__infI2) ).

fof(fact_listrel__Nil,axiom,
    ! [X171,X5] : hAPP(c_Relation_OImage(tc_List_Olist(X5),tc_List_Olist(X5),c_List_Olistrel(X5,X171)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X5)),c_List_Olist_ONil(X5)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X5),tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X5)),c_List_Olist_ONil(X5)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X5),tc_HOL_Obool))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__Nil) ).

fof(fact_setsum__eq__0__iff,axiom,
    ! [X2,X205,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X205))
     => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),X2),X205) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      <=> ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X205))
           => hAPP(X2,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__eq__0__iff) ).

fof(fact_setprod__eq__1__iff,axiom,
    ! [X2,X205,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X205))
     => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,tc_Nat_Onat),X2),X205) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
      <=> ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X205))
           => hAPP(X2,X3) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__eq__1__iff) ).

fof(fact_nat__diff__split,axiom,
    ! [X24,X6,X18] :
      ( hBOOL(hAPP(X18,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X6),X24)))
    <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),X24))
         => hBOOL(hAPP(X18,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
        & ! [X158] :
            ( X6 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),X158)
           => hBOOL(hAPP(X18,X158)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__diff__split) ).

fof(fact_finite__compl,axiom,
    ! [X21,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X21)))
      <=> hBOOL(hAPP(c_Finite__Set_Ofinite(X5),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__compl) ).

fof(fact_less__nat__number__of,axiom,
    ! [X168,X123] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X123)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X168)))
    <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X123),X168))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X168)) )
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X123),X168)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__nat__number__of) ).

fof(fact_Un__insert__left,axiom,
    ! [X112,X113,X6,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X6),X113)),X112) = hAPP(hAPP(c_Set_Oinsert(X5),X6),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X113),X112)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__insert__left) ).

fof(fact_fun__left__comm__idem_Ofun__comp__idem,axiom,
    ! [X25,X2,X20,X5] :
      ( c_Finite__Set_Ofun__left__comm__idem(X5,X20,X2)
     => hAPP(c_Fun_Ocomp(X20,X20,X20,hAPP(X2,X25)),hAPP(X2,X25)) = hAPP(X2,X25) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__idem_Ofun__comp__idem) ).

fof(fact_com_Osize_I12_J,axiom,
    ! [X37,X38] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSemi(X38,X37)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X38)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X37))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osize_I12_J) ).

fof(fact_divmod__int__rel__mod,axiom,
    ! [X134,X140,X90,X62] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X62,X90),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X140),X134)))
     => ( X90 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,X62,X90) = X134 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__int__rel__mod) ).

fof(fact_snd__def,axiom,
    ! [X160,X5,X20] : hAPP(c_Product__Type_Osnd(X20,X5),X160) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X20,X5,X5),hAPP(c_COMBK(tc_fun(X5,X5),X20),c_COMBI(X5))),X160),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_snd__def) ).

fof(fact_Ints__odd__nonzero,axiom,
    ! [X6,X5] :
      ( class_Int_Oring__char__0(X5)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X6),c_Int_Oring__1__class_OInts(X5)))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),c_Groups_Oone__class_Oone(X5)),X6)),X6) != c_Groups_Ozero__class_Ozero(X5) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__odd__nonzero) ).

fof(fact_finite__Int,axiom,
    ! [X4,X205,X5] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X205))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4)) )
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X205),X4))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Int) ).

fof(fact_finite__Diff,axiom,
    ! [X113,X21,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),X113))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Diff) ).

fof(fact_sorted__many__eq,axiom,
    ! [X250,X33,X25,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X25),hAPP(hAPP(c_List_Olist_OCons(X5),X33),X250)))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X25),X33))
          & c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X33),X250)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__many__eq) ).

fof(fact_sorted__many,axiom,
    ! [X248,X65,X66,X58] :
      ( class_Orderings_Olinorder(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X66),X65))
       => ( c_List_Olinorder__class_Osorted(X58,hAPP(hAPP(c_List_Olist_OCons(X58),X65),X248))
         => c_List_Olinorder__class_Osorted(X58,hAPP(hAPP(c_List_Olist_OCons(X58),X66),hAPP(hAPP(c_List_Olist_OCons(X58),X65),X248))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__many) ).

fof(fact_mod__eq,axiom,
    ! [X134,X140,X57,X72] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X72,X57),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X140),X134)))
     => c_Divides_Odiv__class_Omod(tc_Nat_Onat,X72,X57) = X134 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__eq) ).

fof(fact_zmod__le__nonneg__dividend,axiom,
    ! [X96,X72] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X72))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X72,X96)),X72)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__le__nonneg__dividend) ).

fof(fact_mod__le__divisor,axiom,
    ! [X72,X57] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X57))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X72,X57)),X57)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__le__divisor) ).

fof(fact_pos__mod__conj,axiom,
    ! [X62,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)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X62,X90)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X62,X90)),X90)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__mod__conj) ).

fof(fact_pos__mod__bound,axiom,
    ! [X62,X90] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X90))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X62,X90)),X90)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__mod__bound) ).

fof(fact_mod__less__divisor,axiom,
    ! [X72,X57] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X57))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X72,X57)),X57)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__less__divisor) ).

fof(fact_length__remdups__leq,axiom,
    ! [X242,X58] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),c_List_Oremdups(X58,X242))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__remdups__leq) ).

fof(fact_card__length,axiom,
    ! [X239,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),hAPP(c_List_Oset(X5),X239))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__length) ).

fof(fact_image__Pow__surj,axiom,
    ! [X113,X21,X2,X5,X20] :
      ( hAPP(c_Set_Oimage(X20,X5,X2),X21) = X113
     => hAPP(c_Set_Oimage(tc_fun(X20,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool),c_Set_Oimage(X20,X5,X2)),hAPP(c_Set_OPow(X20),X21)) = hAPP(c_Set_OPow(X5),X113) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__Pow__surj) ).

fof(fact_surj__image__vimage__eq,axiom,
    ! [X21,X2,X5,X20] :
      ( hAPP(c_Set_Oimage(X20,X5,X2),c_Orderings_Otop__class_Otop(tc_fun(X20,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))
     => hAPP(c_Set_Oimage(X20,X5,X2),hAPP(c_Set_Ovimage(X20,X5,X2),X21)) = X21 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surj__image__vimage__eq) ).

fof(fact_divmod__int__rel__div,axiom,
    ! [X134,X140,X90,X62] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X62,X90),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X140),X134)))
     => ( X90 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X62),X90) = X140 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__int__rel__div) ).

fof(fact_abs__le__D2,axiom,
    ! [X90,X62,X58] :
      ( class_Groups_Oordered__ab__group__add__abs(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(c_Groups_Oabs__class_Oabs(X58),X62)),X90))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(c_Groups_Ouminus__class_Ouminus(X58),X62)),X90)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__le__D2) ).

fof(fact_minus__le__iff,axiom,
    ! [X24,X6,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X6)),X24))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X24)),X6)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__le__iff) ).

fof(fact_minus__less__iff,axiom,
    ! [X24,X6,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X6)),X24))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X24)),X6)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__less__iff) ).

fof(fact_neg__mod__conj,axiom,
    ! [X62,X90] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X90),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X62,X90)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X90),c_Divides_Odiv__class_Omod(tc_Int_Oint,X62,X90))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__mod__conj) ).

fof(fact_neg__mod__sign,axiom,
    ! [X62,X90] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X90),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X62,X90)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__mod__sign) ).

fof(fact_vimage__Collect__eq,axiom,
    ! [X18,X2,X20,X5] : hAPP(c_Set_Ovimage(X5,X20,X2),hAPP(c_Set_OCollect(X20),X18)) = hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(X20,tc_HOL_Obool,X5),X18),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__Collect__eq) ).

fof(fact_div__eq,axiom,
    ! [X134,X140,X57,X72] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X72,X57),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X140),X134)))
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X72),X57) = X140 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__eq) ).

fof(fact_card__image,axiom,
    ! [X21,X2,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,X2,X21)
     => hAPP(c_Finite__Set_Ocard(X20),hAPP(c_Set_Oimage(X5,X20,X2),X21)) = hAPP(c_Finite__Set_Ocard(X5),X21) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__image) ).

fof(fact_take__drop,axiom,
    ! [X242,X72,X57,X58] : hAPP(hAPP(c_List_Otake(X58),X57),hAPP(hAPP(c_List_Odrop(X58),X72),X242)) = hAPP(hAPP(c_List_Odrop(X58),X72),hAPP(hAPP(c_List_Otake(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X57),X72)),X242)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__drop) ).

fof(fact_sorted__filter,axiom,
    ! [X18,X239,X2,X20,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Omap(X20,X5),X2),X239))
       => c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Omap(X20,X5),X2),hAPP(c_List_Ofilter(X20,X18),X239))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__filter) ).

fof(fact_nat__mod__eq__lemma,axiom,
    ! [X65,X57,X66] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X66,X57) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X65,X57)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X65),X66))
       => ? [X151] : X66 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X65),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X57),X151)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mod__eq__lemma) ).

fof(fact_takeWhile__eq__all__conv,axiom,
    ! [X239,X18,X5] :
      ( c_List_OtakeWhile(X5,X18,X239) = X239
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X239)))
         => hBOOL(hAPP(X18,X3)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_takeWhile__eq__all__conv) ).

fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
    ! [X6,X5] :
      ( class_Groups_Olinordered__ab__group__add(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),X6)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),X6)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__double__add__iff__zero__le__single__add) ).

fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
    ! [X6,X5] :
      ( class_Groups_Olinordered__ab__group__add(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),X6)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X6)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__double__add__iff__zero__less__single__add) ).

fof(fact_Ball__set__list__all,axiom,
    ! [X18,X239,X5] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X239)))
         => hBOOL(hAPP(X18,X3)) )
    <=> c_List_Olist__all(X5,X18,X239) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ball__set__list__all) ).

fof(fact_list__all__iff__raw,axiom,
    ! [X239,X18,X5] :
      ( c_List_Olist__all(X5,X18,X239)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X239)))
         => hBOOL(hAPP(X18,X3)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__all__iff__raw) ).

fof(fact_list__all__iff,axiom,
    ! [X239,X18,X5] :
      ( c_List_Olist__all(X5,X18,X239)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X239)))
         => hBOOL(hAPP(X18,X3)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__all__iff) ).

fof(fact_add__gr__0,axiom,
    ! [X50,X95] :
      ( 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),X95),X50)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X95))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X50)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__gr__0) ).

fof(fact_asm,axiom,
    ! [X4,X13,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool)),X13),X4))
     => c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,X13) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_asm) ).

fof(fact_mod__diff__cong,axiom,
    ! [X143,X90,X150,X56,X62,X58] :
      ( class_Divides_Oring__div(X58)
     => ( c_Divides_Odiv__class_Omod(X58,X62,X56) = c_Divides_Odiv__class_Omod(X58,X150,X56)
       => ( c_Divides_Odiv__class_Omod(X58,X90,X56) = c_Divides_Odiv__class_Omod(X58,X143,X56)
         => c_Divides_Odiv__class_Omod(X58,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X58),X62),X90),X56) = c_Divides_Odiv__class_Omod(X58,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X58),X150),X143),X56) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__diff__cong) ).

fof(fact_mod__mult__cong,axiom,
    ! [X143,X90,X150,X56,X62,X58] :
      ( class_Divides_Osemiring__div(X58)
     => ( c_Divides_Odiv__class_Omod(X58,X62,X56) = c_Divides_Odiv__class_Omod(X58,X150,X56)
       => ( c_Divides_Odiv__class_Omod(X58,X90,X56) = c_Divides_Odiv__class_Omod(X58,X143,X56)
         => c_Divides_Odiv__class_Omod(X58,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X90),X56) = c_Divides_Odiv__class_Omod(X58,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X150),X143),X56) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__cong) ).

fof(fact_mod__add__cong,axiom,
    ! [X143,X90,X150,X56,X62,X58] :
      ( class_Divides_Osemiring__div(X58)
     => ( c_Divides_Odiv__class_Omod(X58,X62,X56) = c_Divides_Odiv__class_Omod(X58,X150,X56)
       => ( c_Divides_Odiv__class_Omod(X58,X90,X56) = c_Divides_Odiv__class_Omod(X58,X143,X56)
         => c_Divides_Odiv__class_Omod(X58,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),X90),X56) = c_Divides_Odiv__class_Omod(X58,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X150),X143),X56) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__add__cong) ).

fof(fact_power__diff,axiom,
    ! [X72,X57,X62,X58] :
      ( class_Fields_Ofield(X58)
     => ( X62 != c_Groups_Ozero__class_Ozero(X58)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X57),X72))
         => hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X72),X57)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),X72)),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),X57)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__diff) ).

fof(fact_divmod__int__rel__neg,axiom,
    ! [X182,X90,X62] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X62),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X90)),X182))
     => hBOOL(hAPP(c_Divides_Odivmod__int__rel(X62,X90),hAPP(c_Divides_OnegateSnd,X182))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__int__rel__neg) ).

fof(fact_evaln__Suc,axiom,
    ! [X75,X57,X48,X56] :
      ( c_Natural_Oevaln(X56,X48,X57,X75)
     => c_Natural_Oevaln(X56,X48,hAPP(c_Nat_OSuc,X57),X75) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln__Suc) ).

fof(fact_insert__Diff1,axiom,
    ! [X21,X113,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X25),X113))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)),X113) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),X113) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__Diff1) ).

fof(fact_Nat_Odiff__diff__eq,axiom,
    ! [X57,X72,X96] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X96),X72))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X96),X57))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X72),X96)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X57),X96)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X72),X57) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat_Odiff__diff__eq) ).

fof(fact_takeWhile__eq__take,axiom,
    ! [X239,X18,X5] : c_List_OtakeWhile(X5,X18,X239) = hAPP(hAPP(c_List_Otake(X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_OtakeWhile(X5,X18,X239))),X239),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_takeWhile__eq__take) ).

fof(fact_ex__nat__less__eq,axiom,
    ! [X18,X50] :
      ( ? [X86] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X86),X50))
          & hBOOL(hAPP(X18,X86)) )
    <=> ? [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)),X50)))
          & hBOOL(hAPP(X18,X3)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ex__nat__less__eq) ).

fof(fact_Suc__diff__diff,axiom,
    ! [X96,X57,X72] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X72)),X57)),hAPP(c_Nat_OSuc,X96)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X72),X57)),X96),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__diff__diff) ).

fof(fact_power__inject__base,axiom,
    ! [X90,X57,X62,X58] :
      ( class_Rings_Olinordered__semidom(X58)
     => ( hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),hAPP(c_Nat_OSuc,X57)) = hAPP(hAPP(c_Power_Opower__class_Opower(X58),X90),hAPP(c_Nat_OSuc,X57))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),X62))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),X90))
           => X62 = X90 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__inject__base) ).

fof(fact_int__zle__neg,axiom,
    ! [X95,X50] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X50)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X95))))
    <=> ( X50 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        & X95 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__zle__neg) ).

fof(fact_wf,axiom,
    ! [X5] :
      ( class_Orderings_Owellorder(X5)
     => c_Wellfounded_Owf(X5,hAPP(c_Set_OCollect(tc_prod(X5,X5)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X5,tc_HOL_Obool),c_Orderings_Oord__class_Oless(X5)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf) ).

fof(fact_inf__greatest,axiom,
    ! [X94,X65,X66,X58] :
      ( class_Lattices_Osemilattice__inf(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X66),X65))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X66),X94))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X66),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X65),X94))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__greatest) ).

fof(fact_le__infI,axiom,
    ! [X90,X62,X66,X58] :
      ( class_Lattices_Osemilattice__inf(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X66),X62))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X66),X90))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X66),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X62),X90))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__infI) ).

fof(fact_le__inf__iff,axiom,
    ! [X120,X33,X25,X5] :
      ( class_Lattices_Osemilattice__inf(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X25),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X33),X120)))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X25),X33))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X25),X120)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__inf__iff) ).

fof(fact_min__max_Ole__inf__iff,axiom,
    ! [X120,X33,X25,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X25),hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X33),X120)))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X25),X33))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X25),X120)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ole__inf__iff) ).

fof(fact_min__max_Ole__infI,axiom,
    ! [X90,X62,X66,X58] :
      ( class_Orderings_Olinorder(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X66),X62))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X66),X90))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X66),hAPP(hAPP(c_Orderings_Oord__class_Omin(X58),X62),X90))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ole__infI) ).

fof(fact_min__max_Oinf__greatest,axiom,
    ! [X94,X65,X66,X58] :
      ( class_Orderings_Olinorder(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X66),X65))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X66),X94))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X66),hAPP(hAPP(c_Orderings_Oord__class_Omin(X58),X65),X94))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__greatest) ).

fof(fact_min__less__iff__conj,axiom,
    ! [X33,X25,X120,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X120),hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X25),X33)))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X120),X25))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X120),X33)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__less__iff__conj) ).

fof(fact_self__quotient__aux2,axiom,
    ! [X140,X134,X62] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X62))
     => ( X62 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X134),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X62),X140))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X134))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X140),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_self__quotient__aux2) ).

fof(fact_filter__id__conv,axiom,
    ! [X239,X18,X5] :
      ( hAPP(c_List_Ofilter(X5,X18),X239) = X239
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X239)))
         => hBOOL(hAPP(X18,X3)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter__id__conv) ).

fof(fact_Divides_Otransfer__nat__int__function__closures_I2_J,axiom,
    ! [X65,X66] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X66))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X65))
       => 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,X66,X65))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Divides_Otransfer__nat__int__function__closures_I2_J) ).

fof(fact_evalc_OSemi,axiom,
    ! [X51,X52,X45,X46,X53] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X53),X46),X45))
     => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X52),X45),X51))
       => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(X53,X52)),X46),X51)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_OSemi) ).

fof(fact_nth__append__length__plus,axiom,
    ! [X57,X241,X242,X58] : hAPP(hAPP(c_List_Onth(X58),hAPP(hAPP(c_List_Oappend(X58),X242),X241)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242)),X57)) = hAPP(hAPP(c_List_Onth(X58),X241),X57),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__append__length__plus) ).

fof(fact_list_Osimps_I5_J,axiom,
    ! [X254,X6,X89,X19,X20,X5] : hAPP(c_List_Olist_Olist__case(X5,X20,X19,X89),hAPP(hAPP(c_List_Olist_OCons(X20),X6),X254)) = hAPP(hAPP(X89,X6),X254),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list_Osimps_I5_J) ).

fof(fact_sup1I1,axiom,
    ! [X113,X5,X25,X21] :
      ( hBOOL(hAPP(X21,X25))
     => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113),X25)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup1I1) ).

fof(fact_sup1I2,axiom,
    ! [X21,X5,X25,X113] :
      ( hBOOL(hAPP(X113,X25))
     => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113),X25)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup1I2) ).

fof(fact_zero__le__power__abs,axiom,
    ! [X57,X62,X58] :
      ( class_Rings_Olinordered__idom(X58)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),hAPP(hAPP(c_Power_Opower__class_Opower(X58),hAPP(c_Groups_Oabs__class_Oabs(X58),X62)),X57))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__power__abs) ).

fof(fact_diff__Suc__diff__eq1,axiom,
    ! [X72,X97,X96] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X96),X97))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X72),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X97),X96))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X72),X96)),hAPP(c_Nat_OSuc,X97)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__diff__eq1) ).

fof(fact_subset__empty,axiom,
    ! [X21,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))
    <=> X21 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__empty) ).

fof(fact_wfP__acyclicP,axiom,
    ! [X171,X5] :
      ( c_Wellfounded_OwfP(X5,X171)
     => c_Wellfounded_Oacyclic(X5,hAPP(c_Set_OCollect(tc_prod(X5,X5)),hAPP(c_Product__Type_Oprod_Oprod__case(X5,X5,tc_HOL_Obool),X171))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfP__acyclicP) ).

fof(fact_rel__comp__empty1,axiom,
    ! [X32,X20,X116,X5] : hAPP(hAPP(c_Relation_Orel__comp(X5,X116,X20),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X116),tc_HOL_Obool))),X32) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X20),tc_HOL_Obool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__comp__empty1) ).

fof(fact_zdiv__zminus1__eq__if,axiom,
    ! [X62,X90] :
      ( X90 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
     => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X62,X90) = 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),X62)),X90) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X62),X90)) )
        & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X62,X90) != 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),X62)),X90) = 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),X62),X90))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zminus1__eq__if) ).

fof(fact_compl__le__compl__iff,axiom,
    ! [X33,X25,X5] :
      ( class_Lattices_Oboolean__algebra(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X25)),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X33)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X33),X25)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compl__le__compl__iff) ).

fof(fact_neg__le__iff__le,axiom,
    ! [X6,X24,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X24)),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X6)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),X24)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__le__iff__le) ).

fof(fact_neg__less__iff__less,axiom,
    ! [X6,X24,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X24)),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X6)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),X24)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__less__iff__less) ).

fof(fact_all__nat__less__eq,axiom,
    ! [X18,X50] :
      ( ! [X86] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X86),X50))
         => hBOOL(hAPP(X18,X86)) )
    <=> ! [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)),X50)))
         => hBOOL(hAPP(X18,X3)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_all__nat__less__eq) ).

fof(fact_power__gt1,axiom,
    ! [X57,X62,X58] :
      ( class_Rings_Olinordered__semidom(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Oone__class_Oone(X58)),X62))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Oone__class_Oone(X58)),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),hAPP(c_Nat_OSuc,X57)))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__gt1) ).

fof(fact_self__quotient__aux1,axiom,
    ! [X140,X134,X62] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X62))
     => ( X62 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X134),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X62),X140))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X134),X62))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X140)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_self__quotient__aux1) ).

fof(fact_conversep_Ointros,axiom,
    ! [X20,X5,X24,X6,X171] :
      ( hBOOL(hAPP(hAPP(X171,X6),X24))
     => hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X5,X20,X171),X24),X6)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_conversep_Ointros) ).

fof(fact_le__number__of,axiom,
    ! [X33,X25,X5] :
      ( ( class_Int_Onumber__ring(X5)
        & class_Rings_Olinordered__idom(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X25)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X33)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25),X33)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__number__of) ).

fof(fact_less__number__of,axiom,
    ! [X33,X25,X5] :
      ( ( class_Int_Onumber__ring(X5)
        & class_Rings_Olinordered__idom(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X25)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X33)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25),X33)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__number__of) ).

fof(fact_list__update__beyond,axiom,
    ! [X66,X98,X242,X58] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242)),X98))
     => hAPP(hAPP(c_List_Olist__update(X58,X242),X98),X66) = X242 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update__beyond) ).

fof(fact_le__cube,axiom,
    ! [X72] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X72),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X72),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X72),X72)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__cube) ).

fof(fact_in__set__butlastD,axiom,
    ! [X239,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),c_List_Obutlast(X5,X239))))
     => hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X239))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__set__butlastD) ).

fof(fact_insert__image,axiom,
    ! [X2,X20,X21,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
     => hAPP(hAPP(c_Set_Oinsert(X20),hAPP(X2,X25)),hAPP(c_Set_Oimage(X5,X20,X2),X21)) = hAPP(c_Set_Oimage(X5,X20,X2),X21) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__image) ).

fof(fact_self__quotient,axiom,
    ! [X134,X140,X62] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X62,X62),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X140),X134)))
     => ( X62 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => X140 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_self__quotient) ).

fof(fact_self__remainder,axiom,
    ! [X134,X140,X62] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X62,X62),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X140),X134)))
     => ( X62 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => X134 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_self__remainder) ).

fof(fact_wf__exp,axiom,
    ! [X32,X50,X5] :
      ( c_Wellfounded_Owf(X5,hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X50),X32))
     => c_Wellfounded_Owf(X5,X32) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__exp) ).

fof(fact_of__int__le__iff,axiom,
    ! [X120,X121,X5] :
      ( class_Rings_Olinordered__idom(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Int_Oring__1__class_Oof__int(X5),X121)),hAPP(c_Int_Oring__1__class_Oof__int(X5),X120)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X121),X120)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__le__iff) ).

fof(fact_of__nat__le__iff,axiom,
    ! [X50,X95,X5] :
      ( class_Rings_Olinordered__semidom(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X95)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X50)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X50)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__le__iff) ).

fof(fact_of__int__less__iff,axiom,
    ! [X120,X121,X5] :
      ( class_Rings_Olinordered__idom(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Oring__1__class_Oof__int(X5),X121)),hAPP(c_Int_Oring__1__class_Oof__int(X5),X120)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X121),X120)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__less__iff) ).

fof(fact_of__nat__less__iff,axiom,
    ! [X50,X95,X5] :
      ( class_Rings_Olinordered__semidom(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X95)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X50)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),X50)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__less__iff) ).

fof(fact_of__nat__less__imp__less,axiom,
    ! [X57,X72,X58] :
      ( class_Rings_Olinordered__semidom(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X58),X72)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X58),X57)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X72),X57)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__less__imp__less) ).

fof(fact_nonzero__power__divide,axiom,
    ! [X57,X62,X90,X58] :
      ( class_Fields_Ofield(X58)
     => ( X90 != c_Groups_Ozero__class_Ozero(X58)
       => hAPP(hAPP(c_Power_Opower__class_Opower(X58),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X62),X90)),X57) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),X57)),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X90),X57)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__power__divide) ).

fof(fact_zless__imp__add1__zle,axiom,
    ! [X94,X128] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X128),X94))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X128),c_Groups_Oone__class_Oone(tc_Int_Oint))),X94)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__imp__add1__zle) ).

fof(fact_Min__Un,axiom,
    ! [X113,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X113))
           => ( X113 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => c_Big__Operators_Olinorder__class_OMin(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),c_Big__Operators_Olinorder__class_OMin(X5,X21)),c_Big__Operators_Olinorder__class_OMin(X5,X113)) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min__Un) ).

fof(fact_Max__Un,axiom,
    ! [X113,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X113))
           => ( X113 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => c_Big__Operators_Olinorder__class_OMax(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),c_Big__Operators_Olinorder__class_OMax(X5,X21)),c_Big__Operators_Olinorder__class_OMax(X5,X113)) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max__Un) ).

fof(fact_Sup__fin_Ounion__idem,axiom,
    ! [X113,X21,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X113))
           => ( X113 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => c_Big__Operators_Olattice__class_OSup__fin(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),c_Big__Operators_Olattice__class_OSup__fin(X5,X21)),c_Big__Operators_Olattice__class_OSup__fin(X5,X113)) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_Ounion__idem) ).

fof(fact_Inf__fin_Ounion__idem,axiom,
    ! [X113,X21,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X113))
           => ( X113 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
             => c_Big__Operators_Olattice__class_OInf__fin(X5,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),c_Big__Operators_Olattice__class_OInf__fin(X5,X21)),c_Big__Operators_Olattice__class_OInf__fin(X5,X113)) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_Ounion__idem) ).

fof(fact_splice_Osimps_I3_J,axiom,
    ! [X241,X65,X242,X66,X58] : c_List_Osplice(X58,hAPP(hAPP(c_List_Olist_OCons(X58),X66),X242),hAPP(hAPP(c_List_Olist_OCons(X58),X65),X241)) = hAPP(hAPP(c_List_Olist_OCons(X58),X66),hAPP(hAPP(c_List_Olist_OCons(X58),X65),c_List_Osplice(X58,X242,X241))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_splice_Osimps_I3_J) ).

fof(fact_code__numeral_Oof__nat__inject,axiom,
    ! [X33,X25] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X25),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X33),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
       => ( hAPP(c_Code__Numeral_Oof__nat,X25) = hAPP(c_Code__Numeral_Oof__nat,X33)
        <=> X25 = X33 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_code__numeral_Oof__nat__inject) ).

fof(fact_nat__le__eq__zle,axiom,
    ! [X120,X121] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X121))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X120)) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X121)),hAPP(c_Int_Onat,X120)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X121),X120)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__eq__zle) ).

fof(fact_nat__less__eq__zless,axiom,
    ! [X120,X121] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X121))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X121)),hAPP(c_Int_Onat,X120)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X121),X120)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__eq__zless) ).

fof(fact_nat__mono__iff,axiom,
    ! [X121,X120] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X120))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X121)),hAPP(c_Int_Onat,X120)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X121),X120)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mono__iff) ).

fof(fact_funpow__swap1,axiom,
    ! [X25,X50,X5,X2] : hAPP(X2,hAPP(hAPP(hAPP(c_Nat_Ocompow(X5,X5),X50),X2),X25)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(X5,X5),X50),X2),hAPP(X2,X25)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funpow__swap1) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
    ! [X90,X72,X62,X58] :
      ( class_Rings_Ocomm__semiring__1(X58)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X72)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X90),X72)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),X90)),X72) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).

fof(fact_inf__sup__distrib2,axiom,
    ! [X66,X94,X65,X58] :
      ( class_Lattices_Odistrib__lattice(X58)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X65),X94)),X66) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X65),X66)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X94),X66)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__distrib2) ).

fof(fact_sup__inf__distrib2,axiom,
    ! [X66,X94,X65,X58] :
      ( class_Lattices_Odistrib__lattice(X58)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X65),X94)),X66) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X65),X66)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X94),X66)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__inf__distrib2) ).

fof(fact_min__max_Osup__inf__distrib2,axiom,
    ! [X66,X94,X65,X58] :
      ( class_Orderings_Olinorder(X58)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(X58),hAPP(hAPP(c_Orderings_Oord__class_Omin(X58),X65),X94)),X66) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X58),hAPP(hAPP(c_Orderings_Oord__class_Omax(X58),X65),X66)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X58),X94),X66)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup__inf__distrib2) ).

fof(fact_min__max_Oinf__sup__distrib2,axiom,
    ! [X66,X94,X65,X58] :
      ( class_Orderings_Olinorder(X58)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(X58),hAPP(hAPP(c_Orderings_Oord__class_Omax(X58),X65),X94)),X66) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X58),hAPP(hAPP(c_Orderings_Oord__class_Omin(X58),X65),X66)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X58),X94),X66)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__sup__distrib2) ).

fof(fact_diff__divide__distrib,axiom,
    ! [X56,X90,X62,X58] :
      ( class_Rings_Odivision__ring(X58)
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X58),X62),X90)),X56) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X58),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X62),X56)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X90),X56)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__divide__distrib) ).

fof(fact_add__divide__distrib,axiom,
    ! [X56,X90,X62,X58] :
      ( class_Rings_Odivision__ring(X58)
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),X90)),X56) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X62),X56)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X90),X56)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__divide__distrib) ).

fof(fact_power__divide,axiom,
    ! [X57,X90,X62,X58] :
      ( class_Fields_Ofield__inverse__zero(X58)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X58),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X62),X90)),X57) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),X57)),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X90),X57)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__divide) ).

fof(fact_power__mult__distrib,axiom,
    ! [X57,X90,X62,X58] :
      ( class_Groups_Ocomm__monoid__mult(X58)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X90)),X57) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),X57)),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X90),X57)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__mult__distrib) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
    ! [X140,X65,X66,X58] :
      ( class_Rings_Ocomm__semiring__1(X58)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X66),X65)),X140) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X66),X140)),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X65),X140)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).

fof(fact_max__diff__distrib__left,axiom,
    ! [X94,X65,X66,X58] :
      ( class_Groups_Oordered__ab__group__add(X58)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X58),hAPP(hAPP(c_Orderings_Oord__class_Omax(X58),X66),X65)),X94) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X58),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X58),X66),X94)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X58),X65),X94)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__diff__distrib__left) ).

fof(fact_min__diff__distrib__left,axiom,
    ! [X94,X65,X66,X58] :
      ( class_Groups_Oordered__ab__group__add(X58)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X58),hAPP(hAPP(c_Orderings_Oord__class_Omin(X58),X66),X65)),X94) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X58),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X58),X66),X94)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X58),X65),X94)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__diff__distrib__left) ).

fof(fact_comm__semiring__class_Odistrib,axiom,
    ! [X56,X90,X62,X58] :
      ( class_Rings_Ocomm__semiring(X58)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),X90)),X56) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X56)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X90),X56)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__class_Odistrib) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
    ! [X56,X90,X62,X58] :
      ( class_Rings_Ocomm__semiring__1(X58)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),X90)),X56) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X56)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X90),X56)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).

fof(fact_max__add__distrib__left,axiom,
    ! [X94,X65,X66,X58] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X58)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(hAPP(c_Orderings_Oord__class_Omax(X58),X66),X65)),X94) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X66),X94)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X65),X94)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__add__distrib__left) ).

fof(fact_min__add__distrib__left,axiom,
    ! [X94,X65,X66,X58] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X58)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(hAPP(c_Orderings_Oord__class_Omin(X58),X66),X65)),X94) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X66),X94)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X65),X94)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__add__distrib__left) ).

fof(fact_set__insort,axiom,
    ! [X239,X25,X2,X5,X20] :
      ( class_Orderings_Olinorder(X20)
     => hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X20,X2),X25),X239)) = hAPP(hAPP(c_Set_Oinsert(X5),X25),hAPP(c_List_Oset(X5),X239)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__insort) ).

fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom,
    ! [X65,X66] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X66))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X65))
       => 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),X66),X65))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Divides_Otransfer__nat__int__function__closures_I1_J) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
    ! [X65,X66] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X66))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X65))
       => 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),X66),X65))) ) ),
    file('/export/starexec/sandbox/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,
    ! [X65,X66] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X66))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X65))
       => 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),X66),X65))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).

fof(fact_nat__0__less__mult__iff,axiom,
    ! [X50,X95] :
      ( 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),X95),X50)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X95))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X50)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__0__less__mult__iff) ).

fof(fact_ivl__disj__un_I1_J,axiom,
    ! [X156,X5] :
      ( class_Orderings_Olinorder(X5)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X156),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(X5),X156)) = hAPP(c_SetInterval_Oord__class_OatLeast(X5),X156) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I1_J) ).

fof(fact_finite__converse,axiom,
    ! [X171,X20,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X5,X20)),hAPP(c_Relation_Oconverse(X20,X5),X171)))
    <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X20,X5)),X171)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__converse) ).

fof(fact_finite__UNIV__card__ge__0,axiom,
    ! [X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X5),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UNIV__card__ge__0) ).

fof(fact_set__remove1__eq,axiom,
    ! [X25,X239,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),X239))
     => hAPP(c_List_Oset(X5),c_List_Oremove1(X5,X25,X239)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),X239)),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__remove1__eq) ).

fof(fact_Int__Union,axiom,
    ! [X113,X21,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X113)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X113),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__Union) ).

fof(fact_Un__Inter,axiom,
    ! [X113,X21,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),X113)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X113),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Inter) ).

fof(fact_length__insort,axiom,
    ! [X239,X25,X2,X5,X20] :
      ( class_Orderings_Olinorder(X20)
     => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X20,X2),X25),X239)) = hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__insort) ).

fof(fact_nat__less__iff,axiom,
    ! [X95,X121] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X121))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X121)),X95))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X121),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X95))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__iff) ).

fof(fact_remove1__insort,axiom,
    ! [X239,X25,X5] :
      ( class_Orderings_Olinorder(X5)
     => c_List_Oremove1(X5,X25,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X5,c_COMBI(X5)),X25),X239)) = X239 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_remove1__insort) ).

fof(fact_Powp__def,axiom,
    ! [X113,X21,X5] :
      ( hBOOL(hAPP(c_Predicate_OPowp(X5,X21),X113))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),X113))
         => hBOOL(hAPP(X21,X3)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Powp__def) ).

fof(fact_split__curry,axiom,
    ! [X2,X116,X20,X5] : hAPP(c_Product__Type_Oprod_Oprod__case(X5,X20,X116),c_Product__Type_Ocurry(X5,X20,X116,X2)) = X2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__curry) ).

fof(fact_eq__number__of__eq,axiom,
    ! [X33,X25,X5] :
      ( class_Int_Onumber__ring(X5)
     => ( hAPP(c_Int_Onumber__class_Onumber__of(X5),X25) = hAPP(c_Int_Onumber__class_Onumber__of(X5),X33)
      <=> c_Int_Oiszero(X5,hAPP(c_Int_Onumber__class_Onumber__of(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X33)))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__number__of__eq) ).

fof(fact_append__eq__conv__conj,axiom,
    ! [X250,X251,X239,X5] :
      ( hAPP(hAPP(c_List_Oappend(X5),X239),X251) = X250
    <=> ( X239 = hAPP(hAPP(c_List_Otake(X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239)),X250)
        & X251 = hAPP(hAPP(c_List_Odrop(X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239)),X250) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__eq__conv__conj) ).

fof(fact_zdiv__zminus2__eq__if,axiom,
    ! [X62,X90] :
      ( X90 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
     => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X62,X90) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X62),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X90)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X62),X90)) )
        & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X62,X90) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X62),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X90)) = 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),X62),X90))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zminus2__eq__if) ).

fof(fact_singleton__conv,axiom,
    ! [X6,X5] : hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X6)) = hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_singleton__conv) ).

fof(fact_insert__is__Un,axiom,
    ! [X21,X6,X5] : hAPP(hAPP(c_Set_Oinsert(X5),X6),X21) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),X21),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__is__Un) ).

fof(fact_evalc__elim__cases_I2_J,axiom,
    ! [X15,X76,X6,X194] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(X194,X6)),X76),X15))
     => X15 = hAPP(hAPP(hAPP(c_Natural_Oupdate,X76),X194),hAPP(X6,X76)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc__elim__cases_I2_J) ).

fof(fact_nat__of__induct,axiom,
    ! [X18,X33] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X33),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
     => ( ! [X3] : hBOOL(hAPP(X18,hAPP(c_Code__Numeral_Onat__of,X3)))
       => hBOOL(hAPP(X18,X33)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__of__induct) ).

fof(fact_less__imp__diff__less,axiom,
    ! [X57,X96,X97] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X97),X96))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X97),X57)),X96)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__diff__less) ).

fof(fact_add__diff__assoc2,axiom,
    ! [X98,X97,X96] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X96),X97))
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X97),X96)),X98) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X97),X98)),X96) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__diff__assoc2) ).

fof(fact_diff__add__assoc2,axiom,
    ! [X98,X97,X96] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X96),X97))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X97),X98)),X96) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X97),X96)),X98) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__assoc2) ).

fof(fact_Int__absorb2,axiom,
    ! [X113,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),X113))
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113) = X21 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__absorb2) ).

fof(fact_Int__absorb1,axiom,
    ! [X21,X113,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X113),X21))
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113) = X113 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__absorb1) ).

fof(fact_subset__Un__eq,axiom,
    ! [X113,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),X113))
    <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113) = X113 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__Un__eq) ).

fof(fact_Un__absorb1,axiom,
    ! [X113,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),X113))
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113) = X113 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__absorb1) ).

fof(fact_Un__absorb2,axiom,
    ! [X21,X113,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X113),X21))
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113) = X21 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__absorb2) ).

fof(fact_Collect__neg__eq,axiom,
    ! [X18,X5] : hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),X18)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_OCollect(X5),X18)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__neg__eq) ).

fof(fact_drop__all,axiom,
    ! [X57,X242,X58] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242)),X57))
     => hAPP(hAPP(c_List_Odrop(X58),X57),X242) = c_List_Olist_ONil(X58) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__all) ).

fof(fact_drop__eq__Nil,axiom,
    ! [X239,X50,X5] :
      ( hAPP(hAPP(c_List_Odrop(X5),X50),X239) = c_List_Olist_ONil(X5)
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239)),X50)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__eq__Nil) ).

fof(fact_insert__iff,axiom,
    ! [X21,X24,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(hAPP(c_Set_Oinsert(X5),X24),X21)))
    <=> ( X6 = X24
        | hBOOL(hAPP(hAPP(c_member(X5),X6),X21)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__iff) ).

fof(fact_insertE,axiom,
    ! [X21,X24,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(hAPP(c_Set_Oinsert(X5),X24),X21)))
     => ( X6 != X24
       => hBOOL(hAPP(hAPP(c_member(X5),X6),X21)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertE) ).

fof(fact_take__all,axiom,
    ! [X57,X242,X58] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242)),X57))
     => hAPP(hAPP(c_List_Otake(X58),X57),X242) = X242 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__all) ).

fof(fact_ivl__diff,axiom,
    ! [X95,X50,X82,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X82),X50))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X82),X95)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X82),X50)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X50),X95) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__diff) ).

fof(fact_accp_Osimps,axiom,
    ! [X6,X171,X5] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(X5,X171),X6))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(X171,X3),X6))
         => hBOOL(hAPP(c_Wellfounded_Oaccp(X5,X171),X3)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_accp_Osimps) ).

fof(fact_accp_Oequations,axiom,
    ! [X6,X171,X5] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(X5,X171),X6))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(X171,X3),X6))
         => hBOOL(hAPP(c_Wellfounded_Oaccp(X5,X171),X3)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_accp_Oequations) ).

fof(fact_Times__empty,axiom,
    ! [X113,X21,X20,X5] :
      ( hAPP(hAPP(c_Product__Type_OSigma(X5,X20),X21),hAPP(c_COMBK(tc_fun(X20,tc_HOL_Obool),X5),X113)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X20),tc_HOL_Obool))
    <=> ( X21 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
        | X113 = c_Orderings_Obot__class_Obot(tc_fun(X20,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Times__empty) ).

fof(fact_ivl__disj__un_I13_J,axiom,
    ! [X159,X156,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X156),X159))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X156,X159)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X5),X159)) = hAPP(c_SetInterval_Oord__class_OatLeast(X5),X156) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I13_J) ).

fof(fact_ivl__disj__un_I11_J,axiom,
    ! [X159,X156,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X156),X159))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X156,X159)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X5),X159)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X5),X156) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I11_J) ).

fof(fact_ivl__disj__un_I12_J,axiom,
    ! [X159,X156,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X156),X159))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X156,X159)),hAPP(c_SetInterval_Oord__class_OatLeast(X5),X159)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X5),X156) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I12_J) ).

fof(fact_Inf__set__fold,axiom,
    ! [X239,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => c_Complete__Lattice_OInf__class_OInf(X5,hAPP(c_List_Oset(X5),X239)) = hAPP(c_List_Ofoldl(X5,X5,c_Lattices_Osemilattice__inf__class_Oinf(X5),c_Orderings_Otop__class_Otop(X5)),X239) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__set__fold) ).

fof(fact_Sup__set__fold,axiom,
    ! [X239,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => c_Complete__Lattice_OSup__class_OSup(X5,hAPP(c_List_Oset(X5),X239)) = hAPP(c_List_Ofoldl(X5,X5,c_Lattices_Osemilattice__sup__class_Osup(X5),c_Orderings_Obot__class_Obot(X5)),X239) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__set__fold) ).

fof(fact_card__atLeastAtMost__int,axiom,
    ! [X159,X156] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X156,X159)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X159),X156)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__atLeastAtMost__int) ).

fof(fact_finite__imageI,axiom,
    ! [X122,X20,X205,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X205))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X20),hAPP(c_Set_Oimage(X5,X20,X122),X205))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__imageI) ).

fof(fact_Inf__binary,axiom,
    ! [X24,X6,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => c_Complete__Lattice_OInf__class_OInf(X5,hAPP(hAPP(c_Set_Oinsert(X5),X6),hAPP(hAPP(c_Set_Oinsert(X5),X24),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X6),X24) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__binary) ).

fof(fact_Sup__binary,axiom,
    ! [X24,X6,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => c_Complete__Lattice_OSup__class_OSup(X5,hAPP(hAPP(c_Set_Oinsert(X5),X6),hAPP(hAPP(c_Set_Oinsert(X5),X24),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X6),X24) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__binary) ).

fof(fact_ord_OlessThan__iff,axiom,
    ! [X87,X209,X82,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X82),c_SetInterval_Oord_OlessThan(X5,X209,X87)))
    <=> hBOOL(hAPP(hAPP(X209,X82),X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord_OlessThan__iff) ).

fof(fact_ord_OatMost__iff,axiom,
    ! [X87,X208,X82,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X82),c_SetInterval_Oord_OatMost(X5,X208,X87)))
    <=> hBOOL(hAPP(hAPP(X208,X82),X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord_OatMost__iff) ).

fof(fact_ord_OgreaterThan__iff,axiom,
    ! [X87,X209,X82,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X82),c_SetInterval_Oord_OgreaterThan(X5,X209,X87)))
    <=> hBOOL(hAPP(hAPP(X209,X87),X82)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord_OgreaterThan__iff) ).

fof(fact_ord_OatLeast__iff,axiom,
    ! [X87,X208,X82,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X82),c_SetInterval_Oord_OatLeast(X5,X208,X87)))
    <=> hBOOL(hAPP(hAPP(X208,X87),X82)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord_OatLeast__iff) ).

fof(fact_partition__set,axiom,
    ! [X278,X279,X239,X18,X5] :
      ( c_List_Opartition(X5,X18,X239) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X279),X278)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),X279)),hAPP(c_List_Oset(X5),X278)) = hAPP(c_List_Oset(X5),X239) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_partition__set) ).

fof(fact_nth__Cons__number__of,axiom,
    ! [X242,X66,X58,X136] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Onth(X58),hAPP(hAPP(c_List_Olist_OCons(X58),X66),X242)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)) = X66 )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Onth(X58),hAPP(hAPP(c_List_Olist_OCons(X58),X66),X242)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)) = hAPP(hAPP(c_List_Onth(X58),X242),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__Cons__number__of) ).

fof(fact_r__comp__rtrancl__eq,axiom,
    ! [X171,X5] : hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),X171),c_Transitive__Closure_Ortrancl(X5,X171)) = hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),c_Transitive__Closure_Ortrancl(X5,X171)),X171),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_r__comp__rtrancl__eq) ).

fof(help_c__COMBS__1,axiom,
    ! [X32,X16,X18,X5,X116,X20] : hAPP(hAPP(hAPP(c_COMBS(X20,X116,X5),X18),X16),X32) = hAPP(hAPP(X18,X32),hAPP(X16,X32)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBS__1) ).

fof(fact_abs__minus__le__zero,axiom,
    ! [X62,X58] :
      ( class_Groups_Oordered__ab__group__add__abs(X58)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(c_Groups_Ouminus__class_Ouminus(X58),hAPP(c_Groups_Oabs__class_Oabs(X58),X62))),c_Groups_Ozero__class_Ozero(X58))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__minus__le__zero) ).

fof(fact_Un__insert__right,axiom,
    ! [X113,X6,X21,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X6),X113)) = hAPP(hAPP(c_Set_Oinsert(X5),X6),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__insert__right) ).

fof(fact_sum__squares__eq__zero__iff,axiom,
    ! [X33,X25,X5] :
      ( class_Rings_Olinordered__ring__strict(X5)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X25),X25)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X33),X33)) = c_Groups_Ozero__class_Ozero(X5)
      <=> ( X25 = c_Groups_Ozero__class_Ozero(X5)
          & X33 = c_Groups_Ozero__class_Ozero(X5) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__squares__eq__zero__iff) ).

fof(fact_union__fold__insert,axiom,
    ! [X113,X21,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113) = hAPP(hAPP(c_Finite__Set_Ofold(X5,tc_fun(X5,tc_HOL_Obool),c_Set_Oinsert(X5)),X113),X21) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_union__fold__insert) ).

fof(fact_eq__special_I3_J,axiom,
    ! [X25,X5] :
      ( class_Int_Onumber__ring(X5)
     => ( hAPP(c_Int_Onumber__class_Onumber__of(X5),X25) = c_Groups_Ozero__class_Ozero(X5)
      <=> c_Int_Oiszero(X5,hAPP(c_Int_Onumber__class_Onumber__of(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls)))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__special_I3_J) ).

fof(fact_eq__special_I1_J,axiom,
    ! [X33,X5] :
      ( class_Int_Onumber__ring(X5)
     => ( c_Groups_Ozero__class_Ozero(X5) = hAPP(c_Int_Onumber__class_Onumber__of(X5),X33)
      <=> c_Int_Oiszero(X5,hAPP(c_Int_Onumber__class_Onumber__of(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X33)))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__special_I1_J) ).

fof(fact_trans__lex__prod,axiom,
    ! [X189,X20,X190,X5] :
      ( c_Relation_Otrans(X5,X190)
     => ( c_Relation_Otrans(X20,X189)
       => c_Relation_Otrans(tc_prod(X5,X20),c_Wellfounded_Olex__prod(X5,X20,X190,X189)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__lex__prod) ).

fof(fact_wf__lex__prod,axiom,
    ! [X245,X20,X246,X5] :
      ( c_Wellfounded_Owf(X5,X246)
     => ( c_Wellfounded_Owf(X20,X245)
       => c_Wellfounded_Owf(tc_prod(X5,X20),c_Wellfounded_Olex__prod(X5,X20,X246,X245)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__lex__prod) ).

fof(fact_distinct__zipI1,axiom,
    ! [X241,X5,X242,X58] :
      ( hBOOL(hAPP(c_List_Odistinct(X58),X242))
     => hBOOL(hAPP(c_List_Odistinct(tc_prod(X58,X5)),hAPP(hAPP(c_List_Ozip(X58,X5),X242),X241))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__zipI1) ).

fof(fact_distinct__zipI2,axiom,
    ! [X242,X5,X241,X58] :
      ( hBOOL(hAPP(c_List_Odistinct(X58),X241))
     => hBOOL(hAPP(c_List_Odistinct(tc_prod(X5,X58)),hAPP(hAPP(c_List_Ozip(X5,X58),X242),X241))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__zipI2) ).

fof(fact_vimage__Union,axiom,
    ! [X21,X2,X20,X5] : hAPP(c_Set_Ovimage(X5,X20,X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X20,tc_HOL_Obool),X21)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X20,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X21),c_Set_Ovimage(X5,X20,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__Union) ).

fof(fact_image__Union,axiom,
    ! [X192,X2,X5,X20] : hAPP(c_Set_Oimage(X20,X5,X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X20,tc_HOL_Obool),X192)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X20,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X192),c_Set_Oimage(X20,X5,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__Union) ).

fof(fact_Pow__bottom,axiom,
    ! [X113,X5] : hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),hAPP(c_Set_OPow(X5),X113))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__bottom) ).

fof(fact_listsum__0,axiom,
    ! [X239,X20,X5] :
      ( class_Groups_Omonoid__add(X5)
     => hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(X20,X5),hAPP(c_COMBK(X5,X20),c_Groups_Ozero__class_Ozero(X5))),X239)) = c_Groups_Ozero__class_Ozero(X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__0) ).

fof(fact_Int__left__absorb,axiom,
    ! [X113,X21,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__left__absorb) ).

fof(fact_Un__left__absorb,axiom,
    ! [X113,X21,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__left__absorb) ).

fof(fact_Un__Diff__cancel,axiom,
    ! [X113,X21,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X113),X21)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Diff__cancel) ).

fof(fact_rotate1__length01,axiom,
    ! [X242,X58] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
     => hAPP(c_List_Orotate1(X58),X242) = X242 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate1__length01) ).

fof(fact_fold__image__empty,axiom,
    ! [X120,X1,X2,X20,X5] : hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X5,X20,X2),X1),X120),c_Orderings_Obot__class_Obot(tc_fun(X20,tc_HOL_Obool))) = X120,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__image__empty) ).

fof(fact_mult__eq__if,axiom,
    ! [X57,X72] :
      ( ( X72 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X72),X57) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X72 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X72),X57) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X57),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X72),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X57)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__eq__if) ).

fof(fact_listsp__inf__eq,axiom,
    ! [X113,X21,X5] : c_List_Olistsp(X5,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),c_List_Olistsp(X5,X21)),c_List_Olistsp(X5,X113)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsp__inf__eq) ).

fof(fact_triple_Osimps_I2_J,axiom,
    ! [X10,X11,X12,X19,X5,X20] : c_Hoare__Mirabelle_Otriple_Otriple__case(X20,X5,X19,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X20),X12),X11),X10)) = hAPP(hAPP(hAPP(X19,X12),X11),X10),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_triple_Osimps_I2_J) ).

fof(fact_triple_Orecs,axiom,
    ! [X10,X11,X12,X19,X5,X20] : c_Hoare__Mirabelle_Otriple_Otriple__rec(X20,X5,X19,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X20),X12),X11),X10)) = hAPP(hAPP(hAPP(X19,X12),X11),X10),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_triple_Orecs) ).

fof(fact_RangeP_Oequations,axiom,
    ! [X26,X171,X20,X5] :
      ( hBOOL(hAPP(c_Predicate_ORangeP(X5,X20,X171),X26))
    <=> ? [X187] : hBOOL(hAPP(hAPP(X171,X187),X26)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_RangeP_Oequations) ).

fof(fact_nat__mult__distrib__neg,axiom,
    ! [X135,X94] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X94),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X94),X135)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X94))),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X135))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__distrib__neg) ).

fof(fact_pair__box_Osize_I2_J,axiom,
    ! [X90,X62,X5,X58] : hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(X58,X5)),c_Nitpick_Opair__box_OPairBox(X58,X5,X62,X90)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__box_Osize_I2_J) ).

fof(fact_butlast__list__update,axiom,
    ! [X66,X242,X58,X96] :
      ( ( X96 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
       => c_List_Obutlast(X58,hAPP(hAPP(c_List_Olist__update(X58,X242),X96),X66)) = c_List_Obutlast(X58,X242) )
      & ( X96 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
       => c_List_Obutlast(X58,hAPP(hAPP(c_List_Olist__update(X58,X242),X96),X66)) = hAPP(hAPP(c_List_Olist__update(X58,c_List_Obutlast(X58,X242)),X96),X66) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_butlast__list__update) ).

fof(fact_image__insert,axiom,
    ! [X113,X6,X2,X5,X20] : hAPP(c_Set_Oimage(X20,X5,X2),hAPP(hAPP(c_Set_Oinsert(X20),X6),X113)) = hAPP(hAPP(c_Set_Oinsert(X5),hAPP(X2,X6)),hAPP(c_Set_Oimage(X20,X5,X2),X113)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__insert) ).

fof(fact_finite__subset,axiom,
    ! [X113,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),X113))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X113))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__subset) ).

fof(fact_rev__finite__subset,axiom,
    ! [X21,X113,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X113))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),X113))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__finite__subset) ).

fof(fact_neg__le__0__iff__le,axiom,
    ! [X6,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X6)),c_Groups_Ozero__class_Ozero(X5)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),X6)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__le__0__iff__le) ).

fof(fact_neg__less__0__iff__less,axiom,
    ! [X6,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X6)),c_Groups_Ozero__class_Ozero(X5)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X6)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__less__0__iff__less) ).

fof(fact_length__sort,axiom,
    ! [X239,X2,X5,X20] :
      ( class_Orderings_Olinorder(X20)
     => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_Olinorder__class_Osort__key(X5,X20,X2,X239)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__sort) ).

fof(fact_zip__rev,axiom,
    ! [X241,X5,X242,X58] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X241)
     => hAPP(hAPP(c_List_Ozip(X58,X5),hAPP(c_List_Orev(X58),X242)),hAPP(c_List_Orev(X5),X241)) = hAPP(c_List_Orev(tc_prod(X58,X5)),hAPP(hAPP(c_List_Ozip(X58,X5),X242),X241)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__rev) ).

fof(fact_nat__zero__less__power__iff,axiom,
    ! [X50,X25] :
      ( 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),X25),X50)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25))
        | X50 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__zero__less__power__iff) ).

fof(fact_Int__atLeastAtMostL2,axiom,
    ! [X23,X24,X6,X5] :
      ( class_Orderings_Olinorder(X5)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,X24)),hAPP(c_SetInterval_Oord__class_OatLeast(X5),X23)) = c_SetInterval_Oord__class_OatLeastAtMost(X5,hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X6),X23),X24) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__atLeastAtMostL2) ).

fof(fact_Int__atLeastAtMostL1,axiom,
    ! [X22,X24,X6,X5] :
      ( class_Orderings_Olinorder(X5)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,X24)),hAPP(c_SetInterval_Oord__class_OatMost(X5),X22)) = c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X24),X22)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__atLeastAtMostL1) ).

fof(fact_list__update__code_I2_J,axiom,
    ! [X65,X242,X66,X58] : hAPP(hAPP(c_List_Olist__update(X58,hAPP(hAPP(c_List_Olist_OCons(X58),X66),X242)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X65) = hAPP(hAPP(c_List_Olist_OCons(X58),X65),X242),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update__code_I2_J) ).

fof(help_c__COMBC__1,axiom,
    ! [X32,X16,X18,X5,X116,X20] : hAPP(hAPP(hAPP(c_COMBC(X20,X116,X5),X18),X16),X32) = hAPP(hAPP(X18,X32),X16),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBC__1) ).

fof(help_c__COMBB__1,axiom,
    ! [X32,X16,X18,X116,X5,X20] : hAPP(hAPP(hAPP(c_COMBB(X20,X5,X116),X18),X16),X32) = hAPP(X18,hAPP(X16,X32)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBB__1) ).

fof(fact_vimage__Compl,axiom,
    ! [X21,X2,X20,X5] : hAPP(c_Set_Ovimage(X5,X20,X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20,tc_HOL_Obool)),X21)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X5,X20,X2),X21)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__Compl) ).

fof(fact_mod__mult__self3,axiom,
    ! [X72,X57,X96] : 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),X96),X57)),X72),X57) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X72,X57),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__self3) ).

fof(fact_Divides_Otransfer__nat__int__functions_I1_J,axiom,
    ! [X65,X66] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X66))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X65))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,X66)),hAPP(c_Int_Onat,X65)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X66),X65)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Divides_Otransfer__nat__int__functions_I1_J) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J,axiom,
    ! [X65,X66] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X66))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X65))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,X66)),hAPP(c_Int_Onat,X65)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X66),X65)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J,axiom,
    ! [X65,X66] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X66))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X65))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,X66)),hAPP(c_Int_Onat,X65)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X66),X65)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J) ).

fof(fact_nat__add__distrib,axiom,
    ! [X135,X94] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X94))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X135))
       => hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X94),X135)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,X94)),hAPP(c_Int_Onat,X135)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__distrib) ).

fof(fact_length__zip,axiom,
    ! [X241,X242,X5,X58] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(X58,X5))),hAPP(hAPP(c_List_Ozip(X58,X5),X242),X241)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X241)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__zip) ).

fof(fact_Inter__image__eq,axiom,
    ! [X21,X113,X20,X5] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),hAPP(c_Set_Oimage(X20,tc_fun(X5,tc_HOL_Obool),X113),X21)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X20,tc_fun(X5,tc_HOL_Obool)),X21),X113),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__image__eq) ).

fof(fact_Union__image__eq,axiom,
    ! [X21,X113,X20,X5] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),hAPP(c_Set_Oimage(X20,tc_fun(X5,tc_HOL_Obool),X113),X21)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,tc_fun(X5,tc_HOL_Obool)),X21),X113),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__image__eq) ).

fof(fact_INTER__eq__Inter__image,axiom,
    ! [X113,X21,X5,X20] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X20,tc_fun(X5,tc_HOL_Obool)),X21),X113) = c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),hAPP(c_Set_Oimage(X20,tc_fun(X5,tc_HOL_Obool),X113),X21)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INTER__eq__Inter__image) ).

fof(fact_UNION__eq__Union__image,axiom,
    ! [X113,X21,X5,X20] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,tc_fun(X5,tc_HOL_Obool)),X21),X113) = c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),hAPP(c_Set_Oimage(X20,tc_fun(X5,tc_HOL_Obool),X113),X21)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNION__eq__Union__image) ).

fof(fact_of__nat__aux_Osimps_I2_J,axiom,
    ! [X82,X50,X83,X5] :
      ( class_Rings_Osemiring__1(X5)
     => c_Nat_Osemiring__1__class_Oof__nat__aux(X5,X83,hAPP(c_Nat_OSuc,X50),X82) = c_Nat_Osemiring__1__class_Oof__nat__aux(X5,X83,X50,hAPP(X83,X82)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__aux_Osimps_I2_J) ).

fof(fact_Divides_Otransfer__nat__int__functions_I2_J,axiom,
    ! [X65,X66] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X66))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X65))
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,X66),hAPP(c_Int_Onat,X65)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,X66,X65)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Divides_Otransfer__nat__int__functions_I2_J) ).

fof(fact_nat__mod__distrib,axiom,
    ! [X65,X66] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X66))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X65))
       => hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,X66,X65)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,X66),hAPP(c_Int_Onat,X65)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mod__distrib) ).

fof(fact_zmod__zdiv__equality_H,axiom,
    ! [X57,X72] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X72,X57) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X72),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X72),X57)),X57)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zdiv__equality_H) ).

fof(fact_Divides_Omod__div__equality_H,axiom,
    ! [X57,X72] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X72,X57) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X72),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X72),X57)),X57)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Divides_Omod__div__equality_H) ).

fof(fact_one__le__power,axiom,
    ! [X57,X62,X58] :
      ( class_Rings_Olinordered__semidom(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Oone__class_Oone(X58)),X62))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Oone__class_Oone(X58)),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),X57))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__le__power) ).

fof(fact_zero__le__power,axiom,
    ! [X57,X62,X58] :
      ( class_Rings_Olinordered__semidom(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),X62))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),X57))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__power) ).

fof(fact_zero__less__power,axiom,
    ! [X57,X62,X58] :
      ( class_Rings_Olinordered__semidom(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),X62))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),X57))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__power) ).

fof(fact_image__constant,axiom,
    ! [X23,X20,X21,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
     => hAPP(c_Set_Oimage(X5,X20,hAPP(c_COMBK(X20,X5),X23)),X21) = hAPP(hAPP(c_Set_Oinsert(X20),X23),c_Orderings_Obot__class_Obot(tc_fun(X20,tc_HOL_Obool))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__constant) ).

fof(fact_zless__nat__conj,axiom,
    ! [X120,X121] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X121)),hAPP(c_Int_Onat,X120)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X120))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X121),X120)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__nat__conj) ).

fof(fact_UNIV__Times__UNIV,axiom,
    ! [X20,X5] : hAPP(hAPP(c_Product__Type_OSigma(X5,X20),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X20,tc_HOL_Obool),X5),c_Orderings_Otop__class_Otop(tc_fun(X20,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X5,X20),tc_HOL_Obool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__Times__UNIV) ).

fof(fact_zless__add1__eq,axiom,
    ! [X120,X121] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X121),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X120),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X121),X120))
        | X121 = X120 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__add1__eq) ).

fof(fact_minus__le__self__iff,axiom,
    ! [X6,X5] :
      ( class_Groups_Olinordered__ab__group__add(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X6)),X6))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),X6)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__le__self__iff) ).

fof(fact_neg__less__nonneg,axiom,
    ! [X6,X5] :
      ( class_Groups_Olinordered__ab__group__add(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X6)),X6))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X6)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__less__nonneg) ).

fof(fact_append__in__listsp__conv,axiom,
    ! [X251,X239,X21,X5] :
      ( hBOOL(hAPP(c_List_Olistsp(X5,X21),hAPP(hAPP(c_List_Oappend(X5),X239),X251)))
    <=> ( hBOOL(hAPP(c_List_Olistsp(X5,X21),X239))
        & hBOOL(hAPP(c_List_Olistsp(X5,X21),X251)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__in__listsp__conv) ).

fof(fact_funpow__mult,axiom,
    ! [X2,X95,X50,X5] : hAPP(hAPP(c_Nat_Ocompow(X5,X5),X50),hAPP(hAPP(c_Nat_Ocompow(X5,X5),X95),X2)) = hAPP(hAPP(c_Nat_Ocompow(X5,X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X95),X50)),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funpow__mult) ).

fof(fact_less__eq__number__of__int__code,axiom,
    ! [X156,X87] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X87)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X156)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X87),X156)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__number__of__int__code) ).

fof(fact_zle__int,axiom,
    ! [X50,X95] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X95)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X50)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X50)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__int) ).

fof(fact_transfer__int__nat__relations_I3_J,axiom,
    ! [X33,X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(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),X33)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25),X33)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__relations_I3_J) ).

fof(fact_less__number__of__int__code,axiom,
    ! [X156,X87] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X87)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X156)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X87),X156)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__number__of__int__code) ).

fof(fact_transfer__int__nat__relations_I2_J,axiom,
    ! [X33,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_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X33)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),X33)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__relations_I2_J) ).

fof(fact_zless__int,axiom,
    ! [X50,X95] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X95)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X50)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),X50)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__int) ).

fof(fact_zero__less__diff,axiom,
    ! [X95,X50] :
      ( 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),X50),X95)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),X50)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__diff) ).

fof(fact_zle__add1__eq__le,axiom,
    ! [X120,X121] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X121),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X120),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X121),X120)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__add1__eq__le) ).

fof(fact_zle__diff1__eq,axiom,
    ! [X120,X121] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X121),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X120),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X121),X120)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__diff1__eq) ).

fof(fact_minus__number__of__mult,axiom,
    ! [X94,X128,X58] :
      ( class_Int_Onumber__ring(X58)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),hAPP(c_Groups_Ouminus__class_Ouminus(X58),hAPP(c_Int_Onumber__class_Onumber__of(X58),X128))),X94) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),hAPP(c_Int_Onumber__class_Onumber__of(X58),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X128))),X94) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__number__of__mult) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
    ! [X72,X62,X58] :
      ( class_Rings_Ocomm__semiring__1(X58)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X72)),X72) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),c_Groups_Oone__class_Oone(X58))),X72) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).

fof(fact_list__update__same__conv,axiom,
    ! [X25,X239,X5,X82] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X82),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239)))
     => ( hAPP(hAPP(c_List_Olist__update(X5,X239),X82),X25) = X239
      <=> hAPP(hAPP(c_List_Onth(X5),X239),X82) = X25 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update__same__conv) ).

fof(fact_evaln__elim__cases_I2_J,axiom,
    ! [X15,X50,X76,X6,X194] :
      ( c_Natural_Oevaln(c_Com_Ocom_OAss(X194,X6),X76,X50,X15)
     => X15 = hAPP(hAPP(hAPP(c_Natural_Oupdate,X76),X194),hAPP(X6,X76)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln__elim__cases_I2_J) ).

fof(fact_negative__zle,axiom,
    ! [X72,X57] : 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),X57))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X72))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negative__zle) ).

fof(fact_zero__le__zpower__abs,axiom,
    ! [X57,X66] : 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),X66)),X57))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__zpower__abs) ).

fof(fact_min__diff,axiom,
    ! [X57,X98,X72] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X72),X98)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X57),X98)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X72),X57)),X98),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__diff) ).

fof(fact_zdiff__zmult__distrib,axiom,
    ! [X128,X126,X127] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X127),X126)),X128) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X127),X128)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X126),X128)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiff__zmult__distrib) ).

fof(fact_zadd__zmult__distrib,axiom,
    ! [X128,X126,X127] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X127),X126)),X128) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X127),X128)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X126),X128)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__zmult__distrib) ).

fof(fact_diff__mult__distrib,axiom,
    ! [X96,X57,X72] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X72),X57)),X96) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X72),X96)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X57),X96)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__mult__distrib) ).

fof(fact_add__mult__distrib,axiom,
    ! [X96,X57,X72] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X72),X57)),X96) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X72),X96)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X57),X96)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__mult__distrib) ).

fof(fact_nth_Osimps,axiom,
    ! [X50,X239,X25,X5] : hAPP(hAPP(c_List_Onth(X5),hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239)),X50) = c_Nat_Onat_Onat__case(X5,X25,hAPP(c_List_Onth(X5),X239),X50),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth_Osimps) ).

fof(fact_replicate__length__filter,axiom,
    ! [X239,X25,X5] : c_List_Oreplicate(X5,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),hAPP(c_List_Ofilter(X5,hAPP(c_fequal,X25)),X239)),X25) = hAPP(c_List_Ofilter(X5,hAPP(c_fequal,X25)),X239),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_replicate__length__filter) ).

fof(fact_Plus__eq__empty__conv,axiom,
    ! [X113,X21,X20,X5] :
      ( c_Sum__Type_OPlus(X5,X20,X21,X113) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X5,X20),tc_HOL_Obool))
    <=> ( X21 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
        & X113 = c_Orderings_Obot__class_Obot(tc_fun(X20,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Plus__eq__empty__conv) ).

fof(fact_set__sort,axiom,
    ! [X239,X2,X5,X20] :
      ( class_Orderings_Olinorder(X20)
     => hAPP(c_List_Oset(X5),c_List_Olinorder__class_Osort__key(X5,X20,X2,X239)) = hAPP(c_List_Oset(X5),X239) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__sort) ).

fof(fact_replicate__append__same,axiom,
    ! [X66,X98,X58] : hAPP(hAPP(c_List_Oappend(X58),c_List_Oreplicate(X58,X98,X66)),hAPP(hAPP(c_List_Olist_OCons(X58),X66),c_List_Olist_ONil(X58))) = hAPP(hAPP(c_List_Olist_OCons(X58),X66),c_List_Oreplicate(X58,X98,X66)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_replicate__append__same) ).

fof(fact_Inter__insert,axiom,
    ! [X113,X6,X5] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X5,tc_HOL_Obool)),X6),X113)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X6),c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),X113)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__insert) ).

fof(fact_Union__insert,axiom,
    ! [X113,X6,X5] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X5,tc_HOL_Obool)),X6),X113)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X6),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X113)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__insert) ).

fof(fact_wf__no__loop,axiom,
    ! [X32,X5] :
      ( hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),X32),X32) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X5),tc_HOL_Obool))
     => c_Wellfounded_Owf(X5,X32) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__no__loop) ).

fof(fact_add__eq__if,axiom,
    ! [X57,X72] :
      ( ( X72 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X72),X57) = X57 )
      & ( X72 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X72),X57) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X72),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X57)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__eq__if) ).

fof(fact_setsum__constant,axiom,
    ! [X21,X33,X20,X5] :
      ( class_Rings_Osemiring__1(X5)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X20,X5),hAPP(c_COMBK(X5,X20),X33)),X21) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),hAPP(c_Finite__Set_Ocard(X20),X21))),X33) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__constant) ).

fof(fact_of__int__le__0__iff,axiom,
    ! [X120,X5] :
      ( class_Rings_Olinordered__idom(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Int_Oring__1__class_Oof__int(X5),X120)),c_Groups_Ozero__class_Ozero(X5)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X120),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__le__0__iff) ).

fof(fact_of__int__less__0__iff,axiom,
    ! [X120,X5] :
      ( class_Rings_Olinordered__idom(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Oring__1__class_Oof__int(X5),X120)),c_Groups_Ozero__class_Ozero(X5)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X120),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__less__0__iff) ).

fof(fact_zmod__simps_I2_J,axiom,
    ! [X56,X90,X62,X58] :
      ( class_Divides_Osemiring__div(X58)
     => c_Divides_Odiv__class_Omod(X58,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),c_Divides_Odiv__class_Omod(X58,X90,X56)),X56) = c_Divides_Odiv__class_Omod(X58,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),X90),X56) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__simps_I2_J) ).

fof(fact_mod__diff__right__eq,axiom,
    ! [X56,X90,X62,X58] :
      ( class_Divides_Oring__div(X58)
     => c_Divides_Odiv__class_Omod(X58,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X58),X62),X90),X56) = c_Divides_Odiv__class_Omod(X58,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X58),X62),c_Divides_Odiv__class_Omod(X58,X90,X56)),X56) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__diff__right__eq) ).

fof(fact_mod__mult__right__eq,axiom,
    ! [X56,X90,X62,X58] :
      ( class_Divides_Osemiring__div(X58)
     => c_Divides_Odiv__class_Omod(X58,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X90),X56) = c_Divides_Odiv__class_Omod(X58,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),c_Divides_Odiv__class_Omod(X58,X90,X56)),X56) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__right__eq) ).

fof(fact_mod__add__right__eq,axiom,
    ! [X56,X90,X62,X58] :
      ( class_Divides_Osemiring__div(X58)
     => c_Divides_Odiv__class_Omod(X58,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),X90),X56) = c_Divides_Odiv__class_Omod(X58,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),c_Divides_Odiv__class_Omod(X58,X90,X56)),X56) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__add__right__eq) ).

fof(fact_predicate1D,axiom,
    ! [X25,X16,X18,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X18),X16))
     => ( hBOOL(hAPP(X18,X25))
       => hBOOL(hAPP(X16,X25)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_predicate1D) ).

fof(fact_rev__predicate1D,axiom,
    ! [X16,X5,X25,X18] :
      ( hBOOL(hAPP(X18,X25))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X18),X16))
       => hBOOL(hAPP(X16,X25)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__predicate1D) ).

fof(fact_nat__diff__distrib,axiom,
    ! [X94,X135] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X135))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X135),X94))
       => hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X94),X135)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X94)),hAPP(c_Int_Onat,X135)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__diff__distrib) ).

fof(fact_listsp_Oequations_I2_J,axiom,
    ! [X26,X27,X21,X5] :
      ( hBOOL(hAPP(c_List_Olistsp(X5,X21),hAPP(hAPP(c_List_Olist_OCons(X5),X27),X26)))
    <=> ( hBOOL(hAPP(X21,X27))
        & hBOOL(hAPP(c_List_Olistsp(X5,X21),X26)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsp_Oequations_I2_J) ).

fof(fact_ivl__disj__un_I14_J,axiom,
    ! [X159,X156,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X156),X159))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X156),X159)),hAPP(c_SetInterval_Oord__class_OatLeast(X5),X159)) = hAPP(c_SetInterval_Oord__class_OatLeast(X5),X156) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I14_J) ).

fof(fact_le__special_I3_J,axiom,
    ! [X25,X5] :
      ( ( class_Int_Onumber__ring(X5)
        & class_Rings_Olinordered__idom(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X25)),c_Groups_Ozero__class_Ozero(X5)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25),c_Int_OPls)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__special_I3_J) ).

fof(fact_less__special_I3_J,axiom,
    ! [X25,X5] :
      ( ( class_Int_Onumber__ring(X5)
        & class_Rings_Olinordered__idom(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X25)),c_Groups_Ozero__class_Ozero(X5)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25),c_Int_OPls)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__special_I3_J) ).

fof(fact_map__fst__zip,axiom,
    ! [X251,X20,X239,X5] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X20)),X251)
     => hAPP(hAPP(c_List_Omap(tc_prod(X5,X20),X5),c_Product__Type_Ofst(X5,X20)),hAPP(hAPP(c_List_Ozip(X5,X20),X239),X251)) = X239 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__fst__zip) ).

fof(fact_map__snd__zip,axiom,
    ! [X251,X20,X239,X5] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X20)),X251)
     => hAPP(hAPP(c_List_Omap(tc_prod(X5,X20),X20),c_Product__Type_Osnd(X5,X20)),hAPP(hAPP(c_List_Ozip(X5,X20),X239),X251)) = X251 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__snd__zip) ).

fof(fact_div__add__self1,axiom,
    ! [X62,X90,X58] :
      ( class_Divides_Osemiring__div(X58)
     => ( X90 != c_Groups_Ozero__class_Ozero(X58)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X90),X62)),X90) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X58),X62),X90)),c_Groups_Oone__class_Oone(X58)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__add__self1) ).

fof(fact_div__add__self2,axiom,
    ! [X62,X90,X58] :
      ( class_Divides_Osemiring__div(X58)
     => ( X90 != c_Groups_Ozero__class_Ozero(X58)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),X90)),X90) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X58),X62),X90)),c_Groups_Oone__class_Oone(X58)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__add__self2) ).

fof(fact_mod__mult__mult2,axiom,
    ! [X90,X56,X62,X58] :
      ( class_Divides_Osemiring__div(X58)
     => c_Divides_Odiv__class_Omod(X58,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X56),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X90),X56)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),c_Divides_Odiv__class_Omod(X58,X62,X90)),X56) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__mult2) ).

fof(fact_nat__abs__mult__distrib,axiom,
    ! [X94,X128] : hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X128),X94))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X128))),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X94))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__abs__mult__distrib) ).

fof(fact_nat__mult__div__cancel1,axiom,
    ! [X57,X72,X96] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X96))
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X96),X72)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X96),X57)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X72),X57) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__div__cancel1) ).

fof(fact_zdiv__zmult2__eq,axiom,
    ! [X90,X62,X56] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X56))
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X62),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X90),X56)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X62),X90)),X56) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zmult2__eq) ).

fof(fact_split__def,axiom,
    ! [X160,X23,X5,X116,X20] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X20,X116,X5),X23),X160) = hAPP(hAPP(X23,hAPP(c_Product__Type_Ofst(X20,X116),X160)),hAPP(c_Product__Type_Osnd(X20,X116),X160)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__def) ).

fof(fact_split__beta,axiom,
    ! [X120,X18,X5,X116,X20] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X20,X116,X5),X18),X120) = hAPP(hAPP(X18,hAPP(c_Product__Type_Ofst(X20,X116),X120)),hAPP(c_Product__Type_Osnd(X20,X116),X120)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__beta) ).

fof(fact_prod__case__beta,axiom,
    ! [X160,X2,X5,X116,X20] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X20,X116,X5),X2),X160) = hAPP(hAPP(X2,hAPP(c_Product__Type_Ofst(X20,X116),X160)),hAPP(c_Product__Type_Osnd(X20,X116),X160)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_prod__case__beta) ).

fof(fact_sorted__sort,axiom,
    ! [X239,X5] :
      ( class_Orderings_Olinorder(X5)
     => c_List_Olinorder__class_Osorted(X5,c_List_Olinorder__class_Osort__key(X5,X5,c_COMBI(X5),X239)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__sort) ).

fof(fact_append1__eq__conv,axiom,
    ! [X33,X251,X25,X239,X5] :
      ( hAPP(hAPP(c_List_Oappend(X5),X239),hAPP(hAPP(c_List_Olist_OCons(X5),X25),c_List_Olist_ONil(X5))) = hAPP(hAPP(c_List_Oappend(X5),X251),hAPP(hAPP(c_List_Olist_OCons(X5),X33),c_List_Olist_ONil(X5)))
    <=> ( X239 = X251
        & X25 = X33 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append1__eq__conv) ).

fof(fact_hd__drop__conv__nth,axiom,
    ! [X57,X58,X242] :
      ( X242 != c_List_Olist_ONil(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X57),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242)))
       => hAPP(c_List_Ohd(X58),hAPP(hAPP(c_List_Odrop(X58),X57),X242)) = hAPP(hAPP(c_List_Onth(X58),X242),X57) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hd__drop__conv__nth) ).

fof(fact_abs__add__abs,axiom,
    ! [X90,X62,X58] :
      ( class_Groups_Oordered__ab__group__add__abs(X58)
     => hAPP(c_Groups_Oabs__class_Oabs(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(c_Groups_Oabs__class_Oabs(X58),X62)),hAPP(c_Groups_Oabs__class_Oabs(X58),X90))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(c_Groups_Oabs__class_Oabs(X58),X62)),hAPP(c_Groups_Oabs__class_Oabs(X58),X90)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__add__abs) ).

fof(fact_folding__one__idem_Oeq__fold__idem_H,axiom,
    ! [X6,X21,X205,X2,X5] :
      ( c_Finite__Set_Ofolding__one__idem(X5,X2,X205)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => hAPP(X205,hAPP(hAPP(c_Set_Oinsert(X5),X6),X21)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,X2),X6),X21) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Oeq__fold__idem_H) ).

fof(fact_inf__le1,axiom,
    ! [X65,X66,X58] :
      ( class_Lattices_Osemilattice__inf(X58)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X66),X65)),X66)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__le1) ).

fof(fact_inf__sup__ord_I1_J,axiom,
    ! [X65,X66,X58] :
      ( class_Lattices_Olattice(X58)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X66),X65)),X66)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__ord_I1_J) ).

fof(fact_inf__le2,axiom,
    ! [X65,X66,X58] :
      ( class_Lattices_Osemilattice__inf(X58)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X66),X65)),X65)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__le2) ).

fof(fact_inf__sup__ord_I2_J,axiom,
    ! [X65,X66,X58] :
      ( class_Lattices_Olattice(X58)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X66),X65)),X65)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__ord_I2_J) ).

fof(fact_min__max_Oinf__le1,axiom,
    ! [X65,X66,X58] :
      ( class_Orderings_Olinorder(X58)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Orderings_Oord__class_Omin(X58),X66),X65)),X66)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__le1) ).

fof(fact_min__max_Oinf__le2,axiom,
    ! [X65,X66,X58] :
      ( class_Orderings_Olinorder(X58)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Orderings_Oord__class_Omin(X58),X66),X65)),X65)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__le2) ).

fof(fact_expand__Suc,axiom,
    ! [X136] :
      ( 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),X136)))
     => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_expand__Suc) ).

fof(fact_evalc__evaln,axiom,
    ! [X54,X48,X56] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X56),X48),X54))
     => ? [X69] : c_Natural_Oevaln(X56,X48,X69,X54) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc__evaln) ).

fof(fact_eval__eq,axiom,
    ! [X15,X76,X23] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X23),X76),X15))
    <=> ? [X69] : c_Natural_Oevaln(X23,X76,X69,X15) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eval__eq) ).

fof(fact_ivl__disj__un_I10_J,axiom,
    ! [X159,X156,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X156),X159))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X5),X156)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X156,X159)) = hAPP(c_SetInterval_Oord__class_OatMost(X5),X159) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I10_J) ).

fof(fact_ivl__disj__un_I9_J,axiom,
    ! [X159,X156,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X156),X159))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X5),X156)),c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X156,X159)) = hAPP(c_SetInterval_Oord__class_OatMost(X5),X159) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I9_J) ).

fof(fact_ivl__disj__un_I7_J,axiom,
    ! [X159,X156,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X156),X159))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X5),X156)),c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X156,X159)) = hAPP(c_SetInterval_Oord__class_OlessThan(X5),X159) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I7_J) ).

fof(fact_abs__le__D1,axiom,
    ! [X90,X62,X58] :
      ( class_Groups_Oordered__ab__group__add__abs(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(c_Groups_Oabs__class_Oabs(X58),X62)),X90))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X62),X90)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__le__D1) ).

fof(fact_inf__sup__distrib1,axiom,
    ! [X94,X65,X66,X58] :
      ( class_Lattices_Odistrib__lattice(X58)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X66),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X65),X94)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X66),X65)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X66),X94)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__distrib1) ).

fof(fact_sup__inf__distrib1,axiom,
    ! [X94,X65,X66,X58] :
      ( class_Lattices_Odistrib__lattice(X58)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X66),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X65),X94)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X66),X65)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X66),X94)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__inf__distrib1) ).

fof(fact_min__max_Osup__inf__distrib1,axiom,
    ! [X94,X65,X66,X58] :
      ( class_Orderings_Olinorder(X58)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(X58),X66),hAPP(hAPP(c_Orderings_Oord__class_Omin(X58),X65),X94)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X58),hAPP(hAPP(c_Orderings_Oord__class_Omax(X58),X66),X65)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X58),X66),X94)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup__inf__distrib1) ).

fof(fact_min__max_Oinf__sup__distrib1,axiom,
    ! [X94,X65,X66,X58] :
      ( class_Orderings_Olinorder(X58)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(X58),X66),hAPP(hAPP(c_Orderings_Oord__class_Omax(X58),X65),X94)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X58),hAPP(hAPP(c_Orderings_Oord__class_Omin(X58),X66),X65)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X58),X66),X94)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__sup__distrib1) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
    ! [X94,X65,X66,X58] :
      ( class_Rings_Ocomm__semiring__1(X58)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X66),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X65),X94)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X66),X65)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X66),X94)) ),
    file('/export/starexec/sandbox/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,
    ! [X130,X131,X132,X58] :
      ( class_Rings_Ocomm__semiring__1(X58)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X132),X131)),X130) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X132),X130)),X131) ),
    file('/export/starexec/sandbox/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,
    ! [X56,X90,X62,X58] :
      ( class_Rings_Ocomm__semiring__1(X58)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),X90)),X56) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),X56)),X90) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).

fof(fact_id__o,axiom,
    ! [X1,X5,X20] : hAPP(c_Fun_Ocomp(X20,X20,X5,c_Fun_Oid(X20)),X1) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_id__o) ).

fof(fact_length__pos__if__in__set,axiom,
    ! [X239,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X239)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__pos__if__in__set) ).

fof(fact_single__valued__rel__pow,axiom,
    ! [X50,X32,X5] :
      ( c_Relation_Osingle__valued(X5,X5,X32)
     => c_Relation_Osingle__valued(X5,X5,hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X50),X32)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valued__rel__pow) ).

fof(fact_Random__Sequence_Osingle__def,axiom,
    ! [X293,X294,X25,X5] : hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(X5),X25),X294),X293) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_DSequence_Osingle(X5),X25)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Random__Sequence_Osingle__def) ).

fof(fact_DomainP_Oequations,axiom,
    ! [X27,X171,X20,X5] :
      ( hBOOL(hAPP(c_Predicate_ODomainP(X5,X20,X171),X27))
    <=> ? [X138] : hBOOL(hAPP(hAPP(X171,X27),X138)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DomainP_Oequations) ).

fof(fact_inj__eq,axiom,
    ! [X33,X25,X2,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => ( hAPP(X2,X25) = hAPP(X2,X33)
      <=> X25 = X33 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__eq) ).

fof(fact_injD,axiom,
    ! [X33,X25,X2,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
     => ( hAPP(X2,X25) = hAPP(X2,X33)
       => X25 = X33 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_injD) ).

fof(fact_replicate__add,axiom,
    ! [X66,X72,X57,X58] : c_List_Oreplicate(X58,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X57),X72),X66) = hAPP(hAPP(c_List_Oappend(X58),c_List_Oreplicate(X58,X57,X66)),c_List_Oreplicate(X58,X72,X66)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_replicate__add) ).

fof(fact_min__max_OInf__fin_Oeq__fold__idem_H,axiom,
    ! [X6,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),hAPP(hAPP(c_Set_Oinsert(X5),X6),X21)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omin(X5)),X6),X21) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Oeq__fold__idem_H) ).

fof(fact_min__max_OSup__fin_Oeq__fold__idem_H,axiom,
    ! [X6,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),hAPP(hAPP(c_Set_Oinsert(X5),X6),X21)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omax(X5)),X6),X21) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Oeq__fold__idem_H) ).

fof(fact_foldl__Nil,axiom,
    ! [X6,X2,X20,X5] : hAPP(c_List_Ofoldl(X5,X20,X2,X6),c_List_Olist_ONil(X20)) = X6,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldl__Nil) ).

fof(fact_list_Osimps_I4_J,axiom,
    ! [X89,X19,X20,X5] : hAPP(c_List_Olist_Olist__case(X5,X20,X19,X89),c_List_Olist_ONil(X20)) = X19,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list_Osimps_I4_J) ).

fof(fact_o__id,axiom,
    ! [X2,X20,X5] : hAPP(c_Fun_Ocomp(X5,X20,X5,X2),c_Fun_Oid(X5)) = X2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__id) ).

fof(fact_add__nonneg__eq__0__iff,axiom,
    ! [X33,X25,X5] :
      ( class_Groups_Oordered__comm__monoid__add(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),X25))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),X33))
         => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X25),X33) = c_Groups_Ozero__class_Ozero(X5)
          <=> ( X25 = c_Groups_Ozero__class_Ozero(X5)
              & X33 = c_Groups_Ozero__class_Ozero(X5) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonneg__eq__0__iff) ).

fof(fact_diff__add__assoc,axiom,
    ! [X98,X97,X96] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X96),X97))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),X97)),X96) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X97),X96)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__assoc) ).

fof(fact_diff__diff__right,axiom,
    ! [X98,X97,X96] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X96),X97))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X98),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X97),X96)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),X96)),X97) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__diff__right) ).

fof(fact_add__diff__assoc,axiom,
    ! [X98,X97,X96] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X96),X97))
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X97),X96)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),X97)),X96) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__diff__assoc) ).

fof(fact_compl__mono,axiom,
    ! [X65,X66,X58] :
      ( class_Lattices_Oboolean__algebra(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X66),X65))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(c_Groups_Ouminus__class_Ouminus(X58),X65)),hAPP(c_Groups_Ouminus__class_Ouminus(X58),X66))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compl__mono) ).

fof(fact_le__imp__neg__le,axiom,
    ! [X90,X62,X58] :
      ( class_Groups_Oordered__ab__group__add(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X62),X90))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(c_Groups_Ouminus__class_Ouminus(X58),X90)),hAPP(c_Groups_Ouminus__class_Ouminus(X58),X62))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__neg__le) ).

fof(fact_one__less__nat__eq,axiom,
    ! [X120] :
      ( 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,X120)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X120)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__less__nat__eq) ).

fof(fact_mod__less__eq__dividend,axiom,
    ! [X57,X72] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X72,X57)),X72)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__less__eq__dividend) ).

fof(fact_greaterThan__Suc,axiom,
    ! [X87] : hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X87)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),X87)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X87)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThan__Suc) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
    ! [X140,X162,X66,X58] :
      ( class_Rings_Ocomm__semiring__1(X58)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X66),X162)),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X66),X140)) = hAPP(hAPP(c_Power_Opower__class_Opower(X58),X66),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X162),X140)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).

fof(fact_power__add,axiom,
    ! [X57,X72,X62,X58] :
      ( class_Groups_Omonoid__mult(X58)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X72),X57)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),X72)),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),X57)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__add) ).

fof(fact_fold1__eq__fold__idem,axiom,
    ! [X6,X21,X5] :
      ( class_Lattices_Oab__semigroup__idem__mult(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),hAPP(hAPP(c_Set_Oinsert(X5),X6),X21)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Groups_Otimes__class_Otimes(X5)),X6),X21) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__eq__fold__idem) ).

fof(fact_add__scale__eq__noteq,axiom,
    ! [X91,X56,X90,X62,X134,X58] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X58)
     => ( X134 != c_Groups_Ozero__class_Ozero(X58)
       => ( ( X62 = X90
            & X56 != X91 )
         => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X134),X56)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X90),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X134),X91)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__scale__eq__noteq) ).

fof(fact_some__eq__trivial,axiom,
    ! [X25,X5] : c_Hilbert__Choice_OEps(X5,hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X25)) = X25,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_some__eq__trivial) ).

fof(fact_the__eq__trivial,axiom,
    ! [X6,X5] : c_HOL_OThe(X5,hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X6)) = X6,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__eq__trivial) ).

fof(fact_diff__less__Suc,axiom,
    ! [X57,X72] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X72),X57)),hAPP(c_Nat_OSuc,X72))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__less__Suc) ).

fof(fact_less__add__Suc1,axiom,
    ! [X72,X98] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),X72)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__Suc1) ).

fof(fact_less__add__Suc2,axiom,
    ! [X72,X98] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X72),X98)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__Suc2) ).

fof(fact_ivl__disj__int_I16_J,axiom,
    ! [X159,X95,X156,X5] :
      ( class_Orderings_Oorder(X5)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X156,X95)),c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X95,X159)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I16_J) ).

fof(fact_ivl__disj__int_I12_J,axiom,
    ! [X159,X95,X156,X5] :
      ( class_Orderings_Oorder(X5)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X156,X95)),c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X95,X159)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I12_J) ).

fof(fact_ivl__disj__int_I14_J,axiom,
    ! [X159,X95,X156,X5] :
      ( class_Orderings_Oorder(X5)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X156,X95)),c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X95,X159)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I14_J) ).

fof(fact_ivl__disj__int_I10_J,axiom,
    ! [X159,X95,X156,X5] :
      ( class_Orderings_Oorder(X5)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X156,X95)),c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X95,X159)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I10_J) ).

fof(fact_ivl__disj__int_I13_J,axiom,
    ! [X159,X95,X156,X5] :
      ( class_Orderings_Oorder(X5)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X156,X95)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X95,X159)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I13_J) ).

fof(fact_empty__subsetI,axiom,
    ! [X21,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),X21)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__subsetI) ).

fof(fact_equiv__comp__eq,axiom,
    ! [X171,X21,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X21,X171)
     => hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),hAPP(c_Relation_Oconverse(X5,X5),X171)),X171) = X171 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equiv__comp__eq) ).

fof(fact_evaln__evalc,axiom,
    ! [X54,X57,X48,X56] :
      ( c_Natural_Oevaln(X56,X48,X57,X54)
     => hBOOL(hAPP(hAPP(c_Natural_Oevalc(X56),X48),X54)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln__evalc) ).

fof(fact_evaln_Oequations_I2_J,axiom,
    ! [X60,X63,X26,X27] : c_Natural_Oevaln(c_Com_Ocom_OAss(X27,X26),X63,X60,hAPP(hAPP(hAPP(c_Natural_Oupdate,X63),X27),hAPP(X26,X63))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_Oequations_I2_J) ).

fof(fact_evaln_OAssign,axiom,
    ! [X50,X76,X6,X194] : c_Natural_Oevaln(c_Com_Ocom_OAss(X194,X6),X76,X50,hAPP(hAPP(hAPP(c_Natural_Oupdate,X76),X194),hAPP(X6,X76))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_OAssign) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom,
    ! [X65,X66] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X66))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X65))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat__Transfer_Otsub(X66,X65))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J) ).

fof(fact_subset__insertI,axiom,
    ! [X6,X113,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X113),hAPP(hAPP(c_Set_Oinsert(X5),X6),X113))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__insertI) ).

fof(fact_zdiff__zmod__right,axiom,
    ! [X72,X65,X66] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X66),c_Divides_Odiv__class_Omod(tc_Int_Oint,X65,X72)),X72) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X66),X65),X72),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiff__zmod__right) ).

fof(fact_zmod__simps_I3_J,axiom,
    ! [X56,X90,X62] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X62),c_Divides_Odiv__class_Omod(tc_Int_Oint,X90,X56)),X56) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X62),X90),X56),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__simps_I3_J) ).

fof(fact_zmod__zmult1__eq,axiom,
    ! [X56,X90,X62] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X62),X90),X56) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X62),c_Divides_Odiv__class_Omod(tc_Int_Oint,X90,X56)),X56),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zmult1__eq) ).

fof(fact_ivl__disj__un_I8_J,axiom,
    ! [X159,X156,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X156),X159))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X5),X156)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X156),X159)) = hAPP(c_SetInterval_Oord__class_OlessThan(X5),X159) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I8_J) ).

fof(fact_atLeastAtMostSuc__conv,axiom,
    ! [X50,X95] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),hAPP(c_Nat_OSuc,X50)))
     => c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X95,hAPP(c_Nat_OSuc,X50)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X50)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X95,X50)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastAtMostSuc__conv) ).

fof(fact_finite__option__UNIV,axiom,
    ! [X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X5)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X5),tc_HOL_Obool))))
    <=> hBOOL(hAPP(c_Finite__Set_Ofinite(X5),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__option__UNIV) ).

fof(fact_less__imp__of__nat__less,axiom,
    ! [X57,X72,X58] :
      ( class_Rings_Olinordered__semidom(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X72),X57))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X58),X72)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X58),X57))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__of__nat__less) ).

fof(fact_Int__atLeastAtMostR2,axiom,
    ! [X22,X23,X6,X5] :
      ( class_Orderings_Olinorder(X5)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X5),X6)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X23,X22)) = c_SetInterval_Oord__class_OatLeastAtMost(X5,hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X6),X23),X22) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__atLeastAtMostR2) ).

fof(fact_Int__atLeastAtMostR1,axiom,
    ! [X22,X23,X24,X5] :
      ( class_Orderings_Olinorder(X5)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X5),X24)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X23,X22)) = c_SetInterval_Oord__class_OatLeastAtMost(X5,X23,hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X24),X22)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__atLeastAtMostR1) ).

fof(fact_zless__nat__eq__int__zless,axiom,
    ! [X120,X95] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),hAPP(c_Int_Onat,X120)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X95)),X120)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__nat__eq__int__zless) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J,axiom,
    ! [X65,X66] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X66))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X65))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X66)),hAPP(c_Int_Onat,X65)) = hAPP(c_Int_Onat,c_Nat__Transfer_Otsub(X66,X65)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J) ).

fof(fact_drop__take,axiom,
    ! [X242,X72,X57,X58] : hAPP(hAPP(c_List_Odrop(X58),X57),hAPP(hAPP(c_List_Otake(X58),X72),X242)) = hAPP(hAPP(c_List_Otake(X58),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X72),X57)),hAPP(hAPP(c_List_Odrop(X58),X57),X242)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__take) ).

fof(fact_rel__comp__empty2,axiom,
    ! [X32,X20,X116,X5] : hAPP(hAPP(c_Relation_Orel__comp(X5,X116,X20),X32),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X116,X20),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X20),tc_HOL_Obool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__comp__empty2) ).

fof(fact_curry__split,axiom,
    ! [X2,X116,X20,X5] : c_Product__Type_Ocurry(X5,X20,X116,hAPP(c_Product__Type_Oprod_Oprod__case(X5,X20,X116),X2)) = X2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_curry__split) ).

fof(fact_mod__pos__pos__1__number__of,axiom,
    ! [X128] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)))
     => 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),X128)) = 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),X128))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__pos__pos__1__number__of) ).

fof(fact_mod__mult__distrib,axiom,
    ! [X96,X57,X72] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X72,X57)),X96) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X72),X96),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X57),X96)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__distrib) ).

fof(fact_le__supI1,axiom,
    ! [X90,X62,X66,X58] :
      ( class_Lattices_Osemilattice__sup(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X66),X62))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X66),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X62),X90))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__supI1) ).

fof(fact_le__supI2,axiom,
    ! [X62,X90,X66,X58] :
      ( class_Lattices_Osemilattice__sup(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X66),X90))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X66),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X62),X90))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__supI2) ).

fof(fact_min__max_Ole__supI1,axiom,
    ! [X90,X62,X66,X58] :
      ( class_Orderings_Olinorder(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X66),X62))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X66),hAPP(hAPP(c_Orderings_Oord__class_Omax(X58),X62),X90))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ole__supI1) ).

fof(fact_min__max_Ole__supI2,axiom,
    ! [X62,X90,X66,X58] :
      ( class_Orderings_Olinorder(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X66),X90))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X66),hAPP(hAPP(c_Orderings_Oord__class_Omax(X58),X62),X90))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ole__supI2) ).

fof(fact_less__supI1,axiom,
    ! [X90,X62,X66,X58] :
      ( class_Lattices_Osemilattice__sup(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X66),X62))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X66),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X62),X90))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__supI1) ).

fof(fact_less__supI2,axiom,
    ! [X62,X90,X66,X58] :
      ( class_Lattices_Osemilattice__sup(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X66),X90))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X66),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X62),X90))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__supI2) ).

fof(fact_min__max_Oless__supI1,axiom,
    ! [X90,X62,X66,X58] :
      ( class_Orderings_Olinorder(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X66),X62))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X66),hAPP(hAPP(c_Orderings_Oord__class_Omax(X58),X62),X90))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oless__supI1) ).

fof(fact_min__max_Oless__supI2,axiom,
    ! [X62,X90,X66,X58] :
      ( class_Orderings_Olinorder(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X66),X90))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X66),hAPP(hAPP(c_Orderings_Oord__class_Omax(X58),X62),X90))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oless__supI2) ).

fof(fact_negative__zle__0,axiom,
    ! [X57] : 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),X57))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negative__zle__0) ).

fof(fact_transpose__empty,axiom,
    ! [X239,X5] :
      ( c_List_Otranspose(X5,X239) = c_List_Olist_ONil(tc_List_Olist(X5))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),X3),hAPP(c_List_Oset(tc_List_Olist(X5)),X239)))
         => X3 = c_List_Olist_ONil(X5) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose__empty) ).

fof(fact_setsum__shift__lb__Suc0__0__upt,axiom,
    ! [X87,X2,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => ( hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(X5)
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X87)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X87)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__shift__lb__Suc0__0__upt) ).

fof(fact_UN__empty2,axiom,
    ! [X21,X5,X20] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X20,tc_fun(X5,tc_HOL_Obool)),X21),hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__empty2) ).

fof(fact_less__trans__Suc,axiom,
    ! [X96,X97,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),X97))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X97),X96))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X98)),X96)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__trans__Suc) ).

fof(fact_div__pos__pos__1__number__of,axiom,
    ! [X128] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)))
     => 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),X128)) = 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),X128))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__pos__pos__1__number__of) ).

fof(fact_pos__mod__sign,axiom,
    ! [X62,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)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X62,X90))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__mod__sign) ).

fof(fact_greaterThanLessThan__upto,axiom,
    ! [X157,X82] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X82,X157) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X82),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X157),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThanLessThan__upto) ).

fof(fact_map_Osimps_I2_J,axiom,
    ! [X239,X25,X2,X5,X20] : hAPP(hAPP(c_List_Omap(X20,X5),X2),hAPP(hAPP(c_List_Olist_OCons(X20),X25),X239)) = hAPP(hAPP(c_List_Olist_OCons(X5),hAPP(X2,X25)),hAPP(hAPP(c_List_Omap(X20,X5),X2),X239)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map_Osimps_I2_J) ).

fof(fact_power__one__over,axiom,
    ! [X57,X62,X58] :
      ( class_Fields_Ofield__inverse__zero(X58)
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),c_Groups_Oone__class_Oone(X58)),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),X57)) = hAPP(hAPP(c_Power_Opower__class_Opower(X58),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),c_Groups_Oone__class_Oone(X58)),X62)),X57) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__one__over) ).

fof(fact_le__imp__0__less,axiom,
    ! [X94] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X94))
     => 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)),X94))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__0__less) ).

fof(fact_insertI2,axiom,
    ! [X24,X113,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),X113))
     => hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(hAPP(c_Set_Oinsert(X5),X24),X113))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertI2) ).

fof(fact_le__minus__iff,axiom,
    ! [X24,X6,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X24)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X24),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X6))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__minus__iff) ).

fof(fact_less__minus__iff,axiom,
    ! [X24,X6,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X24)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X24),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X6))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__minus__iff) ).

fof(fact_last__list__update,axiom,
    ! [X66,X96,X58,X242] :
      ( X242 != c_List_Olist_ONil(X58)
     => ( ( X96 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
         => c_List_Olast(X58,hAPP(hAPP(c_List_Olist__update(X58,X242),X96),X66)) = X66 )
        & ( X96 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
         => c_List_Olast(X58,hAPP(hAPP(c_List_Olist__update(X58,X242),X96),X66)) = c_List_Olast(X58,X242) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__list__update) ).

fof(fact_sgn__less,axiom,
    ! [X6,X5] :
      ( class_Rings_Olinordered__idom(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Osgn__class_Osgn(X5,X6)),c_Groups_Ozero__class_Ozero(X5)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),c_Groups_Ozero__class_Ozero(X5))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__less) ).

fof(fact_take__butlast,axiom,
    ! [X242,X58,X57] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X57),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242)))
     => hAPP(hAPP(c_List_Otake(X58),X57),c_List_Obutlast(X58,X242)) = hAPP(hAPP(c_List_Otake(X58),X57),X242) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__butlast) ).

fof(fact_last__drop,axiom,
    ! [X242,X58,X57] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X57),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242)))
     => c_List_Olast(X58,hAPP(hAPP(c_List_Odrop(X58),X57),X242)) = c_List_Olast(X58,X242) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__drop) ).

fof(fact_prod_Osimps_I2_J,axiom,
    ! [X24,X6,X19,X5,X116,X20] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X20,X116,X5),X19),hAPP(hAPP(c_Product__Type_OPair(X20,X116),X6),X24)) = hAPP(hAPP(X19,X6),X24),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_prod_Osimps_I2_J) ).

fof(fact_split__conv,axiom,
    ! [X24,X6,X2,X5,X116,X20] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X20,X116,X5),X2),hAPP(hAPP(c_Product__Type_OPair(X20,X116),X6),X24)) = hAPP(hAPP(X2,X6),X24),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__conv) ).

fof(fact_min__max_OSup__fin_Oin__idem,axiom,
    ! [X25,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X25),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X21)) = c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X21) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Oin__idem) ).

fof(fact_min__max_OInf__fin_Oin__idem,axiom,
    ! [X25,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X25),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X21)) = c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X21) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Oin__idem) ).

fof(fact_atLeastLessThan__eq__iff,axiom,
    ! [X22,X23,X24,X6,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),X24))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),X22))
         => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X6),X24) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X23),X22)
          <=> ( X6 = X23
              & X24 = X22 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__eq__iff) ).

fof(fact_atLeastLessThan__inj_I1_J,axiom,
    ! [X22,X23,X24,X6,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X6),X24) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X23),X22)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),X24))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),X22))
           => X6 = X23 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__inj_I1_J) ).

fof(fact_atLeastLessThan__inj_I2_J,axiom,
    ! [X22,X23,X24,X6,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X6),X24) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X23),X22)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),X24))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),X22))
           => X24 = X22 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__inj_I2_J) ).

fof(fact_posDivAlg__correct,axiom,
    ! [X90,X62] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X62))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X90))
       => hBOOL(hAPP(c_Divides_Odivmod__int__rel(X62,X90),c_Divides_OposDivAlg(X62,X90))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_posDivAlg__correct) ).

fof(fact_nth__list__update__neq,axiom,
    ! [X66,X242,X58,X97,X98] :
      ( X98 != X97
     => hAPP(hAPP(c_List_Onth(X58),hAPP(hAPP(c_List_Olist__update(X58,X242),X98),X66)),X97) = hAPP(hAPP(c_List_Onth(X58),X242),X97) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__list__update__neq) ).

fof(fact_ivl__disj__int_I9_J,axiom,
    ! [X159,X95,X156,X5] :
      ( class_Orderings_Oorder(X5)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X156,X95)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X95),X159)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I9_J) ).

fof(fact_converse__inv__image,axiom,
    ! [X2,X32,X20,X5] : hAPP(c_Relation_Oconverse(X5,X5),hAPP(hAPP(c_Relation_Oinv__image(X20,X5),X32),X2)) = hAPP(hAPP(c_Relation_Oinv__image(X20,X5),hAPP(c_Relation_Oconverse(X20,X20),X32)),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__inv__image) ).

fof(fact_Min_Oeq__fold__idem_H,axiom,
    ! [X6,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => c_Big__Operators_Olinorder__class_OMin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X6),X21)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omin(X5)),X6),X21) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min_Oeq__fold__idem_H) ).

fof(fact_Max_Oeq__fold__idem_H,axiom,
    ! [X6,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => c_Big__Operators_Olinorder__class_OMax(X5,hAPP(hAPP(c_Set_Oinsert(X5),X6),X21)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omax(X5)),X6),X21) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max_Oeq__fold__idem_H) ).

fof(fact_Sup__fin_Oeq__fold__idem_H,axiom,
    ! [X6,X21,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => c_Big__Operators_Olattice__class_OSup__fin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X6),X21)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Lattices_Osemilattice__sup__class_Osup(X5)),X6),X21) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_Oeq__fold__idem_H) ).

fof(fact_Inf__fin_Oeq__fold__idem_H,axiom,
    ! [X6,X21,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => c_Big__Operators_Olattice__class_OInf__fin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X6),X21)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Lattices_Osemilattice__inf__class_Oinf(X5)),X6),X21) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_Oeq__fold__idem_H) ).

fof(fact_log_Osimps,axiom,
    ! [X98,X90] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X90),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X98),X90)) )
       => c_Random_Olog(X90,X98) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
      & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X90),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X98),X90)) )
       => c_Random_Olog(X90,X98) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),c_Random_Olog(X90,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X98),X90))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_log_Osimps) ).

fof(fact_Ints__minus,axiom,
    ! [X6,X5] :
      ( class_Rings_Oring__1(X5)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X6),c_Int_Oring__1__class_OInts(X5)))
       => hBOOL(hAPP(hAPP(c_member(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X6)),c_Int_Oring__1__class_OInts(X5))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__minus) ).

fof(fact_bot__empty__eq,axiom,
    ! [X25,X5] :
      ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),X25))
    <=> hBOOL(hAPP(hAPP(c_member(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot__empty__eq) ).

fof(fact_abs__div__pos,axiom,
    ! [X66,X65,X58] :
      ( class_Fields_Olinordered__field__inverse__zero(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),X65))
       => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),hAPP(c_Groups_Oabs__class_Oabs(X58),X66)),X65) = hAPP(c_Groups_Oabs__class_Oabs(X58),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X66),X65)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__div__pos) ).

fof(fact_abs__mult__pos,axiom,
    ! [X65,X66,X58] :
      ( class_Rings_Olinordered__idom(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),X66))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),hAPP(c_Groups_Oabs__class_Oabs(X58),X65)),X66) = hAPP(c_Groups_Oabs__class_Oabs(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X65),X66)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__mult__pos) ).

fof(fact_Pow__empty,axiom,
    ! [X5] : hAPP(c_Set_OPow(X5),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__empty) ).

fof(fact_setsum__shift__lb__Suc0__0,axiom,
    ! [X87,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)),X87)) = 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),X87)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__shift__lb__Suc0__0) ).

fof(fact_inf__apply,axiom,
    ! [X25,X1,X2,X20,X5] :
      ( class_Lattices_Olattice(X5)
     => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20,X5)),X2),X1),X25) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),hAPP(X2,X25)),hAPP(X1,X25)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__apply) ).

fof(fact_inf__fun__def,axiom,
    ! [X25,X1,X2,X20,X5] :
      ( class_Lattices_Olattice(X5)
     => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X20,X5)),X2),X1),X25) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),hAPP(X2,X25)),hAPP(X1,X25)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__fun__def) ).

fof(fact_sup__fun__def,axiom,
    ! [X25,X1,X2,X20,X5] :
      ( class_Lattices_Olattice(X5)
     => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20,X5)),X2),X1),X25) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),hAPP(X2,X25)),hAPP(X1,X25)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__fun__def) ).

fof(fact_sup__apply,axiom,
    ! [X25,X1,X2,X20,X5] :
      ( class_Lattices_Olattice(X5)
     => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X20,X5)),X2),X1),X25) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),hAPP(X2,X25)),hAPP(X1,X25)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__apply) ).

fof(fact_fun__diff__def,axiom,
    ! [X25,X113,X21,X20,X5] :
      ( class_Groups_Ominus(X5)
     => hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20,X5)),X21),X113),X25) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),hAPP(X21,X25)),hAPP(X113,X25)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__diff__def) ).

fof(fact_minus__apply,axiom,
    ! [X25,X113,X21,X20,X5] :
      ( class_Groups_Ominus(X5)
     => hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20,X5)),X21),X113),X25) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),hAPP(X21,X25)),hAPP(X113,X25)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__apply) ).

fof(fact_negDivAlg__correct,axiom,
    ! [X90,X62] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X62),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X90))
       => hBOOL(hAPP(c_Divides_Odivmod__int__rel(X62,X90),c_Divides_OnegDivAlg(X62,X90))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negDivAlg__correct) ).

fof(fact_neg__mod__bound,axiom,
    ! [X62,X90] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X90),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X90),c_Divides_Odiv__class_Omod(tc_Int_Oint,X62,X90))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__mod__bound) ).

fof(fact_folding_Oempty,axiom,
    ! [X205,X2,X20,X5] :
      ( c_Finite__Set_Ofolding(X5,X20,X2,X205)
     => hAPP(X205,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) = c_Fun_Oid(X20) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding_Oempty) ).

fof(fact_less__eq__code__numeral__def,axiom,
    ! [X95,X50] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X50),X95))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X50)),hAPP(c_Code__Numeral_Onat__of,X95))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__code__numeral__def) ).

fof(fact_less__eq__code__numeral__code,axiom,
    ! [X95,X50] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X50)),hAPP(c_Code__Numeral_Oof__nat,X95)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X50),X95)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__code__numeral__code) ).

fof(fact_Suc__le__mono,axiom,
    ! [X95,X50] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X50)),hAPP(c_Nat_OSuc,X95)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X50),X95)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__mono) ).

fof(fact_less__code__numeral__def,axiom,
    ! [X95,X50] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X50),X95))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X50)),hAPP(c_Code__Numeral_Onat__of,X95))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__code__numeral__def) ).

fof(fact_less__code__numeral__code,axiom,
    ! [X95,X50] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X50)),hAPP(c_Code__Numeral_Oof__nat,X95)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X50),X95)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__code__numeral__code) ).

fof(fact_Suc__less__SucD,axiom,
    ! [X57,X72] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X72)),hAPP(c_Nat_OSuc,X57)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X72),X57)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__less__SucD) ).

fof(fact_Suc__less__eq,axiom,
    ! [X50,X95] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X95)),hAPP(c_Nat_OSuc,X50)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),X50)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__less__eq) ).

fof(fact_nth__take,axiom,
    ! [X242,X58,X57,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),X57))
     => hAPP(hAPP(c_List_Onth(X58),hAPP(hAPP(c_List_Otake(X58),X57),X242)),X98) = hAPP(hAPP(c_List_Onth(X58),X242),X98) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__take) ).

fof(fact_Diff__disjoint,axiom,
    ! [X113,X21,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X113),X21)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__disjoint) ).

fof(fact_rev__eq__Cons__iff,axiom,
    ! [X251,X33,X239,X5] :
      ( hAPP(c_List_Orev(X5),X239) = hAPP(hAPP(c_List_Olist_OCons(X5),X33),X251)
    <=> X239 = hAPP(hAPP(c_List_Oappend(X5),hAPP(c_List_Orev(X5),X251)),hAPP(hAPP(c_List_Olist_OCons(X5),X33),c_List_Olist_ONil(X5))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__eq__Cons__iff) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
    ! [X57,X66] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X66))
     => 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),X66),X57))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).

fof(fact_diff__le__self,axiom,
    ! [X57,X72] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X72),X57)),X72)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__le__self) ).

fof(fact_div__le__dividend,axiom,
    ! [X57,X72] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X72),X57)),X72)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__le__dividend) ).

fof(fact_ivl__disj__un_I2_J,axiom,
    ! [X159,X5] :
      ( class_Orderings_Olinorder(X5)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X5),X159)),hAPP(hAPP(c_Set_Oinsert(X5),X159),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(X5),X159) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__un_I2_J) ).

fof(fact_Min__le,axiom,
    ! [X25,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Big__Operators_Olinorder__class_OMin(X5,X21)),X25)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min__le) ).

fof(fact_zpower__zadd__distrib,axiom,
    ! [X94,X65,X66] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X66),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X65),X94)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X66),X65)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X66),X94)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zpower__zadd__distrib) ).

fof(fact_zdiff__zmult__distrib2,axiom,
    ! [X126,X127,X128] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X128),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X127),X126)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X128),X127)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X128),X126)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiff__zmult__distrib2) ).

fof(fact_zadd__zmult__distrib2,axiom,
    ! [X126,X127,X128] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X128),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X127),X126)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X128),X127)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X128),X126)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__zmult__distrib2) ).

fof(fact_diff__mult__distrib2,axiom,
    ! [X57,X72,X96] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X96),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X72),X57)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X96),X72)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X96),X57)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__mult__distrib2) ).

fof(fact_add__mult__distrib2,axiom,
    ! [X57,X72,X96] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X96),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X72),X57)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X96),X72)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X96),X57)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__mult__distrib2) ).

fof(fact_diff__commute,axiom,
    ! [X96,X97,X98] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X98),X97)),X96) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X98),X96)),X97),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__commute) ).

fof(fact_neg__0__le__iff__le,axiom,
    ! [X6,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X6)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),c_Groups_Ozero__class_Ozero(X5))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__0__le__iff__le) ).

fof(fact_neg__0__less__iff__less,axiom,
    ! [X6,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X6)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),c_Groups_Ozero__class_Ozero(X5))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__0__less__iff__less) ).

fof(fact_order__trans,axiom,
    ! [X94,X65,X66,X58] :
      ( class_Orderings_Opreorder(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X66),X65))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X65),X94))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X66),X94)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__trans) ).

fof(fact_xt1_I6_J,axiom,
    ! [X94,X66,X65,X58] :
      ( class_Orderings_Oorder(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X65),X66))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X94),X65))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X94),X66)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I6_J) ).

fof(fact_order__less__le__trans,axiom,
    ! [X94,X65,X66,X58] :
      ( class_Orderings_Opreorder(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X66),X65))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X65),X94))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X66),X94)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__le__trans) ).

fof(fact_order__le__less__trans,axiom,
    ! [X94,X65,X66,X58] :
      ( class_Orderings_Opreorder(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X66),X65))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X65),X94))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X66),X94)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__less__trans) ).

fof(fact_order__less__trans,axiom,
    ! [X94,X65,X66,X58] :
      ( class_Orderings_Opreorder(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X66),X65))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X65),X94))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X66),X94)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__trans) ).

fof(fact_xt1_I7_J,axiom,
    ! [X94,X66,X65,X58] :
      ( class_Orderings_Oorder(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X65),X66))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X94),X65))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X94),X66)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I7_J) ).

fof(fact_xt1_I8_J,axiom,
    ! [X94,X66,X65,X58] :
      ( class_Orderings_Oorder(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X65),X66))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X94),X65))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X94),X66)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I8_J) ).

fof(fact_xt1_I10_J,axiom,
    ! [X94,X66,X65,X58] :
      ( class_Orderings_Oorder(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X65),X66))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X94),X65))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X94),X66)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I10_J) ).

fof(fact_divmod__int__rel__0,axiom,
    ! [X90] :
      ( X90 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
     => hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X90),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/sandbox/benchmark/theBenchmark.p',fact_divmod__int__rel__0) ).

fof(fact_mod__pos__pos,axiom,
    ! [X90,X62] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X62))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X90))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,X62,X90) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(X62,X90)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__pos__pos) ).

fof(fact_diff__eq__diff__less__eq,axiom,
    ! [X22,X23,X24,X6,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X6),X24) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X23),X22)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),X24))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X23),X22)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__eq__diff__less__eq) ).

fof(fact_diff__eq__diff__less,axiom,
    ! [X22,X23,X24,X6,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X6),X24) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X23),X22)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),X24))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),X22)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__eq__diff__less) ).

fof(fact_eq__diff__iff,axiom,
    ! [X50,X95,X87] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X87),X95))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X87),X50))
       => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X95),X87) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X50),X87)
        <=> X95 = X50 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__diff__iff) ).

fof(fact_Sigma__empty2,axiom,
    ! [X21,X20,X5] : hAPP(hAPP(c_Product__Type_OSigma(X5,X20),X21),hAPP(c_COMBK(tc_fun(X20,tc_HOL_Obool),X5),c_Orderings_Obot__class_Obot(tc_fun(X20,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X20),tc_HOL_Obool)),
    file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_numeral__1__eq__Suc__0) ).

fof(fact_remdups__map__remdups,axiom,
    ! [X239,X2,X20,X5] : c_List_Oremdups(X5,hAPP(hAPP(c_List_Omap(X20,X5),X2),c_List_Oremdups(X20,X239))) = c_List_Oremdups(X5,hAPP(hAPP(c_List_Omap(X20,X5),X2),X239)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_remdups__map__remdups) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
    ! [X62,X72,X58] :
      ( class_Rings_Ocomm__semiring__1(X58)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X72),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X72)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),c_Groups_Oone__class_Oone(X58))),X72) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).

fof(fact_div__pos__pos,axiom,
    ! [X90,X62] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X62))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X90))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X62),X90) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(X62,X90)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__pos__pos) ).

fof(fact_ivl__disj__int_I15_J,axiom,
    ! [X159,X95,X156,X5] :
      ( class_Orderings_Oorder(X5)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X156),X95)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X95,X159)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I15_J) ).

fof(fact_of__int__0__le__iff,axiom,
    ! [X120,X5] :
      ( class_Rings_Olinordered__idom(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Oring__1__class_Oof__int(X5),X120)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X120)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__0__le__iff) ).

fof(fact_of__int__0__less__iff,axiom,
    ! [X120,X5] :
      ( class_Rings_Olinordered__idom(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Oring__1__class_Oof__int(X5),X120)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X120)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__0__less__iff) ).

fof(fact_of__nat__0__less__iff,axiom,
    ! [X50,X5] :
      ( class_Rings_Olinordered__semidom(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X50)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X50)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__0__less__iff) ).

fof(fact_com_Osize_I5_J,axiom,
    ! [X41,X42,X84] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(X84,X42,X41)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X42)),c_Com_Ocom_Ocom__size(X41))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osize_I5_J) ).

fof(fact_abs__le__zero__iff,axiom,
    ! [X6,X5] :
      ( class_Groups_Oordered__ab__group__add__abs(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Groups_Oabs__class_Oabs(X5),X6)),c_Groups_Ozero__class_Ozero(X5)))
      <=> X6 = c_Groups_Ozero__class_Ozero(X5) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__le__zero__iff) ).

fof(fact_mod__neg__pos,axiom,
    ! [X90,X62] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X62),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X90))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,X62,X90) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(X62,X90)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__neg__pos) ).

fof(fact_min__max_OInf__fin_Oinsert__idem,axiom,
    ! [X25,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X25),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X21)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Oinsert__idem) ).

fof(fact_min__max_OSup__fin_Oinsert__idem,axiom,
    ! [X25,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X25),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X21)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Oinsert__idem) ).

fof(fact_of__nat__diff,axiom,
    ! [X72,X57,X58] :
      ( class_Rings_Oring__1(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X57),X72))
       => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X58),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X72),X57)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X58),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X58),X72)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X58),X57)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__diff) ).

fof(fact_div__neg__pos,axiom,
    ! [X90,X62] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X62),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X90))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X62),X90) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(X62,X90)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__neg__pos) ).

fof(fact_finite__insert,axiom,
    ! [X21,X6,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(hAPP(c_Set_Oinsert(X5),X6),X21)))
    <=> hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__insert) ).

fof(fact_inf__Inf__fold__inf,axiom,
    ! [X113,X21,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X113),c_Complete__Lattice_OInf__class_OInf(X5,X21)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Lattices_Osemilattice__inf__class_Oinf(X5)),X113),X21) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__Inf__fold__inf) ).

fof(fact_sup__Sup__fold__sup,axiom,
    ! [X113,X21,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X113),c_Complete__Lattice_OSup__class_OSup(X5,X21)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Lattices_Osemilattice__sup__class_Osup(X5)),X113),X21) ) ),
    file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_Numeral1__eq1__nat) ).

fof(fact_Compl__disjoint2,axiom,
    ! [X21,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X21)),X21) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__disjoint2) ).

fof(fact_Compl__partition2,axiom,
    ! [X21,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X21)),X21) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__partition2) ).

fof(fact_UNIV__Plus__UNIV,axiom,
    ! [X20,X5] : c_Sum__Type_OPlus(X5,X20,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X20,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X5,X20),tc_HOL_Obool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__Plus__UNIV) ).

fof(fact_ivl__disj__int_I7_J,axiom,
    ! [X159,X156,X5] :
      ( class_Orderings_Oorder(X5)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X156,X159)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X5),X159)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I7_J) ).

fof(fact_ivl__disj__int_I5_J,axiom,
    ! [X159,X156,X5] :
      ( class_Orderings_Oorder(X5)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X156,X159)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X5),X159)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I5_J) ).

fof(fact_ivl__disj__int_I6_J,axiom,
    ! [X159,X156,X5] :
      ( class_Orderings_Oorder(X5)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X156,X159)),hAPP(c_SetInterval_Oord__class_OatLeast(X5),X159)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I6_J) ).

fof(fact_le__special_I1_J,axiom,
    ! [X33,X5] :
      ( ( class_Int_Onumber__ring(X5)
        & class_Rings_Olinordered__idom(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X33)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X33)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__special_I1_J) ).

fof(fact_less__special_I1_J,axiom,
    ! [X33,X5] :
      ( ( class_Int_Onumber__ring(X5)
        & class_Rings_Olinordered__idom(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X33)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X33)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__special_I1_J) ).

fof(fact_finite__Domain,axiom,
    ! [X171,X20,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X5,X20)),X171))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(c_Relation_ODomain(X5,X20),X171))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Domain) ).

fof(fact_finite__Range,axiom,
    ! [X171,X20,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X5,X20)),X171))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X20),hAPP(c_Relation_ORange(X5,X20),X171))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Range) ).

fof(fact_fold1Set__nonempty,axiom,
    ! [X25,X21,X2,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(X5,X2,X21),X25))
     => X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1Set__nonempty) ).

fof(fact_Nitpick_Oint__gcd__def,axiom,
    ! [X65,X66] : hAPP(hAPP(c_Nitpick_Oint__gcd,X66),X65) = 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),X66)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X65)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Oint__gcd__def) ).

fof(fact_drop__map,axiom,
    ! [X239,X2,X20,X50,X5] : hAPP(hAPP(c_List_Odrop(X5),X50),hAPP(hAPP(c_List_Omap(X20,X5),X2),X239)) = hAPP(hAPP(c_List_Omap(X20,X5),X2),hAPP(hAPP(c_List_Odrop(X20),X50),X239)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__map) ).

fof(fact_take__map,axiom,
    ! [X239,X2,X20,X50,X5] : hAPP(hAPP(c_List_Otake(X5),X50),hAPP(hAPP(c_List_Omap(X20,X5),X2),X239)) = hAPP(hAPP(c_List_Omap(X20,X5),X2),hAPP(hAPP(c_List_Otake(X20),X50),X239)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__map) ).

fof(fact_filter__append,axiom,
    ! [X251,X239,X18,X5] : hAPP(c_List_Ofilter(X5,X18),hAPP(hAPP(c_List_Oappend(X5),X239),X251)) = hAPP(hAPP(c_List_Oappend(X5),hAPP(c_List_Ofilter(X5,X18),X239)),hAPP(c_List_Ofilter(X5,X18),X251)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter__append) ).

fof(fact_wf__acc__iff,axiom,
    ! [X171,X5] :
      ( c_Wellfounded_Owf(X5,X171)
    <=> ! [X3] : hBOOL(hAPP(hAPP(c_member(X5),X3),c_Wellfounded_Oacc(X5,X171))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__acc__iff) ).

fof(fact_minus__Min__eq__Max,axiom,
    ! [X192,X5] :
      ( class_Groups_Olinordered__ab__group__add(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X192))
       => ( X192 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => hAPP(c_Groups_Ouminus__class_Ouminus(X5),c_Big__Operators_Olinorder__class_OMin(X5,X192)) = c_Big__Operators_Olinorder__class_OMax(X5,hAPP(c_Set_Oimage(X5,X5,c_Groups_Ouminus__class_Ouminus(X5)),X192)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__Min__eq__Max) ).

fof(fact_minus__Max__eq__Min,axiom,
    ! [X192,X5] :
      ( class_Groups_Olinordered__ab__group__add(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X192))
       => ( X192 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => hAPP(c_Groups_Ouminus__class_Ouminus(X5),c_Big__Operators_Olinorder__class_OMax(X5,X192)) = c_Big__Operators_Olinorder__class_OMin(X5,hAPP(c_Set_Oimage(X5,X5,c_Groups_Ouminus__class_Ouminus(X5)),X192)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__Max__eq__Min) ).

fof(fact_finite__UnionD,axiom,
    ! [X21,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X21)))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X5,tc_HOL_Obool)),X21)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UnionD) ).

fof(fact_Suc__times__mod__eq,axiom,
    ! [X72,X96] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X96))
     => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X96),X72)),X96) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__times__mod__eq) ).

fof(fact_sgn__greater,axiom,
    ! [X6,X5] :
      ( class_Rings_Olinordered__idom(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),c_Groups_Osgn__class_Osgn(X5,X6)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X6)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__greater) ).

fof(fact_mod__mult__mult1,axiom,
    ! [X90,X62,X56,X58] :
      ( class_Divides_Osemiring__div(X58)
     => c_Divides_Odiv__class_Omod(X58,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X56),X62),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X56),X90)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X56),c_Divides_Odiv__class_Omod(X58,X62,X90)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__mult1) ).

fof(fact_INT__constant,axiom,
    ! [X23,X20,X5,X21] :
      ( ( X21 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X20,tc_HOL_Obool)),X21),hAPP(c_COMBK(tc_fun(X20,tc_HOL_Obool),X5),X23)) = c_Orderings_Otop__class_Otop(tc_fun(X20,tc_HOL_Obool)) )
      & ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X20,tc_HOL_Obool)),X21),hAPP(c_COMBK(tc_fun(X20,tc_HOL_Obool),X5),X23)) = X23 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__constant) ).

fof(fact_UN__constant,axiom,
    ! [X23,X20,X5,X21] :
      ( ( X21 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X20,tc_HOL_Obool)),X21),hAPP(c_COMBK(tc_fun(X20,tc_HOL_Obool),X5),X23)) = c_Orderings_Obot__class_Obot(tc_fun(X20,tc_HOL_Obool)) )
      & ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X20,tc_HOL_Obool)),X21),hAPP(c_COMBK(tc_fun(X20,tc_HOL_Obool),X5),X23)) = X23 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__constant) ).

fof(fact_Random__Sequence_Oempty__def,axiom,
    ! [X293,X294,X5] : c_Random__Sequence_Oempty(X5,X294,X293) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(X5)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Random__Sequence_Oempty__def) ).

fof(fact_div__mult__mult1__if,axiom,
    ! [X90,X62,X56,X58] :
      ( class_Divides_Osemiring__div(X58)
     => ( ( X56 = c_Groups_Ozero__class_Ozero(X58)
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X56),X62)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X56),X90)) = c_Groups_Ozero__class_Ozero(X58) )
        & ( X56 != c_Groups_Ozero__class_Ozero(X58)
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X56),X62)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X56),X90)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X58),X62),X90) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__mult1__if) ).

fof(fact_mult__divide__mult__cancel__left,axiom,
    ! [X90,X62,X56,X58] :
      ( class_Fields_Ofield__inverse__zero(X58)
     => ( X56 != c_Groups_Ozero__class_Ozero(X58)
       => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X56),X62)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X56),X90)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X62),X90) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__divide__mult__cancel__left) ).

fof(fact_mult__divide__mult__cancel__right,axiom,
    ! [X90,X62,X56,X58] :
      ( class_Fields_Ofield__inverse__zero(X58)
     => ( X56 != c_Groups_Ozero__class_Ozero(X58)
       => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X56)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X90),X56)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X62),X90) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__divide__mult__cancel__right) ).

fof(fact_div__mult__mult1,axiom,
    ! [X90,X62,X56,X58] :
      ( class_Divides_Osemiring__div(X58)
     => ( X56 != c_Groups_Ozero__class_Ozero(X58)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X56),X62)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X56),X90)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X58),X62),X90) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__mult1) ).

fof(fact_div__mult__mult2,axiom,
    ! [X90,X62,X56,X58] :
      ( class_Divides_Osemiring__div(X58)
     => ( X56 != c_Groups_Ozero__class_Ozero(X58)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X56)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X90),X56)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X58),X62),X90) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__mult2) ).

fof(fact_nat__rec__Suc,axiom,
    ! [X68,X89,X19,X5] : hAPP(c_Nat_Onat_Onat__rec(X5,X19,X89),hAPP(c_Nat_OSuc,X68)) = hAPP(hAPP(X89,X68),hAPP(c_Nat_Onat_Onat__rec(X5,X19,X89),X68)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__rec__Suc) ).

fof(fact_termination__basic__simps_I3_J,axiom,
    ! [X94,X65,X66] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X66),X65))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X66),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X65),X94))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I3_J) ).

fof(fact_trans__le__add1,axiom,
    ! [X72,X97,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X98),X97))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X98),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X97),X72))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__le__add1) ).

fof(fact_termination__basic__simps_I4_J,axiom,
    ! [X65,X94,X66] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X66),X94))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X66),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X65),X94))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I4_J) ).

fof(fact_trans__le__add2,axiom,
    ! [X72,X97,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X98),X97))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X98),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X72),X97))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__le__add2) ).

fof(fact_termination__basic__simps_I1_J,axiom,
    ! [X94,X65,X66] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X66),X65))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X66),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X65),X94))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I1_J) ).

fof(fact_trans__less__add1,axiom,
    ! [X72,X97,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),X97))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X97),X72))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__less__add1) ).

fof(fact_termination__basic__simps_I2_J,axiom,
    ! [X65,X94,X66] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X66),X94))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X66),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X65),X94))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I2_J) ).

fof(fact_trans__less__add2,axiom,
    ! [X72,X97,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),X97))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X72),X97))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__less__add2) ).

fof(fact_mod__mult__self2,axiom,
    ! [X56,X90,X62,X58] :
      ( class_Divides_Osemiring__div(X58)
     => c_Divides_Odiv__class_Omod(X58,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X90),X56)),X90) = c_Divides_Odiv__class_Omod(X58,X62,X90) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__self2) ).

fof(fact_mod__mult__self1,axiom,
    ! [X90,X56,X62,X58] :
      ( class_Divides_Osemiring__div(X58)
     => c_Divides_Odiv__class_Omod(X58,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X56),X90)),X90) = c_Divides_Odiv__class_Omod(X58,X62,X90) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__self1) ).

fof(fact_less__Suc__eq__0__disj,axiom,
    ! [X50,X95] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),hAPP(c_Nat_OSuc,X50)))
    <=> ( X95 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ? [X101] :
            ( X95 = hAPP(c_Nat_OSuc,X101)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X101),X50)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq__0__disj) ).

fof(fact_bex__UNIV,axiom,
    ! [X18,X5] :
      ( ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))))
          & hBOOL(hAPP(X18,X3)) )
    <=> ? [X138] : hBOOL(hAPP(X18,X138)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bex__UNIV) ).

fof(fact_rotate1__hd__tl,axiom,
    ! [X58,X242] :
      ( X242 != c_List_Olist_ONil(X58)
     => hAPP(c_List_Orotate1(X58),X242) = hAPP(hAPP(c_List_Oappend(X58),hAPP(c_List_Otl(X58),X242)),hAPP(hAPP(c_List_Olist_OCons(X58),hAPP(c_List_Ohd(X58),X242)),c_List_Olist_ONil(X58))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate1__hd__tl) ).

fof(fact_setsum__set__upto__conv__listsum__int,axiom,
    ! [X157,X82,X2,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X5),X2),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X82,X157))) = hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(tc_Int_Oint,X5),X2),c_List_Oupto(X82,X157))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__set__upto__conv__listsum__int) ).

fof(fact_interv__listsum__conv__setsum__set__int,axiom,
    ! [X156,X87,X2,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => hAPP(c_List_Omonoid__add__class_Olistsum(X5),hAPP(hAPP(c_List_Omap(tc_Int_Oint,X5),X2),c_List_Oupto(X87,X156))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X5),X2),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X87,X156))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_interv__listsum__conv__setsum__set__int) ).

fof(fact_inf_Oassoc,axiom,
    ! [X56,X90,X62,X58] :
      ( class_Lattices_Osemilattice__inf(X58)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X62),X90)),X56) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X62),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X90),X56)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf_Oassoc) ).

fof(fact_inf__assoc,axiom,
    ! [X94,X65,X66,X58] :
      ( class_Lattices_Osemilattice__inf(X58)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X66),X65)),X94) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X66),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X65),X94)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__assoc) ).

fof(fact_inf__sup__aci_I2_J,axiom,
    ! [X94,X65,X66,X58] :
      ( class_Lattices_Olattice(X58)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X66),X65)),X94) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X66),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X65),X94)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__aci_I2_J) ).

fof(fact_inf__sup__aci_I6_J,axiom,
    ! [X94,X65,X66,X58] :
      ( class_Lattices_Olattice(X58)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X66),X65)),X94) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X66),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X65),X94)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__aci_I6_J) ).

fof(fact_sup__assoc,axiom,
    ! [X94,X65,X66,X58] :
      ( class_Lattices_Osemilattice__sup(X58)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X66),X65)),X94) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X66),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X65),X94)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__assoc) ).

fof(fact_sup_Oassoc,axiom,
    ! [X56,X90,X62,X58] :
      ( class_Lattices_Osemilattice__sup(X58)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X62),X90)),X56) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X62),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X90),X56)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup_Oassoc) ).

fof(fact_min__max_Osup__assoc,axiom,
    ! [X94,X65,X66,X58] :
      ( class_Orderings_Olinorder(X58)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(X58),hAPP(hAPP(c_Orderings_Oord__class_Omax(X58),X66),X65)),X94) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X58),X66),hAPP(hAPP(c_Orderings_Oord__class_Omax(X58),X65),X94)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup__assoc) ).

fof(fact_min__max_Osup_Oassoc,axiom,
    ! [X56,X90,X62,X58] :
      ( class_Orderings_Olinorder(X58)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(X58),hAPP(hAPP(c_Orderings_Oord__class_Omax(X58),X62),X90)),X56) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X58),X62),hAPP(hAPP(c_Orderings_Oord__class_Omax(X58),X90),X56)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup_Oassoc) ).

fof(fact_min__max_Oinf_Oassoc,axiom,
    ! [X56,X90,X62,X58] :
      ( class_Orderings_Olinorder(X58)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(X58),hAPP(hAPP(c_Orderings_Oord__class_Omin(X58),X62),X90)),X56) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X58),X62),hAPP(hAPP(c_Orderings_Oord__class_Omin(X58),X90),X56)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf_Oassoc) ).

fof(fact_min__max_Oinf__assoc,axiom,
    ! [X94,X65,X66,X58] :
      ( class_Orderings_Olinorder(X58)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(X58),hAPP(hAPP(c_Orderings_Oord__class_Omin(X58),X66),X65)),X94) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X58),X66),hAPP(hAPP(c_Orderings_Oord__class_Omin(X58),X65),X94)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__assoc) ).

fof(fact_power__commutes,axiom,
    ! [X57,X62,X58] :
      ( class_Groups_Omonoid__mult(X58)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),X57)),X62) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),X57)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__commutes) ).

fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
    ! [X56,X90,X62,X58] :
      ( class_Groups_Oab__semigroup__mult(X58)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X90)),X56) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X90),X56)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ab__semigroup__mult__class_Omult__ac_I1_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
    ! [X130,X131,X132,X58] :
      ( class_Rings_Ocomm__semiring__1(X58)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X132),X131)),X130) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X132),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X131),X130)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
    ! [X56,X90,X62,X58] :
      ( class_Rings_Ocomm__semiring__1(X58)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),X90)),X56) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X90),X56)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).

fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
    ! [X56,X90,X62,X58] :
      ( class_Groups_Oab__semigroup__add(X58)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),X90)),X56) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X90),X56)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ab__semigroup__add__class_Oadd__ac_I1_J) ).

fof(fact_times__divide__eq__right,axiom,
    ! [X56,X90,X62,X58] :
      ( class_Rings_Odivision__ring(X58)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X90),X56)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X90)),X56) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_times__divide__eq__right) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
    ! [X129,X130,X132,X58] :
      ( class_Rings_Ocomm__semiring__1(X58)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X132),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X130),X129)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X132),X130)),X129) ),
    file('/export/starexec/sandbox/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,
    ! [X91,X56,X62,X58] :
      ( class_Rings_Ocomm__semiring__1(X58)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X56),X91)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),X56)),X91) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).

fof(fact_last__conv__nth,axiom,
    ! [X58,X242] :
      ( X242 != c_List_Olist_ONil(X58)
     => c_List_Olast(X58,X242) = hAPP(hAPP(c_List_Onth(X58),X242),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__conv__nth) ).

fof(fact_Nats__number__of,axiom,
    ! [X121,X5] :
      ( class_Int_Onumber__ring(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X121))
       => hBOOL(hAPP(hAPP(c_member(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)),c_Nat_Osemiring__1__class_ONats(X5))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nats__number__of) ).

fof(fact_card__Pow,axiom,
    ! [X21,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
     => hAPP(c_Finite__Set_Ocard(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_OPow(X5),X21)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Finite__Set_Ocard(X5),X21)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Pow) ).

fof(fact_atLeast__Suc,axiom,
    ! [X87] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,X87)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),X87)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X87),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeast__Suc) ).

fof(fact_Diff__Compl,axiom,
    ! [X113,X21,X5] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X113)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__Compl) ).

fof(fact_Diff__eq,axiom,
    ! [X113,X21,X5] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),X113) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X113)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__eq) ).

fof(fact_zero__less__two,axiom,
    ! [X58] :
      ( class_Rings_Olinordered__semidom(X58)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),c_Groups_Oone__class_Oone(X58)),c_Groups_Oone__class_Oone(X58)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__two) ).

fof(fact_card__greaterThanLessThan__int,axiom,
    ! [X159,X156] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X156,X159)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X159),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X156),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__greaterThanLessThan__int) ).

fof(fact_nth__replicate,axiom,
    ! [X66,X58,X57,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),X57))
     => hAPP(hAPP(c_List_Onth(X58),c_List_Oreplicate(X58,X57,X66)),X98) = X66 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__replicate) ).

fof(fact_min__max_Osup__Inf__absorb,axiom,
    ! [X6,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X21))
         => hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X6),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X21)) = X6 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup__Inf__absorb) ).

fof(fact_min__max_Oinf__Sup__absorb,axiom,
    ! [X6,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X21))
         => hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X6),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X21)) = X6 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__Sup__absorb) ).

fof(fact_le__minus__self__iff,axiom,
    ! [X6,X5] :
      ( class_Groups_Olinordered__ab__group__add(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X6)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),c_Groups_Ozero__class_Ozero(X5))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__minus__self__iff) ).

fof(fact_less__minus__self__iff,axiom,
    ! [X6,X5] :
      ( class_Rings_Olinordered__idom(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X6)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),c_Groups_Ozero__class_Ozero(X5))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__minus__self__iff) ).

fof(fact_Diff__triv,axiom,
    ! [X113,X21,X5] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),X113) = X21 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__triv) ).

fof(fact_insort__not__Nil,axiom,
    ! [X239,X6,X2,X5,X20] :
      ( class_Orderings_Olinorder(X20)
     => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X20,X2),X6),X239) != c_List_Olist_ONil(X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insort__not__Nil) ).

fof(fact_setprod__constant,axiom,
    ! [X33,X21,X5,X20] :
      ( class_Groups_Ocomm__monoid__mult(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),hAPP(c_COMBK(X20,X5),X33)),X21) = hAPP(hAPP(c_Power_Opower__class_Opower(X20),X33),hAPP(c_Finite__Set_Ocard(X5),X21)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__constant) ).

fof(fact_fold1__insert__idem,axiom,
    ! [X25,X21,X5] :
      ( class_Lattices_Oab__semigroup__idem__mult(X5)
     => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
         => hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X25),hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),X21)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__insert__idem) ).

fof(fact_ivl__disj__int_I11_J,axiom,
    ! [X159,X95,X156,X5] :
      ( class_Orderings_Oorder(X5)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X156),X95)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X95),X159)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I11_J) ).

fof(fact_diff__Suc,axiom,
    ! [X50,X95] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X95),hAPP(c_Nat_OSuc,X50)) = 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),X95),X50)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc) ).

fof(fact_append__Cons,axiom,
    ! [X241,X242,X66,X58] : hAPP(hAPP(c_List_Oappend(X58),hAPP(hAPP(c_List_Olist_OCons(X58),X66),X242)),X241) = hAPP(hAPP(c_List_Olist_OCons(X58),X66),hAPP(hAPP(c_List_Oappend(X58),X242),X241)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__Cons) ).

fof(fact_append__assoc,axiom,
    ! [X248,X241,X242,X58] : hAPP(hAPP(c_List_Oappend(X58),hAPP(hAPP(c_List_Oappend(X58),X242),X241)),X248) = hAPP(hAPP(c_List_Oappend(X58),X242),hAPP(hAPP(c_List_Oappend(X58),X241),X248)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__assoc) ).

fof(fact_take__Suc,axiom,
    ! [X57,X58,X242] :
      ( X242 != c_List_Olist_ONil(X58)
     => hAPP(hAPP(c_List_Otake(X58),hAPP(c_Nat_OSuc,X57)),X242) = hAPP(hAPP(c_List_Olist_OCons(X58),hAPP(c_List_Ohd(X58),X242)),hAPP(hAPP(c_List_Otake(X58),X57),hAPP(c_List_Otl(X58),X242))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__Suc) ).

fof(fact_image__atLeastZeroLessThan__int,axiom,
    ! [X159] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X159))
     => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X159) = 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,X159))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__atLeastZeroLessThan__int) ).

fof(fact_nth__Cons_H,axiom,
    ! [X242,X66,X58,X57] :
      ( ( X57 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Onth(X58),hAPP(hAPP(c_List_Olist_OCons(X58),X66),X242)),X57) = X66 )
      & ( X57 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Onth(X58),hAPP(hAPP(c_List_Olist_OCons(X58),X66),X242)),X57) = hAPP(hAPP(c_List_Onth(X58),X242),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X57),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__Cons_H) ).

fof(fact_image__constant__conv,axiom,
    ! [X23,X20,X5,X21] :
      ( ( X21 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(c_Set_Oimage(X5,X20,hAPP(c_COMBK(X20,X5),X23)),X21) = c_Orderings_Obot__class_Obot(tc_fun(X20,tc_HOL_Obool)) )
      & ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(c_Set_Oimage(X5,X20,hAPP(c_COMBK(X20,X5),X23)),X21) = hAPP(hAPP(c_Set_Oinsert(X20),X23),c_Orderings_Obot__class_Obot(tc_fun(X20,tc_HOL_Obool))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__constant__conv) ).

fof(fact_listsum__distinct__conv__setsum__set,axiom,
    ! [X2,X239,X5,X20] :
      ( class_Groups_Ocomm__monoid__add(X20)
     => ( hBOOL(hAPP(c_List_Odistinct(X5),X239))
       => hAPP(c_List_Omonoid__add__class_Olistsum(X20),hAPP(hAPP(c_List_Omap(X5,X20),X2),X239)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X2),hAPP(c_List_Oset(X5),X239)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__distinct__conv__setsum__set) ).

fof(fact_power__mult,axiom,
    ! [X57,X72,X62,X58] :
      ( class_Groups_Omonoid__mult(X58)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X72),X57)) = hAPP(hAPP(c_Power_Opower__class_Opower(X58),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),X72)),X57) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__mult) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
    ! [X140,X162,X66,X58] :
      ( class_Rings_Ocomm__semiring__1(X58)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X58),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X66),X162)),X140) = hAPP(hAPP(c_Power_Opower__class_Opower(X58),X66),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X162),X140)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).

fof(fact_mod__minus__eq,axiom,
    ! [X90,X62,X58] :
      ( class_Divides_Oring__div(X58)
     => c_Divides_Odiv__class_Omod(X58,hAPP(c_Groups_Ouminus__class_Ouminus(X58),X62),X90) = c_Divides_Odiv__class_Omod(X58,hAPP(c_Groups_Ouminus__class_Ouminus(X58),c_Divides_Odiv__class_Omod(X58,X62,X90)),X90) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__minus__eq) ).

fof(fact_tl__take,axiom,
    ! [X242,X57,X58] : hAPP(c_List_Otl(X58),hAPP(hAPP(c_List_Otake(X58),X57),X242)) = hAPP(hAPP(c_List_Otake(X58),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X57),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_List_Otl(X58),X242)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tl__take) ).

fof(fact_abs__power__minus,axiom,
    ! [X57,X62,X58] :
      ( class_Rings_Olinordered__idom(X58)
     => hAPP(c_Groups_Oabs__class_Oabs(X58),hAPP(hAPP(c_Power_Opower__class_Opower(X58),hAPP(c_Groups_Ouminus__class_Ouminus(X58),X62)),X57)) = hAPP(c_Groups_Oabs__class_Oabs(X58),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),X57)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__power__minus) ).

fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom,
    ! [X21,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))))
     => ( hAPP(c_Finite__Set_Ocard(X5),X21) = hAPP(c_Finite__Set_Ocard(X5),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
       => X21 = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__eq__UNIV__imp__eq__UNIV) ).

fof(fact_drop__Cons_H,axiom,
    ! [X242,X66,X58,X57] :
      ( ( X57 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Odrop(X58),X57),hAPP(hAPP(c_List_Olist_OCons(X58),X66),X242)) = hAPP(hAPP(c_List_Olist_OCons(X58),X66),X242) )
      & ( X57 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Odrop(X58),X57),hAPP(hAPP(c_List_Olist_OCons(X58),X66),X242)) = hAPP(hAPP(c_List_Odrop(X58),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X57),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X242) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__Cons_H) ).

fof(fact_neg__zminus__int,axiom,
    ! [X57] : 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,X57))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__zminus__int) ).

fof(fact_insert__code,axiom,
    ! [X25,X21,X33,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X5),X33),X21),X25))
    <=> ( X33 = X25
        | hBOOL(hAPP(X21,X25)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__code) ).

fof(fact_atMost__iff,axiom,
    ! [X87,X82,X5] :
      ( class_Orderings_Oord(X5)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X82),hAPP(c_SetInterval_Oord__class_OatMost(X5),X87)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X82),X87)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atMost__iff) ).

fof(fact_atLeast__iff,axiom,
    ! [X87,X82,X5] :
      ( class_Orderings_Oord(X5)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X82),hAPP(c_SetInterval_Oord__class_OatLeast(X5),X87)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X87),X82)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeast__iff) ).

fof(fact_lessThan__iff,axiom,
    ! [X87,X82,X5] :
      ( class_Orderings_Oord(X5)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X82),hAPP(c_SetInterval_Oord__class_OlessThan(X5),X87)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X82),X87)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lessThan__iff) ).

fof(fact_greaterThan__iff,axiom,
    ! [X87,X82,X5] :
      ( class_Orderings_Oord(X5)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X82),hAPP(c_SetInterval_Oord__class_OgreaterThan(X5),X87)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X87),X82)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThan__iff) ).

fof(fact_image__uminus__greaterThanAtMost,axiom,
    ! [X33,X25,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => hAPP(c_Set_Oimage(X5,X5,c_Groups_Ouminus__class_Ouminus(X5)),c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X25,X33)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,hAPP(c_Groups_Ouminus__class_Ouminus(X5),X33)),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X25)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__uminus__greaterThanAtMost) ).

fof(fact_folding__one__idem_Oin__idem,axiom,
    ! [X25,X21,X205,X2,X5] :
      ( c_Finite__Set_Ofolding__one__idem(X5,X2,X205)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => hAPP(hAPP(X2,X25),hAPP(X205,X21)) = hAPP(X205,X21) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Oin__idem) ).

fof(fact_Max__ge,axiom,
    ! [X25,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X25),c_Big__Operators_Olinorder__class_OMax(X5,X21))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max__ge) ).

fof(fact_listsum__setsum__nth,axiom,
    ! [X239,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => hAPP(c_List_Omonoid__add__class_Olistsum(X5),X239) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),hAPP(c_List_Onth(X5),X239)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__setsum__nth) ).

fof(fact_zdiff__int,axiom,
    ! [X72,X57] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X57),X72))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X72)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X57)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X72),X57)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiff__int) ).

fof(fact_odd__nonzero,axiom,
    ! [X94] : 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)),X94)),X94) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_odd__nonzero) ).

fof(fact_Field__def,axiom,
    ! [X171,X5] : hAPP(c_Relation_OField(X5),X171) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X5,X5),X171)),hAPP(c_Relation_ORange(X5,X5),X171)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Field__def) ).

fof(fact_SetInterval_Otransfer__nat__int__set__functions_I2_J,axiom,
    ! [X50,X95] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X95,X50) = 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),X95),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X50))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SetInterval_Otransfer__nat__int__set__functions_I2_J) ).

fof(fact_div__mult__self1__is__m,axiom,
    ! [X72,X57] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X57))
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X57),X72)),X57) = X72 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__self1__is__m) ).

fof(fact_div__mult__self__is__m,axiom,
    ! [X72,X57] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X57))
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X72),X57)),X57) = X72 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__self__is__m) ).

fof(fact_zmod__zminus2__eq__if,axiom,
    ! [X90,X62] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X62,X90) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,X62,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X90)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X62,X90) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,X62,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X90)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X62,X90)),X90) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zminus2__eq__if) ).

fof(fact_subset__UNIV,axiom,
    ! [X21,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__UNIV) ).

fof(fact_zle__trans,axiom,
    ! [X96,X97,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X98),X97))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X97),X96))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X98),X96)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__trans) ).

fof(fact_le__trans,axiom,
    ! [X96,X97,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X98),X97))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X97),X96))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X98),X96)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__trans) ).

fof(fact_evaln__elim__cases_I1_J,axiom,
    ! [X54,X57,X48] :
      ( c_Natural_Oevaln(c_Com_Ocom_OSKIP,X48,X57,X54)
     => X54 = X48 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln__elim__cases_I1_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
    ! [X72,X58] :
      ( class_Rings_Ocomm__semiring__1(X58)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X72),X72) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),c_Groups_Oone__class_Oone(X58)),c_Groups_Oone__class_Oone(X58))),X72) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).

fof(fact_less__add__eq__less,axiom,
    ! [X57,X72,X99,X96] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X96),X99))
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X72),X99) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X96),X57)
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X72),X57)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__eq__less) ).

fof(fact_Suc__leD,axiom,
    ! [X57,X72] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X72)),X57))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X72),X57)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__leD) ).

fof(fact_less__eq__Suc__le,axiom,
    ! [X95,X50] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X50),X95))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X50)),X95)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__Suc__le) ).

fof(fact_Suc__le__eq,axiom,
    ! [X50,X95] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X95)),X50))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),X50)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__eq) ).

fof(fact_Suc__le__lessD,axiom,
    ! [X57,X72] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X72)),X57))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X72),X57)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__lessD) ).

fof(fact_Suc__lessD,axiom,
    ! [X57,X72] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X72)),X57))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X72),X57)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__lessD) ).

fof(fact_drop__drop,axiom,
    ! [X242,X72,X57,X58] : hAPP(hAPP(c_List_Odrop(X58),X57),hAPP(hAPP(c_List_Odrop(X58),X72),X242)) = hAPP(hAPP(c_List_Odrop(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X57),X72)),X242),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__drop) ).

fof(fact_take__take,axiom,
    ! [X242,X72,X57,X58] : hAPP(hAPP(c_List_Otake(X58),X57),hAPP(hAPP(c_List_Otake(X58),X72),X242)) = hAPP(hAPP(c_List_Otake(X58),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X57),X72)),X242),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__take) ).

fof(fact_Inf__lower,axiom,
    ! [X21,X25,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Complete__Lattice_OInf__class_OInf(X5,X21)),X25)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__lower) ).

fof(fact_transfer__int__nat__quantifiers_I1_J,axiom,
    ! [X18] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
         => hBOOL(hAPP(X18,X3)) )
    <=> ! [X3] : hBOOL(hAPP(X18,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__quantifiers_I1_J) ).

fof(fact_nat__div__distrib,axiom,
    ! [X65,X66] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X66))
     => hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X66),X65)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,X66)),hAPP(c_Int_Onat,X65)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__div__distrib) ).

fof(fact_nat__mult__distrib,axiom,
    ! [X135,X94] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X94))
     => hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X94),X135)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,X94)),hAPP(c_Int_Onat,X135)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__distrib) ).

fof(fact_SetInterval_Otransfer__int__nat__set__functions,axiom,
    ! [X50,X95] :
      ( c_Nat__Transfer_Ois__nat(X95)
     => ( c_Nat__Transfer_Ois__nat(X50)
       => c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X95,X50) = 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,X95),hAPP(c_Int_Onat,X50))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SetInterval_Otransfer__int__nat__set__functions) ).

fof(fact_transpose_Opsimps_I1_J,axiom,
    ! [X5] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(X5)),c_List_Otranspose__rel(X5)),c_List_Olist_ONil(tc_List_Olist(X5))))
     => c_List_Otranspose(X5,c_List_Olist_ONil(tc_List_Olist(X5))) = c_List_Olist_ONil(tc_List_Olist(X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose_Opsimps_I1_J) ).

fof(fact_mod__mult__distrib2,axiom,
    ! [X57,X72,X96] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X96),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X72,X57)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X96),X72),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X96),X57)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__distrib2) ).

fof(fact_transfer__nat__int__set__relations_I3_J,axiom,
    ! [X113,X21] :
      ( X21 = X113
    <=> hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X21) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X113) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__set__relations_I3_J) ).

fof(fact_set__append,axiom,
    ! [X251,X239,X5] : hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Oappend(X5),X239),X251)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),X239)),hAPP(c_List_Oset(X5),X251)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__append) ).

fof(fact_Suc__mono,axiom,
    ! [X57,X72] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X72),X57))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X72)),hAPP(c_Nat_OSuc,X57))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mono) ).

fof(fact_power__inject__exp,axiom,
    ! [X50,X95,X6,X5] :
      ( class_Rings_Olinordered__semidom(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Oone__class_Oone(X5)),X6))
       => ( hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X95) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X50)
        <=> X95 = X50 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__inject__exp) ).

fof(fact_Body__triple__valid__0,axiom,
    ! [X16,X17,X18,X5] : c_Hoare__Mirabelle_Otriple__valid(X5,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),X18),hAPP(c_Com_Ocom_OBODY,X17)),X16)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Body__triple__valid__0) ).

fof(fact_listset_Osimps_I2_J,axiom,
    ! [X261,X21,X5] : c_List_Olistset(X5,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X5,tc_HOL_Obool)),X21),X261)) = c_List_Oset__Cons(X5,X21,c_List_Olistset(X5,X261)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listset_Osimps_I2_J) ).

fof(fact_bex__empty,axiom,
    ! [X18,X5] :
      ~ ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))
          & hBOOL(hAPP(X18,X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bex__empty) ).

fof(fact_Inf__fold__inf,axiom,
    ! [X21,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => c_Complete__Lattice_OInf__class_OInf(X5,X21) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Lattices_Osemilattice__inf__class_Oinf(X5)),c_Orderings_Otop__class_Otop(X5)),X21) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fold__inf) ).

fof(fact_Sup__fold__sup,axiom,
    ! [X21,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => c_Complete__Lattice_OSup__class_OSup(X5,X21) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Lattices_Osemilattice__sup__class_Osup(X5)),c_Orderings_Obot__class_Obot(X5)),X21) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fold__sup) ).

fof(fact_power__eq__if,axiom,
    ! [X162,X72] :
      ( ( X72 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X162),X72) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( X72 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X162),X72) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X162),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X162),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X72),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__eq__if) ).

fof(fact_image__uminus__atLeastAtMost,axiom,
    ! [X33,X25,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => hAPP(c_Set_Oimage(X5,X5,c_Groups_Ouminus__class_Ouminus(X5)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X25,X33)) = c_SetInterval_Oord__class_OatLeastAtMost(X5,hAPP(c_Groups_Ouminus__class_Ouminus(X5),X33),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X25)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__uminus__atLeastAtMost) ).

fof(fact_image__uminus__greaterThanLessThan,axiom,
    ! [X33,X25,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => hAPP(c_Set_Oimage(X5,X5,c_Groups_Ouminus__class_Ouminus(X5)),c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X25,X33)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X5,hAPP(c_Groups_Ouminus__class_Ouminus(X5),X33),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X25)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__uminus__greaterThanLessThan) ).

fof(fact_lessThan__Suc__eq__insert__0,axiom,
    ! [X50] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X50)) = 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),X50))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lessThan__Suc__eq__insert__0) ).

fof(fact_div__mod__code__numeral__def,axiom,
    ! [X72,X57] : c_Code__Numeral_Odiv__mod__code__numeral(X57,X72) = 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),X57),X72)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X57,X72)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mod__code__numeral__def) ).

fof(fact_divmod__int__mod__div,axiom,
    ! [X140,X162] : c_Divides_Odivmod__int(X162,X140) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X162),X140)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X162,X140)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__int__mod__div) ).

fof(fact_zminus__zmod,axiom,
    ! [X72,X66] : 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,X66,X72)),X72) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X66),X72),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zminus__zmod) ).

fof(fact_transfer__nat__int__relations_I1_J,axiom,
    ! [X33,X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X33))
       => ( hAPP(c_Int_Onat,X25) = hAPP(c_Int_Onat,X33)
        <=> X25 = X33 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__relations_I1_J) ).

fof(fact_eq__nat__nat__iff,axiom,
    ! [X137,X120] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X120))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X137))
       => ( hAPP(c_Int_Onat,X120) = hAPP(c_Int_Onat,X137)
        <=> X120 = X137 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__nat__nat__iff) ).

fof(fact_zless__iff__Suc__zadd,axiom,
    ! [X120,X121] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X121),X120))
    <=> ? [X69] : X120 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X121),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X69))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__iff__Suc__zadd) ).

fof(fact_div__mod__equality_H,axiom,
    ! [X57,X72] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X72),X57)),X57) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X72),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X72,X57)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mod__equality_H) ).

fof(fact_le__add__diff__inverse2,axiom,
    ! [X72,X57] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X57),X72))
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X72),X57)),X57) = X72 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add__diff__inverse2) ).

fof(fact_zero__less__int__conv,axiom,
    ! [X50] :
      ( 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),X50)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X50)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__int__conv) ).

fof(fact_int__eq__iff__number__of,axiom,
    ! [X123,X95] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X95) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X123)
    <=> ( X95 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X123))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X123))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__eq__iff__number__of) ).

fof(fact_finite__Pow__iff,axiom,
    ! [X21,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_OPow(X5),X21)))
    <=> hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Pow__iff) ).

fof(fact_DomainP_Ointros,axiom,
    ! [X20,X5,X24,X6,X171] :
      ( hBOOL(hAPP(hAPP(X171,X6),X24))
     => hBOOL(hAPP(c_Predicate_ODomainP(X5,X20,X171),X6)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DomainP_Ointros) ).

fof(fact_RangeP_Ointros,axiom,
    ! [X20,X5,X24,X6,X171] :
      ( hBOOL(hAPP(hAPP(X171,X6),X24))
     => hBOOL(hAPP(c_Predicate_ORangeP(X5,X20,X171),X24)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_RangeP_Ointros) ).

fof(fact_length__splice,axiom,
    ! [X241,X242,X58] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),c_List_Osplice(X58,X242,X241)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X241)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__splice) ).

fof(fact_length__greater__0__conv,axiom,
    ! [X239,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239)))
    <=> X239 != c_List_Olist_ONil(X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__greater__0__conv) ).

fof(fact_ivl__disj__int_I8_J,axiom,
    ! [X159,X156,X5] :
      ( class_Orderings_Oorder(X5)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X156),X159)),hAPP(c_SetInterval_Oord__class_OatLeast(X5),X159)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I8_J) ).

fof(fact_le__less__Suc__eq,axiom,
    ! [X50,X95] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X50))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X50),hAPP(c_Nat_OSuc,X95)))
      <=> X50 = X95 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__less__Suc__eq) ).

fof(fact_nat__induct,axiom,
    ! [X50,X18] :
      ( hBOOL(hAPP(X18,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
     => ( ! [X69] :
            ( hBOOL(hAPP(X18,X69))
           => hBOOL(hAPP(X18,hAPP(c_Nat_OSuc,X69))) )
       => hBOOL(hAPP(X18,X50)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__induct) ).

fof(fact_mod__pos__pos__trivial,axiom,
    ! [X90,X62] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X62))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X62),X90))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,X62,X90) = X62 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__pos__pos__trivial) ).

fof(fact_atMost__Int__atLeast,axiom,
    ! [X50,X5] :
      ( class_Orderings_Oorder(X5)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X5),X50)),hAPP(c_SetInterval_Oord__class_OatLeast(X5),X50)) = hAPP(hAPP(c_Set_Oinsert(X5),X50),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atMost__Int__atLeast) ).

fof(fact_length__append,axiom,
    ! [X241,X242,X58] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),hAPP(hAPP(c_List_Oappend(X58),X242),X241)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X241)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__append) ).

fof(fact_transfer__int__nat__set__relations_I3_J,axiom,
    ! [X113,X21] :
      ( c_Nat__Transfer_Onat__set(X21)
     => ( c_Nat__Transfer_Onat__set(X113)
       => ( X21 = X113
        <=> hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X21) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X113) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__set__relations_I3_J) ).

fof(fact_triple_Oinject,axiom,
    ! [X7,X8,X9,X10,X11,X12,X5] :
      ( hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),X12),X11),X10) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),X9),X8),X7)
    <=> ( X12 = X9
        & X11 = X8
        & X10 = X7 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_triple_Oinject) ).

fof(fact_setprod__zero,axiom,
    ! [X2,X21,X5,X20] :
      ( class_Rings_Ocomm__semiring__1(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( ? [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),X21))
              & hAPP(X2,X3) = c_Groups_Ozero__class_Ozero(X20) )
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X2),X21) = c_Groups_Ozero__class_Ozero(X20) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__zero) ).

fof(fact_nat__mult__div__cancel__disj,axiom,
    ! [X57,X72,X96] :
      ( ( X96 = 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),X96),X72)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X96),X57)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X96 != 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),X96),X72)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X96),X57)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X72),X57) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__div__cancel__disj) ).

fof(fact_Pow__top,axiom,
    ! [X21,X5] : hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(c_Set_OPow(X5),X21))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__top) ).

fof(fact_rev_Osimps_I2_J,axiom,
    ! [X242,X66,X58] : hAPP(c_List_Orev(X58),hAPP(hAPP(c_List_Olist_OCons(X58),X66),X242)) = hAPP(hAPP(c_List_Oappend(X58),hAPP(c_List_Orev(X58),X242)),hAPP(hAPP(c_List_Olist_OCons(X58),X66),c_List_Olist_ONil(X58))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev_Osimps_I2_J) ).

fof(fact_zdiv__eq__0__iff,axiom,
    ! [X87,X82] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X82),X87) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    <=> ( X87 = 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)),X82))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X82),X87)) )
        | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X82),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X87),X82)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__eq__0__iff) ).

fof(fact_div__pos__pos__trivial,axiom,
    ! [X90,X62] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X62))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X62),X90))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X62),X90) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__pos__pos__trivial) ).

fof(fact_Inf__le__Sup,axiom,
    ! [X21,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Big__Operators_Olattice__class_OInf__fin(X5,X21)),c_Big__Operators_Olattice__class_OSup__fin(X5,X21))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__le__Sup) ).

fof(fact_map__replicate__const,axiom,
    ! [X301,X87,X5,X20] : hAPP(hAPP(c_List_Omap(X20,X5),hAPP(c_COMBK(X5,X20),X87)),X301) = c_List_Oreplicate(X5,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X20)),X301),X87),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__replicate__const) ).

fof(fact_part__equivp__transp,axiom,
    ! [X120,X33,X25,X32,X5] :
      ( c_Equiv__Relations_Opart__equivp(X5,X32)
     => ( hBOOL(hAPP(hAPP(X32,X25),X33))
       => ( hBOOL(hAPP(hAPP(X32,X33),X120))
         => hBOOL(hAPP(hAPP(X32,X25),X120)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_part__equivp__transp) ).

fof(fact_transpE,axiom,
    ! [X120,X33,X25,X171,X5] :
      ( c_Predicate_Otransp(X5,X171)
     => ( hBOOL(hAPP(hAPP(X171,X25),X33))
       => ( hBOOL(hAPP(hAPP(X171,X33),X120))
         => hBOOL(hAPP(hAPP(X171,X25),X120)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpE) ).

fof(fact_equivp__transp,axiom,
    ! [X120,X33,X25,X32,X5] :
      ( c_Equiv__Relations_Oequivp(X5,X32)
     => ( hBOOL(hAPP(hAPP(X32,X25),X33))
       => ( hBOOL(hAPP(hAPP(X32,X33),X120))
         => hBOOL(hAPP(hAPP(X32,X25),X120)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equivp__transp) ).

fof(fact_folding__one__idem_Oinsert__idem,axiom,
    ! [X25,X21,X205,X2,X5] :
      ( c_Finite__Set_Ofolding__one__idem(X5,X2,X205)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => hAPP(X205,hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(hAPP(X2,X25),hAPP(X205,X21)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Oinsert__idem) ).

fof(fact_mod__minus__cong,axiom,
    ! [X150,X90,X62,X58] :
      ( class_Divides_Oring__div(X58)
     => ( c_Divides_Odiv__class_Omod(X58,X62,X90) = c_Divides_Odiv__class_Omod(X58,X150,X90)
       => c_Divides_Odiv__class_Omod(X58,hAPP(c_Groups_Ouminus__class_Ouminus(X58),X62),X90) = c_Divides_Odiv__class_Omod(X58,hAPP(c_Groups_Ouminus__class_Ouminus(X58),X150),X90) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__minus__cong) ).

fof(fact_sublists__powset,axiom,
    ! [X239,X5] : hAPP(c_Set_Oimage(tc_List_Olist(X5),tc_fun(X5,tc_HOL_Obool),c_List_Oset(X5)),hAPP(c_List_Oset(tc_List_Olist(X5)),c_Enum_Osublists(X5,X239))) = hAPP(c_Set_OPow(X5),hAPP(c_List_Oset(X5),X239)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sublists__powset) ).

fof(fact_Inter__def,axiom,
    ! [X192,X5] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),X192) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X192),c_COMBI(tc_fun(X5,tc_HOL_Obool))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__def) ).

fof(fact_Union__def,axiom,
    ! [X192,X5] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X192) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X192),c_COMBI(tc_fun(X5,tc_HOL_Obool))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__def) ).

fof(fact_zabs__less__one__iff,axiom,
    ! [X120] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X120)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    <=> X120 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zabs__less__one__iff) ).

fof(fact_int__le__0__conv,axiom,
    ! [X50] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X50)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    <=> X50 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__le__0__conv) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J,axiom,
    ! [X57,X66] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X66))
     => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,X66)),X57) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X66),X57)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J) ).

fof(fact_nat__power__eq,axiom,
    ! [X57,X94] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X94))
     => hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X94),X57)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,X94)),X57) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__power__eq) ).

fof(fact_diff__cancel,axiom,
    ! [X57,X72,X96] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X96),X72)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X96),X57)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X72),X57),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__cancel) ).

fof(fact_diff__cancel2,axiom,
    ! [X57,X96,X72] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X72),X96)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X57),X96)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X72),X57),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__cancel2) ).

fof(fact_zpower__zpower,axiom,
    ! [X94,X65,X66] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X66),X65)),X94) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X66),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X65),X94)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zpower__zpower) ).

fof(fact_diff__diff__left,axiom,
    ! [X96,X97,X98] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X98),X97)),X96) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X98),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X97),X96)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__diff__left) ).

fof(fact_zmult__assoc,axiom,
    ! [X125,X126,X127] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X127),X126)),X125) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X127),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X126),X125)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__assoc) ).

fof(fact_nat__mult__assoc,axiom,
    ! [X96,X57,X72] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X72),X57)),X96) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X72),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X57),X96)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__assoc) ).

fof(fact_zadd__assoc,axiom,
    ! [X125,X126,X127] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X127),X126)),X125) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X127),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X126),X125)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__assoc) ).

fof(fact_nat__add__assoc,axiom,
    ! [X96,X57,X72] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X72),X57)),X96) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X72),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X57),X96)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__assoc) ).

fof(fact_div__mult2__eq,axiom,
    ! [X56,X90,X62] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X62),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X90),X56)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X62),X90)),X56),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult2__eq) ).

fof(fact_ball__empty,axiom,
    ! [X18,X5,X3] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X3),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))
     => hBOOL(hAPP(X18,X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ball__empty) ).

fof(fact_ivl__disj__int_I4_J,axiom,
    ! [X159,X156,X5] :
      ( class_Orderings_Oorder(X5)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X5),X156)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X156,X159)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I4_J) ).

fof(fact_ivl__disj__int_I3_J,axiom,
    ! [X159,X156,X5] :
      ( class_Orderings_Oorder(X5)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X5),X156)),c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X156,X159)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I3_J) ).

fof(fact_ivl__disj__int_I1_J,axiom,
    ! [X159,X156,X5] :
      ( class_Orderings_Oorder(X5)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X5),X156)),c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X156,X159)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I1_J) ).

fof(fact_mod__neg__neg__trivial,axiom,
    ! [X90,X62] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X62),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X90),X62))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,X62,X90) = X62 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__neg__neg__trivial) ).

fof(fact_set__map,axiom,
    ! [X239,X2,X20,X5] : hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Omap(X20,X5),X2),X239)) = hAPP(c_Set_Oimage(X20,X5,X2),hAPP(c_List_Oset(X20),X239)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__map) ).

fof(fact_append__take__drop__id,axiom,
    ! [X242,X57,X58] : hAPP(hAPP(c_List_Oappend(X58),hAPP(hAPP(c_List_Otake(X58),X57),X242)),hAPP(hAPP(c_List_Odrop(X58),X57),X242)) = X242,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__take__drop__id) ).

fof(fact_mod__Suc__eq__Suc__mod,axiom,
    ! [X57,X72] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X72),X57) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X72,X57)),X57),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__Suc__eq__Suc__mod) ).

fof(fact_com_Osize_I4_J,axiom,
    ! [X37,X38] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(X38,X37)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X38)),c_Com_Ocom_Ocom__size(X37))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osize_I4_J) ).

fof(fact_less__0__number__of,axiom,
    ! [X123] :
      ( 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),X123)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X123)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__0__number__of) ).

fof(fact_list__ex__append,axiom,
    ! [X251,X239,X18,X5] :
      ( c_List_Olist__ex(X5,X18,hAPP(hAPP(c_List_Oappend(X5),X239),X251))
    <=> ( c_List_Olist__ex(X5,X18,X239)
        | c_List_Olist__ex(X5,X18,X251) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__ex__append) ).

fof(fact_div__neg__neg__trivial,axiom,
    ! [X90,X62] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X62),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X90),X62))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X62),X90) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__neg__neg__trivial) ).

fof(fact_take__Suc__Cons,axiom,
    ! [X242,X66,X57,X58] : hAPP(hAPP(c_List_Otake(X58),hAPP(c_Nat_OSuc,X57)),hAPP(hAPP(c_List_Olist_OCons(X58),X66),X242)) = hAPP(hAPP(c_List_Olist_OCons(X58),X66),hAPP(hAPP(c_List_Otake(X58),X57),X242)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__Suc__Cons) ).

fof(fact_small__lazy__prod__def,axiom,
    ! [X91,X5,X58] :
      ( ( class_Lazy__Sequence_Osmall__lazy(X58)
        & class_Lazy__Sequence_Osmall__lazy(X5) )
     => c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_prod(X58,X5),X91) = c_Lazy__Sequence_Oproduct(X58,X5,c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(X58,X91),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(X5,X91)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_small__lazy__prod__def) ).

fof(fact_map__eq__imp__length__eq,axiom,
    ! [X251,X1,X116,X239,X2,X5,X20] :
      ( hAPP(hAPP(c_List_Omap(X20,X5),X2),X239) = hAPP(hAPP(c_List_Omap(X116,X5),X1),X251)
     => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X20)),X239) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X116)),X251) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__eq__imp__length__eq) ).

fof(fact_length__sublists,axiom,
    ! [X242,X58] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X58))),c_Enum_Osublists(X58,X242)) = 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(X58)),X242)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__sublists) ).

fof(fact_transfer__int__nat__set__return__embed,axiom,
    ! [X21] : 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)),X21)) = X21,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__set__return__embed) ).

fof(fact_fst__eqD,axiom,
    ! [X62,X65,X66,X5,X58] :
      ( hAPP(c_Product__Type_Ofst(X58,X5),hAPP(hAPP(c_Product__Type_OPair(X58,X5),X66),X65)) = X62
     => X66 = X62 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fst__eqD) ).

fof(fact_snd__eqD,axiom,
    ! [X62,X65,X66,X58,X5] :
      ( hAPP(c_Product__Type_Osnd(X5,X58),hAPP(hAPP(c_Product__Type_OPair(X5,X58),X66),X65)) = X62
     => X65 = X62 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_snd__eqD) ).

fof(fact_transfer__nat__int__set__return__embed,axiom,
    ! [X21] :
      ( c_Nat__Transfer_Onat__set(X21)
     => 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),X21)) = X21 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__set__return__embed) ).

fof(fact_finite__Field,axiom,
    ! [X171,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X5,X5)),X171))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(c_Relation_OField(X5),X171))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Field) ).

fof(fact_image__uminus__atLeastLessThan,axiom,
    ! [X33,X25,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => hAPP(c_Set_Oimage(X5,X5,c_Groups_Ouminus__class_Ouminus(X5)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X25),X33)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X5,hAPP(c_Groups_Ouminus__class_Ouminus(X5),X33),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X25)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__uminus__atLeastLessThan) ).

fof(fact_Suc__lessI,axiom,
    ! [X57,X72] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X72),X57))
     => ( hAPP(c_Nat_OSuc,X72) != X57
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X72)),X57)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__lessI) ).

fof(fact_finite__nat__set__iff__bounded__le,axiom,
    ! [X207] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X207))
    <=> ? [X86] :
        ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),X207))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X86)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__nat__set__iff__bounded__le) ).

fof(fact_finite__nat__set__iff__bounded,axiom,
    ! [X207] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X207))
    <=> ? [X86] :
        ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),X207))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X86)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__nat__set__iff__bounded) ).

fof(fact_diff__number__of__eq,axiom,
    ! [X128,X136,X58] :
      ( class_Int_Onumber__ring(X58)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X58),hAPP(c_Int_Onumber__class_Onumber__of(X58),X136)),hAPP(c_Int_Onumber__class_Onumber__of(X58),X128)) = hAPP(c_Int_Onumber__class_Onumber__of(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X136),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X128))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__number__of__eq) ).

fof(fact_distinct__n__lists,axiom,
    ! [X57,X242,X58] :
      ( hBOOL(hAPP(c_List_Odistinct(X58),X242))
     => hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X58)),c_Enum_On__lists(X58,X57,X242))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__n__lists) ).

fof(fact_zero__less__nat__eq,axiom,
    ! [X120] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,X120)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X120)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__nat__eq) ).

fof(fact_butlast__snoc,axiom,
    ! [X66,X242,X58] : c_List_Obutlast(X58,hAPP(hAPP(c_List_Oappend(X58),X242),hAPP(hAPP(c_List_Olist_OCons(X58),X66),c_List_Olist_ONil(X58)))) = X242,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_butlast__snoc) ).

fof(fact_last__snoc,axiom,
    ! [X66,X242,X58] : c_List_Olast(X58,hAPP(hAPP(c_List_Oappend(X58),X242),hAPP(hAPP(c_List_Olist_OCons(X58),X66),c_List_Olist_ONil(X58)))) = X66,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__snoc) ).

fof(fact_rtrancl__idemp__self__comp,axiom,
    ! [X32,X5] : hAPP(hAPP(c_Relation_Orel__comp(X5,X5,X5),c_Transitive__Closure_Ortrancl(X5,X32)),c_Transitive__Closure_Ortrancl(X5,X32)) = c_Transitive__Closure_Ortrancl(X5,X32),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__idemp__self__comp) ).

fof(fact_fst__def,axiom,
    ! [X160,X20,X5] : hAPP(c_Product__Type_Ofst(X5,X20),X160) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X5,X20,X5),c_COMBK(X5,X20)),X160),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fst__def) ).

fof(fact_finite__acyclic__wf__converse,axiom,
    ! [X171,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X5,X5)),X171))
     => ( c_Wellfounded_Oacyclic(X5,X171)
       => c_Wellfounded_Owf(X5,hAPP(c_Relation_Oconverse(X5,X5),X171)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__acyclic__wf__converse) ).

fof(fact_xt1_I5_J,axiom,
    ! [X66,X65,X58] :
      ( class_Orderings_Oorder(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X65),X66))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X66),X65))
         => X66 = X65 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I5_J) ).

fof(fact_order__antisym,axiom,
    ! [X65,X66,X58] :
      ( class_Orderings_Oorder(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X66),X65))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X65),X66))
         => X66 = X65 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__antisym) ).

fof(fact_order__antisym__conv,axiom,
    ! [X25,X33,X5] :
      ( class_Orderings_Oorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X33),X25))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X25),X33))
        <=> X25 = X33 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__antisym__conv) ).

fof(fact_order__eq__iff,axiom,
    ! [X33,X25,X5] :
      ( class_Orderings_Oorder(X5)
     => ( X25 = X33
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X25),X33))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X33),X25)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__eq__iff) ).

fof(fact_le__mod__geq,axiom,
    ! [X72,X57] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X57),X72))
     => c_Divides_Odiv__class_Omod(tc_Nat_Onat,X72,X57) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X72),X57),X57) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__mod__geq) ).

fof(fact_in__set__insert,axiom,
    ! [X239,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X239)))
     => c_List_Oinsert(X5,X25,X239) = X239 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__set__insert) ).

fof(fact_Suc__diff__le,axiom,
    ! [X72,X57] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X57),X72))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X72)),X57) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X72),X57)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__diff__le) ).

fof(fact_abs__ge__minus__self,axiom,
    ! [X62,X58] :
      ( class_Groups_Oordered__ab__group__add__abs(X58)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(c_Groups_Ouminus__class_Ouminus(X58),X62)),hAPP(c_Groups_Oabs__class_Oabs(X58),X62))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__ge__minus__self) ).

fof(fact_zero__le__square,axiom,
    ! [X62,X58] :
      ( class_Rings_Olinordered__ring(X58)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X62))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__square) ).

fof(fact_less__add__one,axiom,
    ! [X62,X58] :
      ( class_Rings_Olinordered__semidom(X58)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X62),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),c_Groups_Oone__class_Oone(X58)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__one) ).

fof(fact_zero__less__abs__iff,axiom,
    ! [X6,X5] :
      ( class_Groups_Oordered__ab__group__add__abs(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Groups_Oabs__class_Oabs(X5),X6)))
      <=> X6 != c_Groups_Ozero__class_Ozero(X5) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__abs__iff) ).

fof(fact_accp__downward,axiom,
    ! [X6,X24,X171,X5] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(X5,X171),X24))
     => ( hBOOL(hAPP(hAPP(X171,X6),X24))
       => hBOOL(hAPP(c_Wellfounded_Oaccp(X5,X171),X6)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_accp__downward) ).

fof(fact_hd__in__set,axiom,
    ! [X5,X239] :
      ( X239 != c_List_Olist_ONil(X5)
     => hBOOL(hAPP(hAPP(c_member(X5),hAPP(c_List_Ohd(X5),X239)),hAPP(c_List_Oset(X5),X239))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hd__in__set) ).

fof(fact_lazy__sequence_Osize_I4_J,axiom,
    ! [X303,X62,X58] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X58)),c_Lazy__Sequence_Olazy__sequence_OInsert(X58,X62,X303)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X58)),X303)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lazy__sequence_Osize_I4_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom,
    ! [X140,X66,X58] :
      ( class_Rings_Ocomm__semiring__1(X58)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X66),X140)),X66) = hAPP(hAPP(c_Power_Opower__class_Opower(X58),X66),hAPP(c_Nat_OSuc,X140)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J) ).

fof(fact_power__Suc2,axiom,
    ! [X57,X62,X58] :
      ( class_Groups_Omonoid__mult(X58)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),hAPP(c_Nat_OSuc,X57)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),X57)),X62) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__Suc2) ).

fof(fact_sorted__list__of__set__sort__remdups,axiom,
    ! [X239,X5] :
      ( class_Orderings_Olinorder(X5)
     => c_List_Olinorder__class_Osorted__list__of__set(X5,hAPP(c_List_Oset(X5),X239)) = c_List_Olinorder__class_Osort__key(X5,X5,c_COMBI(X5),c_List_Oremdups(X5,X239)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__list__of__set__sort__remdups) ).

fof(fact_com__det,axiom,
    ! [X55,X54,X48,X56] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X56),X48),X54))
     => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X56),X48),X55))
       => X55 = X54 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com__det) ).

fof(fact_list_Osize_I4_J,axiom,
    ! [X255,X62,X58] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),hAPP(hAPP(c_List_Olist_OCons(X58),X62),X255)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X255)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list_Osize_I4_J) ).

fof(fact_length__n__lists,axiom,
    ! [X242,X57,X58] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X58))),c_Enum_On__lists(X58,X57,X242)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242)),X57),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__n__lists) ).

fof(fact_transfer__int__nat__quantifiers_I2_J,axiom,
    ! [X18] :
      ( ? [X3] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
          & hBOOL(hAPP(X18,X3)) )
    <=> ? [X3] : hBOOL(hAPP(X18,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__quantifiers_I2_J) ).

fof(fact_Suc__leI,axiom,
    ! [X57,X72] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X72),X57))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X72)),X57)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__leI) ).

fof(fact_Inf__fin_Oin__idem,axiom,
    ! [X25,X21,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X25),c_Big__Operators_Olattice__class_OInf__fin(X5,X21)) = c_Big__Operators_Olattice__class_OInf__fin(X5,X21) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_Oin__idem) ).

fof(fact_Sup__fin_Oin__idem,axiom,
    ! [X25,X21,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X25),c_Big__Operators_Olattice__class_OSup__fin(X5,X21)) = c_Big__Operators_Olattice__class_OSup__fin(X5,X21) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_Oin__idem) ).

fof(fact_Max_Oin__idem,axiom,
    ! [X25,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X25),c_Big__Operators_Olinorder__class_OMax(X5,X21)) = c_Big__Operators_Olinorder__class_OMax(X5,X21) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max_Oin__idem) ).

fof(fact_Min_Oin__idem,axiom,
    ! [X25,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X25),c_Big__Operators_Olinorder__class_OMin(X5,X21)) = c_Big__Operators_Olinorder__class_OMin(X5,X21) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min_Oin__idem) ).

fof(fact_Sup__upper,axiom,
    ! [X21,X25,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X25),c_Complete__Lattice_OSup__class_OSup(X5,X21))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__upper) ).

fof(fact_list__ex__simps_I1_J,axiom,
    ! [X239,X25,X18,X5] :
      ( c_List_Olist__ex(X5,X18,hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239))
    <=> ( hBOOL(hAPP(X18,X25))
        | c_List_Olist__ex(X5,X18,X239) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__ex__simps_I1_J) ).

fof(fact_ivl__disj__int_I2_J,axiom,
    ! [X159,X156,X5] :
      ( class_Orderings_Oorder(X5)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X5),X156)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X156),X159)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ivl__disj__int_I2_J) ).

fof(fact_card__gt__0__iff,axiom,
    ! [X21,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X5),X21)))
    <=> ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__gt__0__iff) ).

fof(fact_nth__Cons__Suc,axiom,
    ! [X57,X242,X66,X58] : hAPP(hAPP(c_List_Onth(X58),hAPP(hAPP(c_List_Olist_OCons(X58),X66),X242)),hAPP(c_Nat_OSuc,X57)) = hAPP(hAPP(c_List_Onth(X58),X242),X57),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__Cons__Suc) ).

fof(fact_map__tl,axiom,
    ! [X239,X2,X5,X20] : hAPP(hAPP(c_List_Omap(X20,X5),X2),hAPP(c_List_Otl(X20),X239)) = hAPP(c_List_Otl(X5),hAPP(hAPP(c_List_Omap(X20,X5),X2),X239)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__tl) ).

fof(fact_rev__map,axiom,
    ! [X239,X2,X20,X5] : hAPP(c_List_Orev(X5),hAPP(hAPP(c_List_Omap(X20,X5),X2),X239)) = hAPP(hAPP(c_List_Omap(X20,X5),X2),hAPP(c_List_Orev(X20),X239)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__map) ).

fof(fact_ex__nat,axiom,
    ! [X18] :
      ( ? [X138] : hBOOL(hAPP(X18,X138))
    <=> ? [X3] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
          & hBOOL(hAPP(X18,hAPP(c_Int_Onat,X3))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ex__nat) ).

fof(fact_card__ge__0__finite,axiom,
    ! [X21,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X5),X21)))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__ge__0__finite) ).

fof(fact_list__all__append,axiom,
    ! [X251,X239,X18,X5] :
      ( c_List_Olist__all(X5,X18,hAPP(hAPP(c_List_Oappend(X5),X239),X251))
    <=> ( c_List_Olist__all(X5,X18,X239)
        & c_List_Olist__all(X5,X18,X251) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__all__append) ).

fof(fact_Suc__pred,axiom,
    ! [X57] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X57))
     => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X57),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = X57 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__pred) ).

fof(fact_singleton__inject,axiom,
    ! [X24,X6,X5] :
      ( hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(X5),X24),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))
     => X6 = X24 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_singleton__inject) ).

fof(fact_of__nat__inverse,axiom,
    ! [X33] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X33),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,X33)) = X33 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__inverse) ).

fof(fact_divide__eq__eq__number__of,axiom,
    ! [X121,X23,X24,X5] :
      ( ( class_Fields_Ofield__inverse__zero(X5)
        & class_Int_Onumber(X5) )
     => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X24),X23) = hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)
      <=> ( ( X23 != c_Groups_Ozero__class_Ozero(X5)
           => X24 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)),X23) )
          & ( X23 = c_Groups_Ozero__class_Ozero(X5)
           => hAPP(c_Int_Onumber__class_Onumber__of(X5),X121) = c_Groups_Ozero__class_Ozero(X5) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__eq__eq__number__of) ).

fof(fact_eq__divide__eq__number__of,axiom,
    ! [X23,X24,X121,X5] :
      ( ( class_Fields_Ofield__inverse__zero(X5)
        & class_Int_Onumber(X5) )
     => ( hAPP(c_Int_Onumber__class_Onumber__of(X5),X121) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X24),X23)
      <=> ( ( X23 != c_Groups_Ozero__class_Ozero(X5)
           => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)),X23) = X24 )
          & ( X23 = c_Groups_Ozero__class_Ozero(X5)
           => hAPP(c_Int_Onumber__class_Onumber__of(X5),X121) = c_Groups_Ozero__class_Ozero(X5) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__divide__eq__number__of) ).

fof(fact_le__Suc__eq,axiom,
    ! [X50,X95] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),hAPP(c_Nat_OSuc,X50)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X50))
        | X95 = hAPP(c_Nat_OSuc,X50) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__Suc__eq) ).

fof(fact_append__butlast__last__id,axiom,
    ! [X58,X242] :
      ( X242 != c_List_Olist_ONil(X58)
     => hAPP(hAPP(c_List_Oappend(X58),c_List_Obutlast(X58,X242)),hAPP(hAPP(c_List_Olist_OCons(X58),c_List_Olast(X58,X242)),c_List_Olist_ONil(X58))) = X242 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__butlast__last__id) ).

fof(fact_pair__collapse,axiom,
    ! [X162,X5,X58] : hAPP(hAPP(c_Product__Type_OPair(X58,X5),hAPP(c_Product__Type_Ofst(X58,X5),X162)),hAPP(c_Product__Type_Osnd(X58,X5),X162)) = X162,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__collapse) ).

fof(fact_surjective__pairing,axiom,
    ! [X5,X58,X54] : X54 = hAPP(hAPP(c_Product__Type_OPair(X58,X5),hAPP(c_Product__Type_Ofst(X58,X5),X54)),hAPP(c_Product__Type_Osnd(X58,X5),X54)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surjective__pairing) ).

fof(fact_insort__key_Osimps_I1_J,axiom,
    ! [X25,X2,X5,X20] :
      ( class_Orderings_Olinorder(X20)
     => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X20,X2),X25),c_List_Olist_ONil(X5)) = hAPP(hAPP(c_List_Olist_OCons(X5),X25),c_List_Olist_ONil(X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insort__key_Osimps_I1_J) ).

fof(fact_distinct__takeWhile,axiom,
    ! [X18,X239,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),X239))
     => hBOOL(hAPP(c_List_Odistinct(X5),c_List_OtakeWhile(X5,X18,X239))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__takeWhile) ).

fof(fact_distinct__insert,axiom,
    ! [X66,X242,X58] :
      ( hBOOL(hAPP(c_List_Odistinct(X58),X242))
     => hBOOL(hAPP(c_List_Odistinct(X58),c_List_Oinsert(X58,X66,X242))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__insert) ).

fof(fact_distinct__remove1,axiom,
    ! [X66,X242,X58] :
      ( hBOOL(hAPP(c_List_Odistinct(X58),X242))
     => hBOOL(hAPP(c_List_Odistinct(X58),c_List_Oremove1(X58,X66,X242))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__remove1) ).

fof(fact_distinct__sublistI,axiom,
    ! [X221,X239,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),X239))
     => hBOOL(hAPP(c_List_Odistinct(X5),c_List_Osublist(X5,X239,X221))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__sublistI) ).

fof(fact__01,axiom,
    ! [X304,X305,X66,X58] : c_Lazy__Sequence_Oappend(X58,c_Lazy__Sequence_Olazy__sequence_OInsert(X58,X66,X305),X304) = c_Lazy__Sequence_Olazy__sequence_OInsert(X58,X66,c_Lazy__Sequence_Oappend(X58,X305,X304)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__01) ).

fof(fact_remove1__commute,axiom,
    ! [X248,X65,X66,X58] : c_List_Oremove1(X58,X66,c_List_Oremove1(X58,X65,X248)) = c_List_Oremove1(X58,X65,c_List_Oremove1(X58,X66,X248)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_remove1__commute) ).

fof(fact_fun__left__comm_Ofun__left__comm,axiom,
    ! [X120,X33,X25,X2,X20,X5] :
      ( c_Finite__Set_Ofun__left__comm(X5,X20,X2)
     => hAPP(hAPP(X2,X25),hAPP(hAPP(X2,X33),X120)) = hAPP(hAPP(X2,X33),hAPP(hAPP(X2,X25),X120)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm_Ofun__left__comm) ).

fof(fact_inf__Sup__absorb,axiom,
    ! [X6,X21,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X21))
         => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X6),c_Big__Operators_Olattice__class_OSup__fin(X5,X21)) = X6 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__Sup__absorb) ).

fof(fact_sup__Inf__absorb,axiom,
    ! [X6,X21,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X21))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X6),c_Big__Operators_Olattice__class_OInf__fin(X5,X21)) = X6 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__Inf__absorb) ).

fof(fact_wfP__empty,axiom,
    ! [X5] : c_Wellfounded_OwfP(X5,hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X5),hAPP(c_COMBK(tc_HOL_Obool,X5),c_fFalse))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfP__empty) ).

fof(fact_of__nat__induct,axiom,
    ! [X25,X18] :
      ( ! [X177] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X177),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
         => hBOOL(hAPP(X18,hAPP(c_Code__Numeral_Oof__nat,X177))) )
     => hBOOL(hAPP(X18,X25)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__induct) ).

fof(fact_inf__sup__ord_I3_J,axiom,
    ! [X65,X66,X58] :
      ( class_Lattices_Olattice(X58)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X66),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X66),X65))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__ord_I3_J) ).

fof(fact_sup__ge1,axiom,
    ! [X65,X66,X58] :
      ( class_Lattices_Osemilattice__sup(X58)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X66),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X66),X65))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__ge1) ).

fof(fact_inf__sup__ord_I4_J,axiom,
    ! [X66,X65,X58] :
      ( class_Lattices_Olattice(X58)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X65),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X66),X65))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__ord_I4_J) ).

fof(fact_sup__ge2,axiom,
    ! [X66,X65,X58] :
      ( class_Lattices_Osemilattice__sup(X58)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X65),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X66),X65))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__ge2) ).

fof(fact_le__maxI1,axiom,
    ! [X65,X66,X58] :
      ( class_Orderings_Olinorder(X58)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X66),hAPP(hAPP(c_Orderings_Oord__class_Omax(X58),X66),X65))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__maxI1) ).

fof(fact_le__maxI2,axiom,
    ! [X66,X65,X58] :
      ( class_Orderings_Olinorder(X58)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X65),hAPP(hAPP(c_Orderings_Oord__class_Omax(X58),X66),X65))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__maxI2) ).

fof(fact_CollectE,axiom,
    ! [X18,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(c_Set_OCollect(X5),X18)))
     => hBOOL(hAPP(X18,X6)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_CollectE) ).

fof(fact_CollectD,axiom,
    ! [X18,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(c_Set_OCollect(X5),X18)))
     => hBOOL(hAPP(X18,X6)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_CollectD) ).

fof(fact_mem__Collect__eq,axiom,
    ! [X18,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(c_Set_OCollect(X5),X18)))
    <=> hBOOL(hAPP(X18,X6)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__Collect__eq) ).

fof(fact_Suc__nat__eq__nat__zadd1,axiom,
    ! [X94] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X94))
     => hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,X94)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X94)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__nat__eq__nat__zadd1) ).

fof(fact_remove1_Osimps_I2_J,axiom,
    ! [X242,X58,X65,X66] :
      ( ( X66 = X65
       => c_List_Oremove1(X58,X66,hAPP(hAPP(c_List_Olist_OCons(X58),X65),X242)) = X242 )
      & ( X66 != X65
       => c_List_Oremove1(X58,X66,hAPP(hAPP(c_List_Olist_OCons(X58),X65),X242)) = hAPP(hAPP(c_List_Olist_OCons(X58),X65),c_List_Oremove1(X58,X66,X242)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_remove1_Osimps_I2_J) ).

fof(fact_less__Suc__eq,axiom,
    ! [X50,X95] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),hAPP(c_Nat_OSuc,X50)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),X50))
        | X95 = X50 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq) ).

fof(fact_Image__Id__on,axiom,
    ! [X113,X21,X5] : hAPP(c_Relation_OImage(X5,X5,c_Relation_OId__on(X5,X21)),X113) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__Id__on) ).

fof(fact_inf_Oleft__commute,axiom,
    ! [X56,X62,X90,X58] :
      ( class_Lattices_Osemilattice__inf(X58)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X90),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X62),X56)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X62),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X90),X56)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf_Oleft__commute) ).

fof(fact_inf__left__commute,axiom,
    ! [X94,X65,X66,X58] :
      ( class_Lattices_Osemilattice__inf(X58)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X66),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X65),X94)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X65),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X66),X94)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__left__commute) ).

fof(fact_inf__sup__aci_I3_J,axiom,
    ! [X94,X65,X66,X58] :
      ( class_Lattices_Olattice(X58)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X66),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X65),X94)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X65),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X66),X94)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__aci_I3_J) ).

fof(fact_inf__sup__aci_I7_J,axiom,
    ! [X94,X65,X66,X58] :
      ( class_Lattices_Olattice(X58)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X66),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X65),X94)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X65),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X66),X94)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__aci_I7_J) ).

fof(fact_sup__left__commute,axiom,
    ! [X94,X65,X66,X58] :
      ( class_Lattices_Osemilattice__sup(X58)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X66),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X65),X94)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X65),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X66),X94)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__left__commute) ).

fof(fact_sup_Oleft__commute,axiom,
    ! [X56,X62,X90,X58] :
      ( class_Lattices_Osemilattice__sup(X58)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X90),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X62),X56)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X62),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X90),X56)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup_Oleft__commute) ).

fof(fact_min__max_Osup__left__commute,axiom,
    ! [X94,X65,X66,X58] :
      ( class_Orderings_Olinorder(X58)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(X58),X66),hAPP(hAPP(c_Orderings_Oord__class_Omax(X58),X65),X94)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X58),X65),hAPP(hAPP(c_Orderings_Oord__class_Omax(X58),X66),X94)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup__left__commute) ).

fof(fact_min__max_Osup_Oleft__commute,axiom,
    ! [X56,X62,X90,X58] :
      ( class_Orderings_Olinorder(X58)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(X58),X90),hAPP(hAPP(c_Orderings_Oord__class_Omax(X58),X62),X56)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X58),X62),hAPP(hAPP(c_Orderings_Oord__class_Omax(X58),X90),X56)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup_Oleft__commute) ).

fof(fact_min__max_Oinf_Oleft__commute,axiom,
    ! [X56,X62,X90,X58] :
      ( class_Orderings_Olinorder(X58)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(X58),X90),hAPP(hAPP(c_Orderings_Oord__class_Omin(X58),X62),X56)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X58),X62),hAPP(hAPP(c_Orderings_Oord__class_Omin(X58),X90),X56)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf_Oleft__commute) ).

fof(fact_min__max_Oinf__left__commute,axiom,
    ! [X94,X65,X66,X58] :
      ( class_Orderings_Olinorder(X58)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(X58),X66),hAPP(hAPP(c_Orderings_Oord__class_Omin(X58),X65),X94)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X58),X65),hAPP(hAPP(c_Orderings_Oord__class_Omin(X58),X66),X94)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__left__commute) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
    ! [X129,X130,X132,X58] :
      ( class_Rings_Ocomm__semiring__1(X58)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X132),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X130),X129)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X130),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X132),X129)) ),
    file('/export/starexec/sandbox/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,
    ! [X91,X56,X62,X58] :
      ( class_Rings_Ocomm__semiring__1(X58)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X56),X91)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X56),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),X91)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).

fof(fact_add__minus__cancel,axiom,
    ! [X90,X62,X58] :
      ( class_Groups_Ogroup__add(X58)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(c_Groups_Ouminus__class_Ouminus(X58),X62)),X90)) = X90 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__minus__cancel) ).

fof(fact_nat__mult__eq__cancel1,axiom,
    ! [X50,X95,X87] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X87))
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X87),X95) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X87),X50)
      <=> X95 = X50 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel1) ).

fof(fact_less__Suc__eq__le,axiom,
    ! [X50,X95] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),hAPP(c_Nat_OSuc,X50)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X50)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq__le) ).

fof(fact_one__div__nat__number__of,axiom,
    ! [X164] : 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),X164)) = 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),X164))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__div__nat__number__of) ).

fof(fact_split__nat,axiom,
    ! [X82,X18] :
      ( hBOOL(hAPP(X18,hAPP(c_Int_Onat,X82)))
    <=> ( ! [X69] :
            ( X82 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X69)
           => hBOOL(hAPP(X18,X69)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X82),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => hBOOL(hAPP(X18,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__nat) ).

fof(fact_distinct__drop,axiom,
    ! [X98,X242,X58] :
      ( hBOOL(hAPP(c_List_Odistinct(X58),X242))
     => hBOOL(hAPP(c_List_Odistinct(X58),hAPP(hAPP(c_List_Odrop(X58),X98),X242))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__drop) ).

fof(fact_distinct__take,axiom,
    ! [X98,X242,X58] :
      ( hBOOL(hAPP(c_List_Odistinct(X58),X242))
     => hBOOL(hAPP(c_List_Odistinct(X58),hAPP(hAPP(c_List_Otake(X58),X98),X242))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__take) ).

fof(fact_finite_OinsertI,axiom,
    ! [X6,X21,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(hAPP(c_Set_Oinsert(X5),X6),X21))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite_OinsertI) ).

fof(fact_image__Suc__atLeastAtMost,axiom,
    ! [X157,X82] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X82,X157)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X82),hAPP(c_Nat_OSuc,X157)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__Suc__atLeastAtMost) ).

fof(fact_INT__empty,axiom,
    ! [X113,X5,X20] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X20,tc_fun(X5,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X20,tc_HOL_Obool))),X113) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__empty) ).

fof(fact_minus__numeral__code_I6_J,axiom,
    ! [X128,X136] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X136),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X128))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__numeral__code_I6_J) ).

fof(fact_Compl__eq__Diff__UNIV,axiom,
    ! [X21,X5] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X21) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),X21),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__eq__Diff__UNIV) ).

fof(fact_map__butlast,axiom,
    ! [X239,X2,X5,X20] : hAPP(hAPP(c_List_Omap(X20,X5),X2),c_List_Obutlast(X20,X239)) = c_List_Obutlast(X5,hAPP(hAPP(c_List_Omap(X20,X5),X2),X239)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__butlast) ).

fof(fact_Min__in,axiom,
    ! [X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => hBOOL(hAPP(hAPP(c_member(X5),c_Big__Operators_Olinorder__class_OMin(X5,X21)),X21)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min__in) ).

fof(fact_Max__in,axiom,
    ! [X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => hBOOL(hAPP(hAPP(c_member(X5),c_Big__Operators_Olinorder__class_OMax(X5,X21)),X21)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max__in) ).

fof(fact_nat__of__cases,axiom,
    ! [X33] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X33),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
     => ~ ! [X3] : X33 != hAPP(c_Code__Numeral_Onat__of,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__of__cases) ).

fof(fact_all__nat,axiom,
    ! [X18] :
      ( ! [X138] : hBOOL(hAPP(X18,X138))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
         => hBOOL(hAPP(X18,hAPP(c_Int_Onat,X3))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_all__nat) ).

fof(fact_insertI1,axiom,
    ! [X113,X6,X5] : hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(hAPP(c_Set_Oinsert(X5),X6),X113))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertI1) ).

fof(fact_mod__Suc,axiom,
    ! [X57,X72] :
      ( ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X72,X57)) = X57
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X72),X57) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X72,X57)) != X57
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X72),X57) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X72,X57)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__Suc) ).

fof(fact_inv__id,axiom,
    ! [X5] : c_Hilbert__Choice_Oinv__into(X5,X5,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),c_Fun_Oid(X5)) = c_Fun_Oid(X5),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__id) ).

fof(fact_insert__commute,axiom,
    ! [X21,X33,X25,X5] : hAPP(hAPP(c_Set_Oinsert(X5),X25),hAPP(hAPP(c_Set_Oinsert(X5),X33),X21)) = hAPP(hAPP(c_Set_Oinsert(X5),X33),hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__commute) ).

fof(fact_folding__one_Osingleton,axiom,
    ! [X25,X205,X2,X5] :
      ( c_Finite__Set_Ofolding__one(X5,X2,X205)
     => hAPP(X205,hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = X25 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one_Osingleton) ).

fof(fact_diff__Suc__eq__diff__pred,axiom,
    ! [X57,X72] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X72),hAPP(c_Nat_OSuc,X57)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X72),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X57),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__eq__diff__pred) ).

fof(fact_less__imp__add__positive,axiom,
    ! [X97,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),X97))
     => ? [X100] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X100))
          & hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),X100) = X97 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__add__positive) ).

fof(fact_fold__empty,axiom,
    ! [X120,X2,X5,X20] : hAPP(hAPP(c_Finite__Set_Ofold(X20,X5,X2),X120),c_Orderings_Obot__class_Obot(tc_fun(X20,tc_HOL_Obool))) = X120,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__empty) ).

fof(fact_length__drop,axiom,
    ! [X242,X57,X58] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),hAPP(hAPP(c_List_Odrop(X58),X57),X242)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242)),X57),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__drop) ).

fof(fact_length__take,axiom,
    ! [X242,X57,X58] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),hAPP(hAPP(c_List_Otake(X58),X57),X242)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242)),X57),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__take) ).

fof(fact_inj__of__nat,axiom,
    ! [X5] :
      ( class_Nat_Osemiring__char__0(X5)
     => c_Fun_Oinj__on(tc_Nat_Onat,X5,c_Nat_Osemiring__1__class_Oof__nat(X5),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__of__nat) ).

fof(fact_take__tl,axiom,
    ! [X242,X57,X58] : hAPP(hAPP(c_List_Otake(X58),X57),hAPP(c_List_Otl(X58),X242)) = hAPP(c_List_Otl(X58),hAPP(hAPP(c_List_Otake(X58),hAPP(c_Nat_OSuc,X57)),X242)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__tl) ).

fof(fact_less__imp__Suc__add,axiom,
    ! [X57,X72] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X72),X57))
     => ? [X100] : X57 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X72),X100)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__Suc__add) ).

fof(fact_less__iff__Suc__add,axiom,
    ! [X50,X95] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),X50))
    <=> ? [X100] : X50 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X95),X100)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__iff__Suc__add) ).

fof(fact_drop__replicate,axiom,
    ! [X66,X96,X98,X58] : hAPP(hAPP(c_List_Odrop(X58),X98),c_List_Oreplicate(X58,X96,X66)) = c_List_Oreplicate(X58,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X96),X98),X66),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__replicate) ).

fof(fact_take__replicate,axiom,
    ! [X66,X96,X98,X58] : hAPP(hAPP(c_List_Otake(X58),X98),c_List_Oreplicate(X58,X96,X66)) = c_List_Oreplicate(X58,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X98),X96),X66),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__replicate) ).

fof(fact_SetInterval_Otransfer__nat__int__set__functions_I1_J,axiom,
    ! [X50] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X50) = 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),X50))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SetInterval_Otransfer__nat__int__set__functions_I1_J) ).

fof(fact_list__all__simps_I1_J,axiom,
    ! [X239,X25,X18,X5] :
      ( c_List_Olist__all(X5,X18,hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239))
    <=> ( hBOOL(hAPP(X18,X25))
        & c_List_Olist__all(X5,X18,X239) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__all__simps_I1_J) ).

fof(fact_nonzero__abs__divide,axiom,
    ! [X62,X90,X58] :
      ( class_Fields_Olinordered__field(X58)
     => ( X90 != c_Groups_Ozero__class_Ozero(X58)
       => hAPP(c_Groups_Oabs__class_Oabs(X58),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X62),X90)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),hAPP(c_Groups_Oabs__class_Oabs(X58),X62)),hAPP(c_Groups_Oabs__class_Oabs(X58),X90)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__abs__divide) ).

fof(fact_card_Oneutral,axiom,
    ! [X21,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
     => ( ( ? [X3] : hBOOL(hAPP(hAPP(c_member(X5),X3),X21))
         => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
       => hAPP(c_Finite__Set_Ocard(X5),X21) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card_Oneutral) ).

fof(fact_Compl__disjoint,axiom,
    ! [X21,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X21)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__disjoint) ).

fof(fact_Compl__partition,axiom,
    ! [X21,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X21)) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__partition) ).

fof(fact_inj__on__empty,axiom,
    ! [X2,X20,X5] : c_Fun_Oinj__on(X5,X20,X2,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__empty) ).

fof(fact_zle__antisym,axiom,
    ! [X128,X94] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X94),X128))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X128),X94))
       => X94 = X128 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__antisym) ).

fof(fact_le__antisym,axiom,
    ! [X57,X72] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X72),X57))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X57),X72))
       => X72 = X57 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__antisym) ).

fof(fact_zmod__minus1,axiom,
    ! [X90] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X90))
     => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),X90) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X90),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__minus1) ).

fof(fact_Min__insert,axiom,
    ! [X25,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => c_Big__Operators_Olinorder__class_OMin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X25),c_Big__Operators_Olinorder__class_OMin(X5,X21)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min__insert) ).

fof(fact_Max__insert,axiom,
    ! [X25,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => c_Big__Operators_Olinorder__class_OMax(X5,hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X25),c_Big__Operators_Olinorder__class_OMax(X5,X21)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max__insert) ).

fof(fact_Sup__fin_Oinsert__idem,axiom,
    ! [X25,X21,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => c_Big__Operators_Olattice__class_OSup__fin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X25),c_Big__Operators_Olattice__class_OSup__fin(X5,X21)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_Oinsert__idem) ).

fof(fact_Inf__fin_Oinsert__idem,axiom,
    ! [X25,X21,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => c_Big__Operators_Olattice__class_OInf__fin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X25),c_Big__Operators_Olattice__class_OInf__fin(X5,X21)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_Oinsert__idem) ).

fof(fact_Un__empty,axiom,
    ! [X113,X21,X5] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
    <=> ( X21 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
        & X113 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__empty) ).

fof(fact_listsum__append,axiom,
    ! [X241,X242,X58] :
      ( class_Groups_Omonoid__add(X58)
     => hAPP(c_List_Omonoid__add__class_Olistsum(X58),hAPP(hAPP(c_List_Oappend(X58),X242),X241)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(c_List_Omonoid__add__class_Olistsum(X58),X242)),hAPP(c_List_Omonoid__add__class_Olistsum(X58),X241)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__append) ).

fof(fact_abs__divide,axiom,
    ! [X90,X62,X58] :
      ( class_Fields_Olinordered__field__inverse__zero(X58)
     => hAPP(c_Groups_Oabs__class_Oabs(X58),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X62),X90)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),hAPP(c_Groups_Oabs__class_Oabs(X58),X62)),hAPP(c_Groups_Oabs__class_Oabs(X58),X90)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__divide) ).

fof(fact_abs__mult,axiom,
    ! [X90,X62,X58] :
      ( class_Rings_Olinordered__idom(X58)
     => hAPP(c_Groups_Oabs__class_Oabs(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X90)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),hAPP(c_Groups_Oabs__class_Oabs(X58),X62)),hAPP(c_Groups_Oabs__class_Oabs(X58),X90)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__mult) ).

fof(fact_compl__inf,axiom,
    ! [X65,X66,X58] :
      ( class_Lattices_Oboolean__algebra(X58)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X58),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X66),X65)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),hAPP(c_Groups_Ouminus__class_Ouminus(X58),X66)),hAPP(c_Groups_Ouminus__class_Ouminus(X58),X65)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compl__inf) ).

fof(fact_compl__sup,axiom,
    ! [X65,X66,X58] :
      ( class_Lattices_Oboolean__algebra(X58)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X58),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X66),X65)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),hAPP(c_Groups_Ouminus__class_Ouminus(X58),X66)),hAPP(c_Groups_Ouminus__class_Ouminus(X58),X65)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compl__sup) ).

fof(fact_minus__max__eq__min,axiom,
    ! [X65,X66,X58] :
      ( class_Groups_Olinordered__ab__group__add(X58)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X58),hAPP(hAPP(c_Orderings_Oord__class_Omax(X58),X66),X65)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X58),hAPP(c_Groups_Ouminus__class_Ouminus(X58),X66)),hAPP(c_Groups_Ouminus__class_Ouminus(X58),X65)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__max__eq__min) ).

fof(fact_minus__min__eq__max,axiom,
    ! [X65,X66,X58] :
      ( class_Groups_Olinordered__ab__group__add(X58)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X58),hAPP(hAPP(c_Orderings_Oord__class_Omin(X58),X66),X65)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X58),hAPP(c_Groups_Ouminus__class_Ouminus(X58),X66)),hAPP(c_Groups_Ouminus__class_Ouminus(X58),X65)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__min__eq__max) ).

fof(fact_minus__add__distrib,axiom,
    ! [X90,X62,X58] :
      ( class_Groups_Oab__group__add(X58)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),X90)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(c_Groups_Ouminus__class_Ouminus(X58),X62)),hAPP(c_Groups_Ouminus__class_Ouminus(X58),X90)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__add__distrib) ).

fof(fact_minus__add,axiom,
    ! [X90,X62,X58] :
      ( class_Groups_Ogroup__add(X58)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),X90)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(c_Groups_Ouminus__class_Ouminus(X58),X90)),hAPP(c_Groups_Ouminus__class_Ouminus(X58),X62)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__add) ).

fof(fact_Cantors__paradox,axiom,
    ! [X21,X5] :
      ~ ? [X227] : hAPP(c_Set_Oimage(X5,tc_fun(X5,tc_HOL_Obool),X227),X21) = hAPP(c_Set_OPow(X5),X21),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Cantors__paradox) ).

fof(fact_equalityD1,axiom,
    ! [X5,X113,X21] :
      ( X21 = X113
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),X113)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityD1) ).

fof(fact_equalityD2,axiom,
    ! [X5,X113,X21] :
      ( X21 = X113
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X113),X21)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityD2) ).

fof(fact_last__in__set,axiom,
    ! [X5,X273] :
      ( X273 != c_List_Olist_ONil(X5)
     => hBOOL(hAPP(hAPP(c_member(X5),c_List_Olast(X5,X273)),hAPP(c_List_Oset(X5),X273))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__in__set) ).

fof(fact_Suc__mult__cancel1,axiom,
    ! [X50,X95,X87] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X87)),X95) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X87)),X50)
    <=> X95 = X50 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mult__cancel1) ).

fof(fact_Pair__eq,axiom,
    ! [X179,X180,X24,X6,X20,X5] :
      ( hAPP(hAPP(c_Product__Type_OPair(X5,X20),X6),X24) = hAPP(hAPP(c_Product__Type_OPair(X5,X20),X180),X179)
    <=> ( X6 = X180
        & X24 = X179 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pair__eq) ).

fof(fact_Pair__inject,axiom,
    ! [X143,X150,X90,X62,X5,X58] :
      ( hAPP(hAPP(c_Product__Type_OPair(X58,X5),X62),X90) = hAPP(hAPP(c_Product__Type_OPair(X58,X5),X150),X143)
     => ~ ( X62 = X150
         => X90 != X143 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pair__inject) ).

fof(fact_zmod__zminus1__eq__if,axiom,
    ! [X90,X62] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X62,X90) = 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),X62),X90) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X62,X90) != 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),X62),X90) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X90),c_Divides_Odiv__class_Omod(tc_Int_Oint,X62,X90)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zminus1__eq__if) ).

fof(fact_subset__refl,axiom,
    ! [X21,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),X21)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__refl) ).

fof(fact_image__Suc__atLeastLessThan,axiom,
    ! [X157,X82] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X82),X157)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X82)),hAPP(c_Nat_OSuc,X157)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__Suc__atLeastLessThan) ).

fof(fact_rev__append,axiom,
    ! [X241,X242,X58] : hAPP(c_List_Orev(X58),hAPP(hAPP(c_List_Oappend(X58),X242),X241)) = hAPP(hAPP(c_List_Oappend(X58),hAPP(c_List_Orev(X58),X241)),hAPP(c_List_Orev(X58),X242)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__append) ).

fof(fact_rotate__simps,axiom,
    ! [X242,X66,X5,X58] :
      ( hAPP(c_List_Orotate1(X58),c_List_Olist_ONil(X58)) = c_List_Olist_ONil(X58)
      & hAPP(c_List_Orotate1(X5),hAPP(hAPP(c_List_Olist_OCons(X5),X66),X242)) = hAPP(hAPP(c_List_Oappend(X5),X242),hAPP(hAPP(c_List_Olist_OCons(X5),X66),c_List_Olist_ONil(X5))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate__simps) ).

fof(fact_le__SucI,axiom,
    ! [X57,X72] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X72),X57))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X72),hAPP(c_Nat_OSuc,X57))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__SucI) ).

fof(fact_le__imp__less__Suc,axiom,
    ! [X57,X72] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X72),X57))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X72),hAPP(c_Nat_OSuc,X57))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__less__Suc) ).

fof(fact_less__SucI,axiom,
    ! [X57,X72] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X72),X57))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X72),hAPP(c_Nat_OSuc,X57))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__SucI) ).

fof(fact_greaterThanAtMost__upto,axiom,
    ! [X157,X82] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X82,X157) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X82),c_Groups_Oone__class_Oone(tc_Int_Oint)),X157)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThanAtMost__upto) ).

fof(fact_Ints__double__eq__0__iff,axiom,
    ! [X6,X5] :
      ( class_Int_Oring__char__0(X5)
     => ( hBOOL(hAPP(hAPP(c_member(X5),X6),c_Int_Oring__1__class_OInts(X5)))
       => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),X6) = c_Groups_Ozero__class_Ozero(X5)
        <=> X6 = c_Groups_Ozero__class_Ozero(X5) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__double__eq__0__iff) ).

fof(fact_div__eq__minus1,axiom,
    ! [X90] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X90))
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),X90) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__eq__minus1) ).

fof(fact_Int__commute,axiom,
    ! [X113,X21,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X113),X21),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__commute) ).

fof(fact_Un__commute,axiom,
    ! [X113,X21,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X113),X21),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__commute) ).

fof(fact_triple_Osize_I1_J,axiom,
    ! [X10,X11,X12,X80,X5] : c_Hoare__Mirabelle_Otriple_Otriple__size(X5,X80,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),X12),X11),X10)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_triple_Osize_I1_J) ).

fof(fact_zero__less__imp__eq__int,axiom,
    ! [X96] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X96))
     => ? [X69] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X69))
          & X96 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X69) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__imp__eq__int) ).

fof(fact_frac__eq__eq,axiom,
    ! [X121,X25,X120,X33,X5] :
      ( class_Fields_Ofield(X5)
     => ( X33 != c_Groups_Ozero__class_Ozero(X5)
       => ( X120 != c_Groups_Ozero__class_Ozero(X5)
         => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X25),X33) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X121),X120)
          <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X25),X120) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X121),X33) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_frac__eq__eq) ).

fof(fact_zmult__div__cancel,axiom,
    ! [X72,X57] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X57),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X72),X57)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X72),c_Divides_Odiv__class_Omod(tc_Int_Oint,X72,X57)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__div__cancel) ).

fof(fact_mult__div__cancel,axiom,
    ! [X72,X57] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X57),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X72),X57)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X72),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X72,X57)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__div__cancel) ).

fof(fact_minus__code__numeral__def,axiom,
    ! [X72,X57] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X57),X72) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X57)),hAPP(c_Code__Numeral_Onat__of,X72))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__code__numeral__def) ).

fof(fact_div__code__numeral__def,axiom,
    ! [X72,X57] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X57),X72) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X57)),hAPP(c_Code__Numeral_Onat__of,X72))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__code__numeral__def) ).

fof(fact_times__code__numeral__def,axiom,
    ! [X72,X57] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),X57),X72) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X57)),hAPP(c_Code__Numeral_Onat__of,X72))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_times__code__numeral__def) ).

fof(fact_plus__code__numeral__def,axiom,
    ! [X72,X57] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X57),X72) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X57)),hAPP(c_Code__Numeral_Onat__of,X72))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_plus__code__numeral__def) ).

fof(fact_diff__diff__cancel,axiom,
    ! [X57,X98] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X98),X57))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X57),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X57),X98)) = X98 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__diff__cancel) ).

fof(fact_le__add__diff__inverse,axiom,
    ! [X72,X57] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X57),X72))
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X57),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X72),X57)) = X72 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add__diff__inverse) ).

fof(fact_nat__case__Suc,axiom,
    ! [X68,X89,X19,X5] : c_Nat_Onat_Onat__case(X5,X19,X89,hAPP(c_Nat_OSuc,X68)) = hAPP(X89,X68),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__case__Suc) ).

fof(fact_listsum__eq__0__nat__iff__nat,axiom,
    ! [X272] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X272) = 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),X272)))
         => X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__eq__0__nat__iff__nat) ).

fof(fact_xt1_I11_J,axiom,
    ! [X62,X90,X58] :
      ( class_Orderings_Oorder(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X90),X62))
       => ( X62 != X90
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X90),X62)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I11_J) ).

fof(fact_order__le__neq__trans,axiom,
    ! [X90,X62,X58] :
      ( class_Orderings_Oorder(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X62),X90))
       => ( X62 != X90
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X62),X90)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__neq__trans) ).

fof(fact_order__le__imp__less__or__eq,axiom,
    ! [X65,X66,X58] :
      ( class_Orderings_Oorder(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X66),X65))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X66),X65))
          | X66 = X65 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__imp__less__or__eq) ).

fof(fact_order__neq__le__trans,axiom,
    ! [X90,X62,X58] :
      ( class_Orderings_Oorder(X58)
     => ( X62 != X90
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X62),X90))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X62),X90)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__neq__le__trans) ).

fof(fact_order__le__less,axiom,
    ! [X33,X25,X5] :
      ( class_Orderings_Oorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X25),X33))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X25),X33))
          | X25 = X33 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__less) ).

fof(fact_order__less__le,axiom,
    ! [X33,X25,X5] :
      ( class_Orderings_Oorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X25),X33))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X25),X33))
          & X25 != X33 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__le) ).

fof(fact_xt1_I12_J,axiom,
    ! [X90,X62,X58] :
      ( class_Orderings_Oorder(X58)
     => ( X62 != X90
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X90),X62))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X90),X62)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I12_J) ).

fof(fact_arith__simps_I32_J,axiom,
    ! [X128,X136,X58] :
      ( class_Int_Onumber__ring(X58)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),hAPP(c_Int_Onumber__class_Onumber__of(X58),X136)),hAPP(c_Int_Onumber__class_Onumber__of(X58),X128)) = hAPP(c_Int_Onumber__class_Onumber__of(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X136),X128)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_arith__simps_I32_J) ).

fof(fact_add__number__of__eq,axiom,
    ! [X128,X136,X58] :
      ( class_Int_Onumber__ring(X58)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(c_Int_Onumber__class_Onumber__of(X58),X136)),hAPP(c_Int_Onumber__class_Onumber__of(X58),X128)) = hAPP(c_Int_Onumber__class_Onumber__of(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X136),X128)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__number__of__eq) ).

fof(fact_number__of__diff,axiom,
    ! [X128,X136,X58] :
      ( class_Int_Onumber__ring(X58)
     => hAPP(c_Int_Onumber__class_Onumber__of(X58),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X136),X128)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X58),hAPP(c_Int_Onumber__class_Onumber__of(X58),X136)),hAPP(c_Int_Onumber__class_Onumber__of(X58),X128)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__diff) ).

fof(fact_number__of__mult,axiom,
    ! [X128,X136,X58] :
      ( class_Int_Onumber__ring(X58)
     => hAPP(c_Int_Onumber__class_Onumber__of(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X136),X128)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),hAPP(c_Int_Onumber__class_Onumber__of(X58),X136)),hAPP(c_Int_Onumber__class_Onumber__of(X58),X128)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__mult) ).

fof(fact_number__of__add,axiom,
    ! [X128,X136,X58] :
      ( class_Int_Onumber__ring(X58)
     => hAPP(c_Int_Onumber__class_Onumber__of(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X136),X128)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(c_Int_Onumber__class_Onumber__of(X58),X136)),hAPP(c_Int_Onumber__class_Onumber__of(X58),X128)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__add) ).

fof(fact_of__int__diff,axiom,
    ! [X94,X128,X58] :
      ( class_Rings_Oring__1(X58)
     => hAPP(c_Int_Oring__1__class_Oof__int(X58),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X128),X94)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X58),hAPP(c_Int_Oring__1__class_Oof__int(X58),X128)),hAPP(c_Int_Oring__1__class_Oof__int(X58),X94)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__diff) ).

fof(fact_of__int__mult,axiom,
    ! [X94,X128,X58] :
      ( class_Rings_Oring__1(X58)
     => hAPP(c_Int_Oring__1__class_Oof__int(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X128),X94)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),hAPP(c_Int_Oring__1__class_Oof__int(X58),X128)),hAPP(c_Int_Oring__1__class_Oof__int(X58),X94)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__mult) ).

fof(fact_of__int__add,axiom,
    ! [X94,X128,X58] :
      ( class_Rings_Oring__1(X58)
     => hAPP(c_Int_Oring__1__class_Oof__int(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X128),X94)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(c_Int_Oring__1__class_Oof__int(X58),X128)),hAPP(c_Int_Oring__1__class_Oof__int(X58),X94)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__add) ).

fof(fact_of__nat__mult,axiom,
    ! [X57,X72,X58] :
      ( class_Rings_Osemiring__1(X58)
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X72),X57)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X58),X72)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X58),X57)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__mult) ).

fof(fact_of__nat__add,axiom,
    ! [X57,X72,X58] :
      ( class_Rings_Osemiring__1(X58)
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X72),X57)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X58),X72)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X58),X57)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__add) ).

fof(fact_product_Osimps_I1_J,axiom,
    ! [X281,X5,X58] : c_Enum_Oproduct(X58,X5,c_List_Olist_ONil(X58),X281) = c_List_Olist_ONil(tc_prod(X58,X5)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_product_Osimps_I1_J) ).

fof(fact_minus1__divide,axiom,
    ! [X66,X58] :
      ( ( class_Fields_Ofield__inverse__zero(X58)
        & class_Int_Onumber__ring(X58) )
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),hAPP(c_Int_Onumber__class_Onumber__of(X58),c_Int_OMin)),X66) = hAPP(c_Groups_Ouminus__class_Ouminus(X58),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),c_Groups_Oone__class_Oone(X58)),X66)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus1__divide) ).

fof(fact_setsum__0,axiom,
    ! [X21,X20,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X20,X5),hAPP(c_COMBK(X5,X20),c_Groups_Ozero__class_Ozero(X5))),X21) = c_Groups_Ozero__class_Ozero(X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__0) ).

fof(fact_setprod__1,axiom,
    ! [X21,X20,X5] :
      ( class_Groups_Ocomm__monoid__mult(X5)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X20,X5),hAPP(c_COMBK(X5,X20),c_Groups_Oone__class_Oone(X5))),X21) = c_Groups_Oone__class_Oone(X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__1) ).

fof(fact_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
    ! [X159,X156] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X156),c_Groups_Oone__class_Oone(tc_Int_Oint))),X159) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X156,X159),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastPlusOneLessThan__greaterThanLessThan__int) ).

fof(fact_order__less__imp__le,axiom,
    ! [X65,X66,X58] :
      ( class_Orderings_Opreorder(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X66),X65))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X66),X65)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__le) ).

fof(fact_tl__replicate,axiom,
    ! [X66,X58,X57] :
      ( X57 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
     => hAPP(c_List_Otl(X58),c_List_Oreplicate(X58,X57,X66)) = c_List_Oreplicate(X58,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X57),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X66) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tl__replicate) ).

fof(fact_negateSnd__eq,axiom,
    ! [X134,X140] : hAPP(c_Divides_OnegateSnd,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X140),X134)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X140),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X134)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negateSnd__eq) ).

fof(fact_abs__power__minus__one,axiom,
    ! [X57,X58] :
      ( ( class_Int_Onumber__ring(X58)
        & class_Rings_Olinordered__idom(X58) )
     => hAPP(c_Groups_Oabs__class_Oabs(X58),hAPP(hAPP(c_Power_Opower__class_Opower(X58),hAPP(c_Int_Onumber__class_Onumber__of(X58),c_Int_OMin)),X57)) = c_Groups_Oone__class_Oone(X58) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__power__minus__one) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J,axiom,
    ! [X113,X21] :
      ( c_Nat__Transfer_Onat__set(X21)
     => ( c_Nat__Transfer_Onat__set(X113)
       => c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X21),X113)) ) ),
    file('/export/starexec/sandbox/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,
    ! [X113,X21] :
      ( c_Nat__Transfer_Onat__set(X21)
     => ( c_Nat__Transfer_Onat__set(X113)
       => c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X21),X113)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J) ).

fof(fact_zle__iff__zadd,axiom,
    ! [X120,X121] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X121),X120))
    <=> ? [X69] : X120 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X121),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X69)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__iff__zadd) ).

fof(fact_map__replicate,axiom,
    ! [X25,X50,X2,X5,X20] : hAPP(hAPP(c_List_Omap(X20,X5),X2),c_List_Oreplicate(X20,X50,X25)) = c_List_Oreplicate(X5,X50,hAPP(X2,X25)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__replicate) ).

fof(fact_filter__remove1,axiom,
    ! [X239,X25,X16,X5] : hAPP(c_List_Ofilter(X5,X16),c_List_Oremove1(X5,X25,X239)) = c_List_Oremove1(X5,X25,hAPP(c_List_Ofilter(X5,X16),X239)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter__remove1) ).

fof(fact_snoc__eq__iff__butlast,axiom,
    ! [X251,X25,X239,X5] :
      ( hAPP(hAPP(c_List_Oappend(X5),X239),hAPP(hAPP(c_List_Olist_OCons(X5),X25),c_List_Olist_ONil(X5))) = X251
    <=> ( X251 != c_List_Olist_ONil(X5)
        & c_List_Obutlast(X5,X251) = X239
        & c_List_Olast(X5,X251) = X25 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_snoc__eq__iff__butlast) ).

fof(fact_negD,axiom,
    ! [X66] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X66),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ? [X69] : X66 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X69))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negD) ).

fof(fact_Ints__number__of,axiom,
    ! [X121,X5] :
      ( class_Int_Onumber__ring(X5)
     => hBOOL(hAPP(hAPP(c_member(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)),c_Int_Oring__1__class_OInts(X5))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__number__of) ).

fof(fact_Ints__of__int,axiom,
    ! [X120,X5] :
      ( class_Rings_Oring__1(X5)
     => hBOOL(hAPP(hAPP(c_member(X5),hAPP(c_Int_Oring__1__class_Oof__int(X5),X120)),c_Int_Oring__1__class_OInts(X5))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__of__int) ).

fof(fact_of__nat__in__Nats,axiom,
    ! [X50,X5] :
      ( class_Rings_Osemiring__1(X5)
     => hBOOL(hAPP(hAPP(c_member(X5),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X50)),c_Nat_Osemiring__1__class_ONats(X5))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__in__Nats) ).

fof(fact_Ints__of__nat,axiom,
    ! [X50,X5] :
      ( class_Rings_Oring__1(X5)
     => hBOOL(hAPP(hAPP(c_member(X5),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X50)),c_Int_Oring__1__class_OInts(X5))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__of__nat) ).

fof(fact_Suc__diff__1,axiom,
    ! [X57] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X57))
     => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X57),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X57 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__diff__1) ).

fof(fact_Suc__pred_H,axiom,
    ! [X57] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X57))
     => X57 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X57),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__pred_H) ).

fof(fact_nat__of,axiom,
    ! [X25] : hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X25)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__of) ).

fof(fact_mod__div__trivial,axiom,
    ! [X90,X62,X58] :
      ( class_Divides_Osemiring__div(X58)
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(X58),c_Divides_Odiv__class_Omod(X58,X62,X90)),X90) = c_Groups_Ozero__class_Ozero(X58) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__div__trivial) ).

fof(fact_negDivAlg__minus1,axiom,
    ! [X90] : c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),X90) = 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),X90),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negDivAlg__minus1) ).

fof(fact_set__replicate__Suc,axiom,
    ! [X25,X50,X5] : hAPP(c_List_Oset(X5),c_List_Oreplicate(X5,hAPP(c_Nat_OSuc,X50),X25)) = hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__replicate__Suc) ).

fof(fact_SetInterval_Otransfer__nat__int__set__function__closures,axiom,
    ! [X33,X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25))
     => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X25,X33)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SetInterval_Otransfer__nat__int__set__function__closures) ).

fof(fact_min__max_OInf__fin_Osingleton,axiom,
    ! [X25,X5] :
      ( class_Orderings_Olinorder(X5)
     => c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = X25 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Osingleton) ).

fof(fact_min__max_OSup__fin_Osingleton,axiom,
    ! [X25,X5] :
      ( class_Orderings_Olinorder(X5)
     => c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = X25 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Osingleton) ).

fof(fact_int__one__le__iff__zero__less,axiom,
    ! [X120] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X120))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X120)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__one__le__iff__zero__less) ).

fof(fact_Int__empty__left,axiom,
    ! [X113,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),X113) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__empty__left) ).

fof(fact_Un__UNIV__left,axiom,
    ! [X113,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),X113) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__UNIV__left) ).

fof(fact_empty__Diff,axiom,
    ! [X21,X5] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),X21) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__Diff) ).

fof(fact_Sigma__empty1,axiom,
    ! [X113,X20,X5] : hAPP(hAPP(c_Product__Type_OSigma(X5,X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),X113) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X20),tc_HOL_Obool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__empty1) ).

fof(fact_le__square,axiom,
    ! [X72] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X72),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X72),X72))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__square) ).

fof(fact_le__add1,axiom,
    ! [X72,X57] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X57),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X57),X72))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add1) ).

fof(fact_le__add2,axiom,
    ! [X72,X57] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X57),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X72),X57))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add2) ).

fof(fact_divide__eq__eq__number__of1,axiom,
    ! [X6,X121,X24,X5] :
      ( ( class_Fields_Ofield__inverse__zero(X5)
        & class_Int_Onumber(X5) )
     => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X24),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)) = X6
      <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(X5),X121) != c_Groups_Ozero__class_Ozero(X5)
           => X24 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)) )
          & ( hAPP(c_Int_Onumber__class_Onumber__of(X5),X121) = c_Groups_Ozero__class_Ozero(X5)
           => X6 = c_Groups_Ozero__class_Ozero(X5) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__eq__eq__number__of1) ).

fof(fact_eq__divide__eq__number__of1,axiom,
    ! [X121,X24,X6,X5] :
      ( ( class_Fields_Ofield__inverse__zero(X5)
        & class_Int_Onumber(X5) )
     => ( X6 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X24),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121))
      <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(X5),X121) != c_Groups_Ozero__class_Ozero(X5)
           => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)) = X24 )
          & ( hAPP(c_Int_Onumber__class_Onumber__of(X5),X121) = c_Groups_Ozero__class_Ozero(X5)
           => X6 = c_Groups_Ozero__class_Ozero(X5) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__divide__eq__number__of1) ).

fof(fact_nat__less__cases,axiom,
    ! [X18,X50,X95] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),X50))
       => hBOOL(hAPP(hAPP(X18,X50),X95)) )
     => ( ( X95 = X50
         => hBOOL(hAPP(hAPP(X18,X50),X95)) )
       => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X50),X95))
           => hBOOL(hAPP(hAPP(X18,X50),X95)) )
         => hBOOL(hAPP(hAPP(X18,X50),X95)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__cases) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J,axiom,
    ! [X21] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X21) = 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)),X21)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J) ).

fof(fact_Cons__eq__appendI,axiom,
    ! [X248,X242,X241,X249,X66,X58] :
      ( hAPP(hAPP(c_List_Olist_OCons(X58),X66),X249) = X241
     => ( X242 = hAPP(hAPP(c_List_Oappend(X58),X249),X248)
       => hAPP(hAPP(c_List_Olist_OCons(X58),X66),X242) = hAPP(hAPP(c_List_Oappend(X58),X241),X248) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Cons__eq__appendI) ).

fof(fact_append__eq__appendI,axiom,
    ! [X247,X241,X248,X249,X242,X58] :
      ( hAPP(hAPP(c_List_Oappend(X58),X242),X249) = X248
     => ( X241 = hAPP(hAPP(c_List_Oappend(X58),X249),X247)
       => hAPP(hAPP(c_List_Oappend(X58),X242),X241) = hAPP(hAPP(c_List_Oappend(X58),X248),X247) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__eq__appendI) ).

fof(fact_zadd__left__commute,axiom,
    ! [X94,X65,X66] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X66),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X65),X94)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X65),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X66),X94)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__left__commute) ).

fof(fact_nat__add__left__commute,axiom,
    ! [X94,X65,X66] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X66),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X65),X94)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X65),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X66),X94)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__commute) ).

fof(fact_atLeastLessThan__upto,axiom,
    ! [X157,X82] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X82),X157) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X82,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X157),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__upto) ).

fof(fact_nat__minus__add__max,axiom,
    ! [X72,X57] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X57),X72)),X72) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X57),X72),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__minus__add__max) ).

fof(fact_dual__max,axiom,
    ! [X5] :
      ( class_Orderings_Olinorder(X5)
     => c_Orderings_Oord_Omax(X5,hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X5))) = c_Orderings_Oord__class_Omin(X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dual__max) ).

fof(fact_dual__min,axiom,
    ! [X5] :
      ( class_Orderings_Olinorder(X5)
     => c_Orderings_Oord_Omin(X5,hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X5))) = c_Orderings_Oord__class_Omax(X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dual__min) ).

fof(fact_listsum__foldl,axiom,
    ! [X5] :
      ( class_Groups_Omonoid__add(X5)
     => c_List_Omonoid__add__class_Olistsum(X5) = c_List_Ofoldl(X5,X5,c_Groups_Oplus__class_Oplus(X5),c_Groups_Ozero__class_Ozero(X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__foldl) ).

fof(fact_div__mult__self1__is__id,axiom,
    ! [X62,X90,X58] :
      ( class_Divides_Osemiring__div(X58)
     => ( X90 != c_Groups_Ozero__class_Ozero(X58)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X90),X62)),X90) = X62 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__self1__is__id) ).

fof(fact_div__mult__self2__is__id,axiom,
    ! [X62,X90,X58] :
      ( class_Divides_Osemiring__div(X58)
     => ( X90 != c_Groups_Ozero__class_Ozero(X58)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X90)),X90) = X62 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__mult__self2__is__id) ).

fof(fact_le__imp__diff__is__add,axiom,
    ! [X87,X157,X82] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X82),X157))
     => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X157),X82) = X87
      <=> X157 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X87),X82) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__diff__is__add) ).

fof(fact_zmod__zminus2,axiom,
    ! [X90,X62] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X62,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X90)) = 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),X62),X90)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zminus2) ).

fof(fact_remove1__remdups,axiom,
    ! [X66,X242,X58] :
      ( hBOOL(hAPP(c_List_Odistinct(X58),X242))
     => c_List_Oremove1(X58,X66,c_List_Oremdups(X58,X242)) = c_List_Oremdups(X58,c_List_Oremove1(X58,X66,X242)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_remove1__remdups) ).

fof(fact_Nitpick_Owf_H__def,axiom,
    ! [X171,X5] :
      ( c_Nitpick_Owf_H(X5,X171)
    <=> ( c_Wellfounded_Oacyclic(X5,X171)
        & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X5,X5)),X171))
          | c_Nitpick_Ounknown(tc_HOL_Obool) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Owf_H__def) ).

fof(fact_wf__iff__acyclic__if__finite,axiom,
    ! [X171,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X5,X5)),X171))
     => ( c_Wellfounded_Owf(X5,X171)
      <=> c_Wellfounded_Oacyclic(X5,X171) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__iff__acyclic__if__finite) ).

fof(fact_finite__acyclic__wf,axiom,
    ! [X171,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X5,X5)),X171))
     => ( c_Wellfounded_Oacyclic(X5,X171)
       => c_Wellfounded_Owf(X5,X171) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__acyclic__wf) ).

fof(fact_inj__on__rev,axiom,
    ! [X21,X5] : c_Fun_Oinj__on(tc_List_Olist(X5),tc_List_Olist(X5),c_List_Orev(X5),X21),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__rev) ).

fof(fact_distinct__filter,axiom,
    ! [X18,X239,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),X239))
     => hBOOL(hAPP(c_List_Odistinct(X5),hAPP(c_List_Ofilter(X5,X18),X239))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__filter) ).

fof(fact_triple_Osize_I2_J,axiom,
    ! [X10,X11,X12,X5] : hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(X5)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),X12),X11),X10)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_triple_Osize_I2_J) ).

fof(fact_equivp__def,axiom,
    ! [X32,X5] :
      ( c_Equiv__Relations_Oequivp(X5,X32)
    <=> ! [X3,X177] :
          ( hBOOL(hAPP(hAPP(X32,X3),X177))
        <=> hAPP(X32,X3) = hAPP(X32,X177) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equivp__def) ).

fof(fact_add__diff__cancel,axiom,
    ! [X90,X62,X58] :
      ( class_Groups_Ogroup__add(X58)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),X90)),X90) = X62 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__diff__cancel) ).

fof(fact_diff__add__cancel,axiom,
    ! [X90,X62,X58] :
      ( class_Groups_Ogroup__add(X58)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X58),X62),X90)),X90) = X62 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__cancel) ).

fof(fact_sort__key__simps_I1_J,axiom,
    ! [X2,X5,X20] :
      ( class_Orderings_Olinorder(X20)
     => c_List_Olinorder__class_Osort__key(X5,X20,X2,c_List_Olist_ONil(X5)) = c_List_Olist_ONil(X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sort__key__simps_I1_J) ).

fof(fact_fst__eq__Domain,axiom,
    ! [X32,X20,X5] : hAPP(c_Set_Oimage(tc_prod(X5,X20),X5,c_Product__Type_Ofst(X5,X20)),X32) = hAPP(c_Relation_ODomain(X5,X20),X32),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fst__eq__Domain) ).

fof(fact_snd__eq__Range,axiom,
    ! [X32,X5,X20] : hAPP(c_Set_Oimage(tc_prod(X20,X5),X5,c_Product__Type_Osnd(X20,X5)),X32) = hAPP(c_Relation_ORange(X20,X5),X32),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_snd__eq__Range) ).

fof(fact_zero__induct,axiom,
    ! [X87,X18] :
      ( hBOOL(hAPP(X18,X87))
     => ( ! [X69] :
            ( hBOOL(hAPP(X18,hAPP(c_Nat_OSuc,X69)))
           => hBOOL(hAPP(X18,X69)) )
       => hBOOL(hAPP(X18,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__induct) ).

fof(fact_refl__on__converse,axiom,
    ! [X171,X21,X5] :
      ( c_Relation_Orefl__on(X5,X21,hAPP(c_Relation_Oconverse(X5,X5),X171))
    <=> c_Relation_Orefl__on(X5,X21,X171) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__on__converse) ).

fof(fact_total__on__converse,axiom,
    ! [X171,X21,X5] :
      ( c_Relation_Ototal__on(X5,X21,hAPP(c_Relation_Oconverse(X5,X5),X171))
    <=> c_Relation_Ototal__on(X5,X21,X171) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_total__on__converse) ).

fof(fact_com_Osize_I11_J,axiom,
    ! [X11,X84,X102] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OLocal(X102,X84,X11)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X11)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osize_I11_J) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J,axiom,
    ! [X21] :
      ( c_Nat__Transfer_Onat__set(X21)
     => hAPP(c_Finite__Set_Ocard(tc_Int_Oint),X21) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X21)) ),
    file('/export/starexec/sandbox/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,
    ! [X25,X21] :
      ( c_Nat__Transfer_Onat__set(X21)
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X25),X21))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J) ).

fof(fact_nat__set__def,axiom,
    ! [X192] :
      ( c_Nat__Transfer_Onat__set(X192)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X3),X192))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__set__def) ).

fof(fact_refl__on__empty,axiom,
    ! [X5] : c_Relation_Orefl__on(X5,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X5),tc_HOL_Obool))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__on__empty) ).

fof(fact_card__eq__setsum,axiom,
    ! [X21,X5] : hAPP(c_Finite__Set_Ocard(X5),X21) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,X5),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X21),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__eq__setsum) ).

fof(fact_divmod__nat__rel__unique,axiom,
    ! [X181,X182,X57,X72] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X72,X57),X182))
     => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X72,X57),X181))
       => X182 = X181 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__rel__unique) ).

fof(fact_inj__uminus,axiom,
    ! [X21,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => c_Fun_Oinj__on(X5,X5,c_Groups_Ouminus__class_Ouminus(X5),X21) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__uminus) ).

fof(fact_mod__code__numeral__def,axiom,
    ! [X72,X57] : c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X57,X72) = hAPP(c_Code__Numeral_Oof__nat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Code__Numeral_Onat__of,X57),hAPP(c_Code__Numeral_Onat__of,X72))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__code__numeral__def) ).

fof(fact_nth__Cons__0,axiom,
    ! [X242,X66,X58] : hAPP(hAPP(c_List_Onth(X58),hAPP(hAPP(c_List_Olist_OCons(X58),X66),X242)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X66,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__Cons__0) ).

fof(fact_part__equivp__refl__symp__transp,axiom,
    ! [X32,X5] :
      ( c_Equiv__Relations_Opart__equivp(X5,X32)
    <=> ( ? [X3] : hBOOL(hAPP(hAPP(X32,X3),X3))
        & c_Predicate_Osymp(X5,X32)
        & c_Predicate_Otransp(X5,X32) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_part__equivp__refl__symp__transp) ).

fof(fact_image__is__empty,axiom,
    ! [X21,X2,X5,X20] :
      ( hAPP(c_Set_Oimage(X20,X5,X2),X21) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
    <=> X21 = c_Orderings_Obot__class_Obot(tc_fun(X20,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__is__empty) ).

fof(fact_empty__is__image,axiom,
    ! [X21,X2,X20,X5] :
      ( c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) = hAPP(c_Set_Oimage(X20,X5,X2),X21)
    <=> X21 = c_Orderings_Obot__class_Obot(tc_fun(X20,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__is__image) ).

fof(fact_listrelp_Oequations_I1_J,axiom,
    ! [X171,X5] : c_List_Olistrelp(X5,X171,c_List_Olist_ONil(X5),c_List_Olist_ONil(X5)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrelp_Oequations_I1_J) ).

fof(fact_listrelp_ONil,axiom,
    ! [X171,X5] : c_List_Olistrelp(X5,X171,c_List_Olist_ONil(X5),c_List_Olist_ONil(X5)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrelp_ONil) ).

fof(fact_hd__map,axiom,
    ! [X2,X20,X5,X239] :
      ( X239 != c_List_Olist_ONil(X5)
     => hAPP(c_List_Ohd(X20),hAPP(hAPP(c_List_Omap(X5,X20),X2),X239)) = hAPP(X2,hAPP(c_List_Ohd(X5),X239)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hd__map) ).

fof(fact_of__nat__aux_Osimps_I1_J,axiom,
    ! [X82,X83,X5] :
      ( class_Rings_Osemiring__1(X5)
     => c_Nat_Osemiring__1__class_Oof__nat__aux(X5,X83,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X82) = X82 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__aux_Osimps_I1_J) ).

fof(fact_atLeastAtMost__singleton__iff,axiom,
    ! [X23,X24,X6,X5] :
      ( class_Orderings_Oorder(X5)
     => ( c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,X24) = hAPP(hAPP(c_Set_Oinsert(X5),X23),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))
      <=> ( X6 = X24
          & X24 = X23 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastAtMost__singleton__iff) ).

fof(fact_pos__single__def,axiom,
    ! [X292,X293,X294,X25,X5] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(X5),X25),X294),X293),X292) = c_New__DSequence_Opos__single(X5,X25),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__single__def) ).

fof(fact_neg__single__def,axiom,
    ! [X292,X293,X294,X25,X5] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(X5),X25),X294),X293),X292) = c_New__DSequence_Oneg__single(X5,X25),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__single__def) ).

fof(fact_power__abs,axiom,
    ! [X57,X62,X58] :
      ( class_Rings_Olinordered__idom(X58)
     => hAPP(c_Groups_Oabs__class_Oabs(X58),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),X57)) = hAPP(hAPP(c_Power_Opower__class_Opower(X58),hAPP(c_Groups_Oabs__class_Oabs(X58),X62)),X57) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__abs) ).

fof(fact_minus__divide__left,axiom,
    ! [X90,X62,X58] :
      ( class_Rings_Odivision__ring(X58)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X58),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X62),X90)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),hAPP(c_Groups_Ouminus__class_Ouminus(X58),X62)),X90) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__divide__left) ).

fof(fact_minus__mult__left,axiom,
    ! [X90,X62,X58] :
      ( class_Rings_Oring(X58)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X90)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),hAPP(c_Groups_Ouminus__class_Ouminus(X58),X62)),X90) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__mult__left) ).

fof(fact_power_Opower_Opower__0,axiom,
    ! [X6,X166,X167,X5] : hAPP(hAPP(c_Power_Opower_Opower(X5,X167,X166),X6),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X167,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power_Opower_Opower__0) ).

fof(fact_maps__simps_I2_J,axiom,
    ! [X2,X5,X20] : c_List_Omaps(X20,X5,X2,c_List_Olist_ONil(X20)) = c_List_Olist_ONil(X5),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_maps__simps_I2_J) ).

fof(fact_atLeastatMost__empty,axiom,
    ! [X6,X24,X5] :
      ( class_Orderings_Oorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X24),X6))
       => c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,X24) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastatMost__empty) ).

fof(fact_greaterThanAtMost__empty,axiom,
    ! [X87,X156,X5] :
      ( class_Orderings_Oorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X156),X87))
       => c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X87,X156) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThanAtMost__empty) ).

fof(fact_greaterThanLessThan__empty,axiom,
    ! [X87,X156,X5] :
      ( class_Orderings_Oorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X156),X87))
       => c_SetInterval_Oord__class_OgreaterThanLessThan(X5,X87,X156) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThanLessThan__empty) ).

fof(fact_tl__append2,axiom,
    ! [X241,X58,X242] :
      ( X242 != c_List_Olist_ONil(X58)
     => hAPP(c_List_Otl(X58),hAPP(hAPP(c_List_Oappend(X58),X242),X241)) = hAPP(hAPP(c_List_Oappend(X58),hAPP(c_List_Otl(X58),X242)),X241) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tl__append2) ).

fof(fact_zmod__zdiv__trivial,axiom,
    ! [X90,X62] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X62,X90)),X90) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zdiv__trivial) ).

fof(fact_Pair__fst__snd__eq,axiom,
    ! [X20,X5,X15,X76] :
      ( X76 = X15
    <=> ( hAPP(c_Product__Type_Ofst(X5,X20),X76) = hAPP(c_Product__Type_Ofst(X5,X20),X15)
        & hAPP(c_Product__Type_Osnd(X5,X20),X76) = hAPP(c_Product__Type_Osnd(X5,X20),X15) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pair__fst__snd__eq) ).

fof(fact_prod__eqI,axiom,
    ! [X140,X162,X5,X58] :
      ( hAPP(c_Product__Type_Ofst(X58,X5),X162) = hAPP(c_Product__Type_Ofst(X58,X5),X140)
     => ( hAPP(c_Product__Type_Osnd(X58,X5),X162) = hAPP(c_Product__Type_Osnd(X58,X5),X140)
       => X162 = X140 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_prod__eqI) ).

fof(fact_inj__on__id,axiom,
    ! [X21,X5] : c_Fun_Oinj__on(X5,X5,c_Fun_Oid(X5),X21),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__id) ).

fof(fact_inj__on__id2,axiom,
    ! [X21,X5] : c_Fun_Oinj__on(X5,X5,c_COMBI(X5),X21),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__id2) ).

fof(fact_sgn__times,axiom,
    ! [X90,X62,X58] :
      ( class_Rings_Olinordered__idom(X58)
     => c_Groups_Osgn__class_Osgn(X58,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X90)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),c_Groups_Osgn__class_Osgn(X58,X62)),c_Groups_Osgn__class_Osgn(X58,X90)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__times) ).

fof(fact_sorted__distinct__set__unique,axiom,
    ! [X251,X239,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( c_List_Olinorder__class_Osorted(X5,X239)
       => ( hBOOL(hAPP(c_List_Odistinct(X5),X239))
         => ( c_List_Olinorder__class_Osorted(X5,X251)
           => ( hBOOL(hAPP(c_List_Odistinct(X5),X251))
             => ( hAPP(c_List_Oset(X5),X239) = hAPP(c_List_Oset(X5),X251)
               => X239 = X251 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__distinct__set__unique) ).

fof(fact_drop__Suc__Cons,axiom,
    ! [X242,X66,X57,X58] : hAPP(hAPP(c_List_Odrop(X58),hAPP(c_Nat_OSuc,X57)),hAPP(hAPP(c_List_Olist_OCons(X58),X66),X242)) = hAPP(hAPP(c_List_Odrop(X58),X57),X242),
    file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_less__than__def) ).

fof(fact_abs__minus__commute,axiom,
    ! [X90,X62,X58] :
      ( class_Groups_Oordered__ab__group__add__abs(X58)
     => hAPP(c_Groups_Oabs__class_Oabs(X58),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X58),X62),X90)) = hAPP(c_Groups_Oabs__class_Oabs(X58),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X58),X90),X62)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__minus__commute) ).

fof(fact_code__numeral_Orecs_I1_J,axiom,
    ! [X89,X19,X5] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X5,X19,X89,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = X19,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_code__numeral_Orecs_I1_J) ).

fof(fact_code__numeral_Osimps_I4_J,axiom,
    ! [X89,X19,X5] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X5,X19,X89,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = X19,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_code__numeral_Osimps_I4_J) ).

fof(fact_nat__case__0,axiom,
    ! [X89,X19,X5] : c_Nat_Onat_Onat__case(X5,X19,X89,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X19,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__case__0) ).

fof(fact_Divides_Otransfer__int__nat__functions_I1_J,axiom,
    ! [X65,X66] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X66)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X65)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X66),X65)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Divides_Otransfer__int__nat__functions_I1_J) ).

fof(fact_times__numeral__code_I5_J,axiom,
    ! [X128,X136] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X136),X128)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_times__numeral__code_I5_J) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom,
    ! [X65,X66] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X66)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X65)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X66),X65)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J) ).

fof(fact_zmult__int,axiom,
    ! [X57,X72] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X72)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X57)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X72),X57)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__int) ).

fof(fact_plus__numeral__code_I9_J,axiom,
    ! [X128,X136] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X136),X128)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_plus__numeral__code_I9_J) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom,
    ! [X65,X66] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X66)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X65)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X66),X65)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J) ).

fof(fact_zadd__int,axiom,
    ! [X57,X72] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X72)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X57)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X72),X57)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__int) ).

fof(fact_zminus__zadd__distrib,axiom,
    ! [X128,X94] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X94),X128)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X94)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X128)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zminus__zadd__distrib) ).

fof(fact_zdiv__int,axiom,
    ! [X90,X62] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X62),X90)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X62)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X90)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__int) ).

fof(fact_int__mult,axiom,
    ! [X57,X72] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X72),X57)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X72)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X57)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__mult) ).

fof(fact_Int__UNIV__left,axiom,
    ! [X113,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),X113) = X113,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__UNIV__left) ).

fof(fact_Un__empty__left,axiom,
    ! [X113,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),X113) = X113,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__empty__left) ).

fof(fact_pos__zmult__eq__1__iff,axiom,
    ! [X50,X95] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X95))
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X95),X50) = c_Groups_Oone__class_Oone(tc_Int_Oint)
      <=> ( X95 = c_Groups_Oone__class_Oone(tc_Int_Oint)
          & X50 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ),
    file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_succ__Pls) ).

fof(fact_fold1__singleton,axiom,
    ! [X6,X2,X5] : hAPP(c_Finite__Set_Ofold1(X5,X2),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = X6,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__singleton) ).

fof(fact_length__map,axiom,
    ! [X239,X2,X20,X5] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),hAPP(hAPP(c_List_Omap(X20,X5),X2),X239)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X20)),X239),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__map) ).

fof(fact_length__list__update,axiom,
    ! [X66,X98,X242,X58] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),hAPP(hAPP(c_List_Olist__update(X58,X242),X98),X66)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__list__update) ).

fof(fact_evaln_Oequations_I1_J,axiom,
    ! [X78,X79] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,X79,X78,X79),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_Oequations_I1_J) ).

fof(fact_evaln_OSkip,axiom,
    ! [X57,X48] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,X48,X57,X48),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_OSkip) ).

fof(fact_of__int__power,axiom,
    ! [X57,X94,X58] :
      ( class_Rings_Oring__1(X58)
     => hAPP(c_Int_Oring__1__class_Oof__int(X58),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X94),X57)) = hAPP(hAPP(c_Power_Opower__class_Opower(X58),hAPP(c_Int_Oring__1__class_Oof__int(X58),X94)),X57) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__power) ).

fof(fact_of__nat__power,axiom,
    ! [X57,X72,X58] :
      ( class_Rings_Osemiring__1(X58)
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X58),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X72),X57)) = hAPP(hAPP(c_Power_Opower__class_Opower(X58),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X58),X72)),X57) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__power) ).

fof(fact_zless__le,axiom,
    ! [X121,X120] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X120),X121))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X120),X121))
        & X120 != X121 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__le) ).

fof(fact_nat__less__le,axiom,
    ! [X50,X95] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),X50))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X50))
        & X95 != X50 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__le) ).

fof(fact_le__eq__less__or__eq,axiom,
    ! [X50,X95] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X50))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),X50))
        | X95 = X50 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__eq__less__or__eq) ).

fof(fact_le__neq__implies__less,axiom,
    ! [X57,X72] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X72),X57))
     => ( X72 != X57
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X72),X57)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__neq__implies__less) ).

fof(fact_fold1__singleton__def,axiom,
    ! [X6,X2,X5,X1] :
      ( X1 = c_Finite__Set_Ofold1(X5,X2)
     => hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = X6 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__singleton__def) ).

fof(fact_length__tl,axiom,
    ! [X242,X58] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),hAPP(c_List_Otl(X58),X242)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__tl) ).

fof(fact_fun__left__comm__idem_Ofun__left__idem,axiom,
    ! [X120,X25,X2,X20,X5] :
      ( c_Finite__Set_Ofun__left__comm__idem(X5,X20,X2)
     => hAPP(hAPP(X2,X25),hAPP(hAPP(X2,X25),X120)) = hAPP(hAPP(X2,X25),X120) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__idem_Ofun__left__idem) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J,axiom,
    ! [X112] : 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)),X112)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J) ).

fof(fact_finite__atLeastAtMost__int,axiom,
    ! [X159,X156] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X156,X159))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__atLeastAtMost__int) ).

fof(fact_finite__greaterThanAtMost__int,axiom,
    ! [X159,X156] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X156,X159))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__greaterThanAtMost__int) ).

fof(fact_finite__greaterThanLessThan__int,axiom,
    ! [X159,X156] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X156,X159))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__greaterThanLessThan__int) ).

fof(fact_finite__atLeastAtMost,axiom,
    ! [X159,X156] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X156,X159))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__atLeastAtMost) ).

fof(fact_finite__greaterThanAtMost,axiom,
    ! [X159,X156] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X156,X159))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__greaterThanAtMost) ).

fof(fact_finite__greaterThanLessThan,axiom,
    ! [X159,X156] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X156,X159))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__greaterThanLessThan) ).

fof(fact_less__Suc0,axiom,
    ! [X50] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X50),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
    <=> X50 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc0) ).

fof(fact_inj__Suc,axiom,
    ! [X207] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X207),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__Suc) ).

fof(fact_termination__basic__simps_I5_J,axiom,
    ! [X65,X66] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X66),X65))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X66),X65)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I5_J) ).

fof(fact_less__imp__le__nat,axiom,
    ! [X57,X72] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X72),X57))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X72),X57)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__le__nat) ).

fof(fact_less__or__eq__imp__le,axiom,
    ! [X57,X72] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X72),X57))
        | X72 = X57 )
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X72),X57)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__or__eq__imp__le) ).

fof(fact_atLeastLessThan__empty,axiom,
    ! [X6,X24,X5] :
      ( class_Orderings_Oorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X24),X6))
       => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X6),X24) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__empty) ).

fof(fact_eq__mem,axiom,
    ! [X33,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_fequal,X33)))
    <=> X25 = X33 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__mem) ).

fof(fact_last__map,axiom,
    ! [X2,X20,X5,X239] :
      ( X239 != c_List_Olist_ONil(X5)
     => c_List_Olast(X20,hAPP(hAPP(c_List_Omap(X5,X20),X2),X239)) = hAPP(X2,c_List_Olast(X5,X239)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__map) ).

fof(fact_minus__add__cancel,axiom,
    ! [X90,X62,X58] :
      ( class_Groups_Ogroup__add(X58)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(c_Groups_Ouminus__class_Ouminus(X58),X62)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),X90)) = X90 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__add__cancel) ).

fof(fact_ex__in__conv,axiom,
    ! [X21,X5] :
      ( ? [X3] : hBOOL(hAPP(hAPP(c_member(X5),X3),X21))
    <=> X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ex__in__conv) ).

fof(fact_of__nat__nat,axiom,
    ! [X94,X58] :
      ( class_Rings_Oring__1(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X94))
       => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X58),hAPP(c_Int_Onat,X94)) = hAPP(c_Int_Oring__1__class_Oof__int(X58),X94) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__nat) ).

fof(fact_zmod__zminus__zminus,axiom,
    ! [X90,X62] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X62),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X90)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X62,X90)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zminus__zminus) ).

fof(fact_Divides_Otransfer__int__nat__functions_I2_J,axiom,
    ! [X65,X66] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X66),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X65)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X66,X65)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Divides_Otransfer__int__nat__functions_I2_J) ).

fof(fact_zmod__int,axiom,
    ! [X90,X62] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X62,X90)) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X62),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X90)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__int) ).

fof(fact_distinct__listsum__conv__Setsum,axiom,
    ! [X239,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => ( hBOOL(hAPP(c_List_Odistinct(X5),X239))
       => hAPP(c_List_Omonoid__add__class_Olistsum(X5),X239) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X5),c_COMBI(X5)),hAPP(c_List_Oset(X5),X239)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__listsum__conv__Setsum) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom,
    ! [X140,X66,X58] :
      ( class_Rings_Ocomm__semiring__1(X58)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X66),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X66),X140)) = hAPP(hAPP(c_Power_Opower__class_Opower(X58),X66),hAPP(c_Nat_OSuc,X140)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J) ).

fof(fact_power__Suc,axiom,
    ! [X57,X62,X58] :
      ( class_Power_Opower(X58)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),hAPP(c_Nat_OSuc,X57)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),X57)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__Suc) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom,
    ! [X140,X66,X58] :
      ( class_Rings_Ocomm__semiring__1(X58)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X58),X66),hAPP(c_Nat_OSuc,X140)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X66),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X66),X140)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J) ).

fof(fact_image__uminus__greaterThan,axiom,
    ! [X25,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => hAPP(c_Set_Oimage(X5,X5,c_Groups_Ouminus__class_Ouminus(X5)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X5),X25)) = hAPP(c_SetInterval_Oord__class_OlessThan(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X25)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__uminus__greaterThan) ).

fof(fact_image__uminus__atLeast,axiom,
    ! [X25,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => hAPP(c_Set_Oimage(X5,X5,c_Groups_Ouminus__class_Ouminus(X5)),hAPP(c_SetInterval_Oord__class_OatLeast(X5),X25)) = hAPP(c_SetInterval_Oord__class_OatMost(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X25)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__uminus__atLeast) ).

fof(fact_image__uminus__lessThan,axiom,
    ! [X25,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => hAPP(c_Set_Oimage(X5,X5,c_Groups_Ouminus__class_Ouminus(X5)),hAPP(c_SetInterval_Oord__class_OlessThan(X5),X25)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X25)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__uminus__lessThan) ).

fof(fact_image__uminus__atMost,axiom,
    ! [X25,X5] :
      ( class_Groups_Oordered__ab__group__add(X5)
     => hAPP(c_Set_Oimage(X5,X5,c_Groups_Ouminus__class_Ouminus(X5)),hAPP(c_SetInterval_Oord__class_OatMost(X5),X25)) = hAPP(c_SetInterval_Oord__class_OatLeast(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X25)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__uminus__atMost) ).

fof(fact_replicate__Suc,axiom,
    ! [X66,X57,X58] : c_List_Oreplicate(X58,hAPP(c_Nat_OSuc,X57),X66) = hAPP(hAPP(c_List_Olist_OCons(X58),X66),c_List_Oreplicate(X58,X57,X66)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_replicate__Suc) ).

fof(fact_set__replicate,axiom,
    ! [X25,X5,X50] :
      ( X50 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
     => hAPP(c_List_Oset(X5),c_List_Oreplicate(X5,X50,X25)) = hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__replicate) ).

fof(fact_set__replicate__conv__if,axiom,
    ! [X25,X5,X50] :
      ( ( X50 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(c_List_Oset(X5),c_List_Oreplicate(X5,X50,X25)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) )
      & ( X50 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(c_List_Oset(X5),c_List_Oreplicate(X5,X50,X25)) = hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__replicate__conv__if) ).

fof(fact_abs__of__nonneg,axiom,
    ! [X62,X58] :
      ( class_Groups_Oordered__ab__group__add__abs(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),X62))
       => hAPP(c_Groups_Oabs__class_Oabs(X58),X62) = X62 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__of__nonneg) ).

fof(fact_abs__of__pos,axiom,
    ! [X62,X58] :
      ( class_Groups_Oordered__ab__group__add__abs(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),X62))
       => hAPP(c_Groups_Oabs__class_Oabs(X58),X62) = X62 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__of__pos) ).

fof(fact_abs__of__nonpos,axiom,
    ! [X62,X58] :
      ( class_Groups_Oordered__ab__group__add__abs(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X62),c_Groups_Ozero__class_Ozero(X58)))
       => hAPP(c_Groups_Oabs__class_Oabs(X58),X62) = hAPP(c_Groups_Ouminus__class_Ouminus(X58),X62) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__of__nonpos) ).

fof(fact_abs__of__neg,axiom,
    ! [X62,X58] :
      ( class_Groups_Oordered__ab__group__add__abs(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X62),c_Groups_Ozero__class_Ozero(X58)))
       => hAPP(c_Groups_Oabs__class_Oabs(X58),X62) = hAPP(c_Groups_Ouminus__class_Ouminus(X58),X62) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__of__neg) ).

fof(fact_sgn__neg,axiom,
    ! [X62,X58] :
      ( class_Rings_Olinordered__idom(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X62),c_Groups_Ozero__class_Ozero(X58)))
       => c_Groups_Osgn__class_Osgn(X58,X62) = hAPP(c_Groups_Ouminus__class_Ouminus(X58),c_Groups_Oone__class_Oone(X58)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__neg) ).

fof(fact_sgn__1__neg,axiom,
    ! [X6,X5] :
      ( class_Rings_Olinordered__idom(X5)
     => ( c_Groups_Osgn__class_Osgn(X5,X6) = hAPP(c_Groups_Ouminus__class_Ouminus(X5),c_Groups_Oone__class_Oone(X5))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),c_Groups_Ozero__class_Ozero(X5))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__1__neg) ).

fof(fact_part__equivp__symp,axiom,
    ! [X33,X25,X32,X5] :
      ( c_Equiv__Relations_Opart__equivp(X5,X32)
     => ( hBOOL(hAPP(hAPP(X32,X25),X33))
       => hBOOL(hAPP(hAPP(X32,X33),X25)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_part__equivp__symp) ).

fof(fact_sympE,axiom,
    ! [X33,X25,X171,X5] :
      ( c_Predicate_Osymp(X5,X171)
     => ( hBOOL(hAPP(hAPP(X171,X25),X33))
       => hBOOL(hAPP(hAPP(X171,X33),X25)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sympE) ).

fof(fact_equivp__symp,axiom,
    ! [X33,X25,X32,X5] :
      ( c_Equiv__Relations_Oequivp(X5,X32)
     => ( hBOOL(hAPP(hAPP(X32,X25),X33))
       => hBOOL(hAPP(hAPP(X32,X33),X25)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equivp__symp) ).

fof(fact_length__butlast,axiom,
    ! [X242,X58] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),c_List_Obutlast(X58,X242)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__butlast) ).

fof(fact_lists_ONil,axiom,
    ! [X21,X5] : hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X5)),c_List_Olist_ONil(X5)),c_List_Olists(X5,X21))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lists_ONil) ).

fof(fact_sgn__1__pos,axiom,
    ! [X6,X5] :
      ( class_Rings_Olinordered__idom(X5)
     => ( c_Groups_Osgn__class_Osgn(X5,X6) = c_Groups_Oone__class_Oone(X5)
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X6)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__1__pos) ).

fof(fact_sgn__pos,axiom,
    ! [X62,X58] :
      ( class_Rings_Olinordered__idom(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),X62))
       => c_Groups_Osgn__class_Osgn(X58,X62) = c_Groups_Oone__class_Oone(X58) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__pos) ).

fof(fact_nonzero__minus__divide__divide,axiom,
    ! [X62,X90,X58] :
      ( class_Rings_Odivision__ring(X58)
     => ( X90 != c_Groups_Ozero__class_Ozero(X58)
       => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),hAPP(c_Groups_Ouminus__class_Ouminus(X58),X62)),hAPP(c_Groups_Ouminus__class_Ouminus(X58),X90)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X62),X90) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__minus__divide__divide) ).

fof(fact_lists__empty,axiom,
    ! [X5] : c_List_Olists(X5,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X5)),c_List_Olist_ONil(X5)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X5),tc_HOL_Obool))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lists__empty) ).

fof(fact_listset_Osimps_I1_J,axiom,
    ! [X5] : c_List_Olistset(X5,c_List_Olist_ONil(tc_fun(X5,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X5)),c_List_Olist_ONil(X5)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X5),tc_HOL_Obool))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listset_Osimps_I1_J) ).

fof(fact_CollectI,axiom,
    ! [X5,X6,X18] :
      ( hBOOL(hAPP(X18,X6))
     => hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(c_Set_OCollect(X5),X18))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_CollectI) ).

fof(fact_distinct__rev,axiom,
    ! [X239,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),hAPP(c_List_Orev(X5),X239)))
    <=> hBOOL(hAPP(c_List_Odistinct(X5),X239)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__rev) ).

fof(fact_distinct1__rotate,axiom,
    ! [X239,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),hAPP(c_List_Orotate1(X5),X239)))
    <=> hBOOL(hAPP(c_List_Odistinct(X5),X239)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct1__rotate) ).

fof(fact_quotient__empty,axiom,
    ! [X171,X5] : hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),X171) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotient__empty) ).

fof(fact_split__Pair,axiom,
    ! [X20,X5] : hAPP(c_Product__Type_Oprod_Oprod__case(X5,X20,tc_prod(X5,X20)),c_Product__Type_OPair(X5,X20)) = c_Fun_Oid(tc_prod(X5,X20)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__Pair) ).

fof(fact_inf__absorb1,axiom,
    ! [X65,X66,X58] :
      ( class_Lattices_Osemilattice__inf(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X66),X65))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X66),X65) = X66 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__absorb1) ).

fof(fact_le__iff__inf,axiom,
    ! [X33,X25,X5] :
      ( class_Lattices_Osemilattice__inf(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X25),X33))
      <=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X25),X33) = X25 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__iff__inf) ).

fof(fact_inf__absorb2,axiom,
    ! [X66,X65,X58] :
      ( class_Lattices_Osemilattice__inf(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X65),X66))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X66),X65) = X65 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__absorb2) ).

fof(fact_sup__absorb2,axiom,
    ! [X65,X66,X58] :
      ( class_Lattices_Osemilattice__sup(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X66),X65))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X66),X65) = X65 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__absorb2) ).

fof(fact_le__iff__sup,axiom,
    ! [X33,X25,X5] :
      ( class_Lattices_Osemilattice__sup(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X25),X33))
      <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X25),X33) = X33 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__iff__sup) ).

fof(fact_sup__absorb1,axiom,
    ! [X66,X65,X58] :
      ( class_Lattices_Osemilattice__sup(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X65),X66))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X66),X65) = X66 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__absorb1) ).

fof(fact_min__max_Osup__absorb2,axiom,
    ! [X65,X66,X58] :
      ( class_Orderings_Olinorder(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X66),X65))
       => hAPP(hAPP(c_Orderings_Oord__class_Omax(X58),X66),X65) = X65 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup__absorb2) ).

fof(fact_min__max_Ole__iff__sup,axiom,
    ! [X33,X25,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X25),X33))
      <=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X25),X33) = X33 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ole__iff__sup) ).

fof(fact_min__max_Osup__absorb1,axiom,
    ! [X66,X65,X58] :
      ( class_Orderings_Olinorder(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X65),X66))
       => hAPP(hAPP(c_Orderings_Oord__class_Omax(X58),X66),X65) = X66 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup__absorb1) ).

fof(fact_min__max_Ole__iff__inf,axiom,
    ! [X33,X25,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X25),X33))
      <=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X25),X33) = X25 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ole__iff__inf) ).

fof(fact_min__max_Oinf__absorb1,axiom,
    ! [X65,X66,X58] :
      ( class_Orderings_Olinorder(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X66),X65))
       => hAPP(hAPP(c_Orderings_Oord__class_Omin(X58),X66),X65) = X66 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__absorb1) ).

fof(fact_min__max_Oinf__absorb2,axiom,
    ! [X66,X65,X58] :
      ( class_Orderings_Olinorder(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X65),X66))
       => hAPP(hAPP(c_Orderings_Oord__class_Omin(X58),X66),X65) = X65 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__absorb2) ).

fof(fact_Inf__singleton,axiom,
    ! [X6,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => c_Complete__Lattice_OInf__class_OInf(X5,hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = X6 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__singleton) ).

fof(fact_Sup__singleton,axiom,
    ! [X6,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => c_Complete__Lattice_OSup__class_OSup(X5,hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = X6 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__singleton) ).

fof(fact_Min_Osingleton,axiom,
    ! [X25,X5] :
      ( class_Orderings_Olinorder(X5)
     => c_Big__Operators_Olinorder__class_OMin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = X25 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min_Osingleton) ).

fof(fact_Max_Osingleton,axiom,
    ! [X25,X5] :
      ( class_Orderings_Olinorder(X5)
     => c_Big__Operators_Olinorder__class_OMax(X5,hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = X25 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max_Osingleton) ).

fof(fact_Sup__fin_Osingleton,axiom,
    ! [X25,X5] :
      ( class_Lattices_Olattice(X5)
     => c_Big__Operators_Olattice__class_OSup__fin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = X25 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_Osingleton) ).

fof(fact_Inf__fin_Osingleton,axiom,
    ! [X25,X5] :
      ( class_Lattices_Olattice(X5)
     => c_Big__Operators_Olattice__class_OInf__fin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = X25 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_Osingleton) ).

fof(fact_mult__Suc,axiom,
    ! [X57,X72] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X72)),X57) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X57),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X72),X57)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__Suc) ).

fof(fact_cut,axiom,
    ! [X4,X13,X14,X5] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(X5,X14,X13)
     => ( c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,X14)
       => c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,X13) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_cut) ).

fof(fact_diff__add__inverse,axiom,
    ! [X72,X57] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X57),X72)),X57) = X72,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__inverse) ).

fof(fact_diff__add__inverse2,axiom,
    ! [X57,X72] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X72),X57)),X57) = X72,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__inverse2) ).

fof(fact_New__DSequence_Opos__union__def,axiom,
    ! [X82,X302,X277,X5] : hAPP(c_New__DSequence_Opos__union(X5,X277,X302),X82) = c_Lazy__Sequence_Oappend(X5,hAPP(X277,X82),hAPP(X302,X82)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_New__DSequence_Opos__union__def) ).

fof(fact_Union__quotient,axiom,
    ! [X171,X21,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X21,X171)
     => c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X21),X171)) = X21 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__quotient) ).

fof(fact_minus__divide__divide,axiom,
    ! [X90,X62,X58] :
      ( class_Fields_Ofield__inverse__zero(X58)
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),hAPP(c_Groups_Ouminus__class_Ouminus(X58),X62)),hAPP(c_Groups_Ouminus__class_Ouminus(X58),X90)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X62),X90) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__divide__divide) ).

fof(fact_abs__mult__self,axiom,
    ! [X62,X58] :
      ( class_Rings_Olinordered__idom(X58)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),hAPP(c_Groups_Oabs__class_Oabs(X58),X62)),hAPP(c_Groups_Oabs__class_Oabs(X58),X62)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X62) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__mult__self) ).

fof(fact_minus__mult__minus,axiom,
    ! [X90,X62,X58] :
      ( class_Rings_Oring(X58)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),hAPP(c_Groups_Ouminus__class_Ouminus(X58),X62)),hAPP(c_Groups_Ouminus__class_Ouminus(X58),X90)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X90) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__mult__minus) ).

fof(fact_minus__mult__commute,axiom,
    ! [X90,X62,X58] :
      ( class_Rings_Oring(X58)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),hAPP(c_Groups_Ouminus__class_Ouminus(X58),X62)),X90) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),hAPP(c_Groups_Ouminus__class_Ouminus(X58),X90)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__mult__commute) ).

fof(fact_wfP__accp__iff,axiom,
    ! [X171,X5] :
      ( c_Wellfounded_OwfP(X5,X171)
    <=> ! [X138] : hBOOL(hAPP(c_Wellfounded_Oaccp(X5,X171),X138)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfP__accp__iff) ).

fof(fact_nonzero__minus__divide__right,axiom,
    ! [X62,X90,X58] :
      ( class_Rings_Odivision__ring(X58)
     => ( X90 != c_Groups_Ozero__class_Ozero(X58)
       => hAPP(c_Groups_Ouminus__class_Ouminus(X58),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X62),X90)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X62),hAPP(c_Groups_Ouminus__class_Ouminus(X58),X90)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__minus__divide__right) ).

fof(fact_quotient__is__empty2,axiom,
    ! [X171,X21,X5] :
      ( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X21),X171)
    <=> X21 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotient__is__empty2) ).

fof(fact_quotient__is__empty,axiom,
    ! [X171,X21,X5] :
      ( hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X21),X171) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool))
    <=> X21 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotient__is__empty) ).

fof(fact_card__greaterThanAtMost__int,axiom,
    ! [X159,X156] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X156,X159)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X159),X156)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__greaterThanAtMost__int) ).

fof(fact_linorder__neq__iff,axiom,
    ! [X33,X25,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( X25 != X33
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X25),X33))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X33),X25)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neq__iff) ).

fof(fact_linorder__less__linear,axiom,
    ! [X65,X66,X58] :
      ( class_Orderings_Olinorder(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X66),X65))
        | X66 = X65
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X65),X66)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__less__linear) ).

fof(fact_mod__mod__trivial,axiom,
    ! [X90,X62,X58] :
      ( class_Divides_Osemiring__div(X58)
     => c_Divides_Odiv__class_Omod(X58,c_Divides_Odiv__class_Omod(X58,X62,X90),X90) = c_Divides_Odiv__class_Omod(X58,X62,X90) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mod__trivial) ).

fof(fact_Int__empty__right,axiom,
    ! [X21,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__empty__right) ).

fof(fact_Un__UNIV__right,axiom,
    ! [X21,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__UNIV__right) ).

fof(fact_Diff__UNIV,axiom,
    ! [X21,X5] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__UNIV) ).

fof(fact_Domain__empty,axiom,
    ! [X20,X5] : hAPP(c_Relation_ODomain(X5,X20),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X20),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__empty) ).

fof(fact_Range__empty,axiom,
    ! [X5,X20] : hAPP(c_Relation_ORange(X20,X5),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X20,X5),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__empty) ).

fof(fact_fst__conv,axiom,
    ! [X90,X62,X5,X58] : hAPP(c_Product__Type_Ofst(X58,X5),hAPP(hAPP(c_Product__Type_OPair(X58,X5),X62),X90)) = X62,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fst__conv) ).

fof(fact_snd__conv,axiom,
    ! [X90,X62,X58,X5] : hAPP(c_Product__Type_Osnd(X5,X58),hAPP(hAPP(c_Product__Type_OPair(X5,X58),X62),X90)) = X90,
    file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_minus__Min) ).

fof(fact_le__iff__add,axiom,
    ! [X50,X95] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X50))
    <=> ? [X100] : X50 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X95),X100) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__iff__add) ).

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

fof(fact_the__elem__eq,axiom,
    ! [X25,X5] : c_Set_Othe__elem(X5,hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = X25,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__elem__eq) ).

fof(fact_linorder__linear,axiom,
    ! [X65,X66,X58] :
      ( class_Orderings_Olinorder(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X66),X65))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X65),X66)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__linear) ).

fof(fact_linorder__le__less__linear,axiom,
    ! [X65,X66,X58] :
      ( class_Orderings_Olinorder(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X66),X65))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X65),X66)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__le__less__linear) ).

fof(fact_listsum__simps_I2_J,axiom,
    ! [X242,X66,X58] :
      ( class_Groups_Omonoid__add(X58)
     => hAPP(c_List_Omonoid__add__class_Olistsum(X58),hAPP(hAPP(c_List_Olist_OCons(X58),X66),X242)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X66),hAPP(c_List_Omonoid__add__class_Olistsum(X58),X242)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__simps_I2_J) ).

fof(fact_minus__divide__right,axiom,
    ! [X90,X62,X58] :
      ( class_Fields_Ofield__inverse__zero(X58)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X58),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X62),X90)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X62),hAPP(c_Groups_Ouminus__class_Ouminus(X58),X90)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__divide__right) ).

fof(fact_minus__mult__right,axiom,
    ! [X90,X62,X58] :
      ( class_Rings_Oring(X58)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X90)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),hAPP(c_Groups_Ouminus__class_Ouminus(X58),X90)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__mult__right) ).

fof(fact_partition_Osimps_I1_J,axiom,
    ! [X18,X5] : c_List_Opartition(X5,X18,c_List_Olist_ONil(X5)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olist_ONil(X5)),c_List_Olist_ONil(X5)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_partition_Osimps_I1_J) ).

fof(fact_take__1__Cons,axiom,
    ! [X242,X66,X58] : hAPP(hAPP(c_List_Otake(X58),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(X58),X66),X242)) = hAPP(hAPP(c_List_Olist_OCons(X58),X66),c_List_Olist_ONil(X58)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__1__Cons) ).

fof(fact_sym__inv__image,axiom,
    ! [X2,X20,X171,X5] :
      ( c_Relation_Osym(X5,X171)
     => c_Relation_Osym(X20,hAPP(hAPP(c_Relation_Oinv__image(X5,X20),X171),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sym__inv__image) ).

fof(fact_trans__inv__image,axiom,
    ! [X2,X20,X171,X5] :
      ( c_Relation_Otrans(X5,X171)
     => c_Relation_Otrans(X20,hAPP(hAPP(c_Relation_Oinv__image(X5,X20),X171),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__inv__image) ).

fof(fact_wf__inv__image,axiom,
    ! [X2,X20,X171,X5] :
      ( c_Wellfounded_Owf(X5,X171)
     => c_Wellfounded_Owf(X20,hAPP(hAPP(c_Relation_Oinv__image(X5,X20),X171),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__inv__image) ).

fof(fact_rp__inv__image__rp,axiom,
    ! [X2,X20,X18,X5] :
      ( c_FunDef_Oreduction__pair(X5,X18)
     => c_FunDef_Oreduction__pair(X20,hAPP(hAPP(c_FunDef_Orp__inv__image(X5,X20),X18),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rp__inv__image__rp) ).

fof(fact_mod__add__self1,axiom,
    ! [X62,X90,X58] :
      ( class_Divides_Osemiring__div(X58)
     => c_Divides_Odiv__class_Omod(X58,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X90),X62),X90) = c_Divides_Odiv__class_Omod(X58,X62,X90) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__add__self1) ).

fof(fact_mod__add__self2,axiom,
    ! [X90,X62,X58] :
      ( class_Divides_Osemiring__div(X58)
     => c_Divides_Odiv__class_Omod(X58,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),X90),X90) = c_Divides_Odiv__class_Omod(X58,X62,X90) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__add__self2) ).

fof(fact_nth__via__drop,axiom,
    ! [X241,X65,X242,X57,X58] :
      ( hAPP(hAPP(c_List_Odrop(X58),X57),X242) = hAPP(hAPP(c_List_Olist_OCons(X58),X65),X241)
     => hAPP(hAPP(c_List_Onth(X58),X242),X57) = X65 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nth__via__drop) ).

fof(fact_max__Suc__Suc,axiom,
    ! [X57,X72] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X72)),hAPP(c_Nat_OSuc,X57)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X72),X57)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__Suc__Suc) ).

fof(fact_min__Suc__Suc,axiom,
    ! [X57,X72] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X72)),hAPP(c_Nat_OSuc,X57)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X72),X57)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__Suc__Suc) ).

fof(fact_times__code__numeral__code,axiom,
    ! [X72,X57] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X57)),hAPP(c_Code__Numeral_Oof__nat,X72)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X57),X72)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_times__code__numeral__code) ).

fof(fact_plus__code__numeral__code,axiom,
    ! [X72,X57] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X57)),hAPP(c_Code__Numeral_Oof__nat,X72)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X57),X72)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_plus__code__numeral__code) ).

fof(fact_zpower__int,axiom,
    ! [X57,X72] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X72)),X57) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X72),X57)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zpower__int) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J,axiom,
    ! [X57,X66] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X66)),X57) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X66),X57)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J) ).

fof(fact_zmult__zminus,axiom,
    ! [X128,X94] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X94)),X128) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X94),X128)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__zminus) ).

fof(fact_int__power,axiom,
    ! [X57,X72] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X72),X57)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X72)),X57),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__power) ).

fof(fact_List_Oset__insert,axiom,
    ! [X239,X25,X5] : hAPP(c_List_Oset(X5),c_List_Oinsert(X5,X25,X239)) = hAPP(hAPP(c_Set_Oinsert(X5),X25),hAPP(c_List_Oset(X5),X239)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_List_Oset__insert) ).

fof(fact_splice_Osimps_I2_J,axiom,
    ! [X300,X136,X58] : c_List_Osplice(X58,hAPP(hAPP(c_List_Olist_OCons(X58),X136),X300),c_List_Olist_ONil(X58)) = hAPP(hAPP(c_List_Olist_OCons(X58),X136),X300),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_splice_Osimps_I2_J) ).

fof(fact_abs__ge__zero,axiom,
    ! [X62,X58] :
      ( class_Groups_Oordered__ab__group__add__abs(X58)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),hAPP(c_Groups_Oabs__class_Oabs(X58),X62))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__ge__zero) ).

fof(fact_zero__le__imp__of__nat,axiom,
    ! [X72,X58] :
      ( class_Rings_Olinordered__semidom(X58)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X58),X72))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__imp__of__nat) ).

fof(fact_of__nat__0__le__iff,axiom,
    ! [X57,X58] :
      ( class_Rings_Olinordered__semidom(X58)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X58),X57))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__0__le__iff) ).

fof(fact_inf_Oleft__idem,axiom,
    ! [X90,X62,X58] :
      ( class_Lattices_Osemilattice__inf(X58)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X62),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X62),X90)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X62),X90) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf_Oleft__idem) ).

fof(fact_inf__left__idem,axiom,
    ! [X65,X66,X58] :
      ( class_Lattices_Osemilattice__inf(X58)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X66),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X66),X65)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X66),X65) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__left__idem) ).

fof(fact_inf__sup__aci_I4_J,axiom,
    ! [X65,X66,X58] :
      ( class_Lattices_Olattice(X58)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X66),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X66),X65)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X66),X65) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__aci_I4_J) ).

fof(fact_inf__sup__aci_I8_J,axiom,
    ! [X65,X66,X58] :
      ( class_Lattices_Olattice(X58)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X66),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X66),X65)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X66),X65) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__aci_I8_J) ).

fof(fact_sup__left__idem,axiom,
    ! [X65,X66,X58] :
      ( class_Lattices_Osemilattice__sup(X58)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X66),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X66),X65)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X66),X65) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__left__idem) ).

fof(fact_sup_Oleft__idem,axiom,
    ! [X90,X62,X58] :
      ( class_Lattices_Osemilattice__sup(X58)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X62),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X62),X90)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X62),X90) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup_Oleft__idem) ).

fof(fact_min__max_Osup__left__idem,axiom,
    ! [X65,X66,X58] :
      ( class_Orderings_Olinorder(X58)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(X58),X66),hAPP(hAPP(c_Orderings_Oord__class_Omax(X58),X66),X65)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X58),X66),X65) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup__left__idem) ).

fof(fact_min__max_Osup_Oleft__idem,axiom,
    ! [X90,X62,X58] :
      ( class_Orderings_Olinorder(X58)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(X58),X62),hAPP(hAPP(c_Orderings_Oord__class_Omax(X58),X62),X90)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X58),X62),X90) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup_Oleft__idem) ).

fof(fact_min__max_Oinf_Oleft__idem,axiom,
    ! [X90,X62,X58] :
      ( class_Orderings_Olinorder(X58)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(X58),X62),hAPP(hAPP(c_Orderings_Oord__class_Omin(X58),X62),X90)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X58),X62),X90) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf_Oleft__idem) ).

fof(fact_min__max_Oinf__left__idem,axiom,
    ! [X65,X66,X58] :
      ( class_Orderings_Olinorder(X58)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(X58),X66),hAPP(hAPP(c_Orderings_Oord__class_Omin(X58),X66),X65)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X58),X66),X65) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__left__idem) ).

fof(fact_mult__left__idem,axiom,
    ! [X90,X62,X58] :
      ( class_Lattices_Oab__semigroup__idem__mult(X58)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X90)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X90) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left__idem) ).

fof(fact_finite__sorted__distinct__unique,axiom,
    ! [X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ? [X3] :
            ( hAPP(c_List_Oset(X5),X3) = X21
            & c_List_Olinorder__class_Osorted(X5,X3)
            & hBOOL(hAPP(c_List_Odistinct(X5),X3))
            & ! [X177] :
                ( ( hAPP(c_List_Oset(X5),X177) = X21
                  & c_List_Olinorder__class_Osorted(X5,X177)
                  & hBOOL(hAPP(c_List_Odistinct(X5),X177)) )
               => X177 = X3 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__sorted__distinct__unique) ).

fof(fact_drop__tl,axiom,
    ! [X242,X57,X58] : hAPP(hAPP(c_List_Odrop(X58),X57),hAPP(c_List_Otl(X58),X242)) = hAPP(c_List_Otl(X58),hAPP(hAPP(c_List_Odrop(X58),X57),X242)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__tl) ).

fof(fact_tl__drop,axiom,
    ! [X242,X57,X58] : hAPP(c_List_Otl(X58),hAPP(hAPP(c_List_Odrop(X58),X57),X242)) = hAPP(hAPP(c_List_Odrop(X58),X57),hAPP(c_List_Otl(X58),X242)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tl__drop) ).

fof(fact_List_Oset_Osimps_I2_J,axiom,
    ! [X239,X25,X5] : hAPP(c_List_Oset(X5),hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239)) = hAPP(hAPP(c_Set_Oinsert(X5),X25),hAPP(c_List_Oset(X5),X239)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_List_Oset_Osimps_I2_J) ).

fof(fact_card__atLeastAtMost,axiom,
    ! [X159,X156] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X156,X159)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X159)),X156),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__atLeastAtMost) ).

fof(fact_surj__id,axiom,
    ! [X5] : hAPP(c_Set_Oimage(X5,X5,c_Fun_Oid(X5)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surj__id) ).

fof(fact_some__eq__ex,axiom,
    ! [X5,X18] :
      ( hBOOL(hAPP(X18,c_Hilbert__Choice_OEps(X5,X18)))
    <=> ? [X138] : hBOOL(hAPP(X18,X138)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_some__eq__ex) ).

fof(fact_partition__filter1,axiom,
    ! [X239,X18,X5] : hAPP(c_Product__Type_Ofst(tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Opartition(X5,X18,X239)) = hAPP(c_List_Ofilter(X5,X18),X239),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_partition__filter1) ).

fof(fact_iso__tuple__UNIV__I,axiom,
    ! [X25,X5] : hBOOL(hAPP(hAPP(c_member(X5),X25),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_iso__tuple__UNIV__I) ).

fof(fact_UNIV__I,axiom,
    ! [X25,X5] : hBOOL(hAPP(hAPP(c_member(X5),X25),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__I) ).

fof(fact_Compl__eq__Compl__iff,axiom,
    ! [X113,X21,X5] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X21) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X113)
    <=> X21 = X113 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__eq__Compl__iff) ).

fof(fact_fun__Compl__def,axiom,
    ! [X25,X21,X20,X5] :
      ( class_Groups_Ouminus(X5)
     => hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20,X5)),X21),X25) = hAPP(c_Groups_Ouminus__class_Ouminus(X5),hAPP(X21,X25)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__Compl__def) ).

fof(fact_uminus__apply,axiom,
    ! [X25,X21,X20,X5] :
      ( class_Groups_Ouminus(X5)
     => hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20,X5)),X21),X25) = hAPP(c_Groups_Ouminus__class_Ouminus(X5),hAPP(X21,X25)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_uminus__apply) ).

fof(fact_nat__0__le,axiom,
    ! [X94] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X94))
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X94)) = X94 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__0__le) ).

fof(fact_tsub__eq,axiom,
    ! [X66,X65] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X65),X66))
     => c_Nat__Transfer_Otsub(X66,X65) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X66),X65) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tsub__eq) ).

fof(fact_subtract__code__numeral__code,axiom,
    ! [X72,X57] : hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,hAPP(c_Code__Numeral_Oof__nat,X57)),hAPP(c_Code__Numeral_Oof__nat,X72)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X57),X72)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subtract__code__numeral__code) ).

fof(fact_int__eq__iff,axiom,
    ! [X120,X95] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X95) = X120
    <=> ( X95 = hAPP(c_Int_Onat,X120)
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X120)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__eq__iff) ).

fof(fact_semilattice__big_OF__eq,axiom,
    ! [X21,X205,X2,X5] :
      ( c_Big__Operators_Osemilattice__big(X5,X2,X205)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => hAPP(X205,X21) = hAPP(c_Finite__Set_Ofold1(X5,X2),X21) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_semilattice__big_OF__eq) ).

fof(fact_folding__one_Oeq__fold,axiom,
    ! [X21,X205,X2,X5] :
      ( c_Finite__Set_Ofolding__one(X5,X2,X205)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => hAPP(X205,X21) = hAPP(c_Finite__Set_Ofold1(X5,X2),X21) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one_Oeq__fold) ).

fof(fact_Inter__UNIV,axiom,
    ! [X5] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__UNIV) ).

fof(fact_Inter__empty,axiom,
    ! [X5] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X5,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inter__empty) ).

fof(fact_Union__UNIV,axiom,
    ! [X5] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__UNIV) ).

fof(fact_Union__empty,axiom,
    ! [X5] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__empty) ).

fof(fact_insert__absorb2,axiom,
    ! [X21,X25,X5] : hAPP(hAPP(c_Set_Oinsert(X5),X25),hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(hAPP(c_Set_Oinsert(X5),X25),X21),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__absorb2) ).

fof(fact_Bit1__Min,axiom,
    c_Int_OBit1(c_Int_OMin) = c_Int_OMin,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bit1__Min) ).

fof(fact_INF__const,axiom,
    ! [X210,X5,X21,X20] :
      ( class_Complete__Lattice_Ocomplete__lattice(X20)
     => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,X20),X21),hAPP(c_COMBK(X20,X5),X210)) = X210 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INF__const) ).

fof(fact_SUP__const,axiom,
    ! [X210,X5,X21,X20] :
      ( class_Complete__Lattice_Ocomplete__lattice(X20)
     => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,X20),X21),hAPP(c_COMBK(X20,X5),X210)) = X210 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SUP__const) ).

fof(fact_compl__unique,axiom,
    ! [X65,X66,X58] :
      ( class_Lattices_Oboolean__algebra(X58)
     => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X66),X65) = c_Orderings_Obot__class_Obot(X58)
       => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X66),X65) = c_Orderings_Otop__class_Otop(X58)
         => hAPP(c_Groups_Ouminus__class_Ouminus(X58),X66) = X65 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compl__unique) ).

fof(fact_mult__Suc__right,axiom,
    ! [X57,X72] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X72),hAPP(c_Nat_OSuc,X57)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X72),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X72),X57)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__Suc__right) ).

fof(fact_finite__atLeastZeroLessThan__int,axiom,
    ! [X159] : 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)),X159))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__atLeastZeroLessThan__int) ).

fof(fact_transpose_Osimps_I2_J,axiom,
    ! [X288,X58] : c_List_Otranspose(X58,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X58)),c_List_Olist_ONil(X58)),X288)) = c_List_Otranspose(X58,X288),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose_Osimps_I2_J) ).

fof(fact_Field__empty,axiom,
    ! [X5] : hAPP(c_Relation_OField(X5),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X5),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Field__empty) ).

fof(fact_mod__less,axiom,
    ! [X57,X72] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X72),X57))
     => c_Divides_Odiv__class_Omod(tc_Nat_Onat,X72,X57) = X72 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__less) ).

fof(fact_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
    ! [X159,X156] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X156),c_Groups_Oone__class_Oone(tc_Int_Oint)),X159) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X156,X159),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastPlusOneAtMost__greaterThanAtMost__int) ).

fof(fact_Inf__insert,axiom,
    ! [X21,X6,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => c_Complete__Lattice_OInf__class_OInf(X5,hAPP(hAPP(c_Set_Oinsert(X5),X6),X21)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X6),c_Complete__Lattice_OInf__class_OInf(X5,X21)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__insert) ).

fof(fact_Sup__insert,axiom,
    ! [X21,X6,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => c_Complete__Lattice_OSup__class_OSup(X5,hAPP(hAPP(c_Set_Oinsert(X5),X6),X21)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X6),c_Complete__Lattice_OSup__class_OSup(X5,X21)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__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/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_infinite__UNIV__nat) ).

fof(fact_insert__remdups,axiom,
    ! [X242,X66,X58] : c_List_Oinsert(X58,X66,c_List_Oremdups(X58,X242)) = c_List_Oremdups(X58,c_List_Oinsert(X58,X66,X242)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__remdups) ).

fof(fact_list__all__rev,axiom,
    ! [X239,X18,X5] :
      ( c_List_Olist__all(X5,X18,hAPP(c_List_Orev(X5),X239))
    <=> c_List_Olist__all(X5,X18,X239) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__all__rev) ).

fof(fact_list__ex__rev,axiom,
    ! [X239,X18,X5] :
      ( c_List_Olist__ex(X5,X18,hAPP(c_List_Orev(X5),X239))
    <=> c_List_Olist__ex(X5,X18,X239) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__ex__rev) ).

fof(fact_butlast_Osimps_I2_J,axiom,
    ! [X66,X58,X242] :
      ( ( X242 = c_List_Olist_ONil(X58)
       => c_List_Obutlast(X58,hAPP(hAPP(c_List_Olist_OCons(X58),X66),X242)) = c_List_Olist_ONil(X58) )
      & ( X242 != c_List_Olist_ONil(X58)
       => c_List_Obutlast(X58,hAPP(hAPP(c_List_Olist_OCons(X58),X66),X242)) = hAPP(hAPP(c_List_Olist_OCons(X58),X66),c_List_Obutlast(X58,X242)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_butlast_Osimps_I2_J) ).

fof(fact_butlast__append,axiom,
    ! [X242,X58,X241] :
      ( ( X241 = c_List_Olist_ONil(X58)
       => c_List_Obutlast(X58,hAPP(hAPP(c_List_Oappend(X58),X242),X241)) = c_List_Obutlast(X58,X242) )
      & ( X241 != c_List_Olist_ONil(X58)
       => c_List_Obutlast(X58,hAPP(hAPP(c_List_Oappend(X58),X242),X241)) = hAPP(hAPP(c_List_Oappend(X58),X242),c_List_Obutlast(X58,X241)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_butlast__append) ).

fof(fact_vimage__UNIV,axiom,
    ! [X2,X20,X5] : hAPP(c_Set_Ovimage(X5,X20,X2),c_Orderings_Otop__class_Otop(tc_fun(X20,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__UNIV) ).

fof(fact_vimage__empty,axiom,
    ! [X2,X20,X5] : hAPP(c_Set_Ovimage(X5,X20,X2),c_Orderings_Obot__class_Obot(tc_fun(X20,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__empty) ).

fof(fact_Image__empty,axiom,
    ! [X32,X5,X20] : hAPP(c_Relation_OImage(X20,X5,X32),c_Orderings_Obot__class_Obot(tc_fun(X20,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__empty) ).

fof(fact_image__empty,axiom,
    ! [X2,X5,X20] : hAPP(c_Set_Oimage(X20,X5,X2),c_Orderings_Obot__class_Obot(tc_fun(X20,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__empty) ).

fof(fact_listrel__refl__on,axiom,
    ! [X171,X21,X5] :
      ( c_Relation_Orefl__on(X5,X21,X171)
     => c_Relation_Orefl__on(tc_List_Olist(X5),c_List_Olists(X5,X21),c_List_Olistrel(X5,X171)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__refl__on) ).

fof(fact_equiv__listrel,axiom,
    ! [X171,X21,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X21,X171)
     => c_Equiv__Relations_Oequiv(tc_List_Olist(X5),c_List_Olists(X5,X21),c_List_Olistrel(X5,X171)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equiv__listrel) ).

fof(fact_mem__def,axiom,
    ! [X21,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
    <=> hBOOL(hAPP(X21,X25)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__def) ).

fof(fact_com_Osize_I3_J,axiom,
    ! [X11,X84,X102] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(X102,X84,X11)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X11)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osize_I3_J) ).

fof(fact_diff__is__0__eq,axiom,
    ! [X50,X95] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X95),X50) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X50)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__is__0__eq) ).

fof(fact_diff__is__0__eq_H,axiom,
    ! [X57,X72] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X72),X57))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X72),X57) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__is__0__eq_H) ).

fof(fact_div__less,axiom,
    ! [X57,X72] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X72),X57))
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X72),X57) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__less) ).

fof(fact_Int__UNIV__right,axiom,
    ! [X21,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) = X21,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__UNIV__right) ).

fof(fact_Un__empty__right,axiom,
    ! [X21,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) = X21,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__empty__right) ).

fof(fact_Diff__empty,axiom,
    ! [X21,X5] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) = X21,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__empty) ).

fof(fact_double__complement,axiom,
    ! [X21,X5] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X21)) = X21,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__complement) ).

fof(fact_rel__pow__1,axiom,
    ! [X32,X5] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X32) = X32,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__pow__1) ).

fof(fact_list__update__id,axiom,
    ! [X98,X242,X58] : hAPP(hAPP(c_List_Olist__update(X58,X242),X98),hAPP(hAPP(c_List_Onth(X58),X242),X98)) = X242,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update__id) ).

fof(fact_square__eq__iff,axiom,
    ! [X24,X6,X5] :
      ( class_Rings_Oidom(X5)
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X6) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X24),X24)
      <=> ( X6 = X24
          | X6 = hAPP(c_Groups_Ouminus__class_Ouminus(X5),X24) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_square__eq__iff) ).

fof(fact_add__Suc,axiom,
    ! [X57,X72] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X72)),X57) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X72),X57)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc) ).

fof(fact_drop__butlast,axiom,
    ! [X242,X57,X58] : hAPP(hAPP(c_List_Odrop(X58),X57),c_List_Obutlast(X58,X242)) = c_List_Obutlast(X58,hAPP(hAPP(c_List_Odrop(X58),X57),X242)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__butlast) ).

fof(fact_butlast__drop,axiom,
    ! [X242,X57,X58] : c_List_Obutlast(X58,hAPP(hAPP(c_List_Odrop(X58),X57),X242)) = hAPP(hAPP(c_List_Odrop(X58),X57),c_List_Obutlast(X58,X242)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_butlast__drop) ).

fof(fact_code__numeral__not__eq__zero,axiom,
    ! [X82] :
      ( X82 != 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)),X82)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_code__numeral__not__eq__zero) ).

fof(fact_Domain__empty__iff,axiom,
    ! [X171,X20,X5] :
      ( hAPP(c_Relation_ODomain(X5,X20),X171) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
    <=> X171 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X20),tc_HOL_Obool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__empty__iff) ).

fof(fact_Range__empty__iff,axiom,
    ! [X171,X5,X20] :
      ( hAPP(c_Relation_ORange(X20,X5),X171) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
    <=> X171 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X20,X5),tc_HOL_Obool)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__empty__iff) ).

fof(fact_abs__zmult__eq__1,axiom,
    ! [X57,X72] :
      ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X72),X57)) = c_Groups_Oone__class_Oone(tc_Int_Oint)
     => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X72) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__zmult__eq__1) ).

fof(fact_zless__linear,axiom,
    ! [X65,X66] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X66),X65))
      | X66 = X65
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X65),X66)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__linear) ).

fof(fact_nat__neq__iff,axiom,
    ! [X50,X95] :
      ( X95 != X50
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),X50))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X50),X95)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__neq__iff) ).

fof(fact_card__atLeastLessThan__int,axiom,
    ! [X159,X156] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X156),X159)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X159),X156)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__atLeastLessThan__int) ).

fof(fact_abs__ge__self,axiom,
    ! [X62,X58] :
      ( class_Groups_Oordered__ab__group__add__abs(X58)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X62),hAPP(c_Groups_Oabs__class_Oabs(X58),X62))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__ge__self) ).

fof(fact_card__greaterThanLessThan,axiom,
    ! [X159,X156] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X156,X159)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X159),hAPP(c_Nat_OSuc,X156)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__greaterThanLessThan) ).

fof(fact_part__equivpI,axiom,
    ! [X5,X32] :
      ( ? [X3] : hBOOL(hAPP(hAPP(X32,X3),X3))
     => ( c_Predicate_Osymp(X5,X32)
       => ( c_Predicate_Otransp(X5,X32)
         => c_Equiv__Relations_Opart__equivp(X5,X32) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_part__equivpI) ).

fof(fact_zle__linear,axiom,
    ! [X128,X94] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X94),X128))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X128),X94)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__linear) ).

fof(fact_nat__le__linear,axiom,
    ! [X57,X72] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X72),X57))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X57),X72)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__linear) ).

fof(fact_zdiv__zminus__zminus,axiom,
    ! [X90,X62] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X62)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X90)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X62),X90),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zminus__zminus) ).

fof(fact_zdiv__zminus2,axiom,
    ! [X90,X62] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X62),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X90)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X62)),X90),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zminus2) ).

fof(fact_drop__Suc,axiom,
    ! [X242,X57,X58] : hAPP(hAPP(c_List_Odrop(X58),hAPP(c_Nat_OSuc,X57)),X242) = hAPP(hAPP(c_List_Odrop(X58),X57),hAPP(c_List_Otl(X58),X242)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__Suc) ).

fof(fact_gr0__implies__Suc,axiom,
    ! [X57] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X57))
     => ? [X86] : X57 = hAPP(c_Nat_OSuc,X86) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr0__implies__Suc) ).

fof(fact_gr0__conv__Suc,axiom,
    ! [X50] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X50))
    <=> ? [X86] : X50 = hAPP(c_Nat_OSuc,X86) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr0__conv__Suc) ).

fof(fact_min__max_OInf__fin_OF__eq,axiom,
    ! [X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X21) = hAPP(c_Finite__Set_Ofold1(X5,c_Orderings_Oord__class_Omin(X5)),X21) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__fin_OF__eq) ).

fof(fact_min__max_OSup__fin_OF__eq,axiom,
    ! [X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X21) = hAPP(c_Finite__Set_Ofold1(X5,c_Orderings_Oord__class_Omax(X5)),X21) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OSup__fin_OF__eq) ).

fof(fact_fun__left__comm__insort,axiom,
    ! [X5] :
      ( class_Orderings_Olinorder(X5)
     => c_Finite__Set_Ofun__left__comm(X5,tc_List_Olist(X5),c_List_Olinorder__class_Oinsort__key(X5,X5,c_COMBI(X5))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__insort) ).

fof(fact_equivI,axiom,
    ! [X171,X21,X5] :
      ( c_Relation_Orefl__on(X5,X21,X171)
     => ( c_Relation_Osym(X5,X171)
       => ( c_Relation_Otrans(X5,X171)
         => c_Equiv__Relations_Oequiv(X5,X21,X171) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equivI) ).

fof(fact_equiv__def,axiom,
    ! [X171,X21,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X21,X171)
    <=> ( c_Relation_Orefl__on(X5,X21,X171)
        & c_Relation_Osym(X5,X171)
        & c_Relation_Otrans(X5,X171) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equiv__def) ).

fof(fact_distinct__tl,axiom,
    ! [X242,X58] :
      ( hBOOL(hAPP(c_List_Odistinct(X58),X242))
     => hBOOL(hAPP(c_List_Odistinct(X58),hAPP(c_List_Otl(X58),X242))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__tl) ).

fof(fact_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
    ! [X159,X156] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X156),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X159),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X156,X159),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThanPlusOne__atLeastAtMost__int) ).

fof(fact_neg__def,axiom,
    ! [X165] :
      ( hBOOL(hAPP(c_Nat__Numeral_Oneg,X165))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X165),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__def) ).

fof(fact_card__distinct,axiom,
    ! [X239,X5] :
      ( hAPP(c_Finite__Set_Ocard(X5),hAPP(c_List_Oset(X5),X239)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239)
     => hBOOL(hAPP(c_List_Odistinct(X5),X239)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__distinct) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom,
    ! [X65,X66] : c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X66),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X65)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X66),X65)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J) ).

fof(fact_singleton__rev__conv,axiom,
    ! [X239,X25,X5] :
      ( hAPP(hAPP(c_List_Olist_OCons(X5),X25),c_List_Olist_ONil(X5)) = hAPP(c_List_Orev(X5),X239)
    <=> X239 = hAPP(hAPP(c_List_Olist_OCons(X5),X25),c_List_Olist_ONil(X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_singleton__rev__conv) ).

fof(fact_rev__singleton__conv,axiom,
    ! [X25,X239,X5] :
      ( hAPP(c_List_Orev(X5),X239) = hAPP(hAPP(c_List_Olist_OCons(X5),X25),c_List_Olist_ONil(X5))
    <=> X239 = hAPP(hAPP(c_List_Olist_OCons(X5),X25),c_List_Olist_ONil(X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__singleton__conv) ).

fof(fact_com_Osize_I14_J,axiom,
    ! [X11,X84] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OWhile(X84,X11)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X11)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osize_I14_J) ).

fof(fact_listrel1__converse,axiom,
    ! [X171,X5] : c_List_Olistrel1(X5,hAPP(c_Relation_Oconverse(X5,X5),X171)) = hAPP(c_Relation_Oconverse(tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel1(X5,X171)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel1__converse) ).

fof(fact_minus__diff__eq,axiom,
    ! [X90,X62,X58] :
      ( class_Groups_Oab__group__add(X58)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X58),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X58),X62),X90)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X58),X90),X62) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__diff__eq) ).

fof(fact_rev__replicate,axiom,
    ! [X66,X57,X58] : hAPP(c_List_Orev(X58),c_List_Oreplicate(X58,X57,X66)) = c_List_Oreplicate(X58,X57,X66),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__replicate) ).

fof(fact_acc__wfD,axiom,
    ! [X25,X171,X5] :
      ( c_Wellfounded_Owf(X5,X171)
     => hBOOL(hAPP(hAPP(c_member(X5),X25),c_Wellfounded_Oacc(X5,X171))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc__wfD) ).

fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom,
    ! [X66,X58] :
      ( class_Rings_Ocomm__ring__1(X58)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X58),X66) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),hAPP(c_Groups_Ouminus__class_Ouminus(X58),c_Groups_Oone__class_Oone(X58))),X66) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J) ).

fof(fact_finite__atLeastLessThan__int,axiom,
    ! [X159,X156] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X156),X159))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__atLeastLessThan__int) ).

fof(fact_finite__atLeastLessThan,axiom,
    ! [X159,X156] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X156),X159))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__atLeastLessThan) ).

fof(fact_list__all__iff__all__interval__int,axiom,
    ! [X157,X82,X18] :
      ( c_List_Olist__all(tc_Int_Oint,X18,c_List_Oupto(X82,X157))
    <=> c_List_Oall__interval__int(X18,X82,X157) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__all__iff__all__interval__int) ).

fof(fact_enum__all,axiom,
    ! [X18,X5] :
      ( class_Enum_Oenum(X5)
     => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X5),X18))
      <=> ! [X138] : hBOOL(hAPP(X18,X138)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_enum__all) ).

fof(fact_all__code,axiom,
    ! [X18,X5] :
      ( class_Enum_Oenum(X5)
     => ( ! [X138] : hBOOL(hAPP(X18,X138))
      <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X5),X18)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_all__code) ).

fof(fact_nat_Osize_I4_J,axiom,
    ! [X108] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),hAPP(c_Nat_OSuc,X108)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X108)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osize_I4_J) ).

fof(fact_less__imp__neq,axiom,
    ! [X65,X66,X58] :
      ( class_Orderings_Oorder(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X66),X65))
       => X66 != X65 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__neq) ).

fof(fact_order__less__imp__not__eq,axiom,
    ! [X65,X66,X58] :
      ( class_Orderings_Oorder(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X66),X65))
       => X66 != X65 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__eq) ).

fof(fact_order__less__imp__not__eq2,axiom,
    ! [X65,X66,X58] :
      ( class_Orderings_Oorder(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X66),X65))
       => X65 != X66 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__eq2) ).

fof(fact_replicate__eq__replicate,axiom,
    ! [X33,X50,X25,X95,X5] :
      ( c_List_Oreplicate(X5,X95,X25) = c_List_Oreplicate(X5,X50,X33)
    <=> ( X95 = X50
        & ( X95 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => X25 = X33 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_replicate__eq__replicate) ).

fof(fact_diff__eq__diff__eq,axiom,
    ! [X22,X23,X24,X6,X5] :
      ( class_Groups_Oab__group__add(X5)
     => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X6),X24) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X23),X22)
       => ( X6 = X24
        <=> X23 = X22 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__eq__diff__eq) ).

fof(fact_triple__valid__Suc,axiom,
    ! [X54,X57,X58] :
      ( c_Hoare__Mirabelle_Otriple__valid(X58,hAPP(c_Nat_OSuc,X57),X54)
     => c_Hoare__Mirabelle_Otriple__valid(X58,X57,X54) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_triple__valid__Suc) ).

fof(fact_rev__filter,axiom,
    ! [X239,X18,X5] : hAPP(c_List_Orev(X5),hAPP(c_List_Ofilter(X5,X18),X239)) = hAPP(c_List_Ofilter(X5,X18),hAPP(c_List_Orev(X5),X239)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__filter) ).

fof(fact_zmod__zminus1__not__zero,axiom,
    ! [X99,X96] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X96),X99) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
     => c_Divides_Odiv__class_Omod(tc_Int_Oint,X96,X99) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zminus1__not__zero) ).

fof(fact_zmod__zminus2__not__zero,axiom,
    ! [X99,X96] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X96,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X99)) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
     => c_Divides_Odiv__class_Omod(tc_Int_Oint,X96,X99) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zminus2__not__zero) ).

fof(fact_neq0__conv,axiom,
    ! [X50] :
      ( X50 != 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)),X50)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neq0__conv) ).

fof(fact_n__lists__Nil,axiom,
    ! [X58,X57] :
      ( ( X57 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => c_Enum_On__lists(X58,X57,c_List_Olist_ONil(X58)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X58)),c_List_Olist_ONil(X58)),c_List_Olist_ONil(tc_List_Olist(X58))) )
      & ( X57 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => c_Enum_On__lists(X58,X57,c_List_Olist_ONil(X58)) = c_List_Olist_ONil(tc_List_Olist(X58)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__lists__Nil) ).

fof(fact_add__right__cancel,axiom,
    ! [X23,X6,X24,X5] :
      ( class_Groups_Ocancel__semigroup__add(X5)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X24),X6) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X23),X6)
      <=> X24 = X23 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__right__cancel) ).

fof(fact_add__right__imp__eq,axiom,
    ! [X56,X62,X90,X58] :
      ( class_Groups_Ocancel__semigroup__add(X58)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X90),X62) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X56),X62)
       => X90 = X56 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__right__imp__eq) ).

fof(fact_add__imp__eq,axiom,
    ! [X56,X90,X62,X58] :
      ( class_Groups_Ocancel__ab__semigroup__add(X58)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),X90) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),X56)
       => X90 = X56 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__imp__eq) ).

fof(fact_add__left__cancel,axiom,
    ! [X23,X24,X6,X5] :
      ( class_Groups_Ocancel__semigroup__add(X5)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),X24) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),X23)
      <=> X24 = X23 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__cancel) ).

fof(fact_add__left__imp__eq,axiom,
    ! [X56,X90,X62,X58] :
      ( class_Groups_Ocancel__semigroup__add(X58)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),X90) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),X56)
       => X90 = X56 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__imp__eq) ).

fof(fact_lazy__sequence_Oinject,axiom,
    ! [X306,X180,X307,X6,X5] :
      ( c_Lazy__Sequence_Olazy__sequence_OInsert(X5,X6,X307) = c_Lazy__Sequence_Olazy__sequence_OInsert(X5,X180,X306)
    <=> ( X6 = X180
        & X307 = X306 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lazy__sequence_Oinject) ).

fof(fact_com_Osimps_I2_J,axiom,
    ! [X8,X92,X107,X11,X84,X102] :
      ( c_Com_Ocom_OLocal(X102,X84,X11) = c_Com_Ocom_OLocal(X107,X92,X8)
    <=> ( X102 = X107
        & X84 = X92
        & X11 = X8 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I2_J) ).

fof(fact_com_Osimps_I4_J,axiom,
    ! [X39,X40,X92,X41,X42,X84] :
      ( c_Com_Ocom_OCond(X84,X42,X41) = c_Com_Ocom_OCond(X92,X40,X39)
    <=> ( X84 = X92
        & X42 = X40
        & X41 = X39 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I4_J) ).

fof(fact_com_Osimps_I7_J,axiom,
    ! [X92,X43,X93,X84,X44,X85] :
      ( c_Com_Ocom_OCall(X85,X44,X84) = c_Com_Ocom_OCall(X93,X43,X92)
    <=> ( X85 = X93
        & X44 = X43
        & X84 = X92 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I7_J) ).

fof(fact_nat__0__iff,axiom,
    ! [X82] :
      ( hAPP(c_Int_Onat,X82) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X82),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__0__iff) ).

fof(fact_nat__le__0,axiom,
    ! [X94] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X94),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => hAPP(c_Int_Onat,X94) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__0) ).

fof(fact_is__nat__def,axiom,
    ! [X25] :
      ( c_Nat__Transfer_Ois__nat(X25)
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_is__nat__def) ).

fof(fact_add__Suc__right,axiom,
    ! [X57,X72] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X72),hAPP(c_Nat_OSuc,X57)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X72),X57)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc__right) ).

fof(fact_com_Osimps_I36_J,axiom,
    ! [X39,X40,X92,X11,X84,X102] : c_Com_Ocom_OLocal(X102,X84,X11) != c_Com_Ocom_OCond(X92,X40,X39),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I36_J) ).

fof(fact_com_Osimps_I42_J,axiom,
    ! [X92,X43,X93,X11,X84,X102] : c_Com_Ocom_OLocal(X102,X84,X11) != c_Com_Ocom_OCall(X93,X43,X92),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I42_J) ).

fof(fact_com_Osimps_I37_J,axiom,
    ! [X11,X84,X102,X39,X40,X92] : c_Com_Ocom_OCond(X92,X40,X39) != c_Com_Ocom_OLocal(X102,X84,X11),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I37_J) ).

fof(fact_com_Osimps_I43_J,axiom,
    ! [X11,X84,X102,X92,X43,X93] : c_Com_Ocom_OCall(X93,X43,X92) != c_Com_Ocom_OLocal(X102,X84,X11),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I43_J) ).

fof(fact_com_Osimps_I56_J,axiom,
    ! [X92,X43,X93,X41,X42,X84] : c_Com_Ocom_OCond(X84,X42,X41) != c_Com_Ocom_OCall(X93,X43,X92),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I56_J) ).

fof(fact_com_Osimps_I57_J,axiom,
    ! [X41,X42,X84,X92,X43,X93] : c_Com_Ocom_OCall(X93,X43,X92) != c_Com_Ocom_OCond(X84,X42,X41),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I57_J) ).

fof(fact_lexn_Osimps_I1_J,axiom,
    ! [X171,X5] : hAPP(c_List_Olexn(X5,X171),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)),tc_HOL_Obool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexn_Osimps_I1_J) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom,
    ! [X94] : 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),X94))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J) ).

fof(fact_zero__zle__int,axiom,
    ! [X57] : 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),X57))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__zle__int) ).

fof(fact_Diff__cancel,axiom,
    ! [X21,X5] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),X21) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__cancel) ).

fof(fact_antisym__empty,axiom,
    ! [X5] : c_Relation_Oantisym(X5,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X5),tc_HOL_Obool))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_antisym__empty) ).

fof(fact_wf__empty,axiom,
    ! [X5] : c_Wellfounded_Owf(X5,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X5),tc_HOL_Obool))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__empty) ).

fof(fact_atLeastAtMost__singleton_H,axiom,
    ! [X24,X6,X5] :
      ( class_Orderings_Oorder(X5)
     => ( X6 = X24
       => c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,X24) = hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastAtMost__singleton_H) ).

fof(fact_sorted__list__of__set,axiom,
    ! [X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( hAPP(c_List_Oset(X5),c_List_Olinorder__class_Osorted__list__of__set(X5,X21)) = X21
          & c_List_Olinorder__class_Osorted(X5,c_List_Olinorder__class_Osorted__list__of__set(X5,X21))
          & hBOOL(hAPP(c_List_Odistinct(X5),c_List_Olinorder__class_Osorted__list__of__set(X5,X21))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__list__of__set) ).

fof(fact_mod__mult__self1__is__0,axiom,
    ! [X62,X90,X58] :
      ( class_Divides_Osemiring__div(X58)
     => c_Divides_Odiv__class_Omod(X58,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X90),X62),X90) = c_Groups_Ozero__class_Ozero(X58) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__self1__is__0) ).

fof(fact_mod__mult__self2__is__0,axiom,
    ! [X90,X62,X58] :
      ( class_Divides_Osemiring__div(X58)
     => c_Divides_Odiv__class_Omod(X58,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X90),X90) = c_Groups_Ozero__class_Ozero(X58) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__self2__is__0) ).

fof(fact_distinct__butlast,axiom,
    ! [X58,X242] :
      ( X242 != c_List_Olist_ONil(X58)
     => ( hBOOL(hAPP(c_List_Odistinct(X58),X242))
       => hBOOL(hAPP(c_List_Odistinct(X58),c_List_Obutlast(X58,X242))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__butlast) ).

fof(fact_card__greaterThanAtMost,axiom,
    ! [X159,X156] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X156,X159)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X159),X156),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__greaterThanAtMost) ).

fof(fact_list_Oinject,axiom,
    ! [X253,X180,X254,X6,X5] :
      ( hAPP(hAPP(c_List_Olist_OCons(X5),X6),X254) = hAPP(hAPP(c_List_Olist_OCons(X5),X180),X253)
    <=> ( X6 = X180
        & X254 = X253 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list_Oinject) ).

fof(fact_append__same__eq,axiom,
    ! [X250,X239,X251,X5] :
      ( hAPP(hAPP(c_List_Oappend(X5),X251),X239) = hAPP(hAPP(c_List_Oappend(X5),X250),X239)
    <=> X251 = X250 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__same__eq) ).

fof(fact_same__append__eq,axiom,
    ! [X250,X251,X239,X5] :
      ( hAPP(hAPP(c_List_Oappend(X5),X239),X251) = hAPP(hAPP(c_List_Oappend(X5),X239),X250)
    <=> X251 = X250 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_same__append__eq) ).

fof(fact_atLeastAtMost__singleton,axiom,
    ! [X6,X5] :
      ( class_Orderings_Oorder(X5)
     => c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,X6) = hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastAtMost__singleton) ).

fof(fact_upto__empty,axiom,
    ! [X98,X97] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X97),X98))
     => c_List_Oupto(X98,X97) = c_List_Olist_ONil(tc_Int_Oint) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_upto__empty) ).

fof(fact_n__lists_Osimps_I1_J,axiom,
    ! [X242,X58] : c_Enum_On__lists(X58,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X242) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X58)),c_List_Olist_ONil(X58)),c_List_Olist_ONil(tc_List_Olist(X58))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__lists_Osimps_I1_J) ).

fof(fact_atMost__Suc,axiom,
    ! [X87] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,X87)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X87)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X87)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atMost__Suc) ).

fof(fact_eq__number__of__0,axiom,
    ! [X123] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X123) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X123),c_Int_OPls)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__number__of__0) ).

fof(fact_neg__imp__number__of__eq__0,axiom,
    ! [X136] :
      ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)))
     => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__imp__number__of__eq__0) ).

fof(fact_eq__0__number__of,axiom,
    ! [X123] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X123)
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X123),c_Int_OPls)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__0__number__of) ).

fof(fact_inf__sup__absorb,axiom,
    ! [X65,X66,X58] :
      ( class_Lattices_Olattice(X58)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X66),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X66),X65)) = X66 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__absorb) ).

fof(fact_sup__inf__absorb,axiom,
    ! [X65,X66,X58] :
      ( class_Lattices_Olattice(X58)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X66),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X66),X65)) = X66 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__inf__absorb) ).

fof(fact_min__max_Osup__inf__absorb,axiom,
    ! [X65,X66,X58] :
      ( class_Orderings_Olinorder(X58)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(X58),X66),hAPP(hAPP(c_Orderings_Oord__class_Omin(X58),X66),X65)) = X66 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup__inf__absorb) ).

fof(fact_min__max_Oinf__sup__absorb,axiom,
    ! [X65,X66,X58] :
      ( class_Orderings_Olinorder(X58)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(X58),X66),hAPP(hAPP(c_Orderings_Oord__class_Omax(X58),X66),X65)) = X66 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__sup__absorb) ).

fof(fact_conversep__conversep,axiom,
    ! [X171,X5,X20] : c_Predicate_Oconversep(X20,X5,c_Predicate_Oconversep(X5,X20,X171)) = X171,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_conversep__conversep) ).

fof(fact_le__0__eq,axiom,
    ! [X50] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X50),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    <=> X50 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__0__eq) ).

fof(fact_drop__1__Cons,axiom,
    ! [X242,X66,X58] : hAPP(hAPP(c_List_Odrop(X58),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(X58),X66),X242)) = X242,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__1__Cons) ).

fof(fact_diff__Suc__Suc,axiom,
    ! [X57,X72] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X72)),hAPP(c_Nat_OSuc,X57)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X72),X57),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__Suc) ).

fof(fact_add__Suc__shift,axiom,
    ! [X57,X72] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X72)),X57) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X72),hAPP(c_Nat_OSuc,X57)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc__shift) ).

fof(fact_fold1__def,axiom,
    ! [X21,X2,X5] : hAPP(c_Finite__Set_Ofold1(X5,X2),X21) = c_HOL_OThe(X5,c_Finite__Set_Ofold1Set(X5,X2,X21)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__def) ).

fof(fact_zmod__eq__0__iff,axiom,
    ! [X22,X95] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X95,X22) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    <=> ? [X151] : X95 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22),X151) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__eq__0__iff) ).

fof(fact_mod__eq__0__iff,axiom,
    ! [X22,X95] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X95,X22) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> ? [X151] : X95 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22),X151) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__eq__0__iff) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J,axiom,
    ! [X25,X21] :
      ( c_Nat__Transfer_Onat__set(X21)
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X25),X21))
       => c_Nat__Transfer_Ois__nat(X25) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J) ).

fof(fact_sym__converse,axiom,
    ! [X171,X5] :
      ( c_Relation_Osym(X5,hAPP(c_Relation_Oconverse(X5,X5),X171))
    <=> c_Relation_Osym(X5,X171) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sym__converse) ).

fof(fact_antisym__converse,axiom,
    ! [X171,X5] :
      ( c_Relation_Oantisym(X5,hAPP(c_Relation_Oconverse(X5,X5),X171))
    <=> c_Relation_Oantisym(X5,X171) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_antisym__converse) ).

fof(fact_trans__converse,axiom,
    ! [X171,X5] :
      ( c_Relation_Otrans(X5,hAPP(c_Relation_Oconverse(X5,X5),X171))
    <=> c_Relation_Otrans(X5,X171) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__converse) ).

fof(fact_acyclic__converse,axiom,
    ! [X171,X5] :
      ( c_Wellfounded_Oacyclic(X5,hAPP(c_Relation_Oconverse(X5,X5),X171))
    <=> c_Wellfounded_Oacyclic(X5,X171) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acyclic__converse) ).

fof(fact_distinct__card,axiom,
    ! [X239,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),X239))
     => hAPP(c_Finite__Set_Ocard(X5),hAPP(c_List_Oset(X5),X239)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__card) ).

fof(fact_length__remdups__eq,axiom,
    ! [X239,X5] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_Oremdups(X5,X239)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239)
    <=> c_List_Oremdups(X5,X239) = X239 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__remdups__eq) ).

fof(fact_Domain__converse,axiom,
    ! [X171,X20,X5] : hAPP(c_Relation_ODomain(X5,X20),hAPP(c_Relation_Oconverse(X20,X5),X171)) = hAPP(c_Relation_ORange(X20,X5),X171),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__converse) ).

fof(fact_Range__converse,axiom,
    ! [X171,X5,X20] : hAPP(c_Relation_ORange(X20,X5),hAPP(c_Relation_Oconverse(X5,X20),X171)) = hAPP(c_Relation_ODomain(X5,X20),X171),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__converse) ).

fof(fact_rtrancl__converse,axiom,
    ! [X171,X5] : c_Transitive__Closure_Ortrancl(X5,hAPP(c_Relation_Oconverse(X5,X5),X171)) = hAPP(c_Relation_Oconverse(X5,X5),c_Transitive__Closure_Ortrancl(X5,X171)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__converse) ).

fof(fact_remdups__filter,axiom,
    ! [X239,X18,X5] : c_List_Oremdups(X5,hAPP(c_List_Ofilter(X5,X18),X239)) = hAPP(c_List_Ofilter(X5,X18),c_List_Oremdups(X5,X239)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_remdups__filter) ).

fof(fact_Range__def,axiom,
    ! [X171,X5,X20] : hAPP(c_Relation_ORange(X20,X5),X171) = hAPP(c_Relation_ODomain(X5,X20),hAPP(c_Relation_Oconverse(X20,X5),X171)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__def) ).

fof(fact_exists__code,axiom,
    ! [X18,X5] :
      ( class_Enum_Oenum(X5)
     => ( ? [X138] : hBOOL(hAPP(X18,X138))
      <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X5),X18)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_exists__code) ).

fof(fact_enum__ex,axiom,
    ! [X18,X5] :
      ( class_Enum_Oenum(X5)
     => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X5),X18))
      <=> ? [X138] : hBOOL(hAPP(X18,X138)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_enum__ex) ).

fof(fact_list__update__nonempty,axiom,
    ! [X25,X87,X239,X5] :
      ( hAPP(hAPP(c_List_Olist__update(X5,X239),X87),X25) = c_List_Olist_ONil(X5)
    <=> X239 = c_List_Olist_ONil(X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update__nonempty) ).

fof(fact_map__is__Nil__conv,axiom,
    ! [X239,X2,X5,X20] :
      ( hAPP(hAPP(c_List_Omap(X20,X5),X2),X239) = c_List_Olist_ONil(X5)
    <=> X239 = c_List_Olist_ONil(X20) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__is__Nil__conv) ).

fof(fact_Nil__is__map__conv,axiom,
    ! [X239,X2,X20,X5] :
      ( c_List_Olist_ONil(X5) = hAPP(hAPP(c_List_Omap(X20,X5),X2),X239)
    <=> X239 = c_List_Olist_ONil(X20) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nil__is__map__conv) ).

fof(fact_diffs0__imp__equal,axiom,
    ! [X57,X72] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X72),X57) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
     => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X57),X72) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => X72 = X57 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diffs0__imp__equal) ).

fof(fact_setsum__empty,axiom,
    ! [X2,X20,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X20,X5),X2),c_Orderings_Obot__class_Obot(tc_fun(X20,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__empty) ).

fof(fact_setsum_Oempty,axiom,
    ! [X1,X20,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X20,X5),X1),c_Orderings_Obot__class_Obot(tc_fun(X20,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum_Oempty) ).

fof(fact_setprod__empty,axiom,
    ! [X2,X20,X5] :
      ( class_Groups_Ocomm__monoid__mult(X5)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X20,X5),X2),c_Orderings_Obot__class_Obot(tc_fun(X20,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod__empty) ).

fof(fact_setprod_Oempty,axiom,
    ! [X1,X20,X5] :
      ( class_Groups_Ocomm__monoid__mult(X5)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X20,X5),X1),c_Orderings_Obot__class_Obot(tc_fun(X20,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setprod_Oempty) ).

fof(fact_gr__implies__not0,axiom,
    ! [X57,X72] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X72),X57))
     => X57 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr__implies__not0) ).

fof(fact_finite__UNIV,axiom,
    ! [X5] :
      ( class_Finite__Set_Ofinite(X5)
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X5),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UNIV) ).

fof(fact_divide__eq__eq,axiom,
    ! [X6,X23,X24,X5] :
      ( class_Fields_Ofield__inverse__zero(X5)
     => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X24),X23) = X6
      <=> ( ( X23 != c_Groups_Ozero__class_Ozero(X5)
           => X24 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X23) )
          & ( X23 = c_Groups_Ozero__class_Ozero(X5)
           => X6 = c_Groups_Ozero__class_Ozero(X5) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__eq__eq) ).

fof(fact_eq__divide__eq,axiom,
    ! [X23,X24,X6,X5] :
      ( class_Fields_Ofield__inverse__zero(X5)
     => ( X6 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X24),X23)
      <=> ( ( X23 != c_Groups_Ozero__class_Ozero(X5)
           => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X23) = X24 )
          & ( X23 = c_Groups_Ozero__class_Ozero(X5)
           => X6 = c_Groups_Ozero__class_Ozero(X5) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__divide__eq) ).

fof(fact_of__nat__Suc,axiom,
    ! [X72,X58] :
      ( class_Rings_Osemiring__1(X58)
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X58),hAPP(c_Nat_OSuc,X72)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),c_Groups_Oone__class_Oone(X58)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X58),X72)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__Suc) ).

fof(fact_zero__less__Suc,axiom,
    ! [X57] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X57))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__Suc) ).

fof(fact_less__not__refl2,axiom,
    ! [X72,X57] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X57),X72))
     => X72 != X57 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl2) ).

fof(fact_less__not__refl3,axiom,
    ! [X54,X48] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X48),X54))
     => X48 != X54 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl3) ).

fof(fact_atLeastLessThan__singleton,axiom,
    ! [X95] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X95),hAPP(c_Nat_OSuc,X95)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X95),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__singleton) ).

fof(fact_sorted__takeWhile,axiom,
    ! [X18,X239,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( c_List_Olinorder__class_Osorted(X5,X239)
       => c_List_Olinorder__class_Osorted(X5,c_List_OtakeWhile(X5,X18,X239)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__takeWhile) ).

fof(fact_sorted__remove1,axiom,
    ! [X62,X242,X58] :
      ( class_Orderings_Olinorder(X58)
     => ( c_List_Olinorder__class_Osorted(X58,X242)
       => c_List_Olinorder__class_Osorted(X58,c_List_Oremove1(X58,X62,X242)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__remove1) ).

fof(fact_mult__cancel2,axiom,
    ! [X50,X87,X95] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X95),X87) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X50),X87)
    <=> ( X95 = X50
        | X87 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__cancel2) ).

fof(fact_nat__mult__eq__cancel__disj,axiom,
    ! [X50,X95,X87] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X87),X95) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X87),X50)
    <=> ( X87 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X95 = X50 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel__disj) ).

fof(fact_mult__cancel1,axiom,
    ! [X50,X95,X87] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X87),X95) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X87),X50)
    <=> ( X95 = X50
        | X87 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__cancel1) ).

fof(fact_hd__append,axiom,
    ! [X241,X58,X242] :
      ( ( X242 = c_List_Olist_ONil(X58)
       => hAPP(c_List_Ohd(X58),hAPP(hAPP(c_List_Oappend(X58),X242),X241)) = hAPP(c_List_Ohd(X58),X241) )
      & ( X242 != c_List_Olist_ONil(X58)
       => hAPP(c_List_Ohd(X58),hAPP(hAPP(c_List_Oappend(X58),X242),X241)) = hAPP(c_List_Ohd(X58),X242) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hd__append) ).

fof(fact_evalc__elim__cases_I1_J,axiom,
    ! [X54,X48] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X48),X54))
     => X54 = X48 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc__elim__cases_I1_J) ).

fof(fact_mult__sgn__abs,axiom,
    ! [X66,X58] :
      ( class_Rings_Olinordered__idom(X58)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),c_Groups_Osgn__class_Osgn(X58,X66)),hAPP(c_Groups_Oabs__class_Oabs(X58),X66)) = X66 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__sgn__abs) ).

fof(fact_Nats__1,axiom,
    ! [X5] :
      ( class_Rings_Osemiring__1(X5)
     => hBOOL(hAPP(hAPP(c_member(X5),c_Groups_Oone__class_Oone(X5)),c_Nat_Osemiring__1__class_ONats(X5))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nats__1) ).

fof(fact_Ints__1,axiom,
    ! [X5] :
      ( class_Rings_Oring__1(X5)
     => hBOOL(hAPP(hAPP(c_member(X5),c_Groups_Oone__class_Oone(X5)),c_Int_Oring__1__class_OInts(X5))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__1) ).

fof(fact_Nats__0,axiom,
    ! [X5] :
      ( class_Rings_Osemiring__1(X5)
     => hBOOL(hAPP(hAPP(c_member(X5),c_Groups_Ozero__class_Ozero(X5)),c_Nat_Osemiring__1__class_ONats(X5))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nats__0) ).

fof(fact_Ints__0,axiom,
    ! [X5] :
      ( class_Rings_Oring__1(X5)
     => hBOOL(hAPP(hAPP(c_member(X5),c_Groups_Ozero__class_Ozero(X5)),c_Int_Oring__1__class_OInts(X5))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__0) ).

fof(fact_zero__le__one,axiom,
    ! [X58] :
      ( class_Rings_Olinordered__semidom(X58)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Ozero__class_Ozero(X58)),c_Groups_Oone__class_Oone(X58))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__one) ).

fof(fact_zero__less__one,axiom,
    ! [X58] :
      ( class_Rings_Olinordered__semidom(X58)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),c_Groups_Oone__class_Oone(X58))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__one) ).

fof(fact_divide__eq__imp,axiom,
    ! [X62,X90,X56,X58] :
      ( class_Rings_Odivision__ring(X58)
     => ( X56 != c_Groups_Ozero__class_Ozero(X58)
       => ( X90 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X56)
         => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X90),X56) = X62 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__eq__imp) ).

fof(fact_nonzero__divide__eq__eq,axiom,
    ! [X6,X24,X23,X5] :
      ( class_Rings_Odivision__ring(X5)
     => ( X23 != c_Groups_Ozero__class_Ozero(X5)
       => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X24),X23) = X6
        <=> X24 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X23) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__divide__eq__eq) ).

fof(fact_nonzero__eq__divide__eq,axiom,
    ! [X24,X6,X23,X5] :
      ( class_Rings_Odivision__ring(X5)
     => ( X23 != c_Groups_Ozero__class_Ozero(X5)
       => ( X6 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X24),X23)
        <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X23) = X24 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__eq__divide__eq) ).

fof(fact_eq__divide__imp,axiom,
    ! [X90,X62,X56,X58] :
      ( class_Rings_Odivision__ring(X58)
     => ( X56 != c_Groups_Ozero__class_Ozero(X58)
       => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X56) = X90
         => X62 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X90),X56) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__divide__imp) ).

fof(fact_diff__minus__eq__add,axiom,
    ! [X90,X62,X58] :
      ( class_Groups_Ogroup__add(X58)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X58),X62),hAPP(c_Groups_Ouminus__class_Ouminus(X58),X90)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),X90) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__minus__eq__add) ).

fof(fact_diff__eq,axiom,
    ! [X65,X66,X58] :
      ( class_Lattices_Oboolean__algebra(X58)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X58),X66),X65) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X66),hAPP(c_Groups_Ouminus__class_Ouminus(X58),X65)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__eq) ).

fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom,
    ! [X65,X66,X58] :
      ( class_Rings_Ocomm__ring__1(X58)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X58),X66),X65) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X66),hAPP(c_Groups_Ouminus__class_Ouminus(X58),X65)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J) ).

fof(fact_ab__diff__minus,axiom,
    ! [X90,X62,X58] :
      ( class_Groups_Oab__group__add(X58)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X58),X62),X90) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),hAPP(c_Groups_Ouminus__class_Ouminus(X58),X90)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ab__diff__minus) ).

fof(fact_diff__def,axiom,
    ! [X90,X62,X58] :
      ( class_Groups_Ogroup__add(X58)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X58),X62),X90) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),hAPP(c_Groups_Ouminus__class_Ouminus(X58),X90)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__def) ).

fof(fact_mult__minus1,axiom,
    ! [X94,X58] :
      ( class_Int_Onumber__ring(X58)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),hAPP(c_Int_Onumber__class_Onumber__of(X58),c_Int_OMin)),X94) = hAPP(c_Groups_Ouminus__class_Ouminus(X58),X94) ),
    file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_bin__less__0__simps_I1_J) ).

fof(fact_hd__append2,axiom,
    ! [X241,X58,X242] :
      ( X242 != c_List_Olist_ONil(X58)
     => hAPP(c_List_Ohd(X58),hAPP(hAPP(c_List_Oappend(X58),X242),X241)) = hAPP(c_List_Ohd(X58),X242) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hd__append2) ).

fof(fact_nat__add__right__cancel,axiom,
    ! [X50,X87,X95] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X95),X87) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X50),X87)
    <=> X95 = X50 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__right__cancel) ).

fof(fact_nat__add__left__cancel,axiom,
    ! [X50,X95,X87] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X87),X95) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X87),X50)
    <=> X95 = X50 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel) ).

fof(fact_singleton__conv2,axiom,
    ! [X6,X5] : hAPP(c_Set_OCollect(X5),hAPP(c_fequal,X6)) = hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_singleton__conv2) ).

fof(fact_sorted__drop,axiom,
    ! [X57,X242,X58] :
      ( class_Orderings_Olinorder(X58)
     => ( c_List_Olinorder__class_Osorted(X58,X242)
       => c_List_Olinorder__class_Osorted(X58,hAPP(hAPP(c_List_Odrop(X58),X57),X242)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__drop) ).

fof(fact_sorted__take,axiom,
    ! [X57,X242,X58] :
      ( class_Orderings_Olinorder(X58)
     => ( c_List_Olinorder__class_Osorted(X58,X242)
       => c_List_Olinorder__class_Osorted(X58,hAPP(hAPP(c_List_Otake(X58),X57),X242)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__take) ).

fof(fact_finite_Oequations_I1_J,axiom,
    ! [X5] : hBOOL(hAPP(c_Finite__Set_Ofinite(X5),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite_Oequations_I1_J) ).

fof(fact_finite_OemptyI,axiom,
    ! [X5] : hBOOL(hAPP(c_Finite__Set_Ofinite(X5),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite_OemptyI) ).

fof(fact_Pow__not__empty,axiom,
    ! [X21,X5] : hAPP(c_Set_OPow(X5),X21) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__not__empty) ).

fof(fact_Compl__UNIV__eq,axiom,
    ! [X5] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__UNIV__eq) ).

fof(fact_Compl__empty__eq,axiom,
    ! [X5] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__empty__eq) ).

fof(fact_Pow__UNIV,axiom,
    ! [X5] : hAPP(c_Set_OPow(X5),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__UNIV) ).

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

fof(fact_Int__absorb,axiom,
    ! [X21,X5] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X21) = X21,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__absorb) ).

fof(fact_Un__absorb,axiom,
    ! [X21,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X21) = X21,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__absorb) ).

fof(fact_wf__in__rel,axiom,
    ! [X32,X5] :
      ( c_Wellfounded_Owf(X5,X32)
     => c_Wellfounded_OwfP(X5,c_FunDef_Oin__rel(X5,X5,X32)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__in__rel) ).

fof(fact_wf__mlex,axiom,
    ! [X2,X32,X5] :
      ( c_Wellfounded_Owf(X5,X32)
     => c_Wellfounded_Owf(X5,c_Wellfounded_Omlex__prod(X5,X2,X32)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__mlex) ).

fof(fact_Min_OF__eq,axiom,
    ! [X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => c_Big__Operators_Olinorder__class_OMin(X5,X21) = hAPP(c_Finite__Set_Ofold1(X5,c_Orderings_Oord__class_Omin(X5)),X21) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min_OF__eq) ).

fof(fact_Max_OF__eq,axiom,
    ! [X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => c_Big__Operators_Olinorder__class_OMax(X5,X21) = hAPP(c_Finite__Set_Ofold1(X5,c_Orderings_Oord__class_Omax(X5)),X21) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max_OF__eq) ).

fof(fact_Sup__fin_OF__eq,axiom,
    ! [X21,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => c_Big__Operators_Olattice__class_OSup__fin(X5,X21) = hAPP(c_Finite__Set_Ofold1(X5,c_Lattices_Osemilattice__sup__class_Osup(X5)),X21) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_OF__eq) ).

fof(fact_Inf__fin_OF__eq,axiom,
    ! [X21,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => c_Big__Operators_Olattice__class_OInf__fin(X5,X21) = hAPP(c_Finite__Set_Ofold1(X5,c_Lattices_Osemilattice__inf__class_Oinf(X5)),X21) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_OF__eq) ).

fof(fact_lessI,axiom,
    ! [X57] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X57),hAPP(c_Nat_OSuc,X57))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lessI) ).

fof(fact_length__replicate,axiom,
    ! [X66,X57,X58] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),c_List_Oreplicate(X58,X57,X66)) = X57,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__replicate) ).

fof(fact_compl__inf__bot,axiom,
    ! [X66,X58] :
      ( class_Lattices_Oboolean__algebra(X58)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),hAPP(c_Groups_Ouminus__class_Ouminus(X58),X66)),X66) = c_Orderings_Obot__class_Obot(X58) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compl__inf__bot) ).

fof(fact_compl__sup__top,axiom,
    ! [X66,X58] :
      ( class_Lattices_Oboolean__algebra(X58)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),hAPP(c_Groups_Ouminus__class_Ouminus(X58),X66)),X66) = c_Orderings_Otop__class_Otop(X58) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compl__sup__top) ).

fof(fact_ab__left__minus,axiom,
    ! [X62,X58] :
      ( class_Groups_Oab__group__add(X58)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(c_Groups_Ouminus__class_Ouminus(X58),X62)),X62) = c_Groups_Ozero__class_Ozero(X58) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ab__left__minus) ).

fof(fact_left__minus,axiom,
    ! [X62,X58] :
      ( class_Groups_Ogroup__add(X58)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(c_Groups_Ouminus__class_Ouminus(X58),X62)),X62) = c_Groups_Ozero__class_Ozero(X58) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_left__minus) ).

fof(fact_last__appendL,axiom,
    ! [X242,X58,X241] :
      ( X241 = c_List_Olist_ONil(X58)
     => c_List_Olast(X58,hAPP(hAPP(c_List_Oappend(X58),X242),X241)) = c_List_Olast(X58,X242) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__appendL) ).

fof(fact_last__append,axiom,
    ! [X242,X58,X241] :
      ( ( X241 = c_List_Olist_ONil(X58)
       => c_List_Olast(X58,hAPP(hAPP(c_List_Oappend(X58),X242),X241)) = c_List_Olast(X58,X242) )
      & ( X241 != c_List_Olist_ONil(X58)
       => c_List_Olast(X58,hAPP(hAPP(c_List_Oappend(X58),X242),X241)) = c_List_Olast(X58,X241) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__append) ).

fof(fact_diff__add__0,axiom,
    ! [X72,X57] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X57),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X57),X72)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__0) ).

fof(fact_sublist__upt__eq__take,axiom,
    ! [X50,X156,X5] : c_List_Osublist(X5,X156,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X50)) = hAPP(hAPP(c_List_Otake(X5),X50),X156),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sublist__upt__eq__take) ).

fof(fact_bot__least,axiom,
    ! [X66,X58] :
      ( class_Orderings_Obot(X58)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Orderings_Obot__class_Obot(X58)),X66)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot__least) ).

fof(fact_divmod__int__correct,axiom,
    ! [X62,X90] :
      ( X90 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
     => hBOOL(hAPP(c_Divides_Odivmod__int__rel(X62,X90),c_Divides_Odivmod__int(X62,X90))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__int__correct) ).

fof(fact_pdivmod__posDivAlg,axiom,
    ! [X96,X99] :
      ( ( X99 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Divides_Opdivmod(X96,X99) = 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),X96)) )
      & ( X99 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Divides_Opdivmod(X96,X99) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X96),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X99)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pdivmod__posDivAlg) ).

fof(fact_sorted__single,axiom,
    ! [X66,X58] :
      ( class_Orderings_Olinorder(X58)
     => c_List_Olinorder__class_Osorted(X58,hAPP(hAPP(c_List_Olist_OCons(X58),X66),c_List_Olist_ONil(X58))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__single) ).

fof(fact_last__ConsR,axiom,
    ! [X66,X58,X242] :
      ( X242 != c_List_Olist_ONil(X58)
     => c_List_Olast(X58,hAPP(hAPP(c_List_Olist_OCons(X58),X66),X242)) = c_List_Olast(X58,X242) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__ConsR) ).

fof(fact_last_Osimps,axiom,
    ! [X66,X58,X242] :
      ( ( X242 = c_List_Olist_ONil(X58)
       => c_List_Olast(X58,hAPP(hAPP(c_List_Olist_OCons(X58),X66),X242)) = X66 )
      & ( X242 != c_List_Olist_ONil(X58)
       => c_List_Olast(X58,hAPP(hAPP(c_List_Olist_OCons(X58),X66),X242)) = c_List_Olast(X58,X242) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last_Osimps) ).

fof(fact_last__appendR,axiom,
    ! [X242,X58,X241] :
      ( X241 != c_List_Olist_ONil(X58)
     => c_List_Olast(X58,hAPP(hAPP(c_List_Oappend(X58),X242),X241)) = c_List_Olast(X58,X241) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__appendR) ).

fof(fact_nat__gcd_Osimps,axiom,
    ! [X66,X65] :
      ( ( X65 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => c_Nitpick_Onat__gcd(X66,X65) = X66 )
      & ( X65 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => c_Nitpick_Onat__gcd(X66,X65) = c_Nitpick_Onat__gcd(X65,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X66,X65)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__gcd_Osimps) ).

fof(fact_atLeastSucLessThan__greaterThanLessThan,axiom,
    ! [X159,X156] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X156)),X159) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X156,X159),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastSucLessThan__greaterThanLessThan) ).

fof(fact_card__atLeastLessThan,axiom,
    ! [X159,X156] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X156),X159)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X159),X156),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__atLeastLessThan) ).

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/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I20_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/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I2_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/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I3_J) ).

fof(fact_rel__simps_I7_J,axiom,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I7_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/sandbox/benchmark/theBenchmark.p',fact_not__neg__number__of__Pls) ).

fof(fact_zip__Nil,axiom,
    ! [X241,X5,X58] : hAPP(hAPP(c_List_Ozip(X58,X5),c_List_Olist_ONil(X58)),X241) = c_List_Olist_ONil(tc_prod(X58,X5)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip__Nil) ).

fof(fact_top1I,axiom,
    ! [X25,X5] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X25)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_top1I) ).

fof(fact_vimage__id,axiom,
    ! [X21,X5] : hAPP(c_Set_Ovimage(X5,X5,c_Fun_Oid(X5)),X21) = X21,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__id) ).

fof(fact_vimage__ident,axiom,
    ! [X196,X5] : hAPP(c_Set_Ovimage(X5,X5,c_COMBI(X5)),X196) = X196,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__ident) ).

fof(fact_image__id,axiom,
    ! [X196,X5] : hAPP(c_Set_Oimage(X5,X5,c_Fun_Oid(X5)),X196) = X196,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__id) ).

fof(fact_image__ident,axiom,
    ! [X196,X5] : hAPP(c_Set_Oimage(X5,X5,c_COMBI(X5)),X196) = X196,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__ident) ).

fof(fact_refl__rtrancl,axiom,
    ! [X171,X5] : c_Relation_Orefl__on(X5,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X5,X171)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__rtrancl) ).

fof(fact_hd__replicate,axiom,
    ! [X66,X58,X57] :
      ( X57 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
     => hAPP(c_List_Ohd(X58),c_List_Oreplicate(X58,X57,X66)) = X66 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hd__replicate) ).

fof(fact_Compl__greaterThan,axiom,
    ! [X87,X5] :
      ( class_Orderings_Olinorder(X5)
     => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X5),X87)) = hAPP(c_SetInterval_Oord__class_OatMost(X5),X87) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__greaterThan) ).

fof(fact_Compl__atLeast,axiom,
    ! [X87,X5] :
      ( class_Orderings_Olinorder(X5)
     => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X5),X87)) = hAPP(c_SetInterval_Oord__class_OlessThan(X5),X87) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__atLeast) ).

fof(fact_Compl__lessThan,axiom,
    ! [X87,X5] :
      ( class_Orderings_Olinorder(X5)
     => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X5),X87)) = hAPP(c_SetInterval_Oord__class_OatLeast(X5),X87) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__lessThan) ).

fof(fact_Compl__atMost,axiom,
    ! [X87,X5] :
      ( class_Orderings_Olinorder(X5)
     => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X5),X87)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X5),X87) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__atMost) ).

fof(fact_hoare__derivs_Oequations_I1_J,axiom,
    ! [X6,X5] : c_Hoare__Mirabelle_Ohoare__derivs(X5,X6,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hoare__derivs_Oequations_I1_J) ).

fof(fact_empty,axiom,
    ! [X4,X5] : c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty) ).

fof(fact_Inf__fin__Inf,axiom,
    ! [X21,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => c_Big__Operators_Olattice__class_OInf__fin(X5,X21) = c_Complete__Lattice_OInf__class_OInf(X5,X21) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin__Inf) ).

fof(fact_Sup__fin__Sup,axiom,
    ! [X21,X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
         => c_Big__Operators_Olattice__class_OSup__fin(X5,X21) = c_Complete__Lattice_OSup__class_OSup(X5,X21) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin__Sup) ).

fof(fact_add__numeral__0,axiom,
    ! [X62,X58] :
      ( class_Int_Onumber__ring(X58)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(c_Int_Onumber__class_Onumber__of(X58),c_Int_OPls)),X62) = X62 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__numeral__0) ).

fof(fact_add__is__1,axiom,
    ! [X50,X95] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X95),X50) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    <=> ( ( X95 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & X50 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( X95 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & X50 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__is__1) ).

fof(fact_one__is__add,axiom,
    ! [X50,X95] :
      ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X95),X50)
    <=> ( ( X95 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & X50 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( X95 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & X50 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__is__add) ).

fof(fact_someI__ex,axiom,
    ! [X5,X18] :
      ( ? [X138] : hBOOL(hAPP(X18,X138))
     => hBOOL(hAPP(X18,c_Hilbert__Choice_OEps(X5,X18))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_someI__ex) ).

fof(fact_tfl__some,axiom,
    ! [X5,X276] :
      ( ? [X3] : hBOOL(hAPP(X276,X3))
     => hBOOL(hAPP(X276,c_Hilbert__Choice_OEps(X5,X276))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tfl__some) ).

fof(fact_someI,axiom,
    ! [X5,X25,X18] :
      ( hBOOL(hAPP(X18,X25))
     => hBOOL(hAPP(X18,c_Hilbert__Choice_OEps(X5,X18))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_someI) ).

fof(fact_atLeastSucAtMost__greaterThanAtMost,axiom,
    ! [X159,X156] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X156),X159) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X156,X159),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastSucAtMost__greaterThanAtMost) ).

fof(fact_square__eq__1__iff,axiom,
    ! [X25,X5] :
      ( class_Rings_Oring__1__no__zero__divisors(X5)
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X25),X25) = c_Groups_Oone__class_Oone(X5)
      <=> ( X25 = c_Groups_Oone__class_Oone(X5)
          | X25 = hAPP(c_Groups_Ouminus__class_Ouminus(X5),c_Groups_Oone__class_Oone(X5)) ) ) ),
    file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_ext) ).

fof(fact_zip_Osimps_I1_J,axiom,
    ! [X242,X5,X58] : hAPP(hAPP(c_List_Ozip(X58,X5),X242),c_List_Olist_ONil(X5)) = c_List_Olist_ONil(tc_prod(X58,X5)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zip_Osimps_I1_J) ).

fof(fact_folding__one__idem_Oidem,axiom,
    ! [X25,X205,X2,X5] :
      ( c_Finite__Set_Ofolding__one__idem(X5,X2,X205)
     => hAPP(hAPP(X2,X25),X25) = X25 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Oidem) ).

fof(fact_sublists_Osimps_I1_J,axiom,
    ! [X58] : c_Enum_Osublists(X58,c_List_Olist_ONil(X58)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X58)),c_List_Olist_ONil(X58)),c_List_Olist_ONil(tc_List_Olist(X58))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sublists_Osimps_I1_J) ).

fof(fact_com_Osize_I16_J,axiom,
    ! [X84,X44,X85] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCall(X85,X44,X84)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osize_I16_J) ).

fof(fact_top__greatest,axiom,
    ! [X66,X58] :
      ( class_Orderings_Otop(X58)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X66),c_Orderings_Otop__class_Otop(X58))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_top__greatest) ).

fof(fact_last__ConsL,axiom,
    ! [X66,X58,X242] :
      ( X242 = c_List_Olist_ONil(X58)
     => c_List_Olast(X58,hAPP(hAPP(c_List_Olist_OCons(X58),X66),X242)) = X66 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__ConsL) ).

fof(fact_last__replicate,axiom,
    ! [X66,X58,X57] :
      ( X57 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
     => c_List_Olast(X58,c_List_Oreplicate(X58,X57,X66)) = X66 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__replicate) ).

fof(fact_nat__rec__0,axiom,
    ! [X89,X19,X5] : hAPP(c_Nat_Onat_Onat__rec(X5,X19,X89),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X19,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__rec__0) ).

fof(fact_insert__not__empty,axiom,
    ! [X21,X6,X5] : hAPP(hAPP(c_Set_Oinsert(X5),X6),X21) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__not__empty) ).

fof(fact_empty__not__insert,axiom,
    ! [X21,X6,X5] : c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(X5),X6),X21),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__not__insert) ).

fof(fact_int__Suc,axiom,
    ! [X72] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X72)) = 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),X72)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__Suc) ).

fof(fact_diff__int__def__symmetric,axiom,
    ! [X128,X94] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X94),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X128)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X94),X128),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__int__def__symmetric) ).

fof(fact_diff__int__def,axiom,
    ! [X128,X94] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X94),X128) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X94),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X128)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__int__def) ).

fof(fact_tl_Osimps_I2_J,axiom,
    ! [X242,X66,X58] : hAPP(c_List_Otl(X58),hAPP(hAPP(c_List_Olist_OCons(X58),X66),X242)) = X242,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tl_Osimps_I2_J) ).

fof(fact_hd_Osimps,axiom,
    ! [X242,X66,X58] : hAPP(c_List_Ohd(X58),hAPP(hAPP(c_List_Olist_OCons(X58),X66),X242)) = X66,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hd_Osimps) ).

fof(fact_power__eq__0__iff,axiom,
    ! [X50,X6,X5] :
      ( ( class_Power_Opower(X5)
        & class_Rings_Omult__zero(X5)
        & class_Rings_Ono__zero__divisors(X5)
        & class_Rings_Ozero__neq__one(X5) )
     => ( hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X50) = c_Groups_Ozero__class_Ozero(X5)
      <=> ( X6 = c_Groups_Ozero__class_Ozero(X5)
          & X50 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__eq__0__iff) ).

fof(fact_Divides_Otransfer__int__nat__function__closures_I2_J,axiom,
    ! [X65,X66] :
      ( c_Nat__Transfer_Ois__nat(X66)
     => ( c_Nat__Transfer_Ois__nat(X65)
       => c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,X66,X65)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Divides_Otransfer__int__nat__function__closures_I2_J) ).

fof(fact_divide__minus1,axiom,
    ! [X66,X58] :
      ( ( class_Fields_Ofield__inverse__zero(X58)
        & class_Int_Onumber__ring(X58) )
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X66),hAPP(c_Int_Onumber__class_Onumber__of(X58),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(X58),X66) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__minus1) ).

fof(fact_wf__lexn,axiom,
    ! [X50,X171,X5] :
      ( c_Wellfounded_Owf(X5,X171)
     => c_Wellfounded_Owf(tc_List_Olist(X5),hAPP(c_List_Olexn(X5,X171),X50)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__lexn) ).

fof(fact_list__update_Osimps_I1_J,axiom,
    ! [X136,X98,X58] : hAPP(hAPP(c_List_Olist__update(X58,c_List_Olist_ONil(X58)),X98),X136) = c_List_Olist_ONil(X58),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update_Osimps_I1_J) ).

fof(fact_list__update__code_I1_J,axiom,
    ! [X65,X98,X58] : hAPP(hAPP(c_List_Olist__update(X58,c_List_Olist_ONil(X58)),X98),X65) = c_List_Olist_ONil(X58),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update__code_I1_J) ).

fof(fact_power__Suc__0,axiom,
    ! [X57] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X57) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__Suc__0) ).

fof(fact_insert__Nil,axiom,
    ! [X66,X58] : c_List_Oinsert(X58,X66,c_List_Olist_ONil(X58)) = hAPP(hAPP(c_List_Olist_OCons(X58),X66),c_List_Olist_ONil(X58)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__Nil) ).

fof(fact_finite__set,axiom,
    ! [X239,X5] : hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(c_List_Oset(X5),X239))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__set) ).

fof(fact_converse__converse,axiom,
    ! [X171,X5,X20] : hAPP(c_Relation_Oconverse(X20,X5),hAPP(c_Relation_Oconverse(X5,X20),X171)) = X171,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__converse) ).

fof(fact_lessThan__Suc,axiom,
    ! [X87] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X87)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X87),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X87)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lessThan__Suc) ).

fof(fact_Field__converse,axiom,
    ! [X171,X5] : hAPP(c_Relation_OField(X5),hAPP(c_Relation_Oconverse(X5,X5),X171)) = hAPP(c_Relation_OField(X5),X171),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Field__converse) ).

fof(fact_number__of__minus,axiom,
    ! [X128,X58] :
      ( class_Int_Onumber__ring(X58)
     => hAPP(c_Int_Onumber__class_Onumber__of(X58),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X128)) = hAPP(c_Groups_Ouminus__class_Ouminus(X58),hAPP(c_Int_Onumber__class_Onumber__of(X58),X128)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__minus) ).

fof(fact_of__int__minus,axiom,
    ! [X94,X58] :
      ( class_Rings_Oring__1(X58)
     => hAPP(c_Int_Oring__1__class_Oof__int(X58),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X94)) = hAPP(c_Groups_Ouminus__class_Ouminus(X58),hAPP(c_Int_Oring__1__class_Oof__int(X58),X94)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__minus) ).

fof(fact_arith__simps_I30_J,axiom,
    ! [X128,X58] :
      ( class_Int_Onumber__ring(X58)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X58),hAPP(c_Int_Onumber__class_Onumber__of(X58),X128)) = hAPP(c_Int_Onumber__class_Onumber__of(X58),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X128)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_arith__simps_I30_J) ).

fof(fact_nat__power__eq__Suc__0__iff,axiom,
    ! [X95,X25] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X25),X95) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    <=> ( X95 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X25 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__power__eq__Suc__0__iff) ).

fof(fact_order__eq__refl,axiom,
    ! [X65,X66,X58] :
      ( class_Orderings_Opreorder(X58)
     => ( X66 = X65
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X66),X65)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__eq__refl) ).

fof(fact_com_Osize_I6_J,axiom,
    ! [X11,X84] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(X84,X11)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X11)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osize_I6_J) ).

fof(fact_minus__unique,axiom,
    ! [X90,X62,X58] :
      ( class_Groups_Ogroup__add(X58)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),X90) = c_Groups_Ozero__class_Ozero(X58)
       => hAPP(c_Groups_Ouminus__class_Ouminus(X58),X62) = X90 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__unique) ).

fof(fact_eq__neg__iff__add__eq__0,axiom,
    ! [X24,X6,X5] :
      ( class_Groups_Ogroup__add(X5)
     => ( X6 = hAPP(c_Groups_Ouminus__class_Ouminus(X5),X24)
      <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),X24) = c_Groups_Ozero__class_Ozero(X5) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__neg__iff__add__eq__0) ).

fof(fact_length__remdups__card__conv,axiom,
    ! [X239,X5] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_Oremdups(X5,X239)) = hAPP(c_Finite__Set_Ocard(X5),hAPP(c_List_Oset(X5),X239)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__remdups__card__conv) ).

fof(fact_UNIV__def,axiom,
    ! [X5] : c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X5),hAPP(c_COMBK(tc_HOL_Obool,X5),c_fTrue)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__def) ).

fof(fact_empty__def,axiom,
    ! [X5] : c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X5),hAPP(c_COMBK(tc_HOL_Obool,X5),c_fFalse)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__def) ).

fof(fact_SetInterval_Otransfer__int__nat__set__function__closures,axiom,
    ! [X33,X25] :
      ( c_Nat__Transfer_Ois__nat(X25)
     => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X25,X33)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SetInterval_Otransfer__int__nat__set__function__closures) ).

fof(fact_mult__minus1__right,axiom,
    ! [X94,X58] :
      ( class_Int_Onumber__ring(X58)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X94),hAPP(c_Int_Onumber__class_Onumber__of(X58),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(X58),X94) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__minus1__right) ).

fof(fact_mult__eq__1__iff,axiom,
    ! [X50,X95] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X95),X50) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    <=> ( X95 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        & X50 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__eq__1__iff) ).

fof(fact_nat_Osize_I2_J,axiom,
    ! [X108] : c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,X108)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(X108)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osize_I2_J) ).

fof(fact_order__refl,axiom,
    ! [X66,X58] :
      ( class_Orderings_Opreorder(X58)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X66),X66)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__refl) ).

fof(fact_card__atLeastZeroLessThan__int,axiom,
    ! [X159] : 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)),X159)) = hAPP(c_Int_Onat,X159),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__atLeastZeroLessThan__int) ).

fof(fact_com_Osize_I8_J,axiom,
    ! [X84,X44,X85] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCall(X85,X44,X84)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osize_I8_J) ).

fof(fact_zadd__zminus__inverse2,axiom,
    ! [X94] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X94)),X94) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__zminus__inverse2) ).

fof(fact_atLeastLessThanSuc__atLeastAtMost,axiom,
    ! [X159,X156] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X156),hAPP(c_Nat_OSuc,X159)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X156,X159),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThanSuc__atLeastAtMost) ).

fof(fact_mod__int__def,axiom,
    ! [X90,X62] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X62,X90) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(X62,X90)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__int__def) ).

fof(fact_inf_Ocommute,axiom,
    ! [X90,X62,X58] :
      ( class_Lattices_Osemilattice__inf(X58)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X62),X90) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X90),X62) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf_Ocommute) ).

fof(fact_inf__commute,axiom,
    ! [X65,X66,X58] :
      ( class_Lattices_Osemilattice__inf(X58)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X66),X65) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X65),X66) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__commute) ).

fof(fact_inf__sup__aci_I1_J,axiom,
    ! [X65,X66,X58] :
      ( class_Lattices_Olattice(X58)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X66),X65) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X65),X66) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__aci_I1_J) ).

fof(fact_inf__sup__aci_I5_J,axiom,
    ! [X65,X66,X58] :
      ( class_Lattices_Olattice(X58)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X66),X65) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X65),X66) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__aci_I5_J) ).

fof(fact_sup__commute,axiom,
    ! [X65,X66,X58] :
      ( class_Lattices_Osemilattice__sup(X58)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X66),X65) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X65),X66) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__commute) ).

fof(fact_sup_Ocommute,axiom,
    ! [X90,X62,X58] :
      ( class_Lattices_Osemilattice__sup(X58)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X62),X90) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X90),X62) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup_Ocommute) ).

fof(fact_min__max_Osup__commute,axiom,
    ! [X65,X66,X58] :
      ( class_Orderings_Olinorder(X58)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(X58),X66),X65) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X58),X65),X66) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup__commute) ).

fof(fact_min__max_Osup_Ocommute,axiom,
    ! [X90,X62,X58] :
      ( class_Orderings_Olinorder(X58)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(X58),X62),X90) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X58),X90),X62) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup_Ocommute) ).

fof(fact_min__max_Oinf_Ocommute,axiom,
    ! [X90,X62,X58] :
      ( class_Orderings_Olinorder(X58)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(X58),X62),X90) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X58),X90),X62) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf_Ocommute) ).

fof(fact_min__max_Oinf__commute,axiom,
    ! [X65,X66,X58] :
      ( class_Orderings_Olinorder(X58)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(X58),X66),X65) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X58),X65),X66) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf__commute) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
    ! [X90,X62,X58] :
      ( class_Rings_Ocomm__semiring__1(X58)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X90) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X90),X62) ),
    file('/export/starexec/sandbox/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,
    ! [X56,X62,X58] :
      ( class_Rings_Ocomm__semiring__1(X58)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),X56) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X56),X62) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).

fof(fact_nat__zminus__int,axiom,
    ! [X57] : hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X57))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__zminus__int) ).

fof(fact_gr0I,axiom,
    ! [X57] :
      ( X57 != 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)),X57)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr0I) ).

fof(fact_Divides_Otransfer__int__nat__function__closures_I1_J,axiom,
    ! [X65,X66] :
      ( c_Nat__Transfer_Ois__nat(X66)
     => ( c_Nat__Transfer_Ois__nat(X65)
       => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X66),X65)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Divides_Otransfer__int__nat__function__closures_I1_J) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J,axiom,
    ! [X65,X66] :
      ( c_Nat__Transfer_Ois__nat(X66)
     => ( c_Nat__Transfer_Ois__nat(X65)
       => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X66),X65)) ) ),
    file('/export/starexec/sandbox/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,
    ! [X65,X66] :
      ( c_Nat__Transfer_Ois__nat(X66)
     => ( c_Nat__Transfer_Ois__nat(X65)
       => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X66),X65)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J) ).

fof(fact_negative__eq__positive,axiom,
    ! [X95,X50] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X50)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X95)
    <=> ( X50 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        & X95 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negative__eq__positive) ).

fof(fact_com_Osimps_I38_J,axiom,
    ! [X8,X92,X11,X84,X102] : c_Com_Ocom_OLocal(X102,X84,X11) != c_Com_Ocom_OWhile(X92,X8),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I38_J) ).

fof(fact_com_Osimps_I23_J,axiom,
    ! [X84,X85,X8,X92,X107] : c_Com_Ocom_OLocal(X107,X92,X8) != c_Com_Ocom_OAss(X85,X84),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I23_J) ).

fof(fact_com_Osimps_I34_J,axiom,
    ! [X39,X40,X11,X84,X102] : c_Com_Ocom_OLocal(X102,X84,X11) != c_Com_Ocom_OSemi(X40,X39),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I34_J) ).

fof(fact_com_Osimps_I52_J,axiom,
    ! [X8,X92,X41,X42,X84] : c_Com_Ocom_OCond(X84,X42,X41) != c_Com_Ocom_OWhile(X92,X8),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I52_J) ).

fof(fact_com_Osimps_I27_J,axiom,
    ! [X84,X85,X39,X40,X92] : c_Com_Ocom_OCond(X92,X40,X39) != c_Com_Ocom_OAss(X85,X84),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I27_J) ).

fof(fact_com_Osimps_I45_J,axiom,
    ! [X41,X42,X39,X40,X92] : c_Com_Ocom_OCond(X92,X40,X39) != c_Com_Ocom_OSemi(X42,X41),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I45_J) ).

fof(fact_com_Osimps_I61_J,axiom,
    ! [X11,X84,X92,X43,X93] : c_Com_Ocom_OCall(X93,X43,X92) != c_Com_Ocom_OWhile(X84,X11),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I61_J) ).

fof(fact_com_Osimps_I33_J,axiom,
    ! [X84,X85,X92,X43,X93] : c_Com_Ocom_OCall(X93,X43,X92) != c_Com_Ocom_OAss(X85,X84),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I33_J) ).

fof(fact_com_Osimps_I51_J,axiom,
    ! [X41,X42,X92,X43,X93] : c_Com_Ocom_OCall(X93,X43,X92) != c_Com_Ocom_OSemi(X42,X41),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I51_J) ).

fof(fact_com_Osimps_I39_J,axiom,
    ! [X11,X84,X102,X8,X92] : c_Com_Ocom_OWhile(X92,X8) != c_Com_Ocom_OLocal(X102,X84,X11),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I39_J) ).

fof(fact_com_Osimps_I53_J,axiom,
    ! [X41,X42,X84,X8,X92] : c_Com_Ocom_OWhile(X92,X8) != c_Com_Ocom_OCond(X84,X42,X41),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I53_J) ).

fof(fact_com_Osimps_I60_J,axiom,
    ! [X92,X43,X93,X11,X84] : c_Com_Ocom_OWhile(X84,X11) != c_Com_Ocom_OCall(X93,X43,X92),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I60_J) ).

fof(fact_com_Osimps_I22_J,axiom,
    ! [X8,X92,X107,X84,X85] : c_Com_Ocom_OAss(X85,X84) != c_Com_Ocom_OLocal(X107,X92,X8),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I22_J) ).

fof(fact_com_Osimps_I26_J,axiom,
    ! [X39,X40,X92,X84,X85] : c_Com_Ocom_OAss(X85,X84) != c_Com_Ocom_OCond(X92,X40,X39),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I26_J) ).

fof(fact_com_Osimps_I32_J,axiom,
    ! [X92,X43,X93,X84,X85] : c_Com_Ocom_OAss(X85,X84) != c_Com_Ocom_OCall(X93,X43,X92),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I32_J) ).

fof(fact_com_Osimps_I35_J,axiom,
    ! [X11,X84,X102,X39,X40] : c_Com_Ocom_OSemi(X40,X39) != c_Com_Ocom_OLocal(X102,X84,X11),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I35_J) ).

fof(fact_com_Osimps_I44_J,axiom,
    ! [X39,X40,X92,X41,X42] : c_Com_Ocom_OSemi(X42,X41) != c_Com_Ocom_OCond(X92,X40,X39),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I44_J) ).

fof(fact_com_Osimps_I50_J,axiom,
    ! [X92,X43,X93,X41,X42] : c_Com_Ocom_OSemi(X42,X41) != c_Com_Ocom_OCall(X93,X43,X92),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I50_J) ).

fof(fact_less__eq__nat_Osimps_I1_J,axiom,
    ! [X57] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X57)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I1_J) ).

fof(fact_le0,axiom,
    ! [X57] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X57)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le0) ).

fof(fact_total__on__empty,axiom,
    ! [X171,X5] : c_Relation_Ototal__on(X5,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),X171),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_total__on__empty) ).

fof(fact_divisors__zero,axiom,
    ! [X90,X62,X58] :
      ( class_Rings_Ono__zero__divisors(X58)
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X90) = c_Groups_Ozero__class_Ozero(X58)
       => ( X62 = c_Groups_Ozero__class_Ozero(X58)
          | X90 = c_Groups_Ozero__class_Ozero(X58) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divisors__zero) ).

fof(fact_no__zero__divisors,axiom,
    ! [X90,X62,X58] :
      ( class_Rings_Ono__zero__divisors(X58)
     => ( X62 != c_Groups_Ozero__class_Ozero(X58)
       => ( X90 != c_Groups_Ozero__class_Ozero(X58)
         => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X90) != c_Groups_Ozero__class_Ozero(X58) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_no__zero__divisors) ).

fof(fact_mult__eq__0__iff,axiom,
    ! [X24,X6,X5] :
      ( class_Rings_Oring__no__zero__divisors(X5)
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X24) = c_Groups_Ozero__class_Ozero(X5)
      <=> ( X6 = c_Groups_Ozero__class_Ozero(X5)
          | X24 = c_Groups_Ozero__class_Ozero(X5) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__eq__0__iff) ).

fof(fact_posDivAlg__0,axiom,
    ! [X90] : c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X90) = 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/sandbox/benchmark/theBenchmark.p',fact_posDivAlg__0) ).

fof(fact_div__int__def,axiom,
    ! [X90,X62] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X62),X90) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(X62,X90)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__int__def) ).

fof(fact_power__0__Suc,axiom,
    ! [X57,X58] :
      ( ( class_Power_Opower(X58)
        & class_Rings_Osemiring__0(X58) )
     => hAPP(hAPP(c_Power_Opower__class_Opower(X58),c_Groups_Ozero__class_Ozero(X58)),hAPP(c_Nat_OSuc,X57)) = c_Groups_Ozero__class_Ozero(X58) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__0__Suc) ).

fof(fact_divide__Numeral0,axiom,
    ! [X66,X58] :
      ( ( class_Fields_Ofield__inverse__zero(X58)
        & class_Int_Onumber__ring(X58) )
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X66),hAPP(c_Int_Onumber__class_Onumber__of(X58),c_Int_OPls)) = c_Groups_Ozero__class_Ozero(X58) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__Numeral0) ).

fof(fact_abs__sgn,axiom,
    ! [X96,X58] :
      ( class_Rings_Olinordered__idom(X58)
     => hAPP(c_Groups_Oabs__class_Oabs(X58),X96) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X96),c_Groups_Osgn__class_Osgn(X58,X96)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__sgn) ).

fof(fact_com_Osimps_I40_J,axiom,
    ! [X43,X11,X84,X102] : c_Com_Ocom_OLocal(X102,X84,X11) != hAPP(c_Com_Ocom_OBODY,X43),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I40_J) ).

fof(fact_com_Osimps_I54_J,axiom,
    ! [X43,X41,X42,X84] : c_Com_Ocom_OCond(X84,X42,X41) != hAPP(c_Com_Ocom_OBODY,X43),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I54_J) ).

fof(fact_com_Osimps_I63_J,axiom,
    ! [X44,X92,X43,X93] : c_Com_Ocom_OCall(X93,X43,X92) != hAPP(c_Com_Ocom_OBODY,X44),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I63_J) ).

fof(fact_com_Osimps_I41_J,axiom,
    ! [X11,X84,X102,X43] : hAPP(c_Com_Ocom_OBODY,X43) != c_Com_Ocom_OLocal(X102,X84,X11),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I41_J) ).

fof(fact_com_Osimps_I55_J,axiom,
    ! [X41,X42,X84,X43] : hAPP(c_Com_Ocom_OBODY,X43) != c_Com_Ocom_OCond(X84,X42,X41),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I55_J) ).

fof(fact_com_Osimps_I62_J,axiom,
    ! [X92,X43,X93,X44] : hAPP(c_Com_Ocom_OBODY,X44) != c_Com_Ocom_OCall(X93,X43,X92),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I62_J) ).

fof(fact_lists__UNIV,axiom,
    ! [X5] : c_List_Olists(X5,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X5),tc_HOL_Obool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lists__UNIV) ).

fof(fact_map__ident,axiom,
    ! [X239,X5] : hAPP(hAPP(c_List_Omap(X5,X5),c_COMBI(X5)),X239) = X239,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__ident) ).

fof(fact_accp__wfPD,axiom,
    ! [X25,X171,X5] :
      ( c_Wellfounded_OwfP(X5,X171)
     => hBOOL(hAPP(c_Wellfounded_Oaccp(X5,X171),X25)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_accp__wfPD) ).

fof(fact_reflpE,axiom,
    ! [X25,X171,X5] :
      ( c_Predicate_Oreflp(X5,X171)
     => hBOOL(hAPP(hAPP(X171,X25),X25)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_reflpE) ).

fof(fact_equivp__reflp,axiom,
    ! [X25,X32,X5] :
      ( c_Equiv__Relations_Oequivp(X5,X32)
     => hBOOL(hAPP(hAPP(X32,X25),X25)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equivp__reflp) ).

fof(fact_sublist__empty,axiom,
    ! [X239,X5] : c_List_Osublist(X5,X239,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = c_List_Olist_ONil(X5),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sublist__empty) ).

fof(fact_right__inverse__eq,axiom,
    ! [X6,X24,X5] :
      ( class_Rings_Odivision__ring(X5)
     => ( X24 != c_Groups_Ozero__class_Ozero(X5)
       => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X6),X24) = c_Groups_Oone__class_Oone(X5)
        <=> X6 = X24 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_right__inverse__eq) ).

fof(fact_length__rev,axiom,
    ! [X242,X58] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),hAPP(c_List_Orev(X58),X242)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__rev) ).

fof(fact_length__rotate1,axiom,
    ! [X242,X58] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),hAPP(c_List_Orotate1(X58),X242)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__rotate1) ).

fof(fact_exE__some,axiom,
    ! [X5,X23,X18] :
      ( ? [X138] : hBOOL(hAPP(X18,X138))
     => ( X23 = c_Hilbert__Choice_OEps(X5,X18)
       => hBOOL(hAPP(X18,X23)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_exE__some) ).

fof(fact_funpow_Osimps_I1_J,axiom,
    ! [X2,X5] : hAPP(hAPP(c_Nat_Ocompow(X5,X5),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2) = c_Fun_Oid(X5),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funpow_Osimps_I1_J) ).

fof(fact_map_Osimps_I1_J,axiom,
    ! [X2,X5,X20] : hAPP(hAPP(c_List_Omap(X20,X5),X2),c_List_Olist_ONil(X20)) = c_List_Olist_ONil(X5),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map_Osimps_I1_J) ).

fof(fact_inf__compl__bot,axiom,
    ! [X66,X58] :
      ( class_Lattices_Oboolean__algebra(X58)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X66),hAPP(c_Groups_Ouminus__class_Ouminus(X58),X66)) = c_Orderings_Obot__class_Obot(X58) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__compl__bot) ).

fof(fact_sup__compl__top,axiom,
    ! [X66,X58] :
      ( class_Lattices_Oboolean__algebra(X58)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X66),hAPP(c_Groups_Ouminus__class_Ouminus(X58),X66)) = c_Orderings_Otop__class_Otop(X58) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__compl__top) ).

fof(fact_right__minus,axiom,
    ! [X62,X58] :
      ( class_Groups_Ogroup__add(X58)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),hAPP(c_Groups_Ouminus__class_Ouminus(X58),X62)) = c_Groups_Ozero__class_Ozero(X58) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_right__minus) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J,axiom,
    ! [X57,X66] :
      ( c_Nat__Transfer_Ois__nat(X66)
     => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X66),X57)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J) ).

fof(fact_zmult__eq__1__iff,axiom,
    ! [X50,X95] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X95),X50) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    <=> ( ( X95 = c_Groups_Oone__class_Oone(tc_Int_Oint)
          & X50 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
        | ( X95 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
          & X50 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__eq__1__iff) ).

fof(fact_inf__eq__top__iff,axiom,
    ! [X33,X25,X5] :
      ( class_Lattices_Obounded__lattice__top(X5)
     => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X25),X33) = c_Orderings_Otop__class_Otop(X5)
      <=> ( X25 = c_Orderings_Otop__class_Otop(X5)
          & X33 = c_Orderings_Otop__class_Otop(X5) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__eq__top__iff) ).

fof(fact_sup__eq__bot__iff,axiom,
    ! [X33,X25,X5] :
      ( class_Lattices_Obounded__lattice__bot(X5)
     => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X25),X33) = c_Orderings_Obot__class_Obot(X5)
      <=> ( X25 = c_Orderings_Obot__class_Obot(X5)
          & X33 = c_Orderings_Obot__class_Obot(X5) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__eq__bot__iff) ).

fof(fact_field__power__not__zero,axiom,
    ! [X57,X62,X58] :
      ( class_Rings_Oring__1__no__zero__divisors(X58)
     => ( X62 != c_Groups_Ozero__class_Ozero(X58)
       => hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),X57) != c_Groups_Ozero__class_Ozero(X58) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_field__power__not__zero) ).

fof(fact_double__eq__0__iff,axiom,
    ! [X6,X5] :
      ( class_Groups_Olinordered__ab__group__add(X5)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),X6) = c_Groups_Ozero__class_Ozero(X5)
      <=> X6 = c_Groups_Ozero__class_Ozero(X5) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__eq__0__iff) ).

fof(fact_double__zero__sym,axiom,
    ! [X6,X5] :
      ( class_Groups_Olinordered__ab__group__add(X5)
     => ( c_Groups_Ozero__class_Ozero(X5) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X6),X6)
      <=> X6 = c_Groups_Ozero__class_Ozero(X5) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__zero__sym) ).

fof(fact_finite__lessThan,axiom,
    ! [X87] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X87))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__lessThan) ).

fof(fact_finite__atMost,axiom,
    ! [X87] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X87))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__atMost) ).

fof(fact_minus__numeral__code_I5_J,axiom,
    ! [X128] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X128)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__numeral__code_I5_J) ).

fof(fact_eq__iff__diff__eq__0,axiom,
    ! [X24,X6,X5] :
      ( class_Groups_Oab__group__add(X5)
     => ( X6 = X24
      <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X6),X24) = c_Groups_Ozero__class_Ozero(X5) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__iff__diff__eq__0) ).

fof(fact_right__minus__eq,axiom,
    ! [X24,X6,X5] :
      ( class_Groups_Ogroup__add(X5)
     => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X6),X24) = c_Groups_Ozero__class_Ozero(X5)
      <=> X6 = X24 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_right__minus__eq) ).

fof(fact_eq__imp__le,axiom,
    ! [X57,X72] :
      ( X72 = X57
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X72),X57)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__imp__le) ).

fof(fact_take__eq__Nil,axiom,
    ! [X239,X50,X5] :
      ( hAPP(hAPP(c_List_Otake(X5),X50),X239) = c_List_Olist_ONil(X5)
    <=> ( X50 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X239 = c_List_Olist_ONil(X5) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__eq__Nil) ).

fof(fact_pos__zmult__eq__1__iff__lemma,axiom,
    ! [X57,X72] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X72),X57) = c_Groups_Oone__class_Oone(tc_Int_Oint)
     => ( X72 = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | X72 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__zmult__eq__1__iff__lemma) ).

fof(fact_add__0__iff,axiom,
    ! [X6,X24,X5] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5)
     => ( X24 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X24),X6)
      <=> X6 = c_Groups_Ozero__class_Ozero(X5) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__iff) ).

fof(fact_replicate__empty,axiom,
    ! [X25,X50,X5] :
      ( c_List_Oreplicate(X5,X50,X25) = c_List_Olist_ONil(X5)
    <=> X50 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_replicate__empty) ).

fof(fact_empty__replicate,axiom,
    ! [X25,X50,X5] :
      ( c_List_Olist_ONil(X5) = c_List_Oreplicate(X5,X50,X25)
    <=> X50 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__replicate) ).

fof(fact_diff__Suc__1,axiom,
    ! [X57] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X57)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X57,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__1) ).

fof(fact_set__upto,axiom,
    ! [X157,X82] : hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X82,X157)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X82,X157),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__upto) ).

fof(fact_atLeastAtMost__upto,axiom,
    ! [X157,X82] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X82,X157) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X82,X157)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastAtMost__upto) ).

fof(fact_add__numeral__0__right,axiom,
    ! [X62,X58] :
      ( class_Int_Onumber__ring(X58)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),hAPP(c_Int_Onumber__class_Onumber__of(X58),c_Int_OPls)) = X62 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__numeral__0__right) ).

fof(fact_zle__refl,axiom,
    ! [X128] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X128),X128)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__refl) ).

fof(fact_le__refl,axiom,
    ! [X57] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X57),X57)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__refl) ).

fof(fact_evalc_Oequations_I1_J,axiom,
    ! [X62] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X62),X62)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_Oequations_I1_J) ).

fof(fact_evalc_OSkip,axiom,
    ! [X48] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X48),X48)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_OSkip) ).

fof(fact_listsp_Oequations_I1_J,axiom,
    ! [X21,X5] : hBOOL(hAPP(c_List_Olistsp(X5,X21),c_List_Olist_ONil(X5))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsp_Oequations_I1_J) ).

fof(fact_listsp_ONil,axiom,
    ! [X21,X5] : hBOOL(hAPP(c_List_Olistsp(X5,X21),c_List_Olist_ONil(X5))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsp_ONil) ).

fof(fact_distinct__remdups,axiom,
    ! [X242,X58] : hBOOL(hAPP(c_List_Odistinct(X58),c_List_Oremdups(X58,X242))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__remdups) ).

fof(fact_append__is__Nil__conv,axiom,
    ! [X251,X239,X5] :
      ( hAPP(hAPP(c_List_Oappend(X5),X239),X251) = c_List_Olist_ONil(X5)
    <=> ( X239 = c_List_Olist_ONil(X5)
        & X251 = c_List_Olist_ONil(X5) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__is__Nil__conv) ).

fof(fact_Nil__is__append__conv,axiom,
    ! [X251,X239,X5] :
      ( c_List_Olist_ONil(X5) = hAPP(hAPP(c_List_Oappend(X5),X239),X251)
    <=> ( X239 = c_List_Olist_ONil(X5)
        & X251 = c_List_Olist_ONil(X5) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nil__is__append__conv) ).

fof(fact_Domain__rtrancl,axiom,
    ! [X32,X5] : hAPP(c_Relation_ODomain(X5,X5),c_Transitive__Closure_Ortrancl(X5,X32)) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__rtrancl) ).

fof(fact_Range__rtrancl,axiom,
    ! [X32,X5] : hAPP(c_Relation_ORange(X5,X5),c_Transitive__Closure_Ortrancl(X5,X32)) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__rtrancl) ).

fof(help_c__COMBK__1,axiom,
    ! [X314,X49,X5,X58] : hAPP(hAPP(c_COMBK(X58,X5),X49),X314) = X49,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBK__1) ).

fof(fact_lazy__sequence_Osimps_I3_J,axiom,
    ! [X310,X150,X58] : c_Lazy__Sequence_Olazy__sequence_OInsert(X58,X150,X310) != c_Lazy__Sequence_Olazy__sequence_OEmpty(X58),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lazy__sequence_Osimps_I3_J) ).

fof(fact_lazy__sequence_Osimps_I2_J,axiom,
    ! [X310,X150,X58] : c_Lazy__Sequence_Olazy__sequence_OEmpty(X58) != c_Lazy__Sequence_Olazy__sequence_OInsert(X58,X150,X310),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lazy__sequence_Osimps_I2_J) ).

fof(fact_zdiv__minus1__right,axiom,
    ! [X62] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X62),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X62),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__minus1__right) ).

fof(fact_zmult__commute,axiom,
    ! [X128,X94] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X94),X128) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X128),X94),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__commute) ).

fof(fact_nat__mult__commute,axiom,
    ! [X57,X72] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X72),X57) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X57),X72),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__commute) ).

fof(fact_zadd__commute,axiom,
    ! [X128,X94] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X94),X128) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X128),X94),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__commute) ).

fof(fact_nat__add__commute,axiom,
    ! [X57,X72] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X72),X57) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X57),X72),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__commute) ).

fof(fact_Nitpick_Ofrac__def,axiom,
    ! [X90,X62,X58] : hAPP(hAPP(c_Nitpick_Ofrac(X58),X62),X90) = c_Nitpick_OAbs__Frac(X58,c_Nitpick_Onorm__frac(X62,X90)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Ofrac__def) ).

fof(fact_diff__0,axiom,
    ! [X62,X58] :
      ( class_Groups_Ogroup__add(X58)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X58),c_Groups_Ozero__class_Ozero(X58)),X62) = hAPP(c_Groups_Ouminus__class_Ouminus(X58),X62) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__0) ).

fof(fact_append__self__conv2,axiom,
    ! [X251,X239,X5] :
      ( hAPP(hAPP(c_List_Oappend(X5),X239),X251) = X251
    <=> X239 = c_List_Olist_ONil(X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__self__conv2) ).

fof(fact_append__self__conv,axiom,
    ! [X251,X239,X5] :
      ( hAPP(hAPP(c_List_Oappend(X5),X239),X251) = X239
    <=> X251 = c_List_Olist_ONil(X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__self__conv) ).

fof(fact_self__append__conv,axiom,
    ! [X251,X5,X239] :
      ( X239 = hAPP(hAPP(c_List_Oappend(X5),X239),X251)
    <=> X251 = c_List_Olist_ONil(X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_self__append__conv) ).

fof(fact_self__append__conv2,axiom,
    ! [X239,X5,X251] :
      ( X251 = hAPP(hAPP(c_List_Oappend(X5),X239),X251)
    <=> X239 = c_List_Olist_ONil(X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_self__append__conv2) ).

fof(fact_power__0__left,axiom,
    ! [X57,X58] :
      ( ( class_Power_Opower(X58)
        & class_Rings_Osemiring__0(X58) )
     => ( ( X57 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => hAPP(hAPP(c_Power_Opower__class_Opower(X58),c_Groups_Ozero__class_Ozero(X58)),X57) = c_Groups_Oone__class_Oone(X58) )
        & ( X57 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => hAPP(hAPP(c_Power_Opower__class_Opower(X58),c_Groups_Ozero__class_Ozero(X58)),X57) = c_Groups_Ozero__class_Ozero(X58) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__0__left) ).

fof(fact_list_Osimps_I3_J,axiom,
    ! [X256,X150,X58] : hAPP(hAPP(c_List_Olist_OCons(X58),X150),X256) != c_List_Olist_ONil(X58),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list_Osimps_I3_J) ).

fof(fact_list_Osimps_I2_J,axiom,
    ! [X256,X150,X58] : c_List_Olist_ONil(X58) != hAPP(hAPP(c_List_Olist_OCons(X58),X150),X256),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list_Osimps_I2_J) ).

fof(fact_distinct__upto,axiom,
    ! [X97,X98] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(X98,X97))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__upto) ).

fof(fact_com_Osimps_I11_J,axiom,
    ! [X8,X92,X107] : c_Com_Ocom_OLocal(X107,X92,X8) != c_Com_Ocom_OSKIP,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I11_J) ).

fof(fact_com_Osimps_I15_J,axiom,
    ! [X39,X40,X92] : c_Com_Ocom_OCond(X92,X40,X39) != c_Com_Ocom_OSKIP,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I15_J) ).

fof(fact_com_Osimps_I21_J,axiom,
    ! [X92,X43,X93] : c_Com_Ocom_OCall(X93,X43,X92) != c_Com_Ocom_OSKIP,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I21_J) ).

fof(fact_com_Osimps_I10_J,axiom,
    ! [X8,X92,X107] : c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(X107,X92,X8),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I10_J) ).

fof(fact_com_Osimps_I14_J,axiom,
    ! [X39,X40,X92] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(X92,X40,X39),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I14_J) ).

fof(fact_com_Osimps_I20_J,axiom,
    ! [X92,X43,X93] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCall(X93,X43,X92),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I20_J) ).

fof(fact_listrel__rtrancl__eq__rtrancl__listrel1,axiom,
    ! [X171,X5] : c_List_Olistrel(X5,c_Transitive__Closure_Ortrancl(X5,X171)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(X5),c_List_Olistrel1(X5,X171)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__rtrancl__eq__rtrancl__listrel1) ).

fof(fact_max__ext__wf,axiom,
    ! [X171,X5] :
      ( c_Wellfounded_Owf(X5,X171)
     => c_Wellfounded_Owf(tc_fun(X5,tc_HOL_Obool),c_Wellfounded_Omax__ext(X5,X171)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__ext__wf) ).

fof(fact_min__ext__wf,axiom,
    ! [X171,X5] :
      ( c_Wellfounded_Owf(X5,X171)
     => c_Wellfounded_Owf(tc_fun(X5,tc_HOL_Obool),c_Wellfounded_Omin__ext(X5,X171)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__ext__wf) ).

fof(fact_listsum__rev,axiom,
    ! [X242,X58] :
      ( class_Groups_Ocomm__monoid__add(X58)
     => hAPP(c_List_Omonoid__add__class_Olistsum(X58),hAPP(c_List_Orev(X58),X242)) = hAPP(c_List_Omonoid__add__class_Olistsum(X58),X242) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__rev) ).

fof(fact_abs__idempotent,axiom,
    ! [X62,X58] :
      ( class_Groups_Oordered__ab__group__add__abs(X58)
     => hAPP(c_Groups_Oabs__class_Oabs(X58),hAPP(c_Groups_Oabs__class_Oabs(X58),X62)) = hAPP(c_Groups_Oabs__class_Oabs(X58),X62) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__idempotent) ).

fof(fact_abs__minus__cancel,axiom,
    ! [X62,X58] :
      ( class_Groups_Oordered__ab__group__add__abs(X58)
     => hAPP(c_Groups_Oabs__class_Oabs(X58),hAPP(c_Groups_Ouminus__class_Ouminus(X58),X62)) = hAPP(c_Groups_Oabs__class_Oabs(X58),X62) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__minus__cancel) ).

fof(fact_abs__of__nat,axiom,
    ! [X57,X58] :
      ( class_Rings_Olinordered__idom(X58)
     => hAPP(c_Groups_Oabs__class_Oabs(X58),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X58),X57)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X58),X57) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__of__nat) ).

fof(fact_UNIV__not__empty,axiom,
    ! [X5] : c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__not__empty) ).

fof(fact_zmod__minus1__right,axiom,
    ! [X62] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X62,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__minus1__right) ).

fof(fact_mod__1,axiom,
    ! [X72] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X72,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__1) ).

fof(fact_mult__is__0,axiom,
    ! [X50,X95] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X95),X50) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> ( X95 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X50 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__is__0) ).

fof(fact_not__Cons__self2,axiom,
    ! [X242,X66,X58] : hAPP(hAPP(c_List_Olist_OCons(X58),X66),X242) != X242,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__Cons__self2) ).

fof(fact_not__Cons__self,axiom,
    ! [X66,X58,X242] : X242 != hAPP(hAPP(c_List_Olist_OCons(X58),X66),X242),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__Cons__self) ).

fof(fact_fun__left__comm__idem__insert,axiom,
    ! [X5] : c_Finite__Set_Ofun__left__comm__idem(X5,tc_fun(X5,tc_HOL_Obool),c_Set_Oinsert(X5)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__idem__insert) ).

fof(fact_top__apply,axiom,
    ! [X25,X20,X5] :
      ( class_Orderings_Otop(X5)
     => hAPP(c_Orderings_Otop__class_Otop(tc_fun(X20,X5)),X25) = c_Orderings_Otop__class_Otop(X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_top__apply) ).

fof(fact_bot__fun__def,axiom,
    ! [X25,X20,X5] :
      ( class_Orderings_Obot(X5)
     => hAPP(c_Orderings_Obot__class_Obot(tc_fun(X20,X5)),X25) = c_Orderings_Obot__class_Obot(X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot__fun__def) ).

fof(fact_bot__apply,axiom,
    ! [X25,X20,X5] :
      ( class_Orderings_Obot(X5)
     => hAPP(c_Orderings_Obot__class_Obot(tc_fun(X20,X5)),X25) = c_Orderings_Obot__class_Obot(X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot__apply) ).

fof(fact_minus__code__numeral__code,axiom,
    ! [X72,X57] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X57),X72) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,X57),X72),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__code__numeral__code) ).

fof(fact_equivp__reflp__symp__transp,axiom,
    ! [X32,X5] :
      ( c_Equiv__Relations_Oequivp(X5,X32)
    <=> ( c_Predicate_Oreflp(X5,X32)
        & c_Predicate_Osymp(X5,X32)
        & c_Predicate_Otransp(X5,X32) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equivp__reflp__symp__transp) ).

fof(fact_equivpI,axiom,
    ! [X32,X5] :
      ( c_Predicate_Oreflp(X5,X32)
     => ( c_Predicate_Osymp(X5,X32)
       => ( c_Predicate_Otransp(X5,X32)
         => c_Equiv__Relations_Oequivp(X5,X32) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equivpI) ).

fof(fact_sorted__tl,axiom,
    ! [X242,X58] :
      ( class_Orderings_Olinorder(X58)
     => ( c_List_Olinorder__class_Osorted(X58,X242)
       => c_List_Olinorder__class_Osorted(X58,hAPP(c_List_Otl(X58),X242)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__tl) ).

fof(fact_distinct__remdups__id,axiom,
    ! [X242,X58] :
      ( hBOOL(hAPP(c_List_Odistinct(X58),X242))
     => c_List_Oremdups(X58,X242) = X242 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__remdups__id) ).

fof(fact_remdups__id__iff__distinct,axiom,
    ! [X239,X5] :
      ( c_List_Oremdups(X5,X239) = X239
    <=> hBOOL(hAPP(c_List_Odistinct(X5),X239)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_remdups__id__iff__distinct) ).

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/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__list__functions_I2_J) ).

fof(fact_mult__eq__self__implies__10,axiom,
    ! [X57,X72] :
      ( X72 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X72),X57)
     => ( X57 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | X72 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__eq__self__implies__10) ).

fof(fact_hd__conv__nth,axiom,
    ! [X58,X242] :
      ( X242 != c_List_Olist_ONil(X58)
     => hAPP(c_List_Ohd(X58),X242) = hAPP(hAPP(c_List_Onth(X58),X242),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hd__conv__nth) ).

fof(help_c__fimplies__1,axiom,
    ! [X16,X18] :
      ( hBOOL(X18)
      | hBOOL(hAPP(hAPP(c_fimplies,X18),X16)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fimplies__1) ).

fof(fact_single__valued__Id__on,axiom,
    ! [X21,X5] : c_Relation_Osingle__valued(X5,X5,c_Relation_OId__on(X5,X21)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valued__Id__on) ).

fof(fact_refl__on__Id__on,axiom,
    ! [X21,X5] : c_Relation_Orefl__on(X5,X21,c_Relation_OId__on(X5,X21)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__on__Id__on) ).

fof(fact_nat__mult__eq__1__iff,axiom,
    ! [X50,X95] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X95),X50) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    <=> ( X95 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        & X50 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__eq__1__iff) ).

fof(fact_add__is__0,axiom,
    ! [X50,X95] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X95),X50) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> ( X95 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        & X50 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__is__0) ).

fof(fact_nat__1__eq__mult__iff,axiom,
    ! [X50,X95] :
      ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X95),X50)
    <=> ( X95 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        & X50 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__1__eq__mult__iff) ).

fof(fact_eq__number__of,axiom,
    ! [X33,X25,X5] :
      ( ( class_Int_Onumber__ring(X5)
        & class_Int_Oring__char__0(X5) )
     => ( hAPP(c_Int_Onumber__class_Onumber__of(X5),X25) = hAPP(c_Int_Onumber__class_Onumber__of(X5),X33)
      <=> X25 = X33 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__number__of) ).

fof(fact_converse__Id__on,axiom,
    ! [X21,X5] : hAPP(c_Relation_Oconverse(X5,X5),c_Relation_OId__on(X5,X21)) = c_Relation_OId__on(X5,X21),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__Id__on) ).

fof(help_c__fequal__2,axiom,
    ! [X33,X25] :
      ( X25 != X33
      | hBOOL(hAPP(hAPP(c_fequal,X25),X33)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fequal__2) ).

fof(fact_of__int__number__of__eq,axiom,
    ! [X136,X58] :
      ( class_Int_Onumber__ring(X58)
     => hAPP(c_Int_Oring__1__class_Oof__int(X58),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)) = hAPP(c_Int_Onumber__class_Onumber__of(X58),X136) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__number__of__eq) ).

fof(fact_of__int__of__nat__eq,axiom,
    ! [X57,X58] :
      ( class_Rings_Oring__1(X58)
     => hAPP(c_Int_Oring__1__class_Oof__int(X58),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X57)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X58),X57) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__of__nat__eq) ).

fof(fact_set__empty2,axiom,
    ! [X239,X5] :
      ( c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) = hAPP(c_List_Oset(X5),X239)
    <=> X239 = c_List_Olist_ONil(X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__empty2) ).

fof(fact_set__empty,axiom,
    ! [X239,X5] :
      ( hAPP(c_List_Oset(X5),X239) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
    <=> X239 = c_List_Olist_ONil(X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__empty) ).

fof(fact_sym__conv__converse__eq,axiom,
    ! [X171,X5] :
      ( c_Relation_Osym(X5,X171)
    <=> hAPP(c_Relation_Oconverse(X5,X5),X171) = X171 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sym__conv__converse__eq) ).

fof(fact_set__rev,axiom,
    ! [X239,X5] : hAPP(c_List_Oset(X5),hAPP(c_List_Orev(X5),X239)) = hAPP(c_List_Oset(X5),X239),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__rev) ).

fof(fact_set__rotate1,axiom,
    ! [X239,X5] : hAPP(c_List_Oset(X5),hAPP(c_List_Orotate1(X5),X239)) = hAPP(c_List_Oset(X5),X239),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__rotate1) ).

fof(fact_power__power__power,axiom,
    ! [X5] :
      ( class_Power_Opower(X5)
     => c_Power_Opower__class_Opower(X5) = c_Power_Opower_Opower(X5,c_Groups_Oone__class_Oone(X5),c_Groups_Otimes__class_Otimes(X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__power__power) ).

fof(fact_add__eq__self__zero,axiom,
    ! [X57,X72] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X72),X57) = X72
     => X57 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__eq__self__zero) ).

fof(fact_hd__rev,axiom,
    ! [X58,X242] :
      ( X242 != c_List_Olist_ONil(X58)
     => hAPP(c_List_Ohd(X58),hAPP(c_List_Orev(X58),X242)) = c_List_Olast(X58,X242) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hd__rev) ).

fof(fact_last__rev,axiom,
    ! [X58,X242] :
      ( X242 != c_List_Olist_ONil(X58)
     => c_List_Olast(X58,hAPP(c_List_Orev(X58),X242)) = hAPP(c_List_Ohd(X58),X242) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last__rev) ).

fof(fact_Inf__UNIV,axiom,
    ! [X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => c_Complete__Lattice_OInf__class_OInf(X5,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__UNIV) ).

fof(fact_Inf__empty,axiom,
    ! [X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => c_Complete__Lattice_OInf__class_OInf(X5,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__empty) ).

fof(fact_Sup__UNIV,axiom,
    ! [X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => c_Complete__Lattice_OSup__class_OSup(X5,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__UNIV) ).

fof(fact_Sup__empty,axiom,
    ! [X5] :
      ( class_Complete__Lattice_Ocomplete__lattice(X5)
     => c_Complete__Lattice_OSup__class_OSup(X5,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__empty) ).

fof(fact_sorted__list__of__set__empty,axiom,
    ! [X5] :
      ( class_Orderings_Olinorder(X5)
     => c_List_Olinorder__class_Osorted__list__of__set(X5,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) = c_List_Olist_ONil(X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__list__of__set__empty) ).

fof(fact_div__1,axiom,
    ! [X72] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X72),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = X72,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__1) ).

fof(fact_Union__Pow__eq,axiom,
    ! [X21,X5] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),hAPP(c_Set_OPow(X5),X21)) = X21,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__Pow__eq) ).

fof(fact_inf__bot__left,axiom,
    ! [X66,X58] :
      ( class_Lattices_Obounded__lattice__bot(X58)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),c_Orderings_Obot__class_Obot(X58)),X66) = c_Orderings_Obot__class_Obot(X58) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__bot__left) ).

fof(fact_sup__top__left,axiom,
    ! [X66,X58] :
      ( class_Lattices_Obounded__lattice__top(X58)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),c_Orderings_Otop__class_Otop(X58)),X66) = c_Orderings_Otop__class_Otop(X58) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__top__left) ).

fof(fact_divide__zero__left,axiom,
    ! [X62,X58] :
      ( class_Rings_Odivision__ring(X58)
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),c_Groups_Ozero__class_Ozero(X58)),X62) = c_Groups_Ozero__class_Ozero(X58) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__zero__left) ).

fof(fact_power__one,axiom,
    ! [X57,X58] :
      ( class_Groups_Omonoid__mult(X58)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X58),c_Groups_Oone__class_Oone(X58)),X57) = c_Groups_Oone__class_Oone(X58) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__one) ).

fof(fact_div__0,axiom,
    ! [X62,X58] :
      ( class_Divides_Osemiring__div(X58)
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(X58),c_Groups_Ozero__class_Ozero(X58)),X62) = c_Groups_Ozero__class_Ozero(X58) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__0) ).

fof(fact_mult__zero__left,axiom,
    ! [X62,X58] :
      ( class_Rings_Omult__zero(X58)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),c_Groups_Ozero__class_Ozero(X58)),X62) = c_Groups_Ozero__class_Ozero(X58) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__zero__left) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
    ! [X62,X58] :
      ( class_Rings_Ocomm__semiring__1(X58)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),c_Groups_Ozero__class_Ozero(X58)),X62) = c_Groups_Ozero__class_Ozero(X58) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).

fof(fact_sorted__butlast,axiom,
    ! [X242,X58] :
      ( class_Orderings_Olinorder(X58)
     => ( X242 != c_List_Olist_ONil(X58)
       => ( c_List_Olinorder__class_Osorted(X58,X242)
         => c_List_Olinorder__class_Osorted(X58,c_List_Obutlast(X58,X242)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__butlast) ).

fof(fact_of__int__m1,axiom,
    ! [X58] :
      ( class_Int_Onumber__ring(X58)
     => hAPP(c_Int_Oring__1__class_Oof__int(X58),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(X58),c_Int_OMin) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__m1) ).

fof(fact_card_Oempty,axiom,
    ! [X5] : hAPP(c_Finite__Set_Ocard(X5),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card_Oempty) ).

fof(fact_abs__minus__one,axiom,
    ! [X58] :
      ( ( class_Int_Onumber__ring(X58)
        & class_Rings_Olinordered__idom(X58) )
     => hAPP(c_Groups_Oabs__class_Oabs(X58),hAPP(c_Int_Onumber__class_Onumber__of(X58),c_Int_OMin)) = c_Groups_Oone__class_Oone(X58) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__minus__one) ).

fof(fact_atLeast0AtMost,axiom,
    ! [X50] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X50) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X50),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeast0AtMost) ).

fof(fact_greaterThan__eq__iff,axiom,
    ! [X33,X25,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hAPP(c_SetInterval_Oord__class_OgreaterThan(X5),X25) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X5),X33)
      <=> X25 = X33 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThan__eq__iff) ).

fof(fact_atLeast__eq__iff,axiom,
    ! [X33,X25,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hAPP(c_SetInterval_Oord__class_OatLeast(X5),X25) = hAPP(c_SetInterval_Oord__class_OatLeast(X5),X33)
      <=> X25 = X33 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeast__eq__iff) ).

fof(fact_lessThan__eq__iff,axiom,
    ! [X33,X25,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hAPP(c_SetInterval_Oord__class_OlessThan(X5),X25) = hAPP(c_SetInterval_Oord__class_OlessThan(X5),X33)
      <=> X25 = X33 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lessThan__eq__iff) ).

fof(fact_atMost__eq__iff,axiom,
    ! [X33,X25,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hAPP(c_SetInterval_Oord__class_OatMost(X5),X25) = hAPP(c_SetInterval_Oord__class_OatMost(X5),X33)
      <=> X25 = X33 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atMost__eq__iff) ).

fof(fact_compl__eq__compl__iff,axiom,
    ! [X33,X25,X5] :
      ( class_Lattices_Oboolean__algebra(X5)
     => ( hAPP(c_Groups_Ouminus__class_Ouminus(X5),X25) = hAPP(c_Groups_Ouminus__class_Ouminus(X5),X33)
      <=> X25 = X33 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compl__eq__compl__iff) ).

fof(fact_neg__equal__iff__equal,axiom,
    ! [X24,X6,X5] :
      ( class_Groups_Ogroup__add(X5)
     => ( hAPP(c_Groups_Ouminus__class_Ouminus(X5),X6) = hAPP(c_Groups_Ouminus__class_Ouminus(X5),X24)
      <=> X6 = X24 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__equal__iff__equal) ).

fof(fact_of__int__eq__iff,axiom,
    ! [X120,X121,X5] :
      ( class_Int_Oring__char__0(X5)
     => ( hAPP(c_Int_Oring__1__class_Oof__int(X5),X121) = hAPP(c_Int_Oring__1__class_Oof__int(X5),X120)
      <=> X121 = X120 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__eq__iff) ).

fof(fact_of__nat__eq__iff,axiom,
    ! [X50,X95,X5] :
      ( class_Nat_Osemiring__char__0(X5)
     => ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X95) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X50)
      <=> X95 = X50 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__eq__iff) ).

fof(fact_inf__top__left,axiom,
    ! [X66,X58] :
      ( class_Lattices_Obounded__lattice__top(X58)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),c_Orderings_Otop__class_Otop(X58)),X66) = X66 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__top__left) ).

fof(fact_sup__bot__left,axiom,
    ! [X66,X58] :
      ( class_Lattices_Obounded__lattice__bot(X58)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),c_Orderings_Obot__class_Obot(X58)),X66) = X66 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__bot__left) ).

fof(fact_mult__1,axiom,
    ! [X62,X58] :
      ( class_Groups_Ocomm__monoid__mult(X58)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),c_Groups_Oone__class_Oone(X58)),X62) = X62 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__1) ).

fof(fact_mult__1__left,axiom,
    ! [X62,X58] :
      ( class_Groups_Omonoid__mult(X58)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),c_Groups_Oone__class_Oone(X58)),X62) = X62 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__1__left) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
    ! [X62,X58] :
      ( class_Rings_Ocomm__semiring__1(X58)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),c_Groups_Oone__class_Oone(X58)),X62) = X62 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
    ! [X62,X58] :
      ( class_Rings_Ocomm__semiring__1(X58)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),c_Groups_Ozero__class_Ozero(X58)),X62) = X62 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).

fof(fact_add__0,axiom,
    ! [X62,X58] :
      ( class_Groups_Ocomm__monoid__add(X58)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),c_Groups_Ozero__class_Ozero(X58)),X62) = X62 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0) ).

fof(fact_add__0__left,axiom,
    ! [X62,X58] :
      ( class_Groups_Omonoid__add(X58)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),c_Groups_Ozero__class_Ozero(X58)),X62) = X62 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__left) ).

fof(fact_divide__self__if,axiom,
    ! [X62,X58] :
      ( class_Rings_Odivision__ring__inverse__zero(X58)
     => ( ( X62 = c_Groups_Ozero__class_Ozero(X58)
         => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X62),X62) = c_Groups_Ozero__class_Ozero(X58) )
        & ( X62 != c_Groups_Ozero__class_Ozero(X58)
         => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X62),X62) = c_Groups_Oone__class_Oone(X58) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__self__if) ).

fof(fact_mod__0,axiom,
    ! [X62,X58] :
      ( class_Divides_Osemiring__div(X58)
     => c_Divides_Odiv__class_Omod(X58,c_Groups_Ozero__class_Ozero(X58),X62) = c_Groups_Ozero__class_Ozero(X58) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__0) ).

fof(fact_mod__by__1,axiom,
    ! [X62,X58] :
      ( class_Divides_Osemiring__div(X58)
     => c_Divides_Odiv__class_Omod(X58,X62,c_Groups_Oone__class_Oone(X58)) = c_Groups_Ozero__class_Ozero(X58) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__by__1) ).

fof(fact_sorted__remdups,axiom,
    ! [X99,X58] :
      ( class_Orderings_Olinorder(X58)
     => ( c_List_Olinorder__class_Osorted(X58,X99)
       => c_List_Olinorder__class_Osorted(X58,c_List_Oremdups(X58,X99)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__remdups) ).

fof(fact_inf__bot__right,axiom,
    ! [X66,X58] :
      ( class_Lattices_Obounded__lattice__bot(X58)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X66),c_Orderings_Obot__class_Obot(X58)) = c_Orderings_Obot__class_Obot(X58) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__bot__right) ).

fof(fact_sup__top__right,axiom,
    ! [X66,X58] :
      ( class_Lattices_Obounded__lattice__top(X58)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X66),c_Orderings_Otop__class_Otop(X58)) = c_Orderings_Otop__class_Otop(X58) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__top__right) ).

fof(fact_divide__zero,axiom,
    ! [X62,X58] :
      ( class_Rings_Odivision__ring__inverse__zero(X58)
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X62),c_Groups_Ozero__class_Ozero(X58)) = c_Groups_Ozero__class_Ozero(X58) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__zero) ).

fof(fact_div__by__0,axiom,
    ! [X62,X58] :
      ( class_Divides_Osemiring__div(X58)
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(X58),X62),c_Groups_Ozero__class_Ozero(X58)) = c_Groups_Ozero__class_Ozero(X58) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__by__0) ).

fof(fact_mult__zero__right,axiom,
    ! [X62,X58] :
      ( class_Rings_Omult__zero(X58)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),c_Groups_Ozero__class_Ozero(X58)) = c_Groups_Ozero__class_Ozero(X58) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__zero__right) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
    ! [X62,X58] :
      ( class_Rings_Ocomm__semiring__1(X58)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),c_Groups_Ozero__class_Ozero(X58)) = c_Groups_Ozero__class_Ozero(X58) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).

fof(fact_listrel__sym,axiom,
    ! [X171,X5] :
      ( c_Relation_Osym(X5,X171)
     => c_Relation_Osym(tc_List_Olist(X5),c_List_Olistrel(X5,X171)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__sym) ).

fof(fact_listrel__trans,axiom,
    ! [X171,X5] :
      ( c_Relation_Otrans(X5,X171)
     => c_Relation_Otrans(tc_List_Olist(X5),c_List_Olistrel(X5,X171)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrel__trans) ).

fof(fact_lexord__transI,axiom,
    ! [X171,X5] :
      ( c_Relation_Otrans(X5,X171)
     => c_Relation_Otrans(tc_List_Olist(X5),c_List_Olexord(X5,X171)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lexord__transI) ).

fof(fact_wf__lex,axiom,
    ! [X171,X5] :
      ( c_Wellfounded_Owf(X5,X171)
     => c_Wellfounded_Owf(tc_List_Olist(X5),c_List_Olex(X5,X171)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__lex) ).

fof(fact_wf__lenlex,axiom,
    ! [X171,X5] :
      ( c_Wellfounded_Owf(X5,X171)
     => c_Wellfounded_Owf(tc_List_Olist(X5),c_List_Olenlex(X5,X171)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__lenlex) ).

fof(fact_eq__Nil__appendI,axiom,
    ! [X58,X241,X242] :
      ( X242 = X241
     => X242 = hAPP(hAPP(c_List_Oappend(X58),c_List_Olist_ONil(X58)),X241) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__Nil__appendI) ).

fof(fact_divide__self,axiom,
    ! [X62,X58] :
      ( class_Rings_Odivision__ring(X58)
     => ( X62 != c_Groups_Ozero__class_Ozero(X58)
       => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X62),X62) = c_Groups_Oone__class_Oone(X58) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__self) ).

fof(fact_div__self,axiom,
    ! [X62,X58] :
      ( class_Divides_Osemiring__div(X58)
     => ( X62 != c_Groups_Ozero__class_Ozero(X58)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(X58),X62),X62) = c_Groups_Oone__class_Oone(X58) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__self) ).

fof(fact_mod__by__0,axiom,
    ! [X62,X58] :
      ( class_Divides_Osemiring__div(X58)
     => c_Divides_Odiv__class_Omod(X58,X62,c_Groups_Ozero__class_Ozero(X58)) = X62 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__by__0) ).

fof(fact_fun__left__comm,axiom,
    ! [X5] :
      ( class_Groups_Oab__semigroup__mult(X5)
     => c_Finite__Set_Ofun__left__comm(X5,X5,c_Groups_Otimes__class_Otimes(X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm) ).

fof(fact_fun__left__comm__idem__inf,axiom,
    ! [X5] :
      ( class_Lattices_Osemilattice__inf(X5)
     => c_Finite__Set_Ofun__left__comm__idem(X5,X5,c_Lattices_Osemilattice__inf__class_Oinf(X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__idem__inf) ).

fof(fact_fun__left__comm__idem__sup,axiom,
    ! [X5] :
      ( class_Lattices_Osemilattice__sup(X5)
     => c_Finite__Set_Ofun__left__comm__idem(X5,X5,c_Lattices_Osemilattice__sup__class_Osup(X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__idem__sup) ).

fof(fact_min__max_Ofun__left__comm__idem__sup,axiom,
    ! [X5] :
      ( class_Orderings_Olinorder(X5)
     => c_Finite__Set_Ofun__left__comm__idem(X5,X5,c_Orderings_Oord__class_Omax(X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ofun__left__comm__idem__sup) ).

fof(fact_min__max_Ofun__left__comm__idem__inf,axiom,
    ! [X5] :
      ( class_Orderings_Olinorder(X5)
     => c_Finite__Set_Ofun__left__comm__idem(X5,X5,c_Orderings_Oord__class_Omin(X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ofun__left__comm__idem__inf) ).

fof(fact_fun__left__comm__idem,axiom,
    ! [X5] :
      ( class_Lattices_Oab__semigroup__idem__mult(X5)
     => c_Finite__Set_Ofun__left__comm__idem(X5,X5,c_Groups_Otimes__class_Otimes(X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__idem) ).

fof(fact_Domain__Id__on,axiom,
    ! [X21,X5] : hAPP(c_Relation_ODomain(X5,X5),c_Relation_OId__on(X5,X21)) = X21,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__Id__on) ).

fof(fact_Range__Id__on,axiom,
    ! [X21,X5] : hAPP(c_Relation_ORange(X5,X5),c_Relation_OId__on(X5,X21)) = X21,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__Id__on) ).

fof(fact_power__0,axiom,
    ! [X62,X58] :
      ( class_Power_Opower(X58)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X58) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__0) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
    ! [X66,X58] :
      ( class_Rings_Ocomm__semiring__1(X58)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X58),X66),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X58) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).

fof(fact_inf__top__right,axiom,
    ! [X66,X58] :
      ( class_Lattices_Obounded__lattice__top(X58)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X66),c_Orderings_Otop__class_Otop(X58)) = X66 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__top__right) ).

fof(fact_sup__bot__right,axiom,
    ! [X66,X58] :
      ( class_Lattices_Obounded__lattice__bot(X58)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X66),c_Orderings_Obot__class_Obot(X58)) = X66 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__bot__right) ).

fof(fact_divide__1,axiom,
    ! [X62,X58] :
      ( class_Rings_Odivision__ring(X58)
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X58),X62),c_Groups_Oone__class_Oone(X58)) = X62 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__1) ).

fof(fact_diff__0__right,axiom,
    ! [X62,X58] :
      ( class_Groups_Ogroup__add(X58)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X58),X62),c_Groups_Ozero__class_Ozero(X58)) = X62 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__0__right) ).

fof(fact_div__by__1,axiom,
    ! [X62,X58] :
      ( class_Divides_Osemiring__div(X58)
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(X58),X62),c_Groups_Oone__class_Oone(X58)) = X62 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__by__1) ).

fof(fact_mult_Ocomm__neutral,axiom,
    ! [X62,X58] :
      ( class_Groups_Ocomm__monoid__mult(X58)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),c_Groups_Oone__class_Oone(X58)) = X62 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Ocomm__neutral) ).

fof(fact_mult__1__right,axiom,
    ! [X62,X58] :
      ( class_Groups_Omonoid__mult(X58)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),c_Groups_Oone__class_Oone(X58)) = X62 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__1__right) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
    ! [X62,X58] :
      ( class_Rings_Ocomm__semiring__1(X58)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),c_Groups_Oone__class_Oone(X58)) = X62 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
    ! [X62,X58] :
      ( class_Rings_Ocomm__semiring__1(X58)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),c_Groups_Ozero__class_Ozero(X58)) = X62 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).

fof(fact_add_Ocomm__neutral,axiom,
    ! [X62,X58] :
      ( class_Groups_Ocomm__monoid__add(X58)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),c_Groups_Ozero__class_Ozero(X58)) = X62 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add_Ocomm__neutral) ).

fof(fact_add__0__right,axiom,
    ! [X62,X58] :
      ( class_Groups_Omonoid__add(X58)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),X62),c_Groups_Ozero__class_Ozero(X58)) = X62 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__right) ).

fof(fact_double__compl,axiom,
    ! [X66,X58] :
      ( class_Lattices_Oboolean__algebra(X58)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X58),hAPP(c_Groups_Ouminus__class_Ouminus(X58),X66)) = X66 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__compl) ).

fof(fact_minus__minus,axiom,
    ! [X62,X58] :
      ( class_Groups_Ogroup__add(X58)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X58),hAPP(c_Groups_Ouminus__class_Ouminus(X58),X62)) = X62 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__minus) ).

fof(fact_abs__int__eq,axiom,
    ! [X72] : hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X72)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X72),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__int__eq) ).

fof(fact_of__int__int__eq,axiom,
    ! [X57] : hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X57)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X57),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__int__eq) ).

fof(fact_set__remdups,axiom,
    ! [X239,X5] : hAPP(c_List_Oset(X5),c_List_Oremdups(X5,X239)) = hAPP(c_List_Oset(X5),X239),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__remdups) ).

fof(fact_mod__self,axiom,
    ! [X62,X58] :
      ( class_Divides_Osemiring__div(X58)
     => c_Divides_Odiv__class_Omod(X58,X62,X62) = c_Groups_Ozero__class_Ozero(X58) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__self) ).

fof(fact_rev__is__rev__conv,axiom,
    ! [X251,X239,X5] :
      ( hAPP(c_List_Orev(X5),X239) = hAPP(c_List_Orev(X5),X251)
    <=> X239 = X251 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__is__rev__conv) ).

fof(fact_inc__shift__def,axiom,
    ! [X96,X136] :
      ( ( X136 = X96
       => c_Random_Oinc__shift(X136,X96) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
      & ( X136 != X96
       => c_Random_Oinc__shift(X136,X96) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X96),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inc__shift__def) ).

fof(fact_append__Nil,axiom,
    ! [X241,X58] : hAPP(hAPP(c_List_Oappend(X58),c_List_Olist_ONil(X58)),X241) = X241,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__Nil) ).

fof(fact_Suc__eq__plus1__left,axiom,
    ! [X57] : hAPP(c_Nat_OSuc,X57) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X57),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).

fof(fact_sublist__nil,axiom,
    ! [X21,X5] : c_List_Osublist(X5,c_List_Olist_ONil(X5),X21) = c_List_Olist_ONil(X5),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sublist__nil) ).

fof(fact_takeWhile_Osimps_I1_J,axiom,
    ! [X18,X5] : c_List_OtakeWhile(X5,X18,c_List_Olist_ONil(X5)) = c_List_Olist_ONil(X5),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_takeWhile_Osimps_I1_J) ).

fof(fact_remove1_Osimps_I1_J,axiom,
    ! [X66,X58] : c_List_Oremove1(X58,X66,c_List_Olist_ONil(X58)) = c_List_Olist_ONil(X58),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_remove1_Osimps_I1_J) ).

fof(fact_atLeastLessThan0,axiom,
    ! [X95] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X95),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan0) ).

fof(fact_power__one__right,axiom,
    ! [X62,X58] :
      ( class_Groups_Omonoid__mult(X58)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X62 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__one__right) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
    ! [X66,X58] :
      ( class_Rings_Ocomm__semiring__1(X58)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X58),X66),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X66 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).

fof(fact_diff__self,axiom,
    ! [X62,X58] :
      ( class_Groups_Ogroup__add(X58)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X58),X62),X62) = c_Groups_Ozero__class_Ozero(X58) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__self) ).

fof(fact_list_Osize_I1_J,axiom,
    ! [X80,X5] : c_List_Olist_Olist__size(X5,X80,c_List_Olist_ONil(X5)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list_Osize_I1_J) ).

fof(fact_sym__rtrancl,axiom,
    ! [X171,X5] :
      ( c_Relation_Osym(X5,X171)
     => c_Relation_Osym(X5,c_Transitive__Closure_Ortrancl(X5,X171)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sym__rtrancl) ).

fof(fact_acyclic__impl__antisym__rtrancl,axiom,
    ! [X171,X5] :
      ( c_Wellfounded_Oacyclic(X5,X171)
     => c_Relation_Oantisym(X5,c_Transitive__Closure_Ortrancl(X5,X171)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acyclic__impl__antisym__rtrancl) ).

fof(fact_take__0,axiom,
    ! [X242,X58] : hAPP(hAPP(c_List_Otake(X58),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X242) = c_List_Olist_ONil(X58),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__0) ).

fof(fact_drop__Nil,axiom,
    ! [X57,X58] : hAPP(hAPP(c_List_Odrop(X58),X57),c_List_Olist_ONil(X58)) = c_List_Olist_ONil(X58),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__Nil) ).

fof(fact_take__Nil,axiom,
    ! [X57,X58] : hAPP(hAPP(c_List_Otake(X58),X57),c_List_Olist_ONil(X58)) = c_List_Olist_ONil(X58),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__Nil) ).

fof(fact_minus__equation__iff,axiom,
    ! [X24,X6,X5] :
      ( class_Groups_Ogroup__add(X5)
     => ( hAPP(c_Groups_Ouminus__class_Ouminus(X5),X6) = X24
      <=> hAPP(c_Groups_Ouminus__class_Ouminus(X5),X24) = X6 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__equation__iff) ).

fof(fact_equation__minus__iff,axiom,
    ! [X24,X6,X5] :
      ( class_Groups_Ogroup__add(X5)
     => ( X6 = hAPP(c_Groups_Ouminus__class_Ouminus(X5),X24)
      <=> X24 = hAPP(c_Groups_Ouminus__class_Ouminus(X5),X6) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equation__minus__iff) ).

fof(fact_nat__list__def,axiom,
    ! [X156] :
      ( c_List_Onat__list(X156)
    <=> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X156)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__list__def) ).

fof(fact_card__atMost,axiom,
    ! [X159] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X159)) = hAPP(c_Nat_OSuc,X159),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__atMost) ).

fof(fact_nat__of__number,axiom,
    ! [X96] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),X96)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X96),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__of__number) ).

fof(fact_nat__number__of,axiom,
    ! [X128] : hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X128),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__number__of) ).

fof(fact_nat__number__of__def,axiom,
    ! [X136] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__number__of__def) ).

fof(fact_Suc__eq__plus1,axiom,
    ! [X57] : hAPP(c_Nat_OSuc,X57) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X57),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1) ).

fof(fact_replicate__0,axiom,
    ! [X66,X58] : c_List_Oreplicate(X58,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X66) = c_List_Olist_ONil(X58),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_replicate__0) ).

fof(fact__02,axiom,
    ! [X304,X58] : c_Lazy__Sequence_Oappend(X58,c_Lazy__Sequence_Olazy__sequence_OEmpty(X58),X304) = X304,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__02) ).

fof(fact_splice_Osimps_I1_J,axiom,
    ! [X241,X58] : c_List_Osplice(X58,c_List_Olist_ONil(X58),X241) = X241,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_splice_Osimps_I1_J) ).

fof(fact_splice__Nil2,axiom,
    ! [X242,X58] : c_List_Osplice(X58,X242,c_List_Olist_ONil(X58)) = X242,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_splice__Nil2) ).

fof(fact_sgn__sgn,axiom,
    ! [X62,X58] :
      ( class_Rings_Olinordered__idom(X58)
     => c_Groups_Osgn__class_Osgn(X58,c_Groups_Osgn__class_Osgn(X58,X62)) = c_Groups_Osgn__class_Osgn(X58,X62) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__sgn) ).

fof(fact_list__all__simps_I2_J,axiom,
    ! [X18,X5] : c_List_Olist__all(X5,X18,c_List_Olist_ONil(X5)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__all__simps_I2_J) ).

fof(fact_inf_Oidem,axiom,
    ! [X62,X58] :
      ( class_Lattices_Osemilattice__inf(X58)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X62),X62) = X62 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf_Oidem) ).

fof(fact_inf__idem,axiom,
    ! [X66,X58] :
      ( class_Lattices_Osemilattice__inf(X58)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X66),X66) = X66 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__idem) ).

fof(fact_Inf__fin_Oidem,axiom,
    ! [X66,X58] :
      ( class_Lattices_Olattice(X58)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X66),X66) = X66 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_Oidem) ).

fof(fact_Sup__fin_Oidem,axiom,
    ! [X66,X58] :
      ( class_Lattices_Olattice(X58)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X66),X66) = X66 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_Oidem) ).

fof(fact_sup__idem,axiom,
    ! [X66,X58] :
      ( class_Lattices_Osemilattice__sup(X58)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X66),X66) = X66 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__idem) ).

fof(fact_sup_Oidem,axiom,
    ! [X62,X58] :
      ( class_Lattices_Osemilattice__sup(X58)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X62),X62) = X62 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup_Oidem) ).

fof(fact_Max_Oidem,axiom,
    ! [X66,X58] :
      ( class_Orderings_Olinorder(X58)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(X58),X66),X66) = X66 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max_Oidem) ).

fof(fact_min__max_Osup_Oidem,axiom,
    ! [X62,X58] :
      ( class_Orderings_Olinorder(X58)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(X58),X62),X62) = X62 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Osup_Oidem) ).

fof(fact_Min_Oidem,axiom,
    ! [X66,X58] :
      ( class_Orderings_Olinorder(X58)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(X58),X66),X66) = X66 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min_Oidem) ).

fof(fact_min__max_Oinf_Oidem,axiom,
    ! [X62,X58] :
      ( class_Orderings_Olinorder(X58)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(X58),X62),X62) = X62 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Oinf_Oidem) ).

fof(fact_times_Oidem,axiom,
    ! [X62,X58] :
      ( class_Lattices_Oab__semigroup__idem__mult(X58)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X62) = X62 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_times_Oidem) ).

fof(fact_mult__idem,axiom,
    ! [X66,X58] :
      ( class_Lattices_Oab__semigroup__idem__mult(X58)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X66),X66) = X66 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__idem) ).

fof(fact_length__0__conv,axiom,
    ! [X239,X5] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> X239 = c_List_Olist_ONil(X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__0__conv) ).

fof(fact_mult__Min,axiom,
    ! [X96] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),X96) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X96),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__Min) ).

fof(fact_atLeast0LessThan,axiom,
    ! [X50] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X50) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X50),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeast0LessThan) ).

fof(fact_New__DSequence_Opos__single__def,axiom,
    ! [X299,X66,X58] : hAPP(c_New__DSequence_Opos__single(X58,X66),X299) = hAPP(c_Lazy__Sequence_Osingle(X58),X66),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_New__DSequence_Opos__single__def) ).

fof(fact_drop__0,axiom,
    ! [X242,X58] : hAPP(hAPP(c_List_Odrop(X58),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X242) = X242,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__0) ).

fof(fact_append__Nil2,axiom,
    ! [X242,X58] : hAPP(hAPP(c_List_Oappend(X58),X242),c_List_Olist_ONil(X58)) = X242,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__Nil2) ).

fof(fact_rev__rev__ident,axiom,
    ! [X242,X58] : hAPP(c_List_Orev(X58),hAPP(c_List_Orev(X58),X242)) = X242,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__rev__ident) ).

fof(fact_small__lazy__int__def,axiom,
    ! [X91] : c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint,X91) = c_Lazy__Sequence_Osmall__lazy_H(X91,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X91)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_small__lazy__int__def) ).

fof(fact_zmod__zero,axiom,
    ! [X90] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X90) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zero) ).

fof(fact_neg__nat,axiom,
    ! [X94] :
      ( hBOOL(hAPP(c_Nat__Numeral_Oneg,X94))
     => hAPP(c_Int_Onat,X94) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__nat) ).

fof(fact_atLeast__Suc__greaterThan,axiom,
    ! [X87] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,X87)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),X87),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeast__Suc__greaterThan) ).

fof(fact_lessThan__Suc__atMost,axiom,
    ! [X87] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X87)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X87),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lessThan__Suc__atMost) ).

fof(fact_less__eq__Suc__le__raw,axiom,
    ! [X50] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X50) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X50)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__Suc__le__raw) ).

fof(fact_DIVISION__BY__ZERO,axiom,
    ! [X62] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X62),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      & c_Divides_Odiv__class_Omod(tc_Int_Oint,X62,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X62 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DIVISION__BY__ZERO) ).

fof(fact_iszero__Numeral0,axiom,
    ! [X58] :
      ( class_Int_Onumber__ring(X58)
     => c_Int_Oiszero(X58,hAPP(c_Int_Onumber__class_Onumber__of(X58),c_Int_OPls)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_iszero__Numeral0) ).

fof(fact_List_Omap_Oid,axiom,
    ! [X5] : hAPP(c_List_Omap(X5,X5),c_Fun_Oid(X5)) = c_Fun_Oid(tc_List_Olist(X5)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_List_Omap_Oid) ).

fof(fact_List_Omap_Oidentity,axiom,
    ! [X5] : hAPP(c_List_Omap(X5,X5),c_COMBI(X5)) = c_Fun_Oid(tc_List_Olist(X5)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_List_Omap_Oidentity) ).

fof(fact_transfer__int__nat__relations_I1_J,axiom,
    ! [X33,X25] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X33)
    <=> X25 = X33 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__relations_I1_J) ).

fof(fact_int__int__eq,axiom,
    ! [X50,X95] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X95) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X50)
    <=> X95 = X50 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__int__eq) ).

fof(fact_zmod__self,axiom,
    ! [X62] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X62,X62) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__self) ).

fof(fact_rev__swap,axiom,
    ! [X251,X239,X5] :
      ( hAPP(c_List_Orev(X5),X239) = X251
    <=> X239 = hAPP(c_List_Orev(X5),X251) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__swap) ).

fof(fact_min__0L,axiom,
    ! [X57] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X57) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__0L) ).

fof(fact_diff__0__eq__0,axiom,
    ! [X57] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X57) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__0__eq__0) ).

fof(fact_zdiv__zero,axiom,
    ! [X90] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X90) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zero) ).

fof(fact_mult__0,axiom,
    ! [X57] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X57) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__0) ).

fof(fact_distinct_Osimps_I1_J,axiom,
    ! [X58] : hBOOL(hAPP(c_List_Odistinct(X58),c_List_Olist_ONil(X58))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct_Osimps_I1_J) ).

fof(fact_New__DSequence_Oneg__single__def,axiom,
    ! [X299,X66,X58] : hAPP(c_New__DSequence_Oneg__single(X58,X66),X299) = c_Lazy__Sequence_Ohb__single(X58,X66),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_New__DSequence_Oneg__single__def) ).

fof(fact_rtrancl__idemp,axiom,
    ! [X171,X5] : c_Transitive__Closure_Ortrancl(X5,c_Transitive__Closure_Ortrancl(X5,X171)) = c_Transitive__Closure_Ortrancl(X5,X171),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__idemp) ).

fof(fact_remdups__remdups,axiom,
    ! [X242,X58] : c_List_Oremdups(X58,c_List_Oremdups(X58,X242)) = c_List_Oremdups(X58,X242),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_remdups__remdups) ).

fof(fact_List_Oset_Osimps_I1_J,axiom,
    ! [X5] : hAPP(c_List_Oset(X5),c_List_Olist_ONil(X5)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_List_Oset_Osimps_I1_J) ).

fof(fact_max__0L,axiom,
    ! [X57] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X57) = X57,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__0L) ).

fof(fact_zmult__1,axiom,
    ! [X94] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X94) = X94,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__1) ).

fof(fact_nat__mult__1,axiom,
    ! [X57] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X57) = X57,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__1) ).

fof(fact_zadd__0,axiom,
    ! [X94] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X94) = X94,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__0) ).

fof(fact_plus__nat_Oadd__0,axiom,
    ! [X57] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X57) = X57,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0) ).

fof(fact_conversep__eq,axiom,
    ! [X5] : c_Predicate_Oconversep(X5,X5,c_fequal) = c_fequal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_conversep__eq) ).

fof(fact_not__neg__1,axiom,
    ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__neg__1) ).

fof(fact_not__neg__0,axiom,
    ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__neg__0) ).

fof(fact_zdiv__self,axiom,
    ! [X62] :
      ( X62 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X62),X62) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__self) ).

fof(fact_arith__simps_I31_J,axiom,
    ! [X58] :
      ( class_Int_Onumber__ring(X58)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X58),c_Groups_Oone__class_Oone(X58)) = hAPP(c_Int_Onumber__class_Onumber__of(X58),c_Int_OMin) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_arith__simps_I31_J) ).

fof(fact_number__of__Min,axiom,
    ! [X58] :
      ( class_Int_Onumber__ring(X58)
     => hAPP(c_Int_Onumber__class_Onumber__of(X58),c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(X58),c_Groups_Oone__class_Oone(X58)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__Min) ).

fof(fact_min__0R,axiom,
    ! [X57] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X57),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__0R) ).

fof(fact_mult__0__right,axiom,
    ! [X72] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X72),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__0__right) ).

fof(fact_neg__0__equal__iff__equal,axiom,
    ! [X6,X5] :
      ( class_Groups_Ogroup__add(X5)
     => ( c_Groups_Ozero__class_Ozero(X5) = hAPP(c_Groups_Ouminus__class_Ouminus(X5),X6)
      <=> c_Groups_Ozero__class_Ozero(X5) = X6 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__0__equal__iff__equal) ).

fof(fact_abs__eq__0,axiom,
    ! [X6,X5] :
      ( class_Groups_Oordered__ab__group__add__abs(X5)
     => ( hAPP(c_Groups_Oabs__class_Oabs(X5),X6) = c_Groups_Ozero__class_Ozero(X5)
      <=> X6 = c_Groups_Ozero__class_Ozero(X5) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__eq__0) ).

fof(fact_neg__equal__0__iff__equal,axiom,
    ! [X6,X5] :
      ( class_Groups_Ogroup__add(X5)
     => ( hAPP(c_Groups_Ouminus__class_Ouminus(X5),X6) = c_Groups_Ozero__class_Ozero(X5)
      <=> X6 = c_Groups_Ozero__class_Ozero(X5) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__equal__0__iff__equal) ).

fof(fact_max__0R,axiom,
    ! [X57] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X57),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X57,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__0R) ).

fof(fact_minus__nat_Odiff__0,axiom,
    ! [X72] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X72),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X72,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__nat_Odiff__0) ).

fof(fact_zmult__1__right,axiom,
    ! [X94] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X94),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X94,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__1__right) ).

fof(fact_nat__mult__1__right,axiom,
    ! [X57] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X57),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X57,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__1__right) ).

fof(fact_zadd__0__right,axiom,
    ! [X94] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X94),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X94,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__0__right) ).

fof(fact_Nat_Oadd__0__right,axiom,
    ! [X72] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X72),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X72,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).

fof(fact_card__lessThan,axiom,
    ! [X159] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X159)) = X159,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__lessThan) ).

fof(fact_zminus__zminus,axiom,
    ! [X94] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X94)) = X94,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zminus__zminus) ).

fof(fact_filter_Osimps_I1_J,axiom,
    ! [X18,X5] : hAPP(c_List_Ofilter(X5,X18),c_List_Olist_ONil(X5)) = c_List_Olist_ONil(X5),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter_Osimps_I1_J) ).

fof(fact_finite__code,axiom,
    ! [X21,X5] :
      ( class_Finite__Set_Ofinite(X5)
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__code) ).

fof(fact_finite,axiom,
    ! [X21,X5] :
      ( class_Finite__Set_Ofinite(X5)
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite) ).

fof(fact_of__int__eq__0__iff,axiom,
    ! [X120,X5] :
      ( class_Int_Oring__char__0(X5)
     => ( hAPP(c_Int_Oring__1__class_Oof__int(X5),X120) = c_Groups_Ozero__class_Ozero(X5)
      <=> X120 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__eq__0__iff) ).

fof(fact_of__int__0__eq__iff,axiom,
    ! [X120,X5] :
      ( class_Int_Oring__char__0(X5)
     => ( c_Groups_Ozero__class_Ozero(X5) = hAPP(c_Int_Oring__1__class_Oof__int(X5),X120)
      <=> X120 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__0__eq__iff) ).

fof(fact_diff__self__eq__0,axiom,
    ! [X72] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X72),X72) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__self__eq__0) ).

fof(fact_lazy__sequence_Osize_I1_J,axiom,
    ! [X80,X5] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X5,X80),c_Lazy__Sequence_Olazy__sequence_OEmpty(X5)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lazy__sequence_Osize_I1_J) ).

fof(fact_number__of__eq,axiom,
    ! [X96,X58] :
      ( class_Int_Onumber__ring(X58)
     => hAPP(c_Int_Onumber__class_Onumber__of(X58),X96) = hAPP(c_Int_Oring__1__class_Oof__int(X58),X96) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__eq) ).

fof(fact_com_Osimps_I5_J,axiom,
    ! [X8,X92,X11,X84] :
      ( c_Com_Ocom_OWhile(X84,X11) = c_Com_Ocom_OWhile(X92,X8)
    <=> ( X84 = X92
        & X11 = X8 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I5_J) ).

fof(fact_com_Osimps_I1_J,axiom,
    ! [X92,X93,X84,X85] :
      ( c_Com_Ocom_OAss(X85,X84) = c_Com_Ocom_OAss(X93,X92)
    <=> ( X85 = X93
        & X84 = X92 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I1_J) ).

fof(fact_com_Osimps_I3_J,axiom,
    ! [X39,X40,X41,X42] :
      ( c_Com_Ocom_OSemi(X42,X41) = c_Com_Ocom_OSemi(X40,X39)
    <=> ( X42 = X40
        & X41 = X39 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I3_J) ).

fof(fact_neg__equal__zero,axiom,
    ! [X6,X5] :
      ( class_Groups_Olinordered__ab__group__add(X5)
     => ( hAPP(c_Groups_Ouminus__class_Ouminus(X5),X6) = X6
      <=> X6 = c_Groups_Ozero__class_Ozero(X5) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__equal__zero) ).

fof(fact_equal__neg__zero,axiom,
    ! [X6,X5] :
      ( class_Groups_Olinordered__ab__group__add(X5)
     => ( X6 = hAPP(c_Groups_Ouminus__class_Ouminus(X5),X6)
      <=> X6 = c_Groups_Ozero__class_Ozero(X5) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equal__neg__zero) ).

fof(fact_com_Osize_I10_J,axiom,
    ! [X84,X85] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OAss(X85,X84)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osize_I10_J) ).

fof(fact_diff__bin__simps_I1_J,axiom,
    ! [X96] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X96),c_Int_OPls) = X96,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__bin__simps_I1_J) ).

fof(fact_add__Pls__right,axiom,
    ! [X96] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X96),c_Int_OPls) = X96,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Pls__right) ).

fof(fact_nat__int,axiom,
    ! [X57] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X57)) = X57,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__int) ).

fof(arity_prod__Lazy__Sequence_Osmall__lazy,axiom,
    ! [X313,X312] :
      ( ( class_Lazy__Sequence_Osmall__lazy(X312)
        & class_Lazy__Sequence_Osmall__lazy(X313) )
     => class_Lazy__Sequence_Osmall__lazy(tc_prod(X312,X313)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_prod__Lazy__Sequence_Osmall__lazy) ).

fof(arity_sum__Enum_Oenum,axiom,
    ! [X313,X312] :
      ( ( class_Enum_Oenum(X312)
        & class_Enum_Oenum(X313) )
     => class_Enum_Oenum(tc_sum(X312,X313)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_sum__Enum_Oenum) ).

fof(arity_prod__Enum_Oenum,axiom,
    ! [X313,X312] :
      ( ( class_Enum_Oenum(X312)
        & class_Enum_Oenum(X313) )
     => class_Enum_Oenum(tc_prod(X312,X313)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_prod__Enum_Oenum) ).

fof(arity_fun__Enum_Oenum,axiom,
    ! [X313,X312] :
      ( ( class_Enum_Oenum(X312)
        & class_Enum_Oenum(X313) )
     => class_Enum_Oenum(tc_fun(X312,X313)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Enum_Oenum) ).

fof(arity_sum__Finite__Set_Ofinite,axiom,
    ! [X313,X312] :
      ( ( class_Finite__Set_Ofinite(X312)
        & class_Finite__Set_Ofinite(X313) )
     => class_Finite__Set_Ofinite(tc_sum(X312,X313)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_sum__Finite__Set_Ofinite) ).

fof(arity_prod__Finite__Set_Ofinite,axiom,
    ! [X313,X312] :
      ( ( class_Finite__Set_Ofinite(X312)
        & class_Finite__Set_Ofinite(X313) )
     => class_Finite__Set_Ofinite(tc_prod(X312,X313)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_prod__Finite__Set_Ofinite) ).

fof(arity_fun__Finite__Set_Ofinite,axiom,
    ! [X313,X312] :
      ( ( class_Finite__Set_Ofinite(X312)
        & class_Finite__Set_Ofinite(X313) )
     => class_Finite__Set_Ofinite(tc_fun(X312,X313)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Finite__Set_Ofinite) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J,axiom,
    ! [X65,X66] :
      ( c_Nat__Transfer_Ois__nat(X66)
     => ( c_Nat__Transfer_Ois__nat(X65)
       => c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(X66,X65)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J) ).

fof(fact_com_Osimps_I29_J,axiom,
    ! [X84,X85,X8,X92] : c_Com_Ocom_OWhile(X92,X8) != c_Com_Ocom_OAss(X85,X84),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I29_J) ).

fof(fact_com_Osimps_I47_J,axiom,
    ! [X41,X42,X8,X92] : c_Com_Ocom_OWhile(X92,X8) != c_Com_Ocom_OSemi(X42,X41),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I47_J) ).

fof(fact_com_Osimps_I28_J,axiom,
    ! [X8,X92,X84,X85] : c_Com_Ocom_OAss(X85,X84) != c_Com_Ocom_OWhile(X92,X8),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I28_J) ).

fof(fact_com_Osimps_I46_J,axiom,
    ! [X8,X92,X41,X42] : c_Com_Ocom_OSemi(X42,X41) != c_Com_Ocom_OWhile(X92,X8),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I46_J) ).

fof(fact_com_Osimps_I24_J,axiom,
    ! [X39,X40,X84,X85] : c_Com_Ocom_OAss(X85,X84) != c_Com_Ocom_OSemi(X40,X39),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I24_J) ).

fof(fact_com_Osimps_I25_J,axiom,
    ! [X84,X85,X39,X40] : c_Com_Ocom_OSemi(X40,X39) != c_Com_Ocom_OAss(X85,X84),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I25_J) ).

fof(fact_add__Pls,axiom,
    ! [X96] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X96) = X96,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Pls) ).

fof(fact_rev__is__Nil__conv,axiom,
    ! [X239,X5] :
      ( hAPP(c_List_Orev(X5),X239) = c_List_Olist_ONil(X5)
    <=> X239 = c_List_Olist_ONil(X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__is__Nil__conv) ).

fof(fact_rotate1__is__Nil__conv,axiom,
    ! [X239,X5] :
      ( hAPP(c_List_Orotate1(X5),X239) = c_List_Olist_ONil(X5)
    <=> X239 = c_List_Olist_ONil(X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate1__is__Nil__conv) ).

fof(fact_Nil__is__rev__conv,axiom,
    ! [X239,X5] :
      ( c_List_Olist_ONil(X5) = hAPP(c_List_Orev(X5),X239)
    <=> X239 = c_List_Olist_ONil(X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nil__is__rev__conv) ).

fof(fact_mult__Pls,axiom,
    ! [X128] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),X128) = c_Int_OPls,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__Pls) ).

fof(fact_trans__finite__psubset,axiom,
    ! [X5] : c_Relation_Otrans(tc_fun(X5,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(X5)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__finite__psubset) ).

fof(fact_wf__finite__psubset,axiom,
    ! [X5] : c_Wellfounded_Owf(tc_fun(X5,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(X5)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__finite__psubset) ).

fof(fact_com_Osize_I15_J,axiom,
    ! [X81] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),hAPP(c_Com_Ocom_OBODY,X81)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osize_I15_J) ).

fof(fact_transpose_Osimps_I1_J,axiom,
    ! [X58] : c_List_Otranspose(X58,c_List_Olist_ONil(tc_List_Olist(X58))) = c_List_Olist_ONil(tc_List_Olist(X58)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose_Osimps_I1_J) ).

fof(fact_com_Osimps_I59_J,axiom,
    ! [X11,X84,X43] : hAPP(c_Com_Ocom_OBODY,X43) != c_Com_Ocom_OWhile(X84,X11),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I59_J) ).

fof(fact_com_Osimps_I31_J,axiom,
    ! [X84,X85,X43] : hAPP(c_Com_Ocom_OBODY,X43) != c_Com_Ocom_OAss(X85,X84),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I31_J) ).

fof(fact_com_Osimps_I49_J,axiom,
    ! [X37,X38,X36] : hAPP(c_Com_Ocom_OBODY,X36) != c_Com_Ocom_OSemi(X38,X37),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I49_J) ).

fof(fact_com_Osimps_I58_J,axiom,
    ! [X43,X11,X84] : c_Com_Ocom_OWhile(X84,X11) != hAPP(c_Com_Ocom_OBODY,X43),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I58_J) ).

fof(fact_com_Osimps_I30_J,axiom,
    ! [X43,X84,X85] : c_Com_Ocom_OAss(X85,X84) != hAPP(c_Com_Ocom_OBODY,X43),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I30_J) ).

fof(fact_com_Osimps_I48_J,axiom,
    ! [X36,X37,X38] : c_Com_Ocom_OSemi(X38,X37) != hAPP(c_Com_Ocom_OBODY,X36),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I48_J) ).

fof(fact_succ__Min,axiom,
    c_Int_Osucc(c_Int_OMin) = c_Int_OPls,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_succ__Min) ).

fof(fact_Bit0__Pls,axiom,
    c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bit0__Pls) ).

fof(fact_pred__Pls,axiom,
    c_Int_Opred(c_Int_OPls) = c_Int_OMin,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__Pls) ).

fof(fact_Code__Numeral_Onat__of__inject,axiom,
    ! [X156,X87] :
      ( hAPP(c_Code__Numeral_Onat__of,X87) = hAPP(c_Code__Numeral_Onat__of,X156)
    <=> X87 = X156 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Code__Numeral_Onat__of__inject) ).

fof(fact_code__numeral_Onat__of__inject,axiom,
    ! [X33,X25] :
      ( hAPP(c_Code__Numeral_Onat__of,X25) = hAPP(c_Code__Numeral_Onat__of,X33)
    <=> X25 = X33 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_code__numeral_Onat__of__inject) ).

fof(fact_Code__Numeral_Oof__nat__inject,axiom,
    ! [X95,X50] :
      ( hAPP(c_Code__Numeral_Oof__nat,X50) = hAPP(c_Code__Numeral_Oof__nat,X95)
    <=> X50 = X95 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Code__Numeral_Oof__nat__inject) ).

fof(fact_Rep__Integ__inject,axiom,
    ! [X33,X25] :
      ( hAPP(c_Int_ORep__Integ,X25) = hAPP(c_Int_ORep__Integ,X33)
    <=> X25 = X33 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Rep__Integ__inject) ).

fof(fact_nat_Oinject,axiom,
    ! [X67,X68] :
      ( hAPP(c_Nat_OSuc,X68) = hAPP(c_Nat_OSuc,X67)
    <=> X68 = X67 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Oinject) ).

fof(fact_Suc__inject,axiom,
    ! [X65,X66] :
      ( hAPP(c_Nat_OSuc,X66) = hAPP(c_Nat_OSuc,X65)
     => X66 = X65 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__inject) ).

fof(fact_com_Osimps_I6_J,axiom,
    ! [X43,X44] :
      ( hAPP(c_Com_Ocom_OBODY,X44) = hAPP(c_Com_Ocom_OBODY,X43)
    <=> X44 = X43 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I6_J) ).

fof(fact_sgn__0__0,axiom,
    ! [X6,X5] :
      ( class_Rings_Olinordered__idom(X5)
     => ( c_Groups_Osgn__class_Osgn(X5,X6) = c_Groups_Ozero__class_Ozero(X5)
      <=> X6 = c_Groups_Ozero__class_Ozero(X5) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__0__0) ).

fof(fact_lazy__sequence_Osize_I3_J,axiom,
    ! [X58] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X58)),c_Lazy__Sequence_Olazy__sequence_OEmpty(X58)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lazy__sequence_Osize_I3_J) ).

fof(fact_list_Osize_I3_J,axiom,
    ! [X58] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),c_List_Olist_ONil(X58)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list_Osize_I3_J) ).

fof(fact_sym__Id__on,axiom,
    ! [X21,X5] : c_Relation_Osym(X5,c_Relation_OId__on(X5,X21)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sym__Id__on) ).

fof(fact_antisym__Id__on,axiom,
    ! [X21,X5] : c_Relation_Oantisym(X5,c_Relation_OId__on(X5,X21)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_antisym__Id__on) ).

fof(fact_trans__rtrancl,axiom,
    ! [X171,X5] : c_Relation_Otrans(X5,c_Transitive__Closure_Ortrancl(X5,X171)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__rtrancl) ).

fof(fact_trans__Id__on,axiom,
    ! [X21,X5] : c_Relation_Otrans(X5,c_Relation_OId__on(X5,X21)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__Id__on) ).

fof(fact_wf__measures,axiom,
    ! [X290,X5] : c_Wellfounded_Owf(X5,c_List_Omeasures(X5,X290)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__measures) ).

fof(fact_sorted__upto,axiom,
    ! [X97,X98] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(X98,X97)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__upto) ).

fof(fact_some__sym__eq__trivial,axiom,
    ! [X25,X5] : c_Hilbert__Choice_OEps(X5,hAPP(c_fequal,X25)) = X25,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_some__sym__eq__trivial) ).

fof(fact_the__sym__eq__trivial,axiom,
    ! [X25,X5] : c_HOL_OThe(X5,hAPP(c_fequal,X25)) = X25,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__sym__eq__trivial) ).

fof(fact_listsum__simps_I1_J,axiom,
    ! [X58] :
      ( class_Groups_Omonoid__add(X58)
     => hAPP(c_List_Omonoid__add__class_Olistsum(X58),c_List_Olist_ONil(X58)) = c_Groups_Ozero__class_Ozero(X58) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__simps_I1_J) ).

fof(fact_abs__one,axiom,
    ! [X58] :
      ( class_Rings_Olinordered__idom(X58)
     => hAPP(c_Groups_Oabs__class_Oabs(X58),c_Groups_Oone__class_Oone(X58)) = c_Groups_Oone__class_Oone(X58) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__one) ).

fof(fact_abs__zero,axiom,
    ! [X58] :
      ( class_Groups_Oordered__ab__group__add__abs(X58)
     => hAPP(c_Groups_Oabs__class_Oabs(X58),c_Groups_Ozero__class_Ozero(X58)) = c_Groups_Ozero__class_Ozero(X58) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__zero) ).

fof(fact_compl__top__eq,axiom,
    ! [X58] :
      ( class_Lattices_Oboolean__algebra(X58)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X58),c_Orderings_Otop__class_Otop(X58)) = c_Orderings_Obot__class_Obot(X58) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compl__top__eq) ).

fof(fact_minus__zero,axiom,
    ! [X58] :
      ( class_Groups_Ogroup__add(X58)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X58),c_Groups_Ozero__class_Ozero(X58)) = c_Groups_Ozero__class_Ozero(X58) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__zero) ).

fof(fact_compl__bot__eq,axiom,
    ! [X58] :
      ( class_Lattices_Oboolean__algebra(X58)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X58),c_Orderings_Obot__class_Obot(X58)) = c_Orderings_Otop__class_Otop(X58) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compl__bot__eq) ).

fof(arity_fun__Lattices_Obounded__lattice,axiom,
    ! [X312,X313] :
      ( class_Lattices_Obounded__lattice(X313)
     => class_Lattices_Obounded__lattice(tc_fun(X312,X313)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Obounded__lattice) ).

fof(arity_fun__Lattices_Obounded__lattice__top,axiom,
    ! [X312,X313] :
      ( class_Lattices_Obounded__lattice(X313)
     => class_Lattices_Obounded__lattice__top(tc_fun(X312,X313)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Obounded__lattice__top) ).

fof(arity_fun__Orderings_Otop,axiom,
    ! [X312,X313] :
      ( class_Orderings_Otop(X313)
     => class_Orderings_Otop(tc_fun(X312,X313)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Otop) ).

fof(arity_fun__Complete__Lattice_Ocomplete__lattice,axiom,
    ! [X312,X313] :
      ( class_Complete__Lattice_Ocomplete__lattice(X313)
     => class_Complete__Lattice_Ocomplete__lattice(tc_fun(X312,X313)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Complete__Lattice_Ocomplete__lattice) ).

fof(arity_fun__Lattices_Odistrib__lattice,axiom,
    ! [X312,X313] :
      ( class_Lattices_Odistrib__lattice(X313)
     => class_Lattices_Odistrib__lattice(tc_fun(X312,X313)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Odistrib__lattice) ).

fof(arity_fun__Lattices_Osemilattice__inf,axiom,
    ! [X312,X313] :
      ( class_Lattices_Olattice(X313)
     => class_Lattices_Osemilattice__inf(tc_fun(X312,X313)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Osemilattice__inf) ).

fof(arity_fun__Lattices_Olattice,axiom,
    ! [X312,X313] :
      ( class_Lattices_Olattice(X313)
     => class_Lattices_Olattice(tc_fun(X312,X313)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Olattice) ).

fof(arity_fun__Lattices_Osemilattice__sup,axiom,
    ! [X312,X313] :
      ( class_Lattices_Olattice(X313)
     => class_Lattices_Osemilattice__sup(tc_fun(X312,X313)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Osemilattice__sup) ).

fof(arity_fun__Lattices_Obounded__lattice__bot,axiom,
    ! [X312,X313] :
      ( class_Lattices_Obounded__lattice(X313)
     => class_Lattices_Obounded__lattice__bot(tc_fun(X312,X313)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Obounded__lattice__bot) ).

fof(arity_fun__Groups_Ominus,axiom,
    ! [X312,X313] :
      ( class_Groups_Ominus(X313)
     => class_Groups_Ominus(tc_fun(X312,X313)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Groups_Ominus) ).

fof(arity_fun__Groups_Ouminus,axiom,
    ! [X312,X313] :
      ( class_Groups_Ouminus(X313)
     => class_Groups_Ouminus(tc_fun(X312,X313)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Groups_Ouminus) ).

fof(arity_fun__Lattices_Oboolean__algebra,axiom,
    ! [X312,X313] :
      ( class_Lattices_Oboolean__algebra(X313)
     => class_Lattices_Oboolean__algebra(tc_fun(X312,X313)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Oboolean__algebra) ).

fof(arity_fun__Orderings_Oord,axiom,
    ! [X312,X313] :
      ( class_Orderings_Oord(X313)
     => class_Orderings_Oord(tc_fun(X312,X313)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Oord) ).

fof(arity_fun__Orderings_Oorder,axiom,
    ! [X312,X313] :
      ( class_Orderings_Oorder(X313)
     => class_Orderings_Oorder(tc_fun(X312,X313)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Oorder) ).

fof(arity_fun__Orderings_Opreorder,axiom,
    ! [X312,X313] :
      ( class_Orderings_Opreorder(X313)
     => class_Orderings_Opreorder(tc_fun(X312,X313)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Opreorder) ).

fof(arity_fun__Orderings_Obot,axiom,
    ! [X312,X313] :
      ( class_Orderings_Obot(X313)
     => class_Orderings_Obot(tc_fun(X312,X313)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Obot) ).

fof(fact_equivp__implies__part__equivp,axiom,
    ! [X32,X5] :
      ( c_Equiv__Relations_Oequivp(X5,X32)
     => c_Equiv__Relations_Opart__equivp(X5,X32) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equivp__implies__part__equivp) ).

fof(fact_wf__acyclic,axiom,
    ! [X171,X5] :
      ( c_Wellfounded_Owf(X5,X171)
     => c_Wellfounded_Oacyclic(X5,X171) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__acyclic) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J,axiom,
    ! [X94] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X94)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J) ).

fof(fact_nat__of__of__nat,axiom,
    ! [X57] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,X57)) = X57,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__of__of__nat) ).

fof(fact_nat__of__inverse,axiom,
    ! [X66] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X66)) = X66,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__of__inverse) ).

fof(fact_of__nat__nat__of,axiom,
    ! [X96] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X96)) = X96,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__nat__of) ).

fof(fact_Rep__Integ__inverse,axiom,
    ! [X25] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,X25)) = X25,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Rep__Integ__inverse) ).

fof(fact_iszero__def,axiom,
    ! [X120,X5] :
      ( class_Rings_Osemiring__1(X5)
     => ( c_Int_Oiszero(X5,X120)
      <=> X120 = c_Groups_Ozero__class_Ozero(X5) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_iszero__def) ).

fof(fact_int__eq__0__conv,axiom,
    ! [X50] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X50) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    <=> X50 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__eq__0__conv) ).

fof(fact_of__int__1,axiom,
    ! [X58] :
      ( class_Rings_Oring__1(X58)
     => hAPP(c_Int_Oring__1__class_Oof__int(X58),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(X58) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__1) ).

fof(fact_of__int__0,axiom,
    ! [X58] :
      ( class_Rings_Oring__1(X58)
     => hAPP(c_Int_Oring__1__class_Oof__int(X58),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(X58) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__0) ).

fof(fact_of__nat__1,axiom,
    ! [X58] :
      ( class_Rings_Osemiring__1(X58)
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X58),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X58) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__1) ).

fof(fact_of__nat__0,axiom,
    ! [X58] :
      ( class_Rings_Osemiring__1(X58)
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X58),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(X58) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__0) ).

fof(fact_int__number__of__def,axiom,
    ! [X128] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X128),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__number__of__def) ).

fof(fact_remdups__eq__nil__iff,axiom,
    ! [X25,X5] :
      ( c_List_Oremdups(X5,X25) = c_List_Olist_ONil(X5)
    <=> X25 = c_List_Olist_ONil(X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_remdups__eq__nil__iff) ).

fof(fact_remdups__eq__nil__right__iff,axiom,
    ! [X25,X5] :
      ( c_List_Olist_ONil(X5) = c_List_Oremdups(X5,X25)
    <=> X25 = c_List_Olist_ONil(X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_remdups__eq__nil__right__iff) ).

fof(fact_com_Osize_I2_J,axiom,
    ! [X84,X85] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OAss(X85,X84)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osize_I2_J) ).

fof(fact_sgn0,axiom,
    ! [X58] :
      ( class_Groups_Osgn__if(X58)
     => c_Groups_Osgn__class_Osgn(X58,c_Groups_Ozero__class_Ozero(X58)) = c_Groups_Ozero__class_Ozero(X58) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn0) ).

fof(fact_max__ord__max,axiom,
    ! [X5] :
      ( class_Orderings_Oord(X5)
     => c_Orderings_Oord__class_Omax(X5) = c_Orderings_Oord_Omax(X5,c_Orderings_Oord__class_Oless__eq(X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__ord__max) ).

fof(fact_min__ord__min,axiom,
    ! [X5] :
      ( class_Orderings_Oord(X5)
     => c_Orderings_Oord__class_Omin(X5) = c_Orderings_Oord_Omin(X5,c_Orderings_Oord__class_Oless__eq(X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__ord__min) ).

fof(fact_rev_Osimps_I1_J,axiom,
    ! [X58] : hAPP(c_List_Orev(X58),c_List_Olist_ONil(X58)) = c_List_Olist_ONil(X58),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev_Osimps_I1_J) ).

fof(fact_tl_Osimps_I1_J,axiom,
    ! [X58] : hAPP(c_List_Otl(X58),c_List_Olist_ONil(X58)) = c_List_Olist_ONil(X58),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tl_Osimps_I1_J) ).

fof(arity_sum__Nat_Osize,axiom,
    ! [X313,X312] : class_Nat_Osize(tc_sum(X312,X313)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_sum__Nat_Osize) ).

fof(arity_prod__Nat_Osize,axiom,
    ! [X313,X312] : class_Nat_Osize(tc_prod(X312,X313)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_prod__Nat_Osize) ).

fof(arity_Nitpick__Opair____box__Nat_Osize,axiom,
    ! [X313,X312] : class_Nat_Osize(tc_Nitpick_Opair__box(X312,X313)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nitpick__Opair____box__Nat_Osize) ).

fof(fact_number__of__Pls,axiom,
    ! [X58] :
      ( class_Int_Onumber__ring(X58)
     => hAPP(c_Int_Onumber__class_Onumber__of(X58),c_Int_OPls) = c_Groups_Ozero__class_Ozero(X58) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__Pls) ).

fof(fact_semiring__norm_I112_J,axiom,
    ! [X58] :
      ( class_Int_Onumber__ring(X58)
     => c_Groups_Ozero__class_Ozero(X58) = hAPP(c_Int_Onumber__class_Onumber__of(X58),c_Int_OPls) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_semiring__norm_I112_J) ).

fof(fact_com_Osize_I7_J,axiom,
    ! [X81] : c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY,X81)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osize_I7_J) ).

fof(fact_sorted_Oequations_I1_J,axiom,
    ! [X58] :
      ( class_Orderings_Olinorder(X58)
     => c_List_Olinorder__class_Osorted(X58,c_List_Olist_ONil(X58)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted_Oequations_I1_J) ).

fof(fact_sorted_ONil,axiom,
    ! [X58] :
      ( class_Orderings_Olinorder(X58)
     => c_List_Olinorder__class_Osorted(X58,c_List_Olist_ONil(X58)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted_ONil) ).

fof(fact_iszero__0,axiom,
    ! [X58] :
      ( class_Rings_Osemiring__1(X58)
     => c_Int_Oiszero(X58,c_Groups_Ozero__class_Ozero(X58)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_iszero__0) ).

fof(fact_New__DSequence_Opos__empty__def,axiom,
    ! [X299,X58] : hAPP(c_New__DSequence_Opos__empty(X58),X299) = c_Lazy__Sequence_Oempty(X58),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_New__DSequence_Opos__empty__def) ).

fof(fact_remdups_Osimps_I1_J,axiom,
    ! [X58] : c_List_Oremdups(X58,c_List_Olist_ONil(X58)) = c_List_Olist_ONil(X58),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_remdups_Osimps_I1_J) ).

fof(fact_butlast_Osimps_I1_J,axiom,
    ! [X58] : c_List_Obutlast(X58,c_List_Olist_ONil(X58)) = c_List_Olist_ONil(X58),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_butlast_Osimps_I1_J) ).

fof(fact_Suc__neq__Zero,axiom,
    ! [X72] : hAPP(c_Nat_OSuc,X72) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__neq__Zero) ).

fof(fact_nat_Osimps_I3_J,axiom,
    ! [X74] : hAPP(c_Nat_OSuc,X74) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osimps_I3_J) ).

fof(fact_Suc__not__Zero,axiom,
    ! [X72] : hAPP(c_Nat_OSuc,X72) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__not__Zero) ).

fof(fact_Zero__neq__Suc,axiom,
    ! [X72] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X72),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).

fof(fact_nat_Osimps_I2_J,axiom,
    ! [X73] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X73),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osimps_I2_J) ).

fof(fact_Zero__not__Suc,axiom,
    ! [X72] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X72),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).

fof(fact_nat_Oexhaust,axiom,
    ! [X65] :
      ( X65 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
     => ~ ! [X88] : X65 != hAPP(c_Nat_OSuc,X88) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Oexhaust) ).

fof(fact_not0__implies__Suc,axiom,
    ! [X57] :
      ( X57 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
     => ? [X86] : X57 = hAPP(c_Nat_OSuc,X86) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not0__implies__Suc) ).

fof(fact_com_Osimps_I17_J,axiom,
    ! [X8,X92] : c_Com_Ocom_OWhile(X92,X8) != c_Com_Ocom_OSKIP,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I17_J) ).

fof(fact_com_Osimps_I9_J,axiom,
    ! [X92,X93] : c_Com_Ocom_OAss(X93,X92) != c_Com_Ocom_OSKIP,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I9_J) ).

fof(fact_com_Osimps_I13_J,axiom,
    ! [X34,X35] : c_Com_Ocom_OSemi(X35,X34) != c_Com_Ocom_OSKIP,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I13_J) ).

fof(fact_com_Osimps_I16_J,axiom,
    ! [X8,X92] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(X92,X8),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I16_J) ).

fof(fact_com_Osimps_I8_J,axiom,
    ! [X92,X93] : c_Com_Ocom_OSKIP != c_Com_Ocom_OAss(X93,X92),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I8_J) ).

fof(fact_com_Osimps_I12_J,axiom,
    ! [X34,X35] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(X35,X34),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I12_J) ).

fof(fact_inf__min,axiom,
    ! [X5] :
      ( ( class_Lattices_Osemilattice__inf(X5)
        & class_Orderings_Olinorder(X5) )
     => c_Lattices_Osemilattice__inf__class_Oinf(X5) = c_Orderings_Oord__class_Omin(X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__min) ).

fof(fact_sup__max,axiom,
    ! [X5] :
      ( ( class_Lattices_Osemilattice__sup(X5)
        & class_Orderings_Olinorder(X5) )
     => c_Lattices_Osemilattice__sup__class_Osup(X5) = c_Orderings_Oord__class_Omax(X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__max) ).

fof(fact_Suc__n__not__n,axiom,
    ! [X57] : hAPP(c_Nat_OSuc,X57) != X57,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).

fof(fact_n__not__Suc__n,axiom,
    ! [X57] : X57 != hAPP(c_Nat_OSuc,X57),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).

fof(fact_id__apply,axiom,
    ! [X66,X58] : hAPP(c_Fun_Oid(X58),X66) = X66,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_id__apply) ).

fof(fact_id__def,axiom,
    ! [X240,X58] : hAPP(c_Fun_Oid(X58),X240) = X240,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_id__def) ).

fof(fact_Collect__def,axiom,
    ! [X18,X5] : hAPP(c_Set_OCollect(X5),X18) = X18,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__def) ).

fof(help_c__COMBI__1,axiom,
    ! [X49,X58] : hAPP(c_COMBI(X58),X49) = X49,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBI__1) ).

fof(fact_one__neq__zero,axiom,
    ! [X58] :
      ( class_Rings_Ozero__neq__one(X58)
     => c_Groups_Oone__class_Oone(X58) != c_Groups_Ozero__class_Ozero(X58) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__neq__zero) ).

fof(fact_zero__neq__one,axiom,
    ! [X58] :
      ( class_Rings_Ozero__neq__one(X58)
     => c_Groups_Ozero__class_Ozero(X58) != c_Groups_Oone__class_Oone(X58) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__neq__one) ).

fof(fact_com_Osimps_I19_J,axiom,
    ! [X36] : hAPP(c_Com_Ocom_OBODY,X36) != c_Com_Ocom_OSKIP,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I19_J) ).

fof(fact_com_Osimps_I18_J,axiom,
    ! [X36] : c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,X36),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I18_J) ).

fof(fact_beyond__zero,axiom,
    ! [X96] : c_Quickcheck_Obeyond(X96,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_beyond__zero) ).

fof(fact_wf__int__ge__less__than2,axiom,
    ! [X22] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(X22)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__int__ge__less__than2) ).

fof(fact_wf__int__ge__less__than,axiom,
    ! [X22] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(X22)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__int__ge__less__than) ).

fof(fact_number__of__is__id,axiom,
    ! [X96] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X96) = X96,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__is__id) ).

fof(fact_nat__size,axiom,
    ! [X57] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X57) = X57,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__size) ).

fof(arity_List__Olist__Lazy__Sequence_Osmall__lazy,axiom,
    ! [X313] :
      ( class_Lazy__Sequence_Osmall__lazy(X313)
     => class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(X313)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_List__Olist__Lazy__Sequence_Osmall__lazy) ).

fof(arity_Option__Ooption__Enum_Oenum,axiom,
    ! [X313] :
      ( class_Enum_Oenum(X313)
     => class_Enum_Oenum(tc_Option_Ooption(X313)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Option__Ooption__Enum_Oenum) ).

fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom,
    ! [X313] :
      ( class_Finite__Set_Ofinite(X313)
     => class_Finite__Set_Ofinite(tc_Option_Ooption(X313)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Option__Ooption__Finite__Set_Ofinite) ).

fof(fact_identity__equivp,axiom,
    ! [X5] : c_Equiv__Relations_Oequivp(X5,c_fequal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_identity__equivp) ).

fof(arity_Lazy____Sequence__Olazy____sequence__Nat_Osize,axiom,
    ! [X313] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(X313)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Lazy____Sequence__Olazy____sequence__Nat_Osize) ).

fof(arity_List__Olist__Nat_Osize,axiom,
    ! [X313] : class_Nat_Osize(tc_List_Olist(X313)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_List__Olist__Nat_Osize) ).

fof(arity_Option__Ooption__Nat_Osize,axiom,
    ! [X313] : class_Nat_Osize(tc_Option_Ooption(X313)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Option__Ooption__Nat_Osize) ).

fof(arity_Hoare____Mirabelle__Otriple__Nat_Osize,axiom,
    ! [X313] : class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(X313)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Hoare____Mirabelle__Otriple__Nat_Osize) ).

fof(help_c__fFalse__1,axiom,
    ~ hBOOL(c_fFalse),
    file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_Nitpick_OFrac__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/sandbox/benchmark/theBenchmark.p',fact_max__weak__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/sandbox/benchmark/theBenchmark.p',fact_min__weak__def) ).

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/sandbox/benchmark/theBenchmark.p',fact_min__rpair__set) ).

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/sandbox/benchmark/theBenchmark.p',fact_max__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/sandbox/benchmark/theBenchmark.p',fact_pred__nat__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/sandbox/benchmark/theBenchmark.p',fact_One__int__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/sandbox/benchmark/theBenchmark.p',fact_Zero__int__def) ).

fof(conj_0,hypothesis,
    c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

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/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_type__definition__code__numeral) ).

fof(fact_wf__less,axiom,
    c_Wellfounded_Owf(tc_Nat_Onat,hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)))),
    file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_UN__atLeast__UNIV) ).

fof(fact_UN__lessThan__UNIV,axiom,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__lessThan__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/sandbox/benchmark/theBenchmark.p',fact_UN__atMost__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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_greaterThan__0) ).

fof(fact_number__of2,axiom,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))),
    file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_atMost__0) ).

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/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).

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/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).

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/sandbox/benchmark/theBenchmark.p',fact_int__0__less__1) ).

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/sandbox/benchmark/theBenchmark.p',fact_bin__less__0__simps_I2_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/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I19_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/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I23_J) ).

fof(fact_rel__simps_I24_J,axiom,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I24_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/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I6_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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_lessThan__0) ).

fof(fact_wf__pair__less,axiom,
    c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__pair__less) ).

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/sandbox/benchmark/theBenchmark.p',fact_min__strict__def) ).

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/sandbox/benchmark/theBenchmark.p',fact_max__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/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_zminus__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/sandbox/benchmark/theBenchmark.p',fact_int__1) ).

fof(fact_int__0,axiom,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__0) ).

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/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_nat_Osize_I3_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/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__numerals_I2_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/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__numerals_I1_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/sandbox/benchmark/theBenchmark.p',fact_Int_OMin__def) ).

fof(fact_nat__number__of__Pls,axiom,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__number__of__Pls) ).

fof(fact_com_Osize_I9_J,axiom,
    hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osize_I9_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/sandbox/benchmark/theBenchmark.p',fact_bool_Osize_I4_J) ).

fof(fact_bool_Osize_I3_J,axiom,
    hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bool_Osize_I3_J) ).

fof(fact_nat__0,axiom,
    hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_semiring__norm_I113_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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_One__nat__def) ).

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/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__numerals_I1_J) ).

fof(fact_minus__Pls,axiom,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls,
    file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_int__0__neq__1) ).

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/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J) ).

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/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_sup__nat__def) ).

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/sandbox/benchmark/theBenchmark.p',fact_bool_Osize_I2_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/sandbox/benchmark/theBenchmark.p',fact_bool_Osize_I1_J) ).

fof(fact_com_Osize_I1_J,axiom,
    c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osize_I1_J) ).

fof(fact_bot__nat__def,axiom,
    c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Obounded__lattice) ).

fof(arity_Product____Type__Ounit__Lazy__Sequence_Osmall__lazy,axiom,
    class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit),
    file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Lazy__Sequence_Osmall__lazy) ).

fof(arity_Product____Type__Ounit__Enum_Oenum,axiom,
    class_Enum_Oenum(tc_Product__Type_Ounit),
    file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Enum_Oenum) ).

fof(arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add,axiom,
    class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add) ).

fof(arity_Int__Oint__Groups_Osemigroup__add,axiom,
    class_Groups_Osemigroup__add(tc_Int_Oint),
    file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Owellorder) ).

fof(arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add,axiom,
    class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add) ).

fof(arity_Int__Oint__Groups_Olinordered__ab__semigroup__add,axiom,
    class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint),
    file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add) ).

fof(arity_HOL__Obool__Lattices_Obounded__lattice__top,axiom,
    class_Lattices_Obounded__lattice__top(tc_HOL_Obool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Obounded__lattice__top) ).

fof(arity_HOL__Obool__Orderings_Otop,axiom,
    class_Orderings_Otop(tc_HOL_Obool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Otop) ).

fof(arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice,axiom,
    class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice) ).

fof(arity_Int__Oint__Lattices_Odistrib__lattice,axiom,
    class_Lattices_Odistrib__lattice(tc_Int_Oint),
    file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Odistrib__lattice) ).

fof(arity_Int__Oint__Lattices_Osemilattice__inf,axiom,
    class_Lattices_Osemilattice__inf(tc_Int_Oint),
    file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Osemilattice__inf) ).

fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom,
    class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
    file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Finite__Set_Ofinite) ).

fof(arity_Int__Oint__Lattices_Olattice,axiom,
    class_Lattices_Olattice(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Lattices_Olattice) ).

fof(arity_Nat__Onat__Lattices_Olattice,axiom,
    class_Lattices_Olattice(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Lattices_Olattice) ).

fof(arity_HOL__Obool__Lattices_Olattice,axiom,
    class_Lattices_Olattice(tc_HOL_Obool),
    file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Osemilattice__sup) ).

fof(arity_HOL__Obool__Lattices_Obounded__lattice__bot,axiom,
    class_Lattices_Obounded__lattice__bot(tc_HOL_Obool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Obounded__lattice__bot) ).

fof(arity_Code____Evaluation__Oterm__Nat_Osize,axiom,
    class_Nat_Osize(tc_Code__Evaluation_Oterm),
    file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',arity_Product____Type__Ounit__Nat_Osize) ).

fof(arity_Com__Ovname__Nat_Osize,axiom,
    class_Nat_Osize(tc_Com_Ovname),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Com__Ovname__Nat_Osize) ).

fof(arity_Code____Numeral__Ocode____numeral__Nat_Osize,axiom,
    class_Nat_Osize(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Nat_Osize) ).

fof(arity_Com__Ostate__Nat_Osize,axiom,
    class_Nat_Osize(tc_Com_Ostate),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Com__Ostate__Nat_Osize) ).

fof(arity_Nat__Onat__Nat_Osize,axiom,
    class_Nat_Osize(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Nat_Osize) ).

fof(arity_Com__Ocom__Nat_Osize,axiom,
    class_Nat_Osize(tc_Com_Ocom),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Com__Ocom__Nat_Osize) ).

fof(arity_HOL__Obool__Nat_Osize,axiom,
    class_Nat_Osize(tc_HOL_Obool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Nat_Osize) ).

fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0,axiom,
    class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0) ).

fof(arity_Int__Oint__Rings_Osemiring__0,axiom,
    class_Rings_Osemiring__0(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring__0) ).

fof(arity_Nat__Onat__Rings_Osemiring__0,axiom,
    class_Rings_Osemiring__0(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__0) ).

fof(arity_Code____Numeral__Ocode____numeral__Power_Opower,axiom,
    class_Power_Opower(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Power_Opower) ).

fof(arity_Int__Oint__Power_Opower,axiom,
    class_Power_Opower(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Power_Opower) ).

fof(arity_Nat__Onat__Power_Opower,axiom,
    class_Power_Opower(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Power_Opower) ).

fof(arity_Int__Oint__Groups_Oabs__if,axiom,
    class_Groups_Oabs__if(tc_Int_Oint),
    file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__group__add__abs) ).

fof(arity_Code____Numeral__Ocode____numeral__Int_Onumber,axiom,
    class_Int_Onumber(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Int_Onumber) ).

fof(arity_Int__Oint__Int_Onumber,axiom,
    class_Int_Onumber(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Int_Onumber) ).

fof(arity_Nat__Onat__Int_Onumber,axiom,
    class_Int_Onumber(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Int_Onumber) ).

fof(arity_Int__Oint__Int_Onumber__ring,axiom,
    class_Int_Onumber__ring(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Int_Onumber__ring) ).

fof(arity_Code____Numeral__Ocode____numeral__Groups_Ominus,axiom,
    class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ominus) ).

fof(arity_Int__Oint__Groups_Ominus,axiom,
    class_Groups_Ominus(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ominus) ).

fof(arity_Nat__Onat__Groups_Ominus,axiom,
    class_Groups_Ominus(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ominus) ).

fof(arity_HOL__Obool__Groups_Ominus,axiom,
    class_Groups_Ominus(tc_HOL_Obool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Groups_Ominus) ).

fof(arity_Int__Oint__Groups_Ouminus,axiom,
    class_Groups_Ouminus(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ouminus) ).

fof(arity_HOL__Obool__Groups_Ouminus,axiom,
    class_Groups_Ouminus(tc_HOL_Obool),
    file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Divides_Oring__div) ).

fof(arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div,axiom,
    class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div) ).

fof(arity_Int__Oint__Divides_Osemiring__div,axiom,
    class_Divides_Osemiring__div(tc_Int_Oint),
    file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Divides_Osemiring__div) ).

fof(arity_Int__Oint__Groups_Osgn__if,axiom,
    class_Groups_Osgn__if(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Osgn__if) ).

fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom,
    class_Lattices_Oboolean__algebra(tc_HOL_Obool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Oboolean__algebra) ).

fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring,axiom,
    class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring) ).

fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom,
    class_Rings_Olinordered__semiring(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring) ).

fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom,
    class_Rings_Olinordered__semiring(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring) ).

fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom,
    class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1__no__zero__divisors) ).

fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom,
    class_Rings_Ocomm__ring__1(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring__1) ).

fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring,axiom,
    class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring) ).

fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom,
    class_Rings_Oordered__comm__semiring(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__comm__semiring) ).

fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom,
    class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__comm__semiring) ).

fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring,axiom,
    class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring) ).

fof(arity_Int__Oint__Rings_Oordered__semiring,axiom,
    class_Rings_Oordered__semiring(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__semiring) ).

fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom,
    class_Rings_Oordered__semiring(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__semiring) ).

fof(arity_Int__Oint__Rings_Oordered__ring,axiom,
    class_Rings_Oordered__ring(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring) ).

fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring,axiom,
    class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring) ).

fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom,
    class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__cancel__semiring) ).

fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom,
    class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__cancel__semiring) ).

fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom,
    class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1__strict) ).

fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom,
    class_Rings_Olinordered__semiring__1(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1) ).

fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add,axiom,
    class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add) ).

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    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add) ).

fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) ).

fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add,axiom,
    class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add) ).

fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom,
    class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__ab__semigroup__add) ).

fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
    class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) ).

fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add,axiom,
    class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add) ).

fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom,
    class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__semigroup__add) ).

fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
    class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).

fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le) ).

fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le) ).

fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le) ).

fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1,axiom,
    class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1) ).

fof(arity_Int__Oint__Rings_Osemiring__1,axiom,
    class_Rings_Osemiring__1(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring__1) ).

fof(arity_Nat__Onat__Rings_Osemiring__1,axiom,
    class_Rings_Osemiring__1(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__1) ).

fof(arity_Code____Numeral__Ocode____numeral__Groups_Ozero,axiom,
    class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ozero) ).

fof(arity_Int__Oint__Groups_Ozero,axiom,
    class_Groups_Ozero(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ozero) ).

fof(arity_Nat__Onat__Groups_Ozero,axiom,
    class_Groups_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ozero) ).

fof(help_c__fTrue__1,axiom,
    hBOOL(c_fTrue),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fTrue__1) ).

fof(arity_Nat__Onat__Orderings_Obot,axiom,
    class_Orderings_Obot(tc_Nat_Onat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Obot) ).

fof(arity_HOL__Obool__Orderings_Obot,axiom,
    class_Orderings_Obot(tc_HOL_Obool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Obot) ).

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/sandbox/benchmark/theBenchmark.p',fact_Code__Numeral_Oof__nat__code) ).

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/sandbox/benchmark/theBenchmark.p',fact_subtract__code__numeral__def) ).

fof(fact_Pls__def,axiom,
    c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pls__def) ).

fof(fact_rel__simps_I40_J,axiom,
    c_Int_OMin != c_Int_OPls,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I40_J) ).

fof(fact_rel__simps_I37_J,axiom,
    c_Int_OPls != c_Int_OMin,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I37_J) ).

fof(i_0_5187,plain,
    ! [X87,X5] :
      ( class_Rings_Oring__1(X5)
     => ( ( X87 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hAPP(c_Int_Oring__1__class_Oof__int(X5),X87) = c_Groups_Ozero__class_Ozero(X5) )
        & ( X87 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X87),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
             => hAPP(c_Int_Oring__1__class_Oof__int(X5),X87) = hAPP(c_Groups_Ouminus__class_Ouminus(X5),hAPP(c_Int_Oring__1__class_Oof__int(X5),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X87))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X87),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
             => hAPP(c_Int_Oring__1__class_Oof__int(X5),X87) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,X5),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(X5,X5)),tc_fun(tc_Int_Oint,X5)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X5,X5),X5),tc_fun(tc_fun(tc_Int_Oint,tc_fun(X5,X5)),tc_fun(tc_Int_Oint,X5)),tc_Int_Oint),c_COMBB(tc_fun(X5,X5),X5,tc_Int_Oint)),hAPP(hAPP(c_COMBB(X5,tc_fun(tc_fun(X5,X5),X5),tc_Int_Oint),c_HOL_OLet(X5,X5)),c_Int_Oring__1__class_Oof__int(X5)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X5,X5),tc_fun(X5,X5)),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X5,X5)),tc_fun(tc_fun(X5,X5),tc_fun(X5,X5)),tc_Int_Oint),c_COMBS(X5,X5,X5)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X5,X5),tc_fun(X5,tc_fun(X5,X5))),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_fun(X5,X5)),tc_fun(tc_fun(X5,X5),tc_fun(X5,tc_fun(X5,X5))),tc_Int_Oint),c_COMBB(X5,tc_fun(X5,X5),X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5,tc_fun(X5,X5)),tc_Int_Oint),c_If(X5)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBS(X5,X5,X5),c_Groups_Oplus__class_Oplus(X5)),c_COMBI(X5))))),hAPP(hAPP(c_COMBC(X5,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X5),c_Groups_Oplus__class_Oplus(X5)),hAPP(hAPP(c_COMBS(X5,X5,X5),c_Groups_Oplus__class_Oplus(X5)),c_COMBI(X5)))),c_Groups_Oone__class_Oone(X5))))),c_Divides_Odivmod__int(X87,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_5188,plain,
    ! [X65,X66,X58] :
      ( class_Rings_Olinordered__idom(X58)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X66),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(X58),X65),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X58))) ),
    inference(fof_simplification,[status(thm)],[fact_not__sum__power2__lt__zero]) ).

fof(i_0_5189,plain,
    ! [X62,X58] :
      ( class_Rings_Olinordered__idom(X58)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(hAPP(c_Power_Opower__class_Opower(X58),X62),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X58))) ),
    inference(fof_simplification,[status(thm)],[fact_power2__less__0]) ).

fof(i_0_5190,plain,
    ! [X136,X128] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X136)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X128))) = 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),X136),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)))),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),X128)))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X136)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X128))) = 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),X136)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ),
    inference(fof_simplification,[status(thm)],[fact_zmod__number__of__Bit1]) ).

fof(i_0_5191,plain,
    ! [X128,X136] :
      ( 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),X136)))
     => ( ( 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),X128)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136))))
         => c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)) = 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),X128)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136))) )
        & ( ~ 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),X128)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136))))
         => c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)),c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128),hAPP(hAPP(c_Groups_Otimes__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),X136)))) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_negDivAlg__eqn__number__of]) ).

fof(i_0_5192,plain,
    ! [X128] :
      ( 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),X128)))
     => ( ( 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),X128))))
         => c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)) = 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),X128))) )
        & ( ~ 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),X128))))
         => c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)),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),X128)))) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_negDivAlg__eqn__1__number__of]) ).

fof(i_0_5193,plain,
    ! [X128,X136] :
      ( 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),X136)))
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)))
         => c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)) = 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),X128)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)))
         => c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)),c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128),hAPP(hAPP(c_Groups_Otimes__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),X136)))) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_posDivAlg__eqn__number__of]) ).

fof(i_0_5194,plain,
    ! [X128] :
      ( 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),X128)))
     => ( ( 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),X128)))
         => c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)) = 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),X128)))
         => c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)),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),X128)))) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_posDivAlg__eqn__1__number__of]) ).

fof(i_0_5195,plain,
    ! [X62,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)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X62),X90)))
         => c_Divides_OnegDivAlg(X62,X90) = 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),X62),X90)) )
        & ( ~ 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),X62),X90)))
         => c_Divides_OnegDivAlg(X62,X90) = hAPP(c_Divides_Oadjust(X90),c_Divides_OnegDivAlg(X62,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X90))) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_negDivAlg__eqn]) ).

fof(i_0_5196,plain,
    ! [X62,X90] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X90))
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X62),X90))
         => c_Divides_OposDivAlg(X62,X90) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X62) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X62),X90))
         => c_Divides_OposDivAlg(X62,X90) = hAPP(c_Divides_Oadjust(X90),c_Divides_OposDivAlg(X62,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X90))) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_posDivAlg__eqn]) ).

fof(i_0_5197,plain,
    ! [X239,X18,X5] :
      ( c_List_OdropWhile(X5,X18,X239) != c_List_Olist_ONil(X5)
     => ~ hBOOL(hAPP(X18,hAPP(c_List_Ohd(X5),c_List_OdropWhile(X5,X18,X239)))) ),
    inference(fof_simplification,[status(thm)],[fact_hd__dropWhile]) ).

fof(i_0_5198,plain,
    ! [X123,X121,X5] :
      ( class_Int_Onumber__ring(X5)
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X121)))
         => hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X123)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X121))) = hAPP(hAPP(c_HOL_OLet(X5,X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X123)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X121))),hAPP(hAPP(c_COMBS(X5,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X5),c_Groups_Otimes__class_Otimes(X5)),hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X123)))),c_COMBI(X5))) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X121)))
         => hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X123)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X121))) = c_Groups_Oone__class_Oone(X5) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_power__number__of__odd__number__of]) ).

fof(i_0_5199,plain,
    ! [X239,X18,X5] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),c_List_OdropWhile(X5,X18,X239))))
         => ~ hBOOL(hAPP(X18,X3)) )
     => c_List_OtakeWhile(X5,X18,X239) = hAPP(c_List_Ofilter(X5,X18),X239) ),
    inference(fof_simplification,[status(thm)],[fact_takeWhile__eq__filter]) ).

fof(i_0_5200,plain,
    ! [X120,X121,X5] :
      ( class_Int_Onumber__ring(X5)
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X121)))
         => hAPP(hAPP(c_Power_Opower__class_Opower(X5),X120),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X121))) = hAPP(hAPP(c_HOL_OLet(X5,X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X120),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X121))),hAPP(hAPP(c_COMBS(X5,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X5),c_Groups_Otimes__class_Otimes(X5)),hAPP(c_Groups_Otimes__class_Otimes(X5),X120))),c_COMBI(X5))) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X121)))
         => hAPP(hAPP(c_Power_Opower__class_Opower(X5),X120),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X121))) = c_Groups_Oone__class_Oone(X5) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_power__number__of__odd]) ).

fof(i_0_5201,plain,
    ! [X120,X121] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X121)))
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X120),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X121))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X120),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X121))),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),X120))),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),X121)))
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X120),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X121))) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
    inference(fof_simplification,[status(thm)],[fact_zpower__number__of__odd]) ).

fof(i_0_5202,plain,
    ! [X25,X171,X5] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X5,X5),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X5,X5),X171)),c_Transitive__Closure_Ortrancl(X5,X171)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X5),tc_HOL_Obool))
     => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X25)),c_Transitive__Closure_Otrancl(X5,X171))) ),
    inference(fof_simplification,[status(thm)],[fact_irrefl__tranclI]) ).

fof(i_0_5203,plain,
    ! [X251,X18,X239,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X239)))
     => ( ~ hBOOL(hAPP(X18,X25))
       => c_List_OdropWhile(X5,X18,hAPP(hAPP(c_List_Oappend(X5),X239),X251)) = hAPP(hAPP(c_List_Oappend(X5),c_List_OdropWhile(X5,X18,X239)),X251) ) ),
    inference(fof_simplification,[status(thm)],[fact_dropWhile__append1]) ).

fof(i_0_5204,plain,
    ! [X171,X5] :
      ( c_Wellfounded_Oacyclic(X5,X171)
    <=> ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X3)),c_Transitive__Closure_Otrancl(X5,X171))) ),
    inference(fof_simplification,[status(thm)],[fact_acyclic__def]) ).

fof(i_0_5205,plain,
    ! [X136,X128] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X136))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X128))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X136))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X128))) = 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),X136)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128)) ) ),
    inference(fof_simplification,[status(thm)],[fact_zdiv__number__of__Bit1]) ).

fof(i_0_5206,plain,
    ! [X171,X5] :
      ( ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X3)),c_Transitive__Closure_Otrancl(X5,X171)))
     => c_Wellfounded_Oacyclic(X5,X171) ),
    inference(fof_simplification,[status(thm)],[fact_acyclicI]) ).

fof(i_0_5207,plain,
    ! [X239,X5,X25,X18] :
      ( ( hBOOL(hAPP(X18,X25))
       => c_List_OdropWhile(X5,X18,hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239)) = c_List_OdropWhile(X5,X18,X239) )
      & ( ~ hBOOL(hAPP(X18,X25))
       => c_List_OdropWhile(X5,X18,hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239)) = hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239) ) ),
    inference(fof_simplification,[status(thm)],[fact_dropWhile_Osimps_I2_J]) ).

fof(i_0_5208,plain,
    ! [X121] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X121)))
       => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X121)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X121)))
       => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X121)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X121)),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_5209,plain,
    ! [X57,X72] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X72)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X57)))
       => c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X72),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X57)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X72)),c_List_Oupt(hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X72)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X57))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X72)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X57)))
       => c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X72),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X57)) = c_List_Olist_ONil(tc_Nat_Onat) ) ),
    inference(fof_simplification,[status(thm)],[fact_upt__rec__number__of]) ).

fof(i_0_5210,plain,
    ! [X128,X58] :
      ( ( class_Int_Onumber__ring(X58)
        & class_Int_Oring__char__0(X58) )
     => ~ c_Int_Oiszero(X58,hAPP(c_Int_Onumber__class_Onumber__of(X58),c_Int_OBit1(X128))) ),
    inference(fof_simplification,[status(thm)],[fact_iszero__number__of__Bit1]) ).

fof(i_0_5211,plain,
    ! [X251,X33,X239,X18,X5] :
      ( c_List_OdropWhile(X5,X18,X239) = hAPP(hAPP(c_List_Olist_OCons(X5),X33),X251)
    <=> ( X239 = hAPP(hAPP(c_List_Oappend(X5),c_List_OtakeWhile(X5,X18,X239)),hAPP(hAPP(c_List_Olist_OCons(X5),X33),X251))
        & ~ hBOOL(hAPP(X18,X33)) ) ),
    inference(fof_simplification,[status(thm)],[fact_dropWhile__eq__Cons__conv]) ).

fof(i_0_5212,plain,
    ! [X58] :
      ( class_Int_Onumber__ring(X58)
     => ~ c_Int_Oiszero(X58,hAPP(c_Int_Onumber__class_Onumber__of(X58),c_Int_OBit1(c_Int_OPls))) ),
    inference(fof_simplification,[status(thm)],[fact_not__iszero__Numeral1]) ).

fof(i_0_5213,plain,
    ! [X239,X25,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X239)))
     => hAPP(c_List_OremoveAll(X5,X25),X239) = X239 ),
    inference(fof_simplification,[status(thm)],[fact_removeAll__id]) ).

fof(i_0_5214,plain,
    ! [X239,X5,X25,X18] :
      ( ~ hBOOL(hAPP(X18,X25))
     => hAPP(c_List_OremoveAll(X5,X25),hAPP(c_List_Ofilter(X5,X18),X239)) = hAPP(c_List_Ofilter(X5,X18),X239) ),
    inference(fof_simplification,[status(thm)],[fact_removeAll__filter__not]) ).

fof(i_0_5215,plain,
    ! [X57,X136] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)))
       => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)),X57)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X57) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)))
       => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)),X57)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X136))),X57) ) ),
    inference(fof_simplification,[status(thm)],[fact_Suc__nat__number__of__add]) ).

fof(i_0_5216,plain,
    ! [X97,X98] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X98),X97))
       => c_List_Oupt(X98,hAPP(c_Nat_OSuc,X97)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X98,X97)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X97),c_List_Olist_ONil(tc_Nat_Onat))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X98),X97))
       => c_List_Oupt(X98,hAPP(c_Nat_OSuc,X97)) = c_List_Olist_ONil(tc_Nat_Onat) ) ),
    inference(fof_simplification,[status(thm)],[fact_upt__Suc]) ).

fof(i_0_5217,plain,
    ! [X97,X98] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),X97))
       => c_List_Oupt(X98,X97) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X98),c_List_Oupt(hAPP(c_Nat_OSuc,X98),X97)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X98),X97))
       => c_List_Oupt(X98,X97) = c_List_Olist_ONil(tc_Nat_Onat) ) ),
    inference(fof_simplification,[status(thm)],[fact_upt__rec]) ).

fof(i_0_5218,plain,
    ! [X87,X50,X18] :
      ( epred1_3(X18,X50,X87)
    <=> ( ( X87 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hBOOL(hAPP(X18,X50)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X87))
         => ! [X146,X101] :
              ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X101))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X101),X87))
                & X50 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X87),X146)),X101) )
             => hBOOL(hAPP(X18,X101)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X87),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => ! [X146,X101] :
              ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X87),X101))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X101),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                & X50 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X87),X146)),X101) )
             => hBOOL(hAPP(X18,X101)) ) ) ) ),
    introduced(definition) ).

fof(i_0_5219,plain,
    ! [X87,X50,X18] :
      ( epred2_3(X18,X50,X87)
    <=> ( ( X87 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hBOOL(hAPP(X18,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)),X87))
         => ! [X146] :
              ( ? [X101] :
                  ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X101))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X101),X87))
                  & X50 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X87),X146)),X101) )
             => hBOOL(hAPP(X18,X146)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X87),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => ! [X146] :
              ( ? [X101] :
                  ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X87),X101))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X101),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                  & X50 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X87),X146)),X101) )
             => hBOOL(hAPP(X18,X146)) ) ) ) ),
    introduced(definition) ).

fof(i_0_5220,plain,
    ! [X136] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X136),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)),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),X136),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(X136)) ) ),
    inference(fof_simplification,[status(thm)],[fact_nat__number__of__diff__1]) ).

fof(i_0_5221,plain,
    ! [X136] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X136),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)),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),X136),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X136)) ) ),
    inference(fof_simplification,[status(thm)],[fact_nat__number__of__add__1]) ).

fof(i_0_5222,plain,
    ! [X136] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X136),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),X136)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X136),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),X136)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X136)) ) ),
    inference(fof_simplification,[status(thm)],[fact_nat__1__add__number__of]) ).

fof(i_0_5223,plain,
    ! [X136] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)))
       => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)))
       => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X136)) ) ),
    inference(fof_simplification,[status(thm)],[fact_Suc__nat__number__of]) ).

fof(i_0_5224,plain,
    ! [X65,X58] : ~ hBOOL(hAPP(hAPP(c_List_Omember(X58),c_List_Olist_ONil(X58)),X65)),
    inference(fof_simplification,[status(thm)],[fact_member__rec_I2_J]) ).

fof(i_0_5225,plain,
    ! [X21812] : c_Divides_Oadjust(X21812) = 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)),X21812))))),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)),X21812))))),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_5226,plain,
    ! [X21107] : c_Int_Osucc(c_Int_OBit0(X21107)) = c_Int_OBit1(X21107),
    inference(variable_rename,[status(thm)],[fact_succ__Bit0]) ).

fof(i_0_5227,plain,
    ! [X21066] : c_Int_OBit0(X21066) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21066),X21066),
    inference(variable_rename,[status(thm)],[fact_Bit0__def]) ).

fof(i_0_5228,plain,
    ! [X20867] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20867),c_Int_OMin) = c_Int_Osucc(X20867),
    inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I2_J]) ).

fof(i_0_5229,plain,
    ! [X32,X1,X2,X115,X116,X23,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X20)),X23),hAPP(c_Set_Oimage(tc_prod(X116,X115),tc_prod(X5,X20),c_Product__Type_Omap__pair(X116,X5,X115,X20,X2,X1)),X32)))
     => ~ ! [X3,X177] :
            ( X23 = hAPP(hAPP(c_Product__Type_OPair(X5,X20),hAPP(X2,X3)),hAPP(X1,X177))
           => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X116,X115)),hAPP(hAPP(c_Product__Type_OPair(X116,X115),X3),X177)),X32)) ) ),
    inference(fof_simplification,[status(thm)],[fact_prod__fun__imageE]) ).

fof(i_0_5230,plain,
    ! [X21862,X21863] :
      ( ( X21863 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odivmod__int(X21863,X21862) = 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)) )
      & ( X21862 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odivmod__int(X21863,X21862) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21863)
        | X21863 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( X21862 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odivmod__int(X21863,X21862) = 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,X21862))),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)),X21862)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21863))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21862),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21863),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(X21863,X21862)),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),X21862))))),c_Divides_Opdivmod(X21863,X21862))))
        | X21863 = 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_5231,plain,
    ! [X27956,X27957,X27958,X27959] : c_Product__Type_Oapsnd(X27959,X27958,X27957,X27956) = c_Product__Type_Omap__pair(X27957,X27957,X27959,X27958,c_Fun_Oid(X27957),X27956),
    inference(variable_rename,[status(thm)],[fact_apsnd__def]) ).

fof(i_0_5232,plain,
    ! [X21902,X21903] :
      ( ( X21903 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odivmod__int(X21903,X21902) = 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)) )
      & ( X21902 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odivmod__int(X21903,X21902) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21903)
        | X21903 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( X21902 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odivmod__int(X21903,X21902) = 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,X21902))),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,X21903)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,X21902))),c_Divides_Opdivmod(X21903,X21902)),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),X21902))))),c_Divides_Opdivmod(X21903,X21902))))
        | X21903 = 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_5233,plain,
    ! [X33131,X33132,X33133] : c_Nitpick_Oplus__frac(X33133,X33132,X33131) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X33133),c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(X33133),X33132),hAPP(c_Nitpick_Odenom(X33133),X33131))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,X33133),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,X33133),tc_Int_Oint),c_Nitpick_Ofrac(X33133)),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(X33133),X33132))),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(X33133),X33132))))),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(X33133),X33131))),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(X33133),X33131)))))),c_COMBI(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[fact_Nitpick_Oplus__frac__def]) ).

fof(i_0_5234,plain,
    ! [X33150] : c_Nitpick_Odenom(X33150) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X33150,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X33150)),
    inference(variable_rename,[status(thm)],[fact_Nitpick_Odenom__def]) ).

fof(i_0_5235,plain,
    ! [X33151] : c_Nitpick_Onum(X33151) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X33151,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X33151)),
    inference(variable_rename,[status(thm)],[fact_Nitpick_Onum__def]) ).

fof(i_0_5236,plain,
    ! [X23360,X23361,X23362,X23363] :
      ( ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23363,tc_fun(X23363,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X23363,tc_fun(tc_prod(X23363,X23363),tc_HOL_Obool),tc_fun(X23363,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X23363,tc_fun(tc_fun(tc_prod(X23363,X23363),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X23363,X23363),tc_HOL_Obool),tc_fun(X23363,tc_HOL_Obool)),X23363),c_COMBC(X23363,tc_fun(tc_prod(X23363,X23363),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X23363,tc_prod(X23363,X23363)),tc_fun(X23363,tc_fun(tc_fun(tc_prod(X23363,X23363),tc_HOL_Obool),tc_HOL_Obool)),X23363),hAPP(c_COMBB(tc_prod(X23363,X23363),tc_fun(tc_fun(tc_prod(X23363,X23363),tc_HOL_Obool),tc_HOL_Obool),X23363),c_member(tc_prod(X23363,X23363)))),c_Product__Type_OPair(X23363,X23363)))),X23362)),c_fequal),X23361),X23360))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X23363,X23363)),hAPP(hAPP(c_Product__Type_OPair(X23363,X23363),X23361),X23360)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X23363,X23363),tc_HOL_Obool)),X23362),c_Relation_OId(X23363)))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X23363,X23363)),hAPP(hAPP(c_Product__Type_OPair(X23363,X23363),X23361),X23360)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X23363,X23363),tc_HOL_Obool)),X23362),c_Relation_OId(X23363))))
        | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23363,tc_fun(X23363,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X23363,tc_fun(tc_prod(X23363,X23363),tc_HOL_Obool),tc_fun(X23363,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X23363,tc_fun(tc_fun(tc_prod(X23363,X23363),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X23363,X23363),tc_HOL_Obool),tc_fun(X23363,tc_HOL_Obool)),X23363),c_COMBC(X23363,tc_fun(tc_prod(X23363,X23363),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X23363,tc_prod(X23363,X23363)),tc_fun(X23363,tc_fun(tc_fun(tc_prod(X23363,X23363),tc_HOL_Obool),tc_HOL_Obool)),X23363),hAPP(c_COMBB(tc_prod(X23363,X23363),tc_fun(tc_fun(tc_prod(X23363,X23363),tc_HOL_Obool),tc_HOL_Obool),X23363),c_member(tc_prod(X23363,X23363)))),c_Product__Type_OPair(X23363,X23363)))),X23362)),c_fequal),X23361),X23360)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_reflcl__set__eq])]) ).

fof(i_0_5237,plain,
    ! [X32173] : c_Transitive__Closure_Ortrancl(X32173,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X32173,X32173),tc_HOL_Obool))) = c_Relation_OId(X32173),
    inference(variable_rename,[status(thm)],[fact_rtrancl__empty]) ).

fof(i_0_5238,plain,
    ! [X21760,X21761,X21762] : hAPP(c_Divides_Oadjust(X21762),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X21761),X21760)) = 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),X21760),X21762)),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)))),X21761)),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)))),X21761)),X21760))),
    inference(variable_rename,[status(thm)],[fact_adjust__eq]) ).

fof(i_0_5239,plain,
    ! [X32279,X32280,X32281,X32282] : c_Transitive__Closure_Otrancl(X32282,hAPP(hAPP(c_Set_Oinsert(tc_prod(X32282,X32282)),hAPP(hAPP(c_Product__Type_OPair(X32282,X32282),X32281),X32280)),X32279)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X32282,X32282),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X32282,X32279)),hAPP(c_Set_OCollect(tc_prod(X32282,X32282)),hAPP(c_Product__Type_Oprod_Oprod__case(X32282,X32282,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X32282,tc_fun(X32282,tc_HOL_Obool),tc_fun(X32282,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X32282,tc_HOL_Obool),tc_fun(X32282,tc_HOL_Obool)),X32282),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X32282)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X32282),c_fconj),hAPP(hAPP(c_COMBC(X32282,tc_fun(tc_prod(X32282,X32282),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X32282,X32282),tc_fun(tc_fun(tc_prod(X32282,X32282),tc_HOL_Obool),tc_HOL_Obool),X32282),c_member(tc_prod(X32282,X32282))),hAPP(hAPP(c_COMBC(X32282,X32282,tc_prod(X32282,X32282)),c_Product__Type_OPair(X32282,X32282)),X32281))),c_Transitive__Closure_Ortrancl(X32282,X32279))))),hAPP(hAPP(c_COMBC(X32282,tc_fun(tc_prod(X32282,X32282),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X32282,X32282),tc_fun(tc_fun(tc_prod(X32282,X32282),tc_HOL_Obool),tc_HOL_Obool),X32282),c_member(tc_prod(X32282,X32282))),hAPP(c_Product__Type_OPair(X32282,X32282),X32280))),c_Transitive__Closure_Ortrancl(X32282,X32279)))))),
    inference(variable_rename,[status(thm)],[fact_trancl__insert]) ).

fof(i_0_5240,plain,
    ! [X32331,X32332] : c_Transitive__Closure_Otrancl(X32332,X32331) = hAPP(hAPP(c_Relation_Orel__comp(X32332,X32332,X32332),X32331),c_Transitive__Closure_Ortrancl(X32332,X32331)),
    inference(variable_rename,[status(thm)],[fact_trancl__unfold__left]) ).

fof(i_0_5241,plain,
    ! [X21825,X21826] :
      ( ( X21825 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(c_Int_Oring__1__class_Oof__int(X21826),X21825) = c_Groups_Ozero__class_Ozero(X21826)
        | ~ class_Rings_Oring__1(X21826) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21825),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Int_Oring__1__class_Oof__int(X21826),X21825) = hAPP(c_Groups_Ouminus__class_Ouminus(X21826),hAPP(c_Int_Oring__1__class_Oof__int(X21826),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21825)))
        | X21825 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ class_Rings_Oring__1(X21826) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21825),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Int_Oring__1__class_Oof__int(X21826),X21825) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,X21826),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(X21826,X21826)),tc_fun(tc_Int_Oint,X21826)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X21826,X21826),X21826),tc_fun(tc_fun(tc_Int_Oint,tc_fun(X21826,X21826)),tc_fun(tc_Int_Oint,X21826)),tc_Int_Oint),c_COMBB(tc_fun(X21826,X21826),X21826,tc_Int_Oint)),hAPP(hAPP(c_COMBB(X21826,tc_fun(tc_fun(X21826,X21826),X21826),tc_Int_Oint),c_HOL_OLet(X21826,X21826)),c_Int_Oring__1__class_Oof__int(X21826)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X21826,X21826),tc_fun(X21826,X21826)),hAPP(hAPP(c_COMBB(tc_fun(X21826,tc_fun(X21826,X21826)),tc_fun(tc_fun(X21826,X21826),tc_fun(X21826,X21826)),tc_Int_Oint),c_COMBS(X21826,X21826,X21826)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X21826,X21826),tc_fun(X21826,tc_fun(X21826,X21826))),hAPP(hAPP(c_COMBB(tc_fun(X21826,tc_fun(X21826,X21826)),tc_fun(tc_fun(X21826,X21826),tc_fun(X21826,tc_fun(X21826,X21826))),tc_Int_Oint),c_COMBB(X21826,tc_fun(X21826,X21826),X21826)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X21826,tc_fun(X21826,X21826)),tc_Int_Oint),c_If(X21826)),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(X21826,X21826,X21826),c_Groups_Oplus__class_Oplus(X21826)),c_COMBI(X21826))))),hAPP(hAPP(c_COMBC(X21826,X21826,X21826),hAPP(hAPP(c_COMBB(X21826,tc_fun(X21826,X21826),X21826),c_Groups_Oplus__class_Oplus(X21826)),hAPP(hAPP(c_COMBS(X21826,X21826,X21826),c_Groups_Oplus__class_Oplus(X21826)),c_COMBI(X21826)))),c_Groups_Oone__class_Oone(X21826))))),c_Divides_Odivmod__int(X21825,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
        | X21825 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ class_Rings_Oring__1(X21826) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5187])])]) ).

fof(i_0_5242,plain,
    ! [X23,X24,X113,X21,X116,X20,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X20,tc_fun(X116,tc_HOL_Obool))),X21),X113),X24),X23))
     => ~ ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X21))
           => ~ hBOOL(hAPP(hAPP(hAPP(X113,X3),X24),X23)) ) ),
    inference(fof_simplification,[status(thm)],[fact_SUP2__E]) ).

fof(i_0_5243,plain,
    ! [X21195,X21196,X21197] :
      ( ( X21196 = c_Groups_Ozero__class_Ozero(X21197)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21197),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21197),hAPP(hAPP(c_Power_Opower__class_Opower(X21197),X21196),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(X21197),X21195),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X21197)))
        | ~ class_Rings_Olinordered__idom(X21197) )
      & ( X21195 = c_Groups_Ozero__class_Ozero(X21197)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21197),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21197),hAPP(hAPP(c_Power_Opower__class_Opower(X21197),X21196),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(X21197),X21195),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X21197)))
        | ~ class_Rings_Olinordered__idom(X21197) )
      & ( X21196 != c_Groups_Ozero__class_Ozero(X21197)
        | X21195 != c_Groups_Ozero__class_Ozero(X21197)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21197),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21197),hAPP(hAPP(c_Power_Opower__class_Opower(X21197),X21196),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(X21197),X21195),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X21197)))
        | ~ class_Rings_Olinordered__idom(X21197) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__power2__le__zero__iff])])]) ).

fof(i_0_5244,plain,
    ! [X21198,X21199,X21200] :
      ( ~ class_Rings_Olinordered__idom(X21200)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21200),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21200),hAPP(hAPP(c_Power_Opower__class_Opower(X21200),X21199),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(X21200),X21198),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X21200))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5188])]) ).

fof(i_0_5245,plain,
    ! [X31300,X31301,X31302,X31303] :
      ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(X31303)),c_List_Otranspose__rel(X31303)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X31303)),hAPP(hAPP(c_List_Olist_OCons(X31303),X31302),X31301)),X31300)))
      | c_List_Otranspose(X31303,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X31303)),hAPP(hAPP(c_List_Olist_OCons(X31303),X31302),X31301)),X31300)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X31303)),hAPP(hAPP(c_List_Olist_OCons(X31303),X31302),c_List_Oconcat(X31303,hAPP(hAPP(c_List_Omap(tc_List_Olist(X31303),tc_List_Olist(X31303)),c_List_Olist_Olist__case(tc_List_Olist(X31303),X31303,c_List_Olist_ONil(X31303),hAPP(hAPP(c_COMBB(tc_List_Olist(X31303),tc_fun(tc_List_Olist(X31303),tc_List_Olist(X31303)),X31303),c_COMBK(tc_List_Olist(X31303),tc_List_Olist(X31303))),hAPP(hAPP(c_COMBC(X31303,tc_List_Olist(X31303),tc_List_Olist(X31303)),c_List_Olist_OCons(X31303)),c_List_Olist_ONil(X31303))))),X31300)))),c_List_Otranspose(X31303,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X31303)),X31301),c_List_Oconcat(tc_List_Olist(X31303),hAPP(hAPP(c_List_Omap(tc_List_Olist(X31303),tc_List_Olist(tc_List_Olist(X31303))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(X31303)),X31303,c_List_Olist_ONil(tc_List_Olist(X31303)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X31303),tc_List_Olist(tc_List_Olist(X31303))),X31303),hAPP(hAPP(c_COMBC(tc_List_Olist(X31303),tc_List_Olist(tc_List_Olist(X31303)),tc_List_Olist(tc_List_Olist(X31303))),c_List_Olist_OCons(tc_List_Olist(X31303))),c_List_Olist_ONil(tc_List_Olist(X31303)))))),X31300))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transpose_Opsimps_I3_J])]) ).

fof(i_0_5246,plain,
    ! [X31213,X31214] : c_List_Oconcat(X31214,X31213) = hAPP(c_List_Ofoldl(tc_List_Olist(X31214),tc_List_Olist(X31214),c_List_Oappend(X31214),c_List_Olist_ONil(X31214)),X31213),
    inference(variable_rename,[status(thm)],[fact_concat__conv__foldl]) ).

fof(i_0_5247,plain,
    ! [X31296,X31297,X31298,X31299] : c_List_Otranspose(X31299,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X31299)),hAPP(hAPP(c_List_Olist_OCons(X31299),X31298),X31297)),X31296)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X31299)),hAPP(hAPP(c_List_Olist_OCons(X31299),X31298),c_List_Oconcat(X31299,hAPP(hAPP(c_List_Omap(tc_List_Olist(X31299),tc_List_Olist(X31299)),c_List_Olist_Olist__case(tc_List_Olist(X31299),X31299,c_List_Olist_ONil(X31299),hAPP(hAPP(c_COMBB(tc_List_Olist(X31299),tc_fun(tc_List_Olist(X31299),tc_List_Olist(X31299)),X31299),c_COMBK(tc_List_Olist(X31299),tc_List_Olist(X31299))),hAPP(hAPP(c_COMBC(X31299,tc_List_Olist(X31299),tc_List_Olist(X31299)),c_List_Olist_OCons(X31299)),c_List_Olist_ONil(X31299))))),X31296)))),c_List_Otranspose(X31299,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X31299)),X31297),c_List_Oconcat(tc_List_Olist(X31299),hAPP(hAPP(c_List_Omap(tc_List_Olist(X31299),tc_List_Olist(tc_List_Olist(X31299))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(X31299)),X31299,c_List_Olist_ONil(tc_List_Olist(X31299)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X31299),tc_List_Olist(tc_List_Olist(X31299))),X31299),hAPP(hAPP(c_COMBC(tc_List_Olist(X31299),tc_List_Olist(tc_List_Olist(X31299)),tc_List_Olist(tc_List_Olist(X31299))),c_List_Olist_OCons(tc_List_Olist(X31299))),c_List_Olist_ONil(tc_List_Olist(X31299)))))),X31296))))),
    inference(variable_rename,[status(thm)],[fact_transpose_Osimps_I3_J]) ).

fof(i_0_5248,plain,
    ! [X21228,X21229,X21230] :
      ( ~ class_Rings_Olinordered__idom(X21230)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21230),X21229),c_Groups_Ozero__class_Ozero(X21230)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21230),hAPP(hAPP(c_Power_Opower__class_Opower(X21230),X21229),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)))),X21228)))),c_Groups_Ozero__class_Ozero(X21230))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_odd__power__less__zero])]) ).

fof(i_0_5249,plain,
    ! [X76,X171,X116,X298,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X20)),X298),hAPP(hAPP(c_Relation_Orel__comp(X5,X116,X20),X171),X76)))
     => ~ ! [X3,X177,X154] :
            ( X298 = hAPP(hAPP(c_Product__Type_OPair(X5,X20),X3),X154)
           => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X116)),hAPP(hAPP(c_Product__Type_OPair(X5,X116),X3),X177)),X171))
             => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X116,X20)),hAPP(hAPP(c_Product__Type_OPair(X116,X20),X177),X154)),X76)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_rel__compE]) ).

fof(i_0_5250,plain,
    ! [X21225,X21226,X21227] :
      ( ~ class_Rings_Olinordered__idom(X21227)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21227),c_Groups_Ozero__class_Ozero(X21227)),hAPP(hAPP(c_Power_Opower__class_Opower(X21227),X21226),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)))),X21225)))))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21227),c_Groups_Ozero__class_Ozero(X21227)),X21226)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_odd__0__le__power__imp__0__le])]) ).

fof(i_0_5251,plain,
    ! [X251,X18,X239,X25,X5] :
      ( hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239) = hAPP(c_List_Ofilter(X5,X18),X251)
    <=> ? [X252,X260] :
          ( X251 = hAPP(hAPP(c_List_Oappend(X5),X252),hAPP(hAPP(c_List_Olist_OCons(X5),X25),X260))
          & ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X252)))
             => ~ hBOOL(hAPP(X18,X3)) )
          & hBOOL(hAPP(X18,X25))
          & X239 = hAPP(c_List_Ofilter(X5,X18),X260) ) ),
    inference(fof_simplification,[status(thm)],[fact_Cons__eq__filter__iff]) ).

fof(i_0_5252,plain,
    ! [X239,X25,X251,X18,X5] :
      ( hAPP(c_List_Ofilter(X5,X18),X251) = hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239)
    <=> ? [X252,X260] :
          ( X251 = hAPP(hAPP(c_List_Oappend(X5),X252),hAPP(hAPP(c_List_Olist_OCons(X5),X25),X260))
          & ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X252)))
             => ~ hBOOL(hAPP(X18,X3)) )
          & hBOOL(hAPP(X18,X25))
          & X239 = hAPP(c_List_Ofilter(X5,X18),X260) ) ),
    inference(fof_simplification,[status(thm)],[fact_filter__eq__Cons__iff]) ).

fof(i_0_5253,plain,
    ! [X21222,X21223,X21224] :
      ( ~ class_Int_Onumber__ring(X21224)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X21224),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21224),X21223),X21222)),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(X21224),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21224),hAPP(hAPP(c_Power_Opower__class_Opower(X21224),X21223),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(X21224),X21222),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(X21224),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21224),hAPP(c_Int_Onumber__class_Onumber__of(X21224),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X21223)),X21222)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__diff])]) ).

fof(i_0_5254,plain,
    ! [X21204,X21205,X21206] :
      ( ~ class_Int_Onumber__ring(X21206)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X21206),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21206),X21205),X21204)),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(X21206),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21206),hAPP(hAPP(c_Power_Opower__class_Opower(X21206),X21205),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(X21206),X21204),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(X21206),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21206),hAPP(c_Int_Onumber__class_Onumber__of(X21206),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X21205)),X21204)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__sum])]) ).

fof(i_0_5255,plain,
    ! [X2,X21,X5,X20] :
      ( class_Groups_Ocomm__monoid__add(X20)
     => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
         => c_Nitpick_Osetsum_H(X5,X20,X2,X21) = hAPP(c_List_Omonoid__add__class_Olistsum(X20),hAPP(hAPP(c_List_Omap(X5,X20),X2),c_Hilbert__Choice_OEps(tc_List_Olist(X5),hAPP(hAPP(c_COMBS(tc_List_Olist(X5),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X5)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X5)),c_fequal),c_List_Oset(X5))),X21))),c_List_Odistinct(X5))))) )
        & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
         => c_Nitpick_Osetsum_H(X5,X20,X2,X21) = c_Groups_Ozero__class_Ozero(X20) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_Nitpick_Osetsum_H__def]) ).

fof(i_0_5256,plain,
    ! [X21201,X21202,X21203] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21203),c_Groups_Ozero__class_Ozero(X21203)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21203),hAPP(hAPP(c_Power_Opower__class_Opower(X21203),X21202),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(X21203),X21201),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
        | X21202 != c_Groups_Ozero__class_Ozero(X21203)
        | X21201 != c_Groups_Ozero__class_Ozero(X21203)
        | ~ class_Rings_Olinordered__idom(X21203) )
      & ( X21202 = c_Groups_Ozero__class_Ozero(X21203)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21203),c_Groups_Ozero__class_Ozero(X21203)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21203),hAPP(hAPP(c_Power_Opower__class_Opower(X21203),X21202),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(X21203),X21201),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
        | ~ class_Rings_Olinordered__idom(X21203) )
      & ( X21201 = c_Groups_Ozero__class_Ozero(X21203)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21203),c_Groups_Ozero__class_Ozero(X21203)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21203),hAPP(hAPP(c_Power_Opower__class_Opower(X21203),X21202),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(X21203),X21201),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
        | ~ class_Rings_Olinordered__idom(X21203) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__power2__gt__zero__iff])])]) ).

fof(i_0_5257,plain,
    ! [X31439,X31440,X31441,X31442] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31442)),X31441))),c_List_Ofoldr(tc_List_Olist(X31440),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X31440)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X31440))),X31439,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(X31442)),X31441)),c_List_Ofoldr(tc_List_Olist(X31440),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X31440)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(X31440),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X31440)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X31440)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_List_Ofilter(tc_List_Olist(X31440),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X31440)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X31440),tc_List_Olist(X31440),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X31440)))),X31439),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    inference(variable_rename,[status(thm)],[fact_transpose__aux__max]) ).

fof(i_0_5258,plain,
    ! [X31660,X31661,X31662,X31663,X31664] : c_List_Ofoldr(X31664,X31663,X31662,X31661,X31660) = hAPP(c_List_Ofoldl(X31663,X31664,hAPP(c_COMBC(X31664,X31663,X31663),X31662),X31660),hAPP(c_List_Orev(X31664),X31661)),
    inference(variable_rename,[status(thm)],[fact_foldr__foldl]) ).

fof(i_0_5259,plain,
    ! [X31326,X31327,X31328,X31329] : hAPP(hAPP(c_List_Omap(tc_prod(X31329,tc_Nat_Onat),X31329),c_Product__Type_Ofst(X31329,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X31329,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X31329,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(X31329,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(X31329,tc_Nat_Onat))),X31328)),hAPP(hAPP(c_List_Ozip(X31329,tc_Nat_Onat),X31327),c_List_Oupt(X31326,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31326),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31329)),X31327)))))) = hAPP(hAPP(c_List_Omap(tc_prod(X31329,tc_Nat_Onat),X31329),c_Product__Type_Ofst(X31329,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X31329,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X31329,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(X31329,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(X31329,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(X31329,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(X31329,tc_Nat_Onat))),X31326))),X31328)),hAPP(hAPP(c_List_Ozip(X31329,tc_Nat_Onat),X31327),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31329)),X31327))))),
    inference(variable_rename,[status(thm)],[fact_sublist__shift__lemma]) ).

fof(i_0_5260,plain,
    ! [X31336,X31337] : c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X31337),X31336)) = c_List_Oupt(X31337,X31336),
    inference(variable_rename,[status(thm)],[fact_sorted__list__of__set__range]) ).

fof(i_0_5261,plain,
    ! [X293,X1,X5,X294] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X294),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))
       => c_Random__Sequence_ORandom(X5,X1,X294,X293) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(X5)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X294),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))
       => c_Random__Sequence_ORandom(X5,X1,X294,X293) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X5,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm)),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(X1,X293)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_prod(X5,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random__Sequence_ORandom(X5,X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X294),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X293))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5))))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_prod(X5,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5))))),c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5))))),tc_prod(X5,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Ounion(X5)),hAPP(hAPP(c_COMBB(X5,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X5)))),tc_prod(X5,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Osingle(X5)),c_Product__Type_Ofst(X5,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))))))) ) ),
    inference(fof_simplification,[status(thm)],[fact_Random_Osimps]) ).

fof(i_0_5262,plain,
    ! [X20961,X20962] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X20962)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20961)) = 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)))),X20962)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20961)),
    inference(variable_rename,[status(thm)],[fact_Suc__div__eq__add3__div__number__of]) ).

fof(i_0_5263,plain,
    ! [X21036,X21037] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X21037)))),X21036) = 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)))),X21037)),X21036),
    inference(variable_rename,[status(thm)],[fact_Suc__div__eq__add3__div]) ).

fof(i_0_5264,plain,
    ! [X30420,X30421] : hAPP(c_New__DSequence_Opos__not__seq(X30421),X30420) = c_Lazy__Sequence_Ohb__not__seq(hAPP(X30421,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)))),X30420))),
    inference(variable_rename,[status(thm)],[fact_New__DSequence_Opos__not__seq__def]) ).

fof(i_0_5265,plain,
    ! [X160,X23,X116,X20,X120,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X120),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X20,X116,tc_fun(X5,tc_HOL_Obool)),X23),X160)))
     => ~ ! [X3,X177] :
            ( X160 = hAPP(hAPP(c_Product__Type_OPair(X20,X116),X3),X177)
           => ~ hBOOL(hAPP(hAPP(c_member(X5),X120),hAPP(hAPP(X23,X3),X177))) ) ),
    inference(fof_simplification,[status(thm)],[fact_mem__splitE]) ).

fof(i_0_5266,plain,
    ! [X123,X21,X25,X120,X2,X20,X5] :
      ( c_Finite__Set_Ofun__left__comm(X5,X20,X2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X20,X2,X120,hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)),X123))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => ~ ! [X177] :
                ( X123 = hAPP(hAPP(X2,X25),X177)
               => ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X20,X2,X120,X21),X177)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_fun__left__comm_Ofold__graph__insertE]) ).

fof(i_0_5267,plain,
    ! [X21238] :
      ( ( X21238 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
        | hAPP(c_Code__Numeral_Oint__of,X21238) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X21238,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,X21238) = hAPP(hAPP(c_Groups_Otimes__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),X21238),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
        | X21238 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
      & ( c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X21238,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,X21238) = 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),X21238),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))
        | X21238 = 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_5268,plain,
    ! [X21192,X21193,X21194] :
      ( ~ class_Rings_Olinordered__idom(X21194)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21194),c_Groups_Ozero__class_Ozero(X21194)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21194),hAPP(hAPP(c_Power_Opower__class_Opower(X21194),X21193),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(X21194),X21192),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_5269,plain,
    ! [X2,X20,X21,X5] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X20),hAPP(c_Set_Oimage(X5,X20,X2),X21)))
       => ? [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),X21))
            & ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X21))),hAPP(hAPP(c_COMBC(X5,X20,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X20,tc_fun(X20,tc_HOL_Obool),X5),c_fequal),X2)),hAPP(X2,X3)))))) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_pigeonhole__infinite]) ).

fof(i_0_5270,plain,
    ! [X31288,X31289,X31290] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X31290),tc_List_Olist(X31290))),esk388_3(X31288,X31289,X31290)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(X31290),tc_List_Olist(X31290))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(X31290),tc_List_Olist(X31290)),X31289),X31288))))
        | X31289 = X31288
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31290))),X31289) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31290))),X31288)
        | c_List_Oconcat(X31290,X31289) != c_List_Oconcat(X31290,X31288) )
      & ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X31290),tc_List_Olist(X31290),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X31290),tc_fun(tc_List_Olist(X31290),tc_Nat_Onat),tc_fun(tc_List_Olist(X31290),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X31290),tc_Nat_Onat),tc_fun(tc_List_Olist(X31290),tc_HOL_Obool)),tc_List_Olist(X31290)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X31290))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X31290)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X31290))))),c_Nat_Osize__class_Osize(tc_List_Olist(X31290)))),esk388_3(X31288,X31289,X31290)))
        | X31289 = X31288
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31290))),X31289) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31290))),X31288)
        | c_List_Oconcat(X31290,X31289) != c_List_Oconcat(X31290,X31288) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_concat__injective])])])]) ).

fof(i_0_5271,plain,
    ! [X31284,X31285,X31286] :
      ( ( c_List_Oconcat(X31286,X31285) != c_List_Oconcat(X31286,X31284)
        | X31285 = X31284
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31286))),X31285) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31286))),X31284)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X31286),tc_List_Olist(X31286))),esk387_3(X31284,X31285,X31286)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(X31286),tc_List_Olist(X31286))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(X31286),tc_List_Olist(X31286)),X31285),X31284)))) )
      & ( X31285 != X31284
        | c_List_Oconcat(X31286,X31285) = c_List_Oconcat(X31286,X31284)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31286))),X31285) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31286))),X31284)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X31286),tc_List_Olist(X31286))),esk387_3(X31284,X31285,X31286)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(X31286),tc_List_Olist(X31286))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(X31286),tc_List_Olist(X31286)),X31285),X31284)))) )
      & ( c_List_Oconcat(X31286,X31285) != c_List_Oconcat(X31286,X31284)
        | X31285 = X31284
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31286))),X31285) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31286))),X31284)
        | ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X31286),tc_List_Olist(X31286),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X31286),tc_fun(tc_List_Olist(X31286),tc_Nat_Onat),tc_fun(tc_List_Olist(X31286),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X31286),tc_Nat_Onat),tc_fun(tc_List_Olist(X31286),tc_HOL_Obool)),tc_List_Olist(X31286)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X31286))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X31286)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X31286))))),c_Nat_Osize__class_Osize(tc_List_Olist(X31286)))),esk387_3(X31284,X31285,X31286))) )
      & ( X31285 != X31284
        | c_List_Oconcat(X31286,X31285) = c_List_Oconcat(X31286,X31284)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31286))),X31285) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31286))),X31284)
        | ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X31286),tc_List_Olist(X31286),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X31286),tc_fun(tc_List_Olist(X31286),tc_Nat_Onat),tc_fun(tc_List_Olist(X31286),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X31286),tc_Nat_Onat),tc_fun(tc_List_Olist(X31286),tc_HOL_Obool)),tc_List_Olist(X31286)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X31286))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X31286)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X31286))))),c_Nat_Osize__class_Osize(tc_List_Olist(X31286)))),esk387_3(X31284,X31285,X31286))) ) ),
    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_5272,plain,
    ! [X21837,X21838,X21839,X21840,X21841] : hAPP(c_Nat_Onat_Onat__rec(X21841,X21840,X21839),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21838)),X21837)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X21841),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X21838))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X21841,X21841),hAPP(hAPP(c_COMBC(tc_Int_Oint,X21841,tc_fun(X21841,X21841)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X21841,tc_fun(X21841,X21841)),tc_Int_Oint),c_If(X21841)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(X21841,X21840,X21839),X21837))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X21841,X21841),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X21841,X21841),tc_Int_Oint),X21839),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)),X21837))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X21841,tc_Int_Oint),c_Nat_Onat_Onat__rec(X21841,X21840,X21839)),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)),X21837))))),
    inference(variable_rename,[status(thm)],[fact_nat__rec__add__eq__if]) ).

fof(i_0_5273,plain,
    ! [X20859] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20859),c_Int_OMin) = c_Int_Opred(X20859),
    inference(variable_rename,[status(thm)],[fact_add__Min__right]) ).

fof(i_0_5274,plain,
    ! [X21038,X21039] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21039),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)))),X21038)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X21039)) = 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),X21038),c_Groups_Oone__class_Oone(tc_Int_Oint)),X21039))),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_5275,plain,
    ! [X21042,X21043] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21043),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)))),X21042))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X21043)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21042),c_Groups_Oone__class_Oone(tc_Int_Oint))),X21043) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__zdiv__mult__2])]) ).

fof(i_0_5276,plain,
    ! [X21044,X21045] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21045))
      | 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)))),X21044))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X21045)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X21044),X21045) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__zdiv__mult__2])]) ).

fof(i_0_5277,plain,
    ! [X21768,X21769] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21769) != hAPP(c_Nat_OSuc,X21768)
        | 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(X21769))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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)),X21768))))) )
      & ( ~ 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(X21769))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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)),X21768)))))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21769) = hAPP(c_Nat_OSuc,X21768) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__number__of__Suc])]) ).

fof(i_0_5278,plain,
    ! [X21770,X21771] :
      ( ( hAPP(c_Nat_OSuc,X21771) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21770)
        | 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(X21770))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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)),X21771))))) )
      & ( ~ 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(X21770))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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)),X21771)))))
        | hAPP(c_Nat_OSuc,X21771) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21770) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__eq__number__of])]) ).

fof(i_0_5279,plain,
    ! [X21,X5] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => c_Nitpick_Ocard_H(X5,X21) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_Hilbert__Choice_OEps(tc_List_Olist(X5),hAPP(hAPP(c_COMBS(tc_List_Olist(X5),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X5)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X5),tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X5,tc_HOL_Obool),tc_fun(tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X5)),c_fequal),c_List_Oset(X5))),X21))),c_List_Odistinct(X5)))) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => c_Nitpick_Ocard_H(X5,X21) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_simplification,[status(thm)],[fact_Nitpick_Ocard_H__def]) ).

fof(i_0_5280,plain,
    ! [X82,X210] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X210))
     => 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)),X210))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X82)))) = 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)),X210))),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,X82))))) ),
    inference(fof_simplification,[status(thm)],[fact_card__less__Suc2]) ).

fof(i_0_5281,plain,
    ! [X21165,X21166,X21167] :
      ( ~ class_Rings_Olinordered__semidom(X21167)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21167),hAPP(hAPP(c_Power_Opower__class_Opower(X21167),X21166),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(X21167),X21165),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(X21167),c_Groups_Ozero__class_Ozero(X21167)),X21165))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21167),X21166),X21165)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__le__imp__le])]) ).

fof(i_0_5282,plain,
    ! [X21189,X21190,X21191] :
      ( ~ class_Rings_Olinordered__semidom(X21191)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21191),hAPP(hAPP(c_Power_Opower__class_Opower(X21191),X21190),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(X21191),X21189),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(X21191),c_Groups_Ozero__class_Ozero(X21191)),X21189))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21191),X21190),X21189)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__less__imp__less])]) ).

fof(i_0_5283,plain,
    ! [X113,X20,X22,X21,X23,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X23),X21))
       => ( ( hBOOL(hAPP(hAPP(c_member(X5),X22),X21))
           => hAPP(c_Set_Ovimage(X20,X5,hAPP(hAPP(c_COMBC(X20,X5,X5),hAPP(hAPP(c_COMBC(X20,X5,tc_fun(X5,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5,tc_fun(X5,X5)),X20),c_If(X5)),hAPP(hAPP(c_COMBC(X20,tc_fun(X20,tc_HOL_Obool),tc_HOL_Obool),c_member(X20)),X113))),X23)),X22)),X21) = c_Orderings_Otop__class_Otop(tc_fun(X20,tc_HOL_Obool)) )
          & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X22),X21))
           => hAPP(c_Set_Ovimage(X20,X5,hAPP(hAPP(c_COMBC(X20,X5,X5),hAPP(hAPP(c_COMBC(X20,X5,tc_fun(X5,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5,tc_fun(X5,X5)),X20),c_If(X5)),hAPP(hAPP(c_COMBC(X20,tc_fun(X20,tc_HOL_Obool),tc_HOL_Obool),c_member(X20)),X113))),X23)),X22)),X21) = X113 ) ) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X23),X21))
       => ( ( hBOOL(hAPP(hAPP(c_member(X5),X22),X21))
           => hAPP(c_Set_Ovimage(X20,X5,hAPP(hAPP(c_COMBC(X20,X5,X5),hAPP(hAPP(c_COMBC(X20,X5,tc_fun(X5,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5,tc_fun(X5,X5)),X20),c_If(X5)),hAPP(hAPP(c_COMBC(X20,tc_fun(X20,tc_HOL_Obool),tc_HOL_Obool),c_member(X20)),X113))),X23)),X22)),X21) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20,tc_HOL_Obool)),X113) )
          & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X22),X21))
           => hAPP(c_Set_Ovimage(X20,X5,hAPP(hAPP(c_COMBC(X20,X5,X5),hAPP(hAPP(c_COMBC(X20,X5,tc_fun(X5,X5)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X5,tc_fun(X5,X5)),X20),c_If(X5)),hAPP(hAPP(c_COMBC(X20,tc_fun(X20,tc_HOL_Obool),tc_HOL_Obool),c_member(X20)),X113))),X23)),X22)),X21) = c_Orderings_Obot__class_Obot(tc_fun(X20,tc_HOL_Obool)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_vimage__if]) ).

fof(i_0_5284,plain,
    ! [X21046,X21047] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21047))
      | 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)))),X21046)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X21047)) = 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,X21046,X21047))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__zmod__mult__2])]) ).

fof(i_0_5285,plain,
    ! [X21032,X21033] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X21033))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21032)) = 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)))),X21033),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21032)),
    inference(variable_rename,[status(thm)],[fact_Suc__mod__eq__add3__mod__number__of]) ).

fof(i_0_5286,plain,
    ! [X21207,X21208,X21209] :
      ( ~ class_Rings_Olinordered__idom(X21209)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21209),c_Groups_Ozero__class_Ozero(X21209)),hAPP(hAPP(c_Power_Opower__class_Opower(X21209),X21208),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)))),X21207)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__even__power_H])]) ).

fof(i_0_5287,plain,
    ! [X21030,X21031] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X21031))),X21030) = 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)))),X21031),X21030),
    inference(variable_rename,[status(thm)],[fact_Suc__mod__eq__add3__mod]) ).

fof(i_0_5288,plain,
    ! [X21028,X21029] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21029,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X21028)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21029,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)))),X21028)),
    inference(variable_rename,[status(thm)],[fact_mod__Suc__eq__mod__add3]) ).

fof(i_0_5289,plain,
    ! [X21034,X21035] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X21035),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X21034)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X21035),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)))),X21034)),
    inference(variable_rename,[status(thm)],[fact_div__Suc__eq__div__add3]) ).

fof(i_0_5290,plain,
    ! [X32384,X32385,X32386] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X32386,X32386),tc_HOL_Obool)),X32385),X32384))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X32386,X32386),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X32386,X32386,X32386),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X32386,X32386),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X32386,X32385)),X32384)),X32385)),X32384))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X32386,X32386),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X32386,X32385)),X32384)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__Int__subset])]) ).

fof(i_0_5291,plain,
    ! [X23,X24,X6,X192,X5,X20] :
      ( class_Groups_Ocomm__monoid__mult(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X192))
       => ( ( hBOOL(hAPP(hAPP(c_member(X5),X6),X192))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),hAPP(hAPP(c_COMBC(X5,X20,X20),hAPP(hAPP(c_COMBS(X5,X20,tc_fun(X20,X20)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X20,tc_fun(X20,X20)),X5),c_If(X20)),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X6))),X24)),X23)),X192) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20),hAPP(X24,X6)),hAPP(hAPP(c_Power_Opower__class_Opower(X20),X23),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X192)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
          & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X192))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),hAPP(hAPP(c_COMBC(X5,X20,X20),hAPP(hAPP(c_COMBS(X5,X20,tc_fun(X20,X20)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X20,tc_fun(X20,X20)),X5),c_If(X20)),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X6))),X24)),X23)),X192) = hAPP(hAPP(c_Power_Opower__class_Opower(X20),X23),hAPP(c_Finite__Set_Ocard(X5),X192)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_setprod__gen__delta]) ).

fof(i_0_5292,plain,
    ! [X24,X6,X192,X5,X20] :
      ( class_Groups_Ocomm__monoid__add(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X192))
       => ( ( hBOOL(hAPP(hAPP(c_member(X5),X6),X192))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),hAPP(hAPP(c_COMBC(X5,X20,X20),hAPP(hAPP(c_COMBS(X5,X20,tc_fun(X20,X20)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X20,tc_fun(X20,X20)),X5),c_If(X20)),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X6))),X24)),c_Groups_Ozero__class_Ozero(X20))),X192) = hAPP(X24,X6) )
          & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X192))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),hAPP(hAPP(c_COMBC(X5,X20,X20),hAPP(hAPP(c_COMBS(X5,X20,tc_fun(X20,X20)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X20,tc_fun(X20,X20)),X5),c_If(X20)),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X6))),X24)),c_Groups_Ozero__class_Ozero(X20))),X192) = c_Groups_Ozero__class_Ozero(X20) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_setsum__delta]) ).

fof(i_0_5293,plain,
    ! [X24,X6,X192,X5,X20] :
      ( class_Groups_Ocomm__monoid__mult(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X192))
       => ( ( hBOOL(hAPP(hAPP(c_member(X5),X6),X192))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),hAPP(hAPP(c_COMBC(X5,X20,X20),hAPP(hAPP(c_COMBS(X5,X20,tc_fun(X20,X20)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X20,tc_fun(X20,X20)),X5),c_If(X20)),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X6))),X24)),c_Groups_Oone__class_Oone(X20))),X192) = hAPP(X24,X6) )
          & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X192))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),hAPP(hAPP(c_COMBC(X5,X20,X20),hAPP(hAPP(c_COMBS(X5,X20,tc_fun(X20,X20)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X20,tc_fun(X20,X20)),X5),c_If(X20)),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X6))),X24)),c_Groups_Oone__class_Oone(X20))),X192) = c_Groups_Oone__class_Oone(X20) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_setprod__delta]) ).

fof(i_0_5294,plain,
    ! [X21781,X21782] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21782)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21781)))
        | 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(X21781))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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),X21782)),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(X21781))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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),X21782)),c_Int_Onat)))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21782)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21781))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__Suc__number__of])]) ).

fof(i_0_5295,plain,
    ! [X21777,X21778] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21778)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21777)))
        | 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(X21777))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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),X21778)),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(X21777))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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),X21778)),c_Int_Onat)))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21778)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21777))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__number__of])]) ).

fof(i_0_5296,plain,
    ! [X22712,X22713,X22714,X22715,X22716,X22717,X22718] : hAPP(c_Product__Type_Oapsnd(X22718,X22717,X22716,X22715),hAPP(c_Product__Type_Oapfst(X22714,X22716,X22718,X22713),X22712)) = hAPP(c_Product__Type_Oapfst(X22714,X22716,X22717,X22713),hAPP(c_Product__Type_Oapsnd(X22718,X22717,X22714,X22715),X22712)),
    inference(variable_rename,[status(thm)],[fact_apsnd__apfst__commute]) ).

fof(i_0_5297,plain,
    ! [X27952,X27953,X27954,X27955] : c_Product__Type_Oapfst(X27955,X27954,X27953,X27952) = c_Product__Type_Omap__pair(X27955,X27954,X27953,X27953,X27952,c_Fun_Oid(X27953)),
    inference(variable_rename,[status(thm)],[fact_apfst__def]) ).

fof(i_0_5298,plain,
    ! [X171,X123,X159,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(hAPP(c_List_Oappend(X5),X25),X159)),hAPP(hAPP(c_List_Oappend(X5),X25),X123))),c_List_Olexord(X5,X171)))
     => ( ! [X187] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X187),X187)),X171))
       => 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)),X159),X123)),c_List_Olexord(X5,X171))) ) ),
    inference(fof_simplification,[status(thm)],[fact_lexord__append__leftD]) ).

fof(i_0_5299,plain,
    ! [X21173,X21174] :
      ( ~ class_Rings_Olinordered__idom(X21174)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21174),hAPP(hAPP(c_Power_Opower__class_Opower(X21174),X21173),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X21174))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5189])]) ).

fof(i_0_5300,plain,
    ! [X32,X50,X120,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X120)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X50),X32)))
     => ( ( X50 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => X25 != X120 )
       => ~ ! [X177,X86] :
              ( X50 = hAPP(c_Nat_OSuc,X86)
             => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X177)),X32))
               => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X177),X120)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X86),X32))) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_rel__pow__E2]) ).

fof(i_0_5301,plain,
    ! [X21213,X21214,X21215] :
      ( ~ class_Groups_Omonoid__mult(X21215)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X21215),X21214),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)))),X21213))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21215),X21214),hAPP(hAPP(c_Power_Opower__class_Opower(X21215),hAPP(hAPP(c_Power_Opower__class_Opower(X21215),X21214),X21213)),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_5302,plain,
    ! [X31789,X31790,X31791] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X31791),X31790))
      | ~ hBOOL(hAPP(hAPP(c_member(X31791),X31789),hAPP(c_List_Oset(X31791),X31790)))
      | c_List_OtakeWhile(X31791,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X31791),c_fNot),hAPP(hAPP(c_COMBC(X31791,X31791,tc_HOL_Obool),c_fequal),X31789)),hAPP(c_List_Orev(X31791),X31790)) = hAPP(c_List_Orev(X31791),hAPP(c_List_Otl(X31791),c_List_OdropWhile(X31791,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X31791),c_fNot),hAPP(hAPP(c_COMBC(X31791,X31791,tc_HOL_Obool),c_fequal),X31789)),X31790))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_takeWhile__neq__rev])]) ).

fof(i_0_5303,plain,
    ! [X31839,X31840,X31841] : c_List_OdropWhile(X31841,X31840,X31839) = hAPP(hAPP(c_List_Odrop(X31841),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31841)),c_List_OtakeWhile(X31841,X31840,X31839))),X31839),
    inference(variable_rename,[status(thm)],[fact_dropWhile__eq__drop]) ).

fof(i_0_5304,plain,
    ! [X21990,X21991,X21992,X21993,X21994,X21995,X21996] : hAPP(c_Product__Type_Oapsnd(X21996,X21995,X21994,X21993),hAPP(c_Product__Type_Oapsnd(X21992,X21996,X21994,X21991),X21990)) = hAPP(c_Product__Type_Oapsnd(X21992,X21995,X21994,hAPP(c_Fun_Ocomp(X21996,X21995,X21992,X21993),X21991)),X21990),
    inference(variable_rename,[status(thm)],[fact_apsnd__compose]) ).

fof(i_0_5305,plain,
    ! [X22670,X22671,X22672,X22673,X22674,X22675,X22676] : hAPP(c_Product__Type_Oapfst(X22676,X22675,X22674,X22673),hAPP(c_Product__Type_Oapfst(X22672,X22676,X22674,X22671),X22670)) = hAPP(c_Product__Type_Oapfst(X22672,X22675,X22674,hAPP(c_Fun_Ocomp(X22676,X22675,X22672,X22673),X22671)),X22670),
    inference(variable_rename,[status(thm)],[fact_apfst__compose]) ).

fof(i_0_5306,plain,
    ! [X21175,X21176,X21177] :
      ( ( X21176 = c_Groups_Ozero__class_Ozero(X21177)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21177),hAPP(hAPP(c_Power_Opower__class_Opower(X21177),X21176),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(X21177),X21175),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(X21177)
        | ~ class_Rings_Olinordered__idom(X21177) )
      & ( X21175 = c_Groups_Ozero__class_Ozero(X21177)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21177),hAPP(hAPP(c_Power_Opower__class_Opower(X21177),X21176),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(X21177),X21175),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(X21177)
        | ~ class_Rings_Olinordered__idom(X21177) )
      & ( X21176 != c_Groups_Ozero__class_Ozero(X21177)
        | X21175 != c_Groups_Ozero__class_Ozero(X21177)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21177),hAPP(hAPP(c_Power_Opower__class_Opower(X21177),X21176),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(X21177),X21175),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(X21177)
        | ~ class_Rings_Olinordered__idom(X21177) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__power2__eq__zero__iff])])]) ).

fof(i_0_5307,plain,
    ! [X31400,X31401,X31402] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk390_3(X31400,X31401,X31402)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31401))),X31402)))
        | c_List_Otranspose(X31401,X31402) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X31401)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X31401)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X31401),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X31401)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X31401)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X31401),hAPP(hAPP(c_COMBB(tc_List_Olist(X31401),tc_fun(tc_Nat_Onat,X31401),tc_Nat_Onat),c_List_Onth(X31401)),hAPP(c_List_Onth(tc_List_Olist(X31401)),X31402))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31401))),X31402)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X31400))
        | X31402 = c_List_Olist_ONil(tc_List_Olist(X31401)) )
      & ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31401)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X31401)),X31402),esk390_3(X31400,X31401,X31402))) != X31400
        | c_List_Otranspose(X31401,X31402) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X31401)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X31401)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X31401),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X31401)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X31401)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X31401),hAPP(hAPP(c_COMBB(tc_List_Olist(X31401),tc_fun(tc_Nat_Onat,X31401),tc_Nat_Onat),c_List_Onth(X31401)),hAPP(c_List_Onth(tc_List_Olist(X31401)),X31402))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31401))),X31402)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X31400))
        | X31402 = c_List_Olist_ONil(tc_List_Olist(X31401)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk390_3(X31400,X31401,X31402)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31401))),X31402)))
        | c_List_Otranspose(X31401,X31402) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X31401)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X31401)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X31401),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X31401)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X31401)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X31401),hAPP(hAPP(c_COMBB(tc_List_Olist(X31401),tc_fun(tc_Nat_Onat,X31401),tc_Nat_Onat),c_List_Onth(X31401)),hAPP(c_List_Onth(tc_List_Olist(X31401)),X31402))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31401))),X31402)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X31400))
        | X31400 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31401)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X31401)),X31402),esk390_3(X31400,X31401,X31402))) != X31400
        | c_List_Otranspose(X31401,X31402) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X31401)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X31401)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X31401),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X31401)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X31401)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X31401),hAPP(hAPP(c_COMBB(tc_List_Olist(X31401),tc_fun(tc_Nat_Onat,X31401),tc_Nat_Onat),c_List_Onth(X31401)),hAPP(c_List_Onth(tc_List_Olist(X31401)),X31402))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31401))),X31402)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X31400))
        | X31400 != 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_5308,plain,
    ! [X21040,X21041] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21041)))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X21040)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X21041))) = 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),X21040),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21041)))),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),X21041)))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X21040)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X21041))) = 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),X21040)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21041)))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5190])]) ).

fof(i_0_5309,plain,
    ! [X22134,X22135,X22136] :
      ( ( 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),esk86_3(X22134,X22135,X22136)),esk87_3(X22134,X22135,X22136))))
        | hBOOL(hAPP(hAPP(X22134,X22136),X22135))
        | ~ 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),X22136),X22135))) )
      & ( 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),esk86_3(X22134,X22135,X22136)),esk87_3(X22134,X22135,X22136))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk87_3(X22134,X22135,X22136)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(X22134,esk86_3(X22134,X22135,X22136)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),esk87_3(X22134,X22135,X22136))))
        | hBOOL(hAPP(hAPP(X22134,X22136),X22135))
        | ~ 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),X22136),X22135))) )
      & ( ~ hBOOL(hAPP(hAPP(X22134,esk86_3(X22134,X22135,X22136)),esk87_3(X22134,X22135,X22136)))
        | hBOOL(hAPP(hAPP(X22134,X22136),X22135))
        | ~ 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),X22136),X22135))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_negDivAlg_Opinduct])])])]) ).

fof(i_0_5310,plain,
    ! [X24,X6,X192,X5,X20] :
      ( class_Groups_Ocomm__monoid__add(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X192))
       => ( ( hBOOL(hAPP(hAPP(c_member(X5),X6),X192))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),hAPP(hAPP(c_COMBC(X5,X20,X20),hAPP(hAPP(c_COMBS(X5,X20,tc_fun(X20,X20)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X20,tc_fun(X20,X20)),X5),c_If(X20)),hAPP(c_fequal,X6))),X24)),c_Groups_Ozero__class_Ozero(X20))),X192) = hAPP(X24,X6) )
          & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X192))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),hAPP(hAPP(c_COMBC(X5,X20,X20),hAPP(hAPP(c_COMBS(X5,X20,tc_fun(X20,X20)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X20,tc_fun(X20,X20)),X5),c_If(X20)),hAPP(c_fequal,X6))),X24)),c_Groups_Ozero__class_Ozero(X20))),X192) = c_Groups_Ozero__class_Ozero(X20) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_setsum__delta_H]) ).

fof(i_0_5311,plain,
    ! [X24,X6,X192,X5,X20] :
      ( class_Groups_Ocomm__monoid__mult(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X192))
       => ( ( hBOOL(hAPP(hAPP(c_member(X5),X6),X192))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),hAPP(hAPP(c_COMBC(X5,X20,X20),hAPP(hAPP(c_COMBS(X5,X20,tc_fun(X20,X20)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X20,tc_fun(X20,X20)),X5),c_If(X20)),hAPP(c_fequal,X6))),X24)),c_Groups_Oone__class_Oone(X20))),X192) = hAPP(X24,X6) )
          & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X192))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),hAPP(hAPP(c_COMBC(X5,X20,X20),hAPP(hAPP(c_COMBS(X5,X20,tc_fun(X20,X20)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X20,tc_fun(X20,X20)),X5),c_If(X20)),hAPP(c_fequal,X6))),X24)),c_Groups_Oone__class_Oone(X20))),X192) = c_Groups_Oone__class_Oone(X20) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_setprod__delta_H]) ).

fof(i_0_5312,plain,
    ! [X22139,X22140,X22141] :
      ( ( 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),esk88_3(X22139,X22140,X22141)),esk89_3(X22139,X22140,X22141))))
        | hBOOL(hAPP(hAPP(X22139,X22141),X22140))
        | ~ 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),X22141),X22140))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk88_3(X22139,X22140,X22141)),esk89_3(X22139,X22140,X22141)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk89_3(X22139,X22140,X22141)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(X22139,esk88_3(X22139,X22140,X22141)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),esk89_3(X22139,X22140,X22141))))
        | hBOOL(hAPP(hAPP(X22139,X22141),X22140))
        | ~ 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),X22141),X22140))) )
      & ( ~ hBOOL(hAPP(hAPP(X22139,esk88_3(X22139,X22140,X22141)),esk89_3(X22139,X22140,X22141)))
        | hBOOL(hAPP(hAPP(X22139,X22141),X22140))
        | ~ 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),X22141),X22140))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_posDivAlg_Opinduct])])])]) ).

fof(i_0_5313,plain,
    ! [X171,X251,X33,X239,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X239),hAPP(hAPP(c_List_Olist_OCons(X5),X33),X251))),c_List_Olistrel(X5,X171)))
     => ~ ! [X3,X263] :
            ( X239 = hAPP(hAPP(c_List_Olist_OCons(X5),X3),X263)
           => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X33)),X171))
             => ~ 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)),X263),X251)),c_List_Olistrel(X5,X171))) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_listrel__Cons2]) ).

fof(i_0_5314,plain,
    ! [X32,X50,X120,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X120)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),hAPP(c_Nat_OSuc,X50)),X32)))
     => ~ ! [X177] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X177)),X32))
           => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X177),X120)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X50),X32))) ) ),
    inference(fof_simplification,[status(thm)],[fact_rel__pow__Suc__E2]) ).

fof(i_0_5315,plain,
    ! [X33134,X33135,X33136] : c_Nitpick_Otimes__frac(X33136,X33135,X33134) = hAPP(hAPP(c_Nitpick_Ofrac(X33136),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(X33136),X33135)),hAPP(c_Nitpick_Onum(X33136),X33134))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Odenom(X33136),X33135)),hAPP(c_Nitpick_Odenom(X33136),X33134))),
    inference(variable_rename,[status(thm)],[fact_Nitpick_Otimes__frac__def]) ).

fof(i_0_5316,plain,
    ! [X32,X50,X120,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X120)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X50),X32)))
     => ( ( X50 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => X25 != X120 )
       => ~ ! [X177,X86] :
              ( X50 = hAPP(c_Nat_OSuc,X86)
             => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X177)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X86),X32)))
               => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X177),X120)),X32)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_rel__pow__E]) ).

fof(i_0_5317,plain,
    ! [X32,X50,X120,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X120)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),hAPP(c_Nat_OSuc,X50)),X32)))
     => ~ ! [X177] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X177)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X5,X5),tc_HOL_Obool),X50),X32)))
           => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X177),X120)),X32)) ) ),
    inference(fof_simplification,[status(thm)],[fact_rel__pow__Suc__E]) ).

fof(i_0_5318,plain,
    ! [X21803,X21804] :
      ( ( ~ 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),X21803)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21804))))
        | c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21803),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21804)) = 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),X21803)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21804)))
        | ~ 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),X21804))) )
      & ( 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),X21803)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21804))))
        | c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21803),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21804)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21804)),c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21803),hAPP(hAPP(c_Groups_Otimes__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),X21804))))
        | ~ 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),X21804))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5191])])]) ).

fof(i_0_5319,plain,
    ! [X22024,X22025] :
      ( ( ~ 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),X22025),X22024)))
        | c_Divides_OnegDivAlg(X22025,X22024) = 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),X22025),X22024))
        | ~ 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),X22025),X22024))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22024),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | c_Divides_OnegDivAlg(X22025,X22024) = 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),X22025),X22024))
        | ~ 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),X22025),X22024))) )
      & ( 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),X22025),X22024)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22024),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | c_Divides_OnegDivAlg(X22025,X22024) = hAPP(c_Divides_Oadjust(X22024),c_Divides_OnegDivAlg(X22025,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X22024)))
        | ~ 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),X22025),X22024))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_negDivAlg_Opsimps])])]) ).

fof(i_0_5320,plain,
    ! [X21693] :
      ( ( ~ 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),X21693))))
        | c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21693)) = 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),X21693)))
        | ~ 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),X21693))) )
      & ( 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),X21693))))
        | c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21693)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21693)),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),X21693))))
        | ~ 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),X21693))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5192])])]) ).

fof(i_0_5321,plain,
    ! [X22031,X22032] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22032),X22031))
        | c_Divides_OposDivAlg(X22032,X22031) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22032)
        | ~ 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),X22032),X22031))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22031),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | c_Divides_OposDivAlg(X22032,X22031) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22032)
        | ~ 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),X22032),X22031))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22032),X22031))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22031),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | c_Divides_OposDivAlg(X22032,X22031) = hAPP(c_Divides_Oadjust(X22031),c_Divides_OposDivAlg(X22032,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X22031)))
        | ~ 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),X22032),X22031))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_posDivAlg_Opsimps])])]) ).

fof(i_0_5322,plain,
    ! [X21823,X21824] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21823)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21824)))
        | c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21823),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21824)) = 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),X21823))
        | ~ 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),X21824))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21823)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21824)))
        | c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21823),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21824)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21824)),c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21823),hAPP(hAPP(c_Groups_Otimes__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),X21824))))
        | ~ 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),X21824))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5193])])]) ).

fof(i_0_5323,plain,
    ! [X21210,X21211,X21212] :
      ( ~ class_Rings_Ocomm__semiring__1(X21212)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X21212),X21211),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)))),X21210))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21212),X21211),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21212),hAPP(hAPP(c_Power_Opower__class_Opower(X21212),X21211),X21210)),hAPP(hAPP(c_Power_Opower__class_Opower(X21212),X21211),X21210))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J])]) ).

fof(i_0_5324,plain,
    ! [X26156,X26157,X26158] : hAPP(hAPP(c_Groups_Otimes__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),X26158)),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))),X26157))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X26156))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X26156)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26158),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26158),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),X26156),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X26157)))),
    inference(variable_rename,[status(thm)],[fact_arith__series__int]) ).

fof(i_0_5325,plain,
    ! [X21783,X21784] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21784)),hAPP(c_Nat_OSuc,X21783)))
        | 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(X21784))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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)),X21783)))) )
      & ( ~ 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(X21784))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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)),X21783))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21784)),hAPP(c_Nat_OSuc,X21783))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__number__of__Suc])]) ).

fof(i_0_5326,plain,
    ! [X21779,X21780] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21780)),hAPP(c_Nat_OSuc,X21779)))
        | 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(X21780))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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)),X21779)))) )
      & ( ~ 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(X21780))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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)),X21779))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21780)),hAPP(c_Nat_OSuc,X21779))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__number__of__Suc])]) ).

fof(i_0_5327,plain,
    ! [X21809] :
      ( ( ~ 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),X21809)))
        | c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21809)) = 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),X21809))) )
      & ( 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),X21809)))
        | c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21809)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21809)),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),X21809))))
        | ~ 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),X21809))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5194])])]) ).

fof(i_0_5328,plain,
    ! [X21048,X21049] :
      ( ~ class_Rings_Osemiring__1(X21049)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21048))
      | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X21049),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)))),X21048))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21049),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X21049),hAPP(c_Int_Onat,X21048))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X21049),hAPP(c_Int_Onat,X21048))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__double])]) ).

fof(i_0_5329,plain,
    ! [X21805,X21806] :
      ( ( ~ 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),X21805),X21806)))
        | c_Divides_OnegDivAlg(X21805,X21806) = 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),X21805),X21806))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21806)) )
      & ( 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),X21805),X21806)))
        | c_Divides_OnegDivAlg(X21805,X21806) = hAPP(c_Divides_Oadjust(X21806),c_Divides_OnegDivAlg(X21805,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X21806)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21806)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5195])])]) ).

fof(i_0_5330,plain,
    ! [X21795,X21796] :
      ( ( ~ 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),X21796),X21795)))
        | c_Divides_OnegDivAlg(X21796,X21795) = 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),X21796),X21795)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21795),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | c_Divides_OnegDivAlg(X21796,X21795) = 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),X21796),X21795)) )
      & ( 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),X21796),X21795)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21795),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | c_Divides_OnegDivAlg(X21796,X21795) = hAPP(c_Divides_Oadjust(X21795),c_Divides_OnegDivAlg(X21796,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X21795))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_negDivAlg_Osimps])])]) ).

fof(i_0_5331,plain,
    ! [X21821,X21822] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21821),X21822))
        | c_Divides_OposDivAlg(X21821,X21822) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21821)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21822)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21821),X21822))
        | c_Divides_OposDivAlg(X21821,X21822) = hAPP(c_Divides_Oadjust(X21822),c_Divides_OposDivAlg(X21821,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X21822)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21822)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5196])])]) ).

fof(i_0_5332,plain,
    ! [X21810,X21811] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21811),X21810))
        | c_Divides_OposDivAlg(X21811,X21810) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21811) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21810),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | c_Divides_OposDivAlg(X21811,X21810) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21811) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21811),X21810))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21810),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | c_Divides_OposDivAlg(X21811,X21810) = hAPP(c_Divides_Oadjust(X21810),c_Divides_OposDivAlg(X21811,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X21810))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_posDivAlg_Osimps])])]) ).

fof(i_0_5333,plain,
    ! [X21231,X21232] :
      ( ~ class_Rings_Oring__1(X21232)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X21232),hAPP(c_Groups_Ouminus__class_Ouminus(X21232),c_Groups_Oone__class_Oone(X21232))),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)))),X21231))) = hAPP(c_Groups_Ouminus__class_Ouminus(X21232),c_Groups_Oone__class_Oone(X21232)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__minus1__odd])]) ).

fof(i_0_5334,plain,
    ! [X21186,X21187,X21188] :
      ( ~ class_Rings_Oring__1(X21188)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X21188),hAPP(c_Groups_Ouminus__class_Ouminus(X21188),X21187)),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)))),X21186)) = hAPP(hAPP(c_Power_Opower__class_Opower(X21188),X21187),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)))),X21186)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__minus__even])]) ).

fof(i_0_5335,plain,
    ! [X21235,X21236] :
      ( ~ class_Int_Onumber__ring(X21236)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X21236),hAPP(c_Int_Onumber__class_Onumber__of(X21236),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)))),X21235))) = hAPP(c_Int_Onumber__class_Onumber__of(X21236),c_Int_OMin) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__m1__odd])]) ).

fof(i_0_5336,plain,
    ! [X21013] : hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X21013))) = 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)))),X21013),
    inference(variable_rename,[status(thm)],[fact_Suc3__eq__add__3]) ).

fof(i_0_5337,plain,
    ! [X21,X171,X20,X24,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X24),hAPP(c_Relation_OImage(X20,X5,X171),X21)))
     => ~ ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(X20,X5)),hAPP(hAPP(c_Product__Type_OPair(X20,X5),X3),X24)),X171))
           => ~ hBOOL(hAPP(hAPP(c_member(X20),X3),X21)) ) ),
    inference(fof_simplification,[status(thm)],[fact_ImageE]) ).

fof(i_0_5338,plain,
    ! [X31137,X31138,X31139] : c_Enum_On__lists(X31139,hAPP(c_Nat_OSuc,X31138),X31137) = c_List_Oconcat(tc_List_Olist(X31139),hAPP(hAPP(c_List_Omap(tc_List_Olist(X31139),tc_List_Olist(tc_List_Olist(X31139))),hAPP(hAPP(c_COMBC(tc_List_Olist(X31139),tc_List_Olist(X31139),tc_List_Olist(tc_List_Olist(X31139))),hAPP(hAPP(c_COMBB(tc_fun(X31139,tc_List_Olist(X31139)),tc_fun(tc_List_Olist(X31139),tc_List_Olist(tc_List_Olist(X31139))),tc_List_Olist(X31139)),c_List_Omap(X31139,tc_List_Olist(X31139))),hAPP(c_COMBC(X31139,tc_List_Olist(X31139),tc_List_Olist(X31139)),c_List_Olist_OCons(X31139)))),X31137)),c_Enum_On__lists(X31139,X31138,X31137))),
    inference(variable_rename,[status(thm)],[fact_n__lists_Osimps_I2_J]) ).

fof(i_0_5339,plain,
    ! [X21785,X21786,X21787,X21788,X21789] : c_Nat_Onat_Onat__case(X21789,X21788,X21787,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21786)),X21785)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X21789),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X21786))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X21789,X21789),hAPP(hAPP(c_COMBC(tc_Int_Oint,X21789,tc_fun(X21789,X21789)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X21789,tc_fun(X21789,X21789)),tc_Int_Oint),c_If(X21789)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(X21789,X21788,X21787,X21785))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X21789,tc_Int_Oint),X21787),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)),X21785)))),
    inference(variable_rename,[status(thm)],[fact_nat__case__add__eq__if]) ).

fof(i_0_5340,plain,
    ! [X21220] :
      ( ( ~ 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,X21220,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,X21220,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,X21220,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,X21220,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_5341,plain,
    ! [X22163,X22164,X22165,X22166,X22167,X22168] :
      ( ( hAPP(c_Product__Type_Oapsnd(X22168,X22167,X22166,X22165),X22164) != hAPP(c_Product__Type_Oapsnd(X22168,X22167,X22166,X22163),X22164)
        | hAPP(X22165,hAPP(c_Product__Type_Osnd(X22166,X22168),X22164)) = hAPP(X22163,hAPP(c_Product__Type_Osnd(X22166,X22168),X22164)) )
      & ( hAPP(X22165,hAPP(c_Product__Type_Osnd(X22166,X22168),X22164)) != hAPP(X22163,hAPP(c_Product__Type_Osnd(X22166,X22168),X22164))
        | hAPP(c_Product__Type_Oapsnd(X22168,X22167,X22166,X22165),X22164) = hAPP(c_Product__Type_Oapsnd(X22168,X22167,X22166,X22163),X22164) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_apsnd__eq__conv])]) ).

fof(i_0_5342,plain,
    ! [X22682,X22683,X22684,X22685,X22686,X22687] :
      ( ( hAPP(c_Product__Type_Oapfst(X22687,X22686,X22685,X22684),X22683) != hAPP(c_Product__Type_Oapfst(X22687,X22686,X22685,X22682),X22683)
        | hAPP(X22684,hAPP(c_Product__Type_Ofst(X22687,X22685),X22683)) = hAPP(X22682,hAPP(c_Product__Type_Ofst(X22687,X22685),X22683)) )
      & ( hAPP(X22684,hAPP(c_Product__Type_Ofst(X22687,X22685),X22683)) != hAPP(X22682,hAPP(c_Product__Type_Ofst(X22687,X22685),X22683))
        | hAPP(c_Product__Type_Oapfst(X22687,X22686,X22685,X22684),X22683) = hAPP(c_Product__Type_Oapfst(X22687,X22686,X22685,X22682),X22683) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_apfst__eq__conv])]) ).

fof(i_0_5343,plain,
    ! [X27843] : c_Relation_OId(X27843) = hAPP(c_Set_OCollect(tc_prod(X27843,X27843)),hAPP(hAPP(c_COMBB(tc_fun(X27843,tc_HOL_Obool),tc_HOL_Obool,tc_prod(X27843,X27843)),c_HOL_OEx(X27843)),hAPP(hAPP(c_COMBC(tc_prod(X27843,X27843),tc_fun(X27843,tc_prod(X27843,X27843)),tc_fun(X27843,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X27843,X27843),tc_HOL_Obool),tc_fun(tc_fun(X27843,tc_prod(X27843,X27843)),tc_fun(X27843,tc_HOL_Obool)),tc_prod(X27843,X27843)),c_COMBB(tc_prod(X27843,X27843),tc_HOL_Obool,X27843)),c_fequal)),hAPP(hAPP(c_COMBS(X27843,X27843,tc_prod(X27843,X27843)),c_Product__Type_OPair(X27843,X27843)),c_COMBI(X27843))))),
    inference(variable_rename,[status(thm)],[fact_Id__def]) ).

fof(i_0_5344,plain,
    ! [X22723,X22724,X22725,X22726,X22727,X22728,X22729] : hAPP(c_Product__Type_Oapsnd(X22729,X22728,X22727,X22726),hAPP(c_Product__Type_Oapfst(X22725,X22727,X22729,X22724),X22723)) = hAPP(hAPP(c_Product__Type_OPair(X22727,X22728),hAPP(X22724,hAPP(c_Product__Type_Ofst(X22725,X22729),X22723))),hAPP(X22726,hAPP(c_Product__Type_Osnd(X22725,X22729),X22723))),
    inference(variable_rename,[status(thm)],[fact_apsnd__apfst]) ).

fof(i_0_5345,plain,
    ! [X22529,X22530,X22531,X22532,X22533,X22534,X22535] : hAPP(c_Product__Type_Oapfst(X22535,X22534,X22533,X22532),hAPP(c_Product__Type_Oapsnd(X22531,X22533,X22535,X22530),X22529)) = hAPP(hAPP(c_Product__Type_OPair(X22534,X22533),hAPP(X22532,hAPP(c_Product__Type_Ofst(X22535,X22531),X22529))),hAPP(X22530,hAPP(c_Product__Type_Osnd(X22535,X22531),X22529))),
    inference(variable_rename,[status(thm)],[fact_apfst__apsnd]) ).

fof(i_0_5346,plain,
    ! [X21241,X21242] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21242),c_Groups_Ozero__class_Ozero(X21242)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21242),X21241),hAPP(c_Int_Onumber__class_Onumber__of(X21242),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21242),c_Groups_Ozero__class_Ozero(X21242)),X21241))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21242)
        | ~ class_Int_Onumber__ring(X21242) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21242),c_Groups_Ozero__class_Ozero(X21242)),X21241))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21242),c_Groups_Ozero__class_Ozero(X21242)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21242),X21241),hAPP(c_Int_Onumber__class_Onumber__of(X21242),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21242)
        | ~ class_Int_Onumber__ring(X21242) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_half__gt__zero__iff])])]) ).

fof(i_0_5347,plain,
    ! [X22525,X22526] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X22526)),hAPP(c_Nat_OSuc,X22525)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X22526))),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,X22525))),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)),X22525)))),
    inference(variable_rename,[status(thm)],[fact_max__Suc__number__of]) ).

fof(i_0_5348,plain,
    ! [X21171,X21172] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21172),c_Groups_Ozero__class_Ozero(X21172)),hAPP(hAPP(c_Power_Opower__class_Opower(X21172),X21171),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
        | X21171 != c_Groups_Ozero__class_Ozero(X21172)
        | ~ class_Rings_Olinordered__idom(X21172) )
      & ( X21171 = c_Groups_Ozero__class_Ozero(X21172)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21172),c_Groups_Ozero__class_Ozero(X21172)),hAPP(hAPP(c_Power_Opower__class_Opower(X21172),X21171),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
        | ~ class_Rings_Olinordered__idom(X21172) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__power2])])]) ).

fof(i_0_5349,plain,
    ! [X22357,X22358] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X22358)),hAPP(c_Nat_OSuc,X22357)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X22358))),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)),X22357)))),
    inference(variable_rename,[status(thm)],[fact_min__Suc__number__of]) ).

fof(i_0_5350,plain,
    ! [X21856,X21857,X21858,X21859] : hAPP(c_Nat_Onat_Onat__rec(X21859,X21858,X21857),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21856)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X21859),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X21856))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X21859,X21859),hAPP(hAPP(c_COMBC(tc_Int_Oint,X21859,tc_fun(X21859,X21859)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X21859,tc_fun(X21859,X21859)),tc_Int_Oint),c_If(X21859)),c_Nat__Numeral_Oneg)),X21858)),hAPP(hAPP(c_COMBS(tc_Int_Oint,X21859,X21859),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X21859,X21859),tc_Int_Oint),X21857),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X21859,tc_Int_Oint),c_Nat_Onat_Onat__rec(X21859,X21858,X21857)),c_Int_Onat)))),
    inference(variable_rename,[status(thm)],[fact_nat__rec__number__of]) ).

fof(i_0_5351,plain,
    ! [X31258,X31259] : c_List_Oconcat(X31259,hAPP(hAPP(c_List_Omap(tc_List_Olist(X31259),tc_List_Olist(X31259)),c_List_Olist_Olist__case(tc_List_Olist(X31259),X31259,c_List_Olist_ONil(X31259),hAPP(hAPP(c_COMBB(tc_List_Olist(X31259),tc_fun(tc_List_Olist(X31259),tc_List_Olist(X31259)),X31259),c_COMBK(tc_List_Olist(X31259),tc_List_Olist(X31259))),hAPP(hAPP(c_COMBC(X31259,tc_List_Olist(X31259),tc_List_Olist(X31259)),c_List_Olist_OCons(X31259)),c_List_Olist_ONil(X31259))))),X31258)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(X31259),X31259),c_List_Ohd(X31259)),hAPP(c_List_Ofilter(tc_List_Olist(X31259),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X31259)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X31259),tc_List_Olist(X31259),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X31259)))),X31258)),
    inference(variable_rename,[status(thm)],[fact_transpose__aux__filter__head]) ).

fof(i_0_5352,plain,
    ! [X31246,X31247] : c_List_Oconcat(tc_List_Olist(X31247),hAPP(hAPP(c_List_Omap(tc_List_Olist(X31247),tc_List_Olist(tc_List_Olist(X31247))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(X31247)),X31247,c_List_Olist_ONil(tc_List_Olist(X31247)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X31247),tc_List_Olist(tc_List_Olist(X31247))),X31247),hAPP(hAPP(c_COMBC(tc_List_Olist(X31247),tc_List_Olist(tc_List_Olist(X31247)),tc_List_Olist(tc_List_Olist(X31247))),c_List_Olist_OCons(tc_List_Olist(X31247))),c_List_Olist_ONil(tc_List_Olist(X31247)))))),X31246)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(X31247),tc_List_Olist(X31247)),c_List_Otl(X31247)),hAPP(c_List_Ofilter(tc_List_Olist(X31247),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X31247)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X31247),tc_List_Olist(X31247),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X31247)))),X31246)),
    inference(variable_rename,[status(thm)],[fact_transpose__aux__filter__tail]) ).

fof(i_0_5353,plain,
    ! [X32269,X32270,X32271] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X32271,X32271),tc_HOL_Obool)),c_Relation_OId(X32271)),X32270))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X32271,X32271),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X32271,X32271,X32271),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X32271,X32271),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X32271,X32269)),X32270)),X32269)),X32270))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X32271,X32271),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X32271,X32269)),X32270)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__Int__subset])]) ).

fof(i_0_5354,plain,
    ! [X171,X239,X251,X33,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),hAPP(hAPP(c_List_Olist_OCons(X5),X33),X251)),X239)),c_List_Olistrel(X5,X171)))
     => ~ ! [X177,X262] :
            ( X239 = hAPP(hAPP(c_List_Olist_OCons(X5),X177),X262)
           => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X33),X177)),X171))
             => ~ 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)),X251),X262)),c_List_Olistrel(X5,X171))) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_listrel__Cons1]) ).

fof(i_0_5355,plain,
    ! [X21151,X21152,X21153] :
      ( ~ class_Groups_Omonoid__mult(X21153)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X21153),X21152),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)))),X21151)) = hAPP(hAPP(c_Power_Opower__class_Opower(X21153),hAPP(hAPP(c_Power_Opower__class_Opower(X21153),X21152),X21151)),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_5356,plain,
    ! [X31323,X31324,X31325] : c_List_Osublist(X31325,X31324,X31323) = hAPP(hAPP(c_List_Omap(tc_prod(X31325,tc_Nat_Onat),X31325),c_Product__Type_Ofst(X31325,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X31325,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X31325,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(X31325,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(X31325,tc_Nat_Onat))),X31323)),hAPP(hAPP(c_List_Ozip(X31325,tc_Nat_Onat),X31324),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31325)),X31324))))),
    inference(variable_rename,[status(thm)],[fact_sublist__def]) ).

fof(i_0_5357,plain,
    ! [X63,X26,X27,X2,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(X5,X2,hAPP(hAPP(c_Set_Oinsert(X5),X27),X26)),X63))
    <=> ? [X187,X226] :
          ( hAPP(hAPP(c_Set_Oinsert(X5),X27),X26) = hAPP(hAPP(c_Set_Oinsert(X5),X187),X226)
          & hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X5,X2,X187,X226),X63))
          & ~ hBOOL(hAPP(hAPP(c_member(X5),X187),X226)) ) ),
    inference(fof_simplification,[status(thm)],[fact_fold1Set_Oequations]) ).

fof(i_0_5358,plain,
    ! [X33142,X33143] : c_Nitpick_Ouminus__frac(X33143,X33142) = c_Nitpick_OAbs__Frac(X33143,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(X33143),X33142))),hAPP(c_Nitpick_Odenom(X33143),X33142))),
    inference(variable_rename,[status(thm)],[fact_Nitpick_Ouminus__frac__def]) ).

fof(i_0_5359,plain,
    ! [X22158,X22159,X22160,X22161,X22162] : hAPP(c_Product__Type_Osnd(X22162,X22161),hAPP(c_Product__Type_Oapsnd(X22160,X22161,X22162,X22159),X22158)) = hAPP(X22159,hAPP(c_Product__Type_Osnd(X22162,X22160),X22158)),
    inference(variable_rename,[status(thm)],[fact_snd__apsnd]) ).

fof(i_0_5360,plain,
    ! [X22677,X22678,X22679,X22680,X22681] : hAPP(c_Product__Type_Ofst(X22681,X22680),hAPP(c_Product__Type_Oapfst(X22679,X22681,X22680,X22678),X22677)) = hAPP(X22678,hAPP(c_Product__Type_Ofst(X22679,X22680),X22677)),
    inference(variable_rename,[status(thm)],[fact_fst__apfst]) ).

fof(i_0_5361,plain,
    ! [X22226,X22227,X22228,X22229,X22230] : hAPP(c_Product__Type_Ofst(X22230,X22229),hAPP(c_Product__Type_Oapsnd(X22228,X22229,X22230,X22227),X22226)) = hAPP(c_Product__Type_Ofst(X22230,X22228),X22226),
    inference(variable_rename,[status(thm)],[fact_fst__apsnd]) ).

fof(i_0_5362,plain,
    ! [X22688,X22689,X22690,X22691,X22692] : hAPP(c_Product__Type_Osnd(X22692,X22691),hAPP(c_Product__Type_Oapfst(X22690,X22692,X22691,X22689),X22688)) = hAPP(c_Product__Type_Osnd(X22690,X22691),X22688),
    inference(variable_rename,[status(thm)],[fact_snd__apfst]) ).

fof(i_0_5363,plain,
    ! [X21772,X21773,X21774,X21775] : c_Nat_Onat_Onat__case(X21775,X21774,X21773,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21772)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X21775),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X21772))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X21775,X21775),hAPP(hAPP(c_COMBC(tc_Int_Oint,X21775,tc_fun(X21775,X21775)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X21775,tc_fun(X21775,X21775)),tc_Int_Oint),c_If(X21775)),c_Nat__Numeral_Oneg)),X21774)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X21775,tc_Int_Oint),X21773),c_Int_Onat))),
    inference(variable_rename,[status(thm)],[fact_nat__case__number__of]) ).

fof(i_0_5364,plain,
    ! [X22527,X22528] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X22528)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X22527)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X22527))),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,X22528))),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),X22528)),c_Int_Onat)))),
    inference(variable_rename,[status(thm)],[fact_max__number__of__Suc]) ).

fof(i_0_5365,plain,
    ! [X22359,X22360] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X22360)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X22359)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X22359))),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),X22360)),c_Int_Onat)))),
    inference(variable_rename,[status(thm)],[fact_min__number__of__Suc]) ).

fof(i_0_5366,plain,
    ! [X21237] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X21237))
      | 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),X21237),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_5367,plain,
    ! [X21239,X21240] :
      ( ~ class_Fields_Olinordered__field__inverse__zero(X21240)
      | ~ class_Int_Onumber__ring(X21240)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21240),c_Groups_Ozero__class_Ozero(X21240)),X21239))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21240),c_Groups_Ozero__class_Ozero(X21240)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21240),X21239),hAPP(c_Int_Onumber__class_Onumber__of(X21240),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_5368,plain,
    ! [X21183,X21184,X21185] :
      ( ~ class_Rings_Ocomm__semiring__1(X21185)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X21185),X21184),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)))),X21183)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21185),hAPP(hAPP(c_Power_Opower__class_Opower(X21185),X21184),X21183)),hAPP(hAPP(c_Power_Opower__class_Opower(X21185),X21184),X21183)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J])]) ).

fof(i_0_5369,plain,
    ! [X21221] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X21221))
      | 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),X21221),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_5370,plain,
    ! [X21011,X21012] :
      ( ~ class_Groups_Omonoid__mult(X21012)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X21012),X21011),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(X21012),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21012),X21011),X21011)),X21011) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power3__eq__cube])]) ).

fof(i_0_5371,plain,
    ! [X21163,X21164] :
      ( ~ class_Rings_Olinordered__idom(X21164)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21164),c_Groups_Ozero__class_Ozero(X21164)),hAPP(hAPP(c_Power_Opower__class_Opower(X21164),X21163),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_5372,plain,
    ! [X21216,X21217] :
      ( ~ class_Rings_Oring__1(X21217)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X21217),hAPP(c_Groups_Ouminus__class_Ouminus(X21217),c_Groups_Oone__class_Oone(X21217))),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)))),X21216)) = c_Groups_Oone__class_Oone(X21217) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__minus1__even])]) ).

fof(i_0_5373,plain,
    ! [X21233,X21234] :
      ( ~ class_Int_Onumber__ring(X21234)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X21234),hAPP(c_Int_Onumber__class_Onumber__of(X21234),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)))),X21233)) = c_Groups_Oone__class_Oone(X21234) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__m1__even])]) ).

fof(i_0_5374,plain,
    ! [X123,X168] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X168),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X123)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X168)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X123) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X168),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X123)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X168)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X123),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X168)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat)) ) ),
    inference(fof_simplification,[status(thm)],[fact_diff__nat__number__of]) ).

fof(i_0_5375,plain,
    ! [X31824,X31825,X31826,X31827,X31828] : c_List_OdropWhile(X31828,X31827,hAPP(hAPP(c_List_Omap(X31826,X31828),X31825),X31824)) = hAPP(hAPP(c_List_Omap(X31826,X31828),X31825),c_List_OdropWhile(X31826,hAPP(c_Fun_Ocomp(X31828,tc_HOL_Obool,X31826,X31827),X31825),X31824)),
    inference(variable_rename,[status(thm)],[fact_dropWhile__map]) ).

fof(i_0_5376,plain,
    ! [X120,X137] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,X137))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X120)),hAPP(c_Int_Onat,X137)) = hAPP(c_Int_Onat,X120) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X137))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X120)),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),X120),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_5377,plain,
    ! [X31792,X31793,X31794] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X31794),X31793))
      | ~ hBOOL(hAPP(hAPP(c_member(X31794),X31792),hAPP(c_List_Oset(X31794),X31793)))
      | c_List_OdropWhile(X31794,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X31794),c_fNot),hAPP(hAPP(c_COMBC(X31794,X31794,tc_HOL_Obool),c_fequal),X31792)),hAPP(c_List_Orev(X31794),X31793)) = hAPP(hAPP(c_List_Olist_OCons(X31794),X31792),hAPP(c_List_Orev(X31794),c_List_OtakeWhile(X31794,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X31794),c_fNot),hAPP(hAPP(c_COMBC(X31794,X31794,tc_HOL_Obool),c_fequal),X31792)),X31793))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dropWhile__neq__rev])]) ).

fof(i_0_5378,plain,
    ! [X6,X25,X21,X24,X5] :
      ( class_Groups_Oab__semigroup__mult(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X5,c_Groups_Otimes__class_Otimes(X5),X24,X21),X25))
       => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X21))
         => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X24),X21))
           => hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X5,c_Groups_Otimes__class_Otimes(X5),X6,hAPP(hAPP(c_Set_Oinsert(X5),X24),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))),X25)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_fold__graph__permute__diff]) ).

fof(i_0_5379,plain,
    ! [X31292,X31293,X31294,X31295] : c_List_Oconcat(X31295,hAPP(hAPP(c_List_Omap(X31294,tc_List_Olist(X31295)),hAPP(hAPP(c_COMBC(X31294,tc_List_Olist(X31295),tc_List_Olist(X31295)),hAPP(hAPP(c_COMBB(X31295,tc_fun(tc_List_Olist(X31295),tc_List_Olist(X31295)),X31294),c_List_Olist_OCons(X31295)),X31293)),c_List_Olist_ONil(X31295))),X31292)) = hAPP(hAPP(c_List_Omap(X31294,X31295),X31293),X31292),
    inference(variable_rename,[status(thm)],[fact_concat__map__singleton]) ).

fof(i_0_5380,plain,
    ! [X33147,X33148,X33149] :
      ( ( ~ c_Nitpick_Oless__eq__frac(X33149,X33148,X33147)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(X33149),c_Nitpick_Oplus__frac(X33149,X33148,c_Nitpick_Ouminus__frac(X33149,X33147)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(X33149),c_Nitpick_Oplus__frac(X33149,X33148,c_Nitpick_Ouminus__frac(X33149,X33147)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | c_Nitpick_Oless__eq__frac(X33149,X33148,X33147) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nitpick_Oless__eq__frac__def])]) ).

fof(i_0_5381,plain,
    ! [X33144,X33145,X33146] :
      ( ( ~ c_Nitpick_Oless__frac(X33146,X33145,X33144)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(X33146),c_Nitpick_Oplus__frac(X33146,X33145,c_Nitpick_Ouminus__frac(X33146,X33144)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(X33146),c_Nitpick_Oplus__frac(X33146,X33145,c_Nitpick_Ouminus__frac(X33146,X33144)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | c_Nitpick_Oless__frac(X33146,X33145,X33144) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nitpick_Oless__frac__def])]) ).

fof(i_0_5382,plain,
    ! [X21168,X21169,X21170] :
      ( ~ class_Rings_Olinordered__semidom(X21170)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X21170),X21169),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(X21170),X21168),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(X21170),c_Groups_Ozero__class_Ozero(X21170)),X21169))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21170),c_Groups_Ozero__class_Ozero(X21170)),X21168))
      | X21169 = X21168 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__eq__imp__eq])]) ).

fof(i_0_5383,plain,
    ! [X21180] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21180),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
      | X21180 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | X21180 = 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_5384,plain,
    ! [X21159] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X21159))),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),X21159),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_5385,plain,
    ! [X21156,X21157] :
      ( ~ class_Rings_Olinordered__idom(X21157)
      | hAPP(c_Groups_Oabs__class_Oabs(X21157),hAPP(hAPP(c_Power_Opower__class_Opower(X21157),X21156),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(X21157),X21156),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_5386,plain,
    ! [X33137,X33138,X33139] :
      ( ~ class_Rings_Oinverse(X33139)
      | ~ class_Rings_Oring__1(X33139)
      | c_Nitpick_Oof__frac(X33138,X33139,X33137) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X33139),hAPP(c_Int_Oring__1__class_Oof__int(X33139),hAPP(c_Nitpick_Onum(X33138),X33137))),hAPP(c_Int_Oring__1__class_Oof__int(X33139),hAPP(c_Nitpick_Odenom(X33138),X33137))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nitpick_Oof__frac__def])]) ).

fof(i_0_5387,plain,
    ! [X171,X297,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X20)),X297),hAPP(c_Relation_Oconverse(X20,X5),X171)))
     => ~ ! [X3,X177] :
            ( X297 = hAPP(hAPP(c_Product__Type_OPair(X5,X20),X177),X3)
           => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X20,X5)),hAPP(hAPP(c_Product__Type_OPair(X20,X5),X3),X177)),X171)) ) ),
    inference(fof_simplification,[status(thm)],[fact_converseE]) ).

fof(i_0_5388,plain,
    ! [X2,X50,X95,X5] :
      ( class_Groups_Oab__group__add(X5)
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X50))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(X5)),X2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X5,tc_Nat_Onat),X2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X95,X50)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),hAPP(X2,X95)),hAPP(X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X50),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X50))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X5,X5),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(X5)),X2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X5,tc_Nat_Onat),X2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X95,X50)) = c_Groups_Ozero__class_Ozero(X5) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_setsum__natinterval__difff]) ).

fof(i_0_5389,plain,
    ! [X120,X33,X21,X24,X5] :
      ( class_Groups_Oab__semigroup__mult(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X5,c_Groups_Otimes__class_Otimes(X5),X24,X21),X33))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X24),X21))
         => hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X5,c_Groups_Otimes__class_Otimes(X5),X120,hAPP(hAPP(c_Set_Oinsert(X5),X24),X21)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X120),X33))) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_fold__graph__insert__swap]) ).

fof(i_0_5390,plain,
    ! [X33,X120,X2,X20,X21,X25,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X20,X2,X120,X21),X33))
       => hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X20,X2,X120,hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)),hAPP(hAPP(X2,X25),X33))) ) ),
    inference(fof_simplification,[status(thm)],[fact_fold__graph_OinsertI]) ).

fof(i_0_5391,plain,
    ! [X32631,X32632,X32633,X32634] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X32634,X32634)),hAPP(hAPP(c_Product__Type_OPair(X32634,X32634),X32633),esk460_4(X32631,X32632,X32633,X32634))),X32631))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32634,X32634)),hAPP(hAPP(c_Product__Type_OPair(X32634,X32634),X32633),X32632)),c_Transitive__Closure_Otrancl(X32634,X32631))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X32634,X32634)),hAPP(hAPP(c_Product__Type_OPair(X32634,X32634),esk460_4(X32631,X32632,X32633,X32634)),X32632)),c_Transitive__Closure_Ortrancl(X32634,X32631)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32634,X32634)),hAPP(hAPP(c_Product__Type_OPair(X32634,X32634),X32633),X32632)),c_Transitive__Closure_Otrancl(X32634,X32631))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_tranclD])])])]) ).

fof(i_0_5392,plain,
    ! [X32626,X32627,X32628,X32629] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X32629,X32629)),hAPP(hAPP(c_Product__Type_OPair(X32629,X32629),X32628),esk459_4(X32626,X32627,X32628,X32629))),c_Transitive__Closure_Ortrancl(X32629,X32626)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32629,X32629)),hAPP(hAPP(c_Product__Type_OPair(X32629,X32629),X32628),X32627)),c_Transitive__Closure_Otrancl(X32629,X32626))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X32629,X32629)),hAPP(hAPP(c_Product__Type_OPair(X32629,X32629),esk459_4(X32626,X32627,X32628,X32629)),X32627)),X32626))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32629,X32629)),hAPP(hAPP(c_Product__Type_OPair(X32629,X32629),X32628),X32627)),c_Transitive__Closure_Otrancl(X32629,X32626))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_tranclD2])])])]) ).

fof(i_0_5393,plain,
    ! [X22664,X22665,X22666,X22667,X22668,X22669] : hAPP(c_Product__Type_Oapfst(X22669,X22668,X22667,X22666),hAPP(hAPP(c_Product__Type_OPair(X22669,X22667),X22665),X22664)) = hAPP(hAPP(c_Product__Type_OPair(X22668,X22667),hAPP(X22666,X22665)),X22664),
    inference(variable_rename,[status(thm)],[fact_apfst__conv]) ).

fof(i_0_5394,plain,
    ! [X21984,X21985,X21986,X21987,X21988,X21989] : hAPP(c_Product__Type_Oapsnd(X21989,X21988,X21987,X21986),hAPP(hAPP(c_Product__Type_OPair(X21987,X21989),X21985),X21984)) = hAPP(hAPP(c_Product__Type_OPair(X21987,X21988),X21985),hAPP(X21986,X21984)),
    inference(variable_rename,[status(thm)],[fact_apsnd__conv]) ).

fof(i_0_5395,plain,
    ! [X239,X25,X18,X5] :
      ( c_List_Olist__ex1(X5,X18,hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239))
    <=> ( ( hBOOL(hAPP(X18,X25))
         => c_List_Olist__all(X5,hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),X18))),hAPP(c_fequal,X25)),X239) )
        & ( ~ hBOOL(hAPP(X18,X25))
         => c_List_Olist__ex1(X5,X18,X239) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_list__ex1__simps_I2_J]) ).

fof(i_0_5396,plain,
    ! [X31404,X31405] : c_List_Ofoldr(tc_List_Olist(X31405),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X31405)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X31405))),c_List_Otranspose(X31405,X31404),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31405))),hAPP(c_List_Ofilter(tc_List_Olist(X31405),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X31405)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X31405),tc_List_Olist(X31405),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X31405)))),X31404)),
    inference(variable_rename,[status(thm)],[fact_transpose__max__length]) ).

fof(i_0_5397,plain,
    ! [X31842,X31843,X31844,X31845] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31845),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31844)),c_List_OdropWhile(X31844,X31843,X31842))))
      | hAPP(hAPP(c_List_Onth(X31844),c_List_OdropWhile(X31844,X31843,X31842)),X31845) = hAPP(hAPP(c_List_Onth(X31844),X31842),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31845),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31844)),c_List_OtakeWhile(X31844,X31843,X31842)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dropWhile__nth])]) ).

fof(i_0_5398,plain,
    ! [X21160,X21161] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X21161)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X21160))) = hAPP(hAPP(c_Groups_Otimes__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),X21161),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21160))),
    inference(variable_rename,[status(thm)],[fact_zmod__number__of__Bit0]) ).

fof(i_0_5399,plain,
    ! [X21154,X21155] :
      ( ~ class_Rings_Olinordered__idom(X21155)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X21155),hAPP(c_Groups_Oabs__class_Oabs(X21155),X21154)),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(X21155),X21154),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_5400,plain,
    ! [X21147,X21148] :
      ( ~ class_Rings_Oring__1(X21148)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X21148),hAPP(c_Groups_Ouminus__class_Ouminus(X21148),X21147)),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(X21148),X21147),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_5401,plain,
    ! [X21158] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X21158)),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,X21158,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_5402,plain,
    ! [X18,X21,X205,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X205))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X205),X21))
       => ( hBOOL(hAPP(X18,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))
         => ( ! [X187,X230] :
                ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X230))
               => ( hBOOL(hAPP(hAPP(c_member(X5),X187),X21))
                 => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X187),X230))
                   => ( hBOOL(hAPP(X18,X230))
                     => hBOOL(hAPP(X18,hAPP(hAPP(c_Set_Oinsert(X5),X187),X230))) ) ) ) )
           => hBOOL(hAPP(X18,X205)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_finite__subset__induct]) ).

fof(i_0_5403,plain,
    ! [X21132,X21133] :
      ( ~ class_Int_Onumber__ring(X21133)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21133),hAPP(c_Int_Onumber__class_Onumber__of(X21133),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X21132) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21133),X21132),X21132) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__2])]) ).

fof(i_0_5404,plain,
    ! [X2,X18,X239,X5,X20] :
      ( class_Groups_Omonoid__add(X20)
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X239)))
           => ( ~ hBOOL(hAPP(X18,X3))
             => hAPP(X2,X3) = c_Groups_Ozero__class_Ozero(X20) ) )
       => hAPP(c_List_Omonoid__add__class_Olistsum(X20),hAPP(hAPP(c_List_Omap(X5,X20),X2),hAPP(c_List_Ofilter(X5,X18),X239))) = hAPP(c_List_Omonoid__add__class_Olistsum(X20),hAPP(hAPP(c_List_Omap(X5,X20),X2),X239)) ) ),
    inference(fof_simplification,[status(thm)],[fact_listsum__map__filter]) ).

fof(i_0_5405,plain,
    ! [X21150] : 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)))),X21150) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21150),X21150),
    inference(variable_rename,[status(thm)],[fact_nat__mult__2]) ).

fof(i_0_5406,plain,
    ! [X21144] : 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)))),X21144) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X21144)),
    inference(variable_rename,[status(thm)],[fact_add__2__eq__Suc]) ).

fof(i_0_5407,plain,
    ! [X31815,X31816,X31817] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31817)),c_List_OdropWhile(X31817,X31816,X31815))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31817)),X31815))),
    inference(variable_rename,[status(thm)],[fact_length__dropWhile__le]) ).

fof(i_0_5408,plain,
    ! [X25,X21,X205,X1,X120,X2,X20,X5] :
      ( c_Finite__Set_Ofolding__image__simple(X5,X20,X2,X120,X1,X205)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X20),X21))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X20),X25),X21))
         => hAPP(X205,hAPP(hAPP(c_Set_Oinsert(X20),X25),X21)) = hAPP(hAPP(X2,hAPP(X1,X25)),hAPP(X205,X21)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_folding__image__simple_Oinsert]) ).

fof(i_0_5409,plain,
    ! [X171,X20,X24,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X24),hAPP(c_Relation_ORange(X20,X5),X171)))
     => ~ ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X20,X5)),hAPP(hAPP(c_Product__Type_OPair(X20,X5),X3),X24)),X171)) ),
    inference(fof_simplification,[status(thm)],[fact_RangeE]) ).

fof(i_0_5410,plain,
    ! [X32366,X32367,X32368,X32369,X32370] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32370,X32370)),hAPP(hAPP(c_Product__Type_OPair(X32370,X32370),X32369),X32368)),c_Transitive__Closure_Otrancl(X32370,X32367)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32370,X32370)),hAPP(hAPP(c_Product__Type_OPair(X32370,X32370),X32368),X32366)),c_Transitive__Closure_Otrancl(X32370,X32367)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X32370,X32370)),hAPP(hAPP(c_Product__Type_OPair(X32370,X32370),X32369),X32366)),c_Transitive__Closure_Otrancl(X32370,X32367))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__trans])]) ).

fof(i_0_5411,plain,
    ! [X32498,X32499,X32500,X32501] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32501,X32501)),hAPP(hAPP(c_Product__Type_OPair(X32501,X32501),X32500),X32499)),hAPP(c_Relation_Oconverse(X32501,X32501),c_Transitive__Closure_Otrancl(X32501,X32498))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X32501,X32501)),hAPP(hAPP(c_Product__Type_OPair(X32501,X32501),X32500),X32499)),c_Transitive__Closure_Otrancl(X32501,hAPP(c_Relation_Oconverse(X32501,X32501),X32498)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__converseI])]) ).

fof(i_0_5412,plain,
    ! [X32502,X32503,X32504,X32505] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32505,X32505)),hAPP(hAPP(c_Product__Type_OPair(X32505,X32505),X32504),X32503)),c_Transitive__Closure_Otrancl(X32505,hAPP(c_Relation_Oconverse(X32505,X32505),X32502))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X32505,X32505)),hAPP(hAPP(c_Product__Type_OPair(X32505,X32505),X32504),X32503)),hAPP(c_Relation_Oconverse(X32505,X32505),c_Transitive__Closure_Otrancl(X32505,X32502)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__converseD])]) ).

fof(i_0_5413,plain,
    ! [X25,X21,X6,X2,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X5,X2,X6,X21),X25))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X21))
       => hBOOL(hAPP(c_Finite__Set_Ofold1Set(X5,X2,hAPP(hAPP(c_Set_Oinsert(X5),X6),X21)),X25)) ) ),
    inference(fof_simplification,[status(thm)],[fact_fold1Set_Ointros]) ).

fof(i_0_5414,plain,
    ! [X31821,X31822,X31823] :
      ( c_List_OdropWhile(X31823,X31822,X31821) = c_List_Olist_ONil(X31823)
      | ~ hBOOL(hAPP(X31822,hAPP(c_List_Ohd(X31823),c_List_OdropWhile(X31823,X31822,X31821)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5197])]) ).

fof(i_0_5415,plain,
    ! [X21181,X21182] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(X21182),X21181),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Oone__class_Oone(X21182)
        | X21181 = c_Groups_Oone__class_Oone(X21182)
        | X21181 = hAPP(c_Groups_Ouminus__class_Ouminus(X21182),c_Groups_Oone__class_Oone(X21182))
        | ~ class_Rings_Oring__1__no__zero__divisors(X21182) )
      & ( X21181 != c_Groups_Oone__class_Oone(X21182)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X21182),X21181),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(X21182)
        | ~ class_Rings_Oring__1__no__zero__divisors(X21182) )
      & ( X21181 != hAPP(c_Groups_Ouminus__class_Ouminus(X21182),c_Groups_Oone__class_Oone(X21182))
        | hAPP(hAPP(c_Power_Opower__class_Opower(X21182),X21181),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(X21182)
        | ~ class_Rings_Oring__1__no__zero__divisors(X21182) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__eq__1__iff])])]) ).

fof(i_0_5416,plain,
    ! [X21137,X21138] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(X21138),X21137),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(X21138)
        | X21137 = c_Groups_Ozero__class_Ozero(X21138)
        | ~ class_Rings_Oring__1__no__zero__divisors(X21138) )
      & ( X21137 != c_Groups_Ozero__class_Ozero(X21138)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X21138),X21137),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(X21138)
        | ~ class_Rings_Oring__1__no__zero__divisors(X21138) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__eq__power2])])]) ).

fof(i_0_5417,plain,
    ! [X31102,X31103,X31104,X31105] : hAPP(c_List_OremoveAll(X31105,X31104),hAPP(hAPP(c_List_Oappend(X31105),X31103),X31102)) = hAPP(hAPP(c_List_Oappend(X31105),hAPP(c_List_OremoveAll(X31105,X31104),X31103)),hAPP(c_List_OremoveAll(X31105,X31104),X31102)),
    inference(variable_rename,[status(thm)],[fact_removeAll__append]) ).

fof(i_0_5418,plain,
    ! [X31219,X31220] : c_List_OremoveAll(X31220,X31219) = c_List_Ofilter(X31220,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X31220),c_fNot),hAPP(c_fequal,X31219))),
    inference(variable_rename,[status(thm)],[fact_removeAll__filter__not__eq]) ).

fof(i_0_5419,plain,
    ! [X31691,X31692,X31693] : hAPP(c_List_Orotate(X31693,X31692),hAPP(c_List_Orev(X31693),X31691)) = hAPP(c_List_Orev(X31693),hAPP(c_List_Orotate(X31693,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31693)),X31691)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X31692,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31693)),X31691)))),X31691)),
    inference(variable_rename,[status(thm)],[fact_rotate__rev]) ).

fof(i_0_5420,plain,
    ! [X29450,X29451] : c_List_Orotate(X29451,X29450) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X29451),tc_List_Olist(X29451)),X29450),c_List_Orotate1(X29451)),
    inference(variable_rename,[status(thm)],[fact_rotate__def]) ).

fof(i_0_5421,plain,
    ! [X32320,X32321,X32322,X32323,X32324] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32324,X32324)),hAPP(hAPP(c_Product__Type_OPair(X32324,X32324),X32323),X32322)),c_Transitive__Closure_Ortrancl(X32324,X32321)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32324,X32324)),hAPP(hAPP(c_Product__Type_OPair(X32324,X32324),X32322),X32320)),c_Transitive__Closure_Otrancl(X32324,X32321)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X32324,X32324)),hAPP(hAPP(c_Product__Type_OPair(X32324,X32324),X32323),X32320)),c_Transitive__Closure_Otrancl(X32324,X32321))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__trancl__trancl])]) ).

fof(i_0_5422,plain,
    ! [X32315,X32316,X32317,X32318,X32319] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32319,X32319)),hAPP(hAPP(c_Product__Type_OPair(X32319,X32319),X32318),X32317)),c_Transitive__Closure_Otrancl(X32319,X32316)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32319,X32319)),hAPP(hAPP(c_Product__Type_OPair(X32319,X32319),X32317),X32315)),c_Transitive__Closure_Ortrancl(X32319,X32316)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X32319,X32319)),hAPP(hAPP(c_Product__Type_OPair(X32319,X32319),X32318),X32315)),c_Transitive__Closure_Otrancl(X32319,X32316))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__rtrancl__trancl])]) ).

fof(i_0_5423,plain,
    ! [X32356,X32357,X32358,X32359,X32360] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32360,X32360)),hAPP(hAPP(c_Product__Type_OPair(X32360,X32360),X32359),X32358)),X32357))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32360,X32360)),hAPP(hAPP(c_Product__Type_OPair(X32360,X32360),X32358),X32356)),c_Transitive__Closure_Otrancl(X32360,X32357)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X32360,X32360)),hAPP(hAPP(c_Product__Type_OPair(X32360,X32360),X32359),X32356)),c_Transitive__Closure_Otrancl(X32360,X32357))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__into__trancl2])]) ).

fof(i_0_5424,plain,
    ! [X32361,X32362,X32363,X32364,X32365] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32365,X32365)),hAPP(hAPP(c_Product__Type_OPair(X32365,X32365),X32364),X32363)),c_Transitive__Closure_Otrancl(X32365,X32362)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32365,X32365)),hAPP(hAPP(c_Product__Type_OPair(X32365,X32365),X32363),X32361)),X32362))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X32365,X32365)),hAPP(hAPP(c_Product__Type_OPair(X32365,X32365),X32364),X32361)),c_Transitive__Closure_Otrancl(X32365,X32362))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Transitive__Closure_Otrancl__into__trancl])]) ).

fof(i_0_5425,plain,
    ! [X5,X6,X18] :
      ( ( hBOOL(hAPP(X18,X6))
       => hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X6))),X18)) = hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) )
      & ( ~ hBOOL(hAPP(X18,X6))
       => hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X6))),X18)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ) ),
    inference(fof_simplification,[status(thm)],[fact_Collect__conv__if]) ).

fof(i_0_5426,plain,
    ! [X31425,X31426,X31427,X31428,X31429,X31430,X31431] : c_List_Ofoldr(X31431,X31430,X31429,hAPP(hAPP(c_List_Omap(X31428,X31431),X31427),X31426),X31425) = c_List_Ofoldr(X31428,X31430,hAPP(c_Fun_Ocomp(X31431,tc_fun(X31430,X31430),X31428,X31429),X31427),X31426,X31425),
    inference(variable_rename,[status(thm)],[fact_foldr__map]) ).

fof(i_0_5427,plain,
    ! [X33,X2,X20,X21,X25,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
       => hAPP(c_Set_Oimage(X5,X20,c_Fun_Ofun__upd(X5,X20,X2,X25,X33)),X21) = hAPP(hAPP(c_Set_Oinsert(X20),X33),hAPP(c_Set_Oimage(X5,X20,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
       => hAPP(c_Set_Oimage(X5,X20,c_Fun_Ofun__upd(X5,X20,X2,X25,X33)),X21) = hAPP(c_Set_Oimage(X5,X20,X2),X21) ) ),
    inference(fof_simplification,[status(thm)],[fact_fun__upd__image]) ).

fof(i_0_5428,plain,
    ! [X32371,X32372,X32373] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X32373,X32373),tc_HOL_Obool)),X32372),hAPP(hAPP(c_Product__Type_OSigma(X32373,X32373),X32371),hAPP(c_COMBK(tc_fun(X32373,tc_HOL_Obool),X32373),X32371))))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X32373,X32373),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X32373,X32372)),hAPP(hAPP(c_Product__Type_OSigma(X32373,X32373),X32371),hAPP(c_COMBK(tc_fun(X32373,tc_HOL_Obool),X32373),X32371)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__subset__Sigma])]) ).

fof(i_0_5429,plain,
    ! [X21797,X21798,X21799] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21798)))
        | hAPP(hAPP(c_Power_Opower__class_Opower(X21799),hAPP(c_Int_Onumber__class_Onumber__of(X21799),X21797)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X21798))) = hAPP(hAPP(c_HOL_OLet(X21799,X21799),hAPP(hAPP(c_Power_Opower__class_Opower(X21799),hAPP(c_Int_Onumber__class_Onumber__of(X21799),X21797)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21798))),hAPP(hAPP(c_COMBS(X21799,X21799,X21799),hAPP(hAPP(c_COMBB(X21799,tc_fun(X21799,X21799),X21799),c_Groups_Otimes__class_Otimes(X21799)),hAPP(c_Groups_Otimes__class_Otimes(X21799),hAPP(c_Int_Onumber__class_Onumber__of(X21799),X21797)))),c_COMBI(X21799)))
        | ~ class_Int_Onumber__ring(X21799) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21798)))
        | hAPP(hAPP(c_Power_Opower__class_Opower(X21799),hAPP(c_Int_Onumber__class_Onumber__of(X21799),X21797)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X21798))) = c_Groups_Oone__class_Oone(X21799)
        | ~ class_Int_Onumber__ring(X21799) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5198])])]) ).

fof(i_0_5430,plain,
    ! [X24,X6] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X6),X24)))
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => c_Nitpick_Onorm__frac(X6,X24) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X6),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X24)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => ( ( ( X6 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
                | X24 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
             => c_Nitpick_Onorm__frac(X6,X24) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
            & ( ~ ( X6 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
                  | X24 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
             => c_Nitpick_Onorm__frac(X6,X24) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X6),X24)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X6))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X24))) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_norm__frac_Opsimps]) ).

fof(i_0_5431,plain,
    ! [X31406,X31407,X31408,X31409,X31410,X31411] : c_List_Ofoldr(X31411,X31410,X31409,hAPP(hAPP(c_List_Oappend(X31411),X31408),X31407),X31406) = c_List_Ofoldr(X31411,X31410,X31409,X31408,c_List_Ofoldr(X31411,X31410,X31409,X31407,X31406)),
    inference(variable_rename,[status(thm)],[fact_foldr__append]) ).

fof(i_0_5432,plain,
    ! [X113,X25,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),X113)))
    <=> ( ( hBOOL(hAPP(hAPP(c_member(X5),X25),X113))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X21),X113)) )
        & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X113))
         => ( ( hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),X113)) )
            & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),X113)) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_psubset__insert__iff]) ).

fof(i_0_5433,plain,
    ! [X33,X171,X5] :
      ( ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X3)),X171))
     => ~ 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)),X33),X33)),c_List_Olexord(X5,X171))) ),
    inference(fof_simplification,[status(thm)],[fact_lexord__irreflexive]) ).

fof(i_0_5434,plain,
    ! [X21125,X21126] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(X21126)),c_Int_OBit1(X21125)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_Opred(X21126)),X21125)),
    inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I8_J]) ).

fof(i_0_5435,plain,
    ! [X21,X6,X2,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,X2,hAPP(hAPP(c_Set_Oinsert(X5),X6),X21))
    <=> ( c_Fun_Oinj__on(X5,X20,X2,X21)
        & ~ hBOOL(hAPP(hAPP(c_member(X20),hAPP(X2,X6)),hAPP(c_Set_Oimage(X5,X20,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))) ) ),
    inference(fof_simplification,[status(thm)],[fact_inj__on__insert]) ).

fof(i_0_5436,plain,
    ! [X27923,X27924] : c_Product__Type_Oapfst(X27924,X27924,X27923,c_Fun_Oid(X27924)) = c_Fun_Oid(tc_prod(X27924,X27923)),
    inference(variable_rename,[status(thm)],[fact_apfst__id]) ).

fof(i_0_5437,plain,
    ! [X27929,X27930] : c_Product__Type_Oapsnd(X27930,X27930,X27929,c_Fun_Oid(X27930)) = c_Fun_Oid(tc_prod(X27929,X27930)),
    inference(variable_rename,[status(thm)],[fact_apsnd__id]) ).

fof(i_0_5438,plain,
    ! [X32382,X32383] : c_Transitive__Closure_Otrancl(X32383,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X32383,X32383),tc_HOL_Obool)),X32382),c_Relation_OId(X32383))) = c_Transitive__Closure_Ortrancl(X32383,X32382),
    inference(variable_rename,[status(thm)],[fact_trancl__reflcl]) ).

fof(i_0_5439,plain,
    ! [X113,X25,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),X113)))
    <=> ( ( hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))),X113)) )
        & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),X113)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_subset__insert__iff]) ).

fof(i_0_5440,plain,
    ! [X20955,X20956] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(X20956),X20955) != c_Groups_Oone__class_Oone(X20956)
        | c_Int_Oiszero(X20956,hAPP(c_Int_Onumber__class_Onumber__of(X20956),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20955),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))
        | ~ class_Int_Onumber__ring(X20956) )
      & ( ~ c_Int_Oiszero(X20956,hAPP(c_Int_Onumber__class_Onumber__of(X20956),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20955),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))
        | hAPP(c_Int_Onumber__class_Onumber__of(X20956),X20955) = c_Groups_Oone__class_Oone(X20956)
        | ~ class_Int_Onumber__ring(X20956) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__special_I4_J])])]) ).

fof(i_0_5441,plain,
    ! [X20953,X20954] :
      ( ( c_Groups_Oone__class_Oone(X20954) != hAPP(c_Int_Onumber__class_Onumber__of(X20954),X20953)
        | c_Int_Oiszero(X20954,hAPP(c_Int_Onumber__class_Onumber__of(X20954),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),X20953))))
        | ~ class_Int_Onumber__ring(X20954) )
      & ( ~ c_Int_Oiszero(X20954,hAPP(c_Int_Onumber__class_Onumber__of(X20954),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),X20953))))
        | c_Groups_Oone__class_Oone(X20954) = hAPP(c_Int_Onumber__class_Onumber__of(X20954),X20953)
        | ~ class_Int_Onumber__ring(X20954) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__special_I2_J])])]) ).

fof(i_0_5442,plain,
    ! [X6,X24] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => c_Nitpick_Onorm__frac(X6,X24) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X6),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X24)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => ( ( ( X6 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
              | X24 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
           => c_Nitpick_Onorm__frac(X6,X24) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
          & ( ~ ( X6 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
                | X24 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
           => c_Nitpick_Onorm__frac(X6,X24) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X6),X24)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X6))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X24))) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_norm__frac_Osimps]) ).

fof(i_0_5443,plain,
    ! [X31858,X31859,X31860] :
      ( ( hBOOL(hAPP(hAPP(c_member(X31860),esk402_3(X31858,X31859,X31860)),hAPP(c_List_Oset(X31860),c_List_OdropWhile(X31860,X31859,X31858))))
        | c_List_OtakeWhile(X31860,X31859,X31858) = hAPP(c_List_Ofilter(X31860,X31859),X31858) )
      & ( hBOOL(hAPP(X31859,esk402_3(X31858,X31859,X31860)))
        | c_List_OtakeWhile(X31860,X31859,X31858) = hAPP(c_List_Ofilter(X31860,X31859),X31858) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5199])])])]) ).

fof(i_0_5444,plain,
    ! [X32301,X32302,X32303,X32304,X32305] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32305,X32305)),hAPP(hAPP(c_Product__Type_OPair(X32305,X32305),X32304),X32303)),X32302))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32305,X32305)),hAPP(hAPP(c_Product__Type_OPair(X32305,X32305),X32303),X32301)),c_Transitive__Closure_Ortrancl(X32305,X32302)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X32305,X32305)),hAPP(hAPP(c_Product__Type_OPair(X32305,X32305),X32304),X32301)),c_Transitive__Closure_Otrancl(X32305,X32302))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__into__trancl2])]) ).

fof(i_0_5445,plain,
    ! [X32310,X32311,X32312,X32313,X32314] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32314,X32314)),hAPP(hAPP(c_Product__Type_OPair(X32314,X32314),X32313),X32312)),c_Transitive__Closure_Ortrancl(X32314,X32311)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32314,X32314)),hAPP(hAPP(c_Product__Type_OPair(X32314,X32314),X32312),X32310)),X32311))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X32314,X32314)),hAPP(hAPP(c_Product__Type_OPair(X32314,X32314),X32313),X32310)),c_Transitive__Closure_Otrancl(X32314,X32311))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__into__trancl1])]) ).

fof(i_0_5446,plain,
    ! [X21790,X21791,X21792] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21791)))
        | hAPP(hAPP(c_Power_Opower__class_Opower(X21792),X21790),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X21791))) = hAPP(hAPP(c_HOL_OLet(X21792,X21792),hAPP(hAPP(c_Power_Opower__class_Opower(X21792),X21790),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21791))),hAPP(hAPP(c_COMBS(X21792,X21792,X21792),hAPP(hAPP(c_COMBB(X21792,tc_fun(X21792,X21792),X21792),c_Groups_Otimes__class_Otimes(X21792)),hAPP(c_Groups_Otimes__class_Otimes(X21792),X21790))),c_COMBI(X21792)))
        | ~ class_Int_Onumber__ring(X21792) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21791)))
        | hAPP(hAPP(c_Power_Opower__class_Opower(X21792),X21790),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X21791))) = c_Groups_Oone__class_Oone(X21792)
        | ~ class_Int_Onumber__ring(X21792) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5200])])]) ).

fof(i_0_5447,plain,
    ! [X21178,X21179] :
      ( ~ class_Groups_Omonoid__mult(X21179)
      | ~ class_Int_Onumber(X21179)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X21179),hAPP(c_Int_Onumber__class_Onumber__of(X21179),X21178)),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(X21179),hAPP(c_Int_Onumber__class_Onumber__of(X21179),X21178)),hAPP(c_Int_Onumber__class_Onumber__of(X21179),X21178)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__eq__square__number__of])]) ).

fof(i_0_5448,plain,
    ! [X32351,X32352,X32353,X32354,X32355] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32355,X32355)),hAPP(hAPP(c_Product__Type_OPair(X32355,X32355),X32354),X32353)),X32352))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32355,X32355)),hAPP(hAPP(c_Product__Type_OPair(X32355,X32355),X32353),X32351)),X32352))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X32355,X32355)),hAPP(hAPP(c_Product__Type_OPair(X32355,X32355),X32354),X32351)),c_Transitive__Closure_Otrancl(X32355,X32352))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_r__r__into__trancl])]) ).

fof(i_0_5449,plain,
    ! [X171,X20,X6,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(c_Relation_ODomain(X5,X20),X171)))
     => ~ ! [X177] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X20)),hAPP(hAPP(c_Product__Type_OPair(X5,X20),X6),X177)),X171)) ),
    inference(fof_simplification,[status(thm)],[fact_DomainE]) ).

fof(i_0_5450,plain,
    ! [X21162] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21162),X21162)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = X21162,
    inference(variable_rename,[status(thm)],[fact_add__self__div__2]) ).

fof(i_0_5451,plain,
    ! [X21134,X21135] :
      ( ~ class_Int_Onumber__ring(X21135)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21135),X21134),hAPP(c_Int_Onumber__class_Onumber__of(X21135),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21135),X21134),X21134) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__2__right])]) ).

fof(i_0_5452,plain,
    ! [X21142,X21143] :
      ( ~ class_Groups_Omonoid__mult(X21143)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X21143),X21142),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(X21143),X21142),X21142) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__eq__square])]) ).

fof(i_0_5453,plain,
    ! [X21140,X21141] :
      ( ~ class_Rings_Ocomm__semiring__1(X21141)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21141),X21140),X21140) = hAPP(hAPP(c_Power_Opower__class_Opower(X21141),X21140),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_5454,plain,
    ! [X6,X23,X24,X113,X21,X116,X20,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X20,tc_fun(X116,tc_HOL_Obool))),X21),X113),X24),X23))
     => ( ~ hBOOL(hAPP(hAPP(hAPP(X113,X6),X24),X23))
       => ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X21)) ) ),
    inference(fof_simplification,[status(thm)],[fact_INF2__E]) ).

fof(i_0_5455,plain,
    ! [X21149] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21149),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),X21149),X21149),
    inference(variable_rename,[status(thm)],[fact_nat__mult__2__right]) ).

fof(i_0_5456,plain,
    ! [X21145] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21145),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,X21145)),
    inference(variable_rename,[status(thm)],[fact_add__2__eq__Suc_H]) ).

fof(i_0_5457,plain,
    ! [X21146] :
      ( ~ class_Rings_Osemiring__1(X21146)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X21146),c_Groups_Oone__class_Oone(X21146)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(X21146) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__power2])]) ).

fof(i_0_5458,plain,
    ! [X21139] :
      ( ~ class_Rings_Osemiring__1(X21139)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X21139),c_Groups_Ozero__class_Ozero(X21139)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(X21139) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__power2])]) ).

fof(i_0_5459,plain,
    ! [X123,X2,X20,X239,X33,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X33),hAPP(c_List_Oset(X5),X239)))
     => hAPP(hAPP(c_List_Omap(X5,X20),c_Fun_Ofun__upd(X5,X20,X2,X33,X123)),X239) = hAPP(hAPP(c_List_Omap(X5,X20),X2),X239) ),
    inference(fof_simplification,[status(thm)],[fact_map__fun__upd]) ).

fof(i_0_5460,plain,
    ! [X21793,X21794] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21794)))
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X21793),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X21794))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X21793),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21794))),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),X21793))),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),X21794)))
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X21793),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X21794))) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5201])]) ).

fof(i_0_5461,plain,
    ! [X32335,X32336,X32337,X32338] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32338,X32338)),X32337),c_Transitive__Closure_Otrancl(X32338,X32336)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X32338,X32338),tc_HOL_Obool)),X32336),X32335))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X32338,X32338)),X32337),c_Transitive__Closure_Otrancl(X32338,X32335))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__mono])]) ).

fof(i_0_5462,plain,
    ! [X65,X66,X58] :
      ( class_Rings_Olinordered__ring(X58)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X66),X66)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X65),X65))),c_Groups_Ozero__class_Ozero(X58))) ),
    inference(fof_simplification,[status(thm)],[fact_not__sum__squares__lt__zero]) ).

fof(i_0_5463,plain,
    ! [X32387,X32388] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X32388,X32388),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X32388,X32387)),hAPP(hAPP(c_Product__Type_OSigma(X32388,X32388),hAPP(c_Relation_OField(X32388),X32387)),hAPP(c_COMBK(tc_fun(X32388,tc_HOL_Obool),X32388),hAPP(c_Relation_OField(X32388),X32387))))),
    inference(variable_rename,[status(thm)],[fact_trancl__subset__Field2]) ).

fof(i_0_5464,plain,
    ! [X33,X25,X113,X21,X20,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_fun(X20,tc_HOL_Obool))),X21),X113),X25),X33))
     => ( ~ hBOOL(hAPP(hAPP(X21,X25),X33))
       => hBOOL(hAPP(hAPP(X113,X25),X33)) ) ),
    inference(fof_simplification,[status(thm)],[fact_sup2E]) ).

fof(i_0_5465,plain,
    ! [X32297,X32298,X32299,X32300] :
      ( ( X32299 != X32298
        | X32299 = X32298
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32300,X32300)),hAPP(hAPP(c_Product__Type_OPair(X32300,X32300),X32299),X32298)),c_Transitive__Closure_Ortrancl(X32300,X32297))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X32300,X32300)),hAPP(hAPP(c_Product__Type_OPair(X32300,X32300),X32299),X32298)),c_Transitive__Closure_Otrancl(X32300,X32297)))
        | X32299 = X32298
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32300,X32300)),hAPP(hAPP(c_Product__Type_OPair(X32300,X32300),X32299),X32298)),c_Transitive__Closure_Ortrancl(X32300,X32297))) )
      & ( X32299 != X32298
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X32300,X32300)),hAPP(hAPP(c_Product__Type_OPair(X32300,X32300),X32299),X32298)),c_Transitive__Closure_Ortrancl(X32300,X32297))) )
      & ( X32299 = X32298
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32300,X32300)),hAPP(hAPP(c_Product__Type_OPair(X32300,X32300),X32299),X32298)),c_Transitive__Closure_Otrancl(X32300,X32297)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X32300,X32300)),hAPP(hAPP(c_Product__Type_OPair(X32300,X32300),X32299),X32298)),c_Transitive__Closure_Ortrancl(X32300,X32297))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__eq__or__trancl])])]) ).

fof(i_0_5466,plain,
    ! [X32293,X32294,X32295,X32296] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32296,X32296)),hAPP(hAPP(c_Product__Type_OPair(X32296,X32296),X32295),X32294)),c_Transitive__Closure_Otrancl(X32296,X32293)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X32296,X32296)),hAPP(hAPP(c_Product__Type_OPair(X32296,X32296),X32295),X32294)),c_Transitive__Closure_Ortrancl(X32296,X32293))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__into__rtrancl])]) ).

fof(i_0_5467,plain,
    ! [X33,X25,X113,X21,X20,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_fun(X20,tc_HOL_Obool))),X21),X113),X25),X33))
     => ~ ( hBOOL(hAPP(hAPP(X21,X25),X33))
         => ~ hBOOL(hAPP(hAPP(X113,X25),X33)) ) ),
    inference(fof_simplification,[status(thm)],[fact_inf2E]) ).

fof(i_0_5468,plain,
    ! [X20967,X20968] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X20968)),c_Int_OBit1(X20967)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20968),X20967)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20968),X20967))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X20968)),c_Int_OBit1(X20967))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I16_J])]) ).

fof(i_0_5469,plain,
    ! [X20965,X20966] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X20966)),c_Int_OBit1(X20965)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20966),X20965)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20966),X20965))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X20966)),c_Int_OBit1(X20965))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I34_J])]) ).

fof(i_0_5470,plain,
    ! [X20971,X20972] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X20972)),c_Int_OBit1(X20971)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20972),X20971)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20972),X20971))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X20972)),c_Int_OBit1(X20971))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__int__code_I16_J])]) ).

fof(i_0_5471,plain,
    ! [X20969,X20970] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X20970)),c_Int_OBit1(X20969)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20970),X20969)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20970),X20969))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X20970)),c_Int_OBit1(X20969))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I17_J])]) ).

fof(i_0_5472,plain,
    ! [X31093,X31094,X31095] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X31095),X31094))
      | hBOOL(hAPP(c_List_Odistinct(X31095),hAPP(c_List_OremoveAll(X31095,X31093),X31094))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__removeAll])]) ).

fof(i_0_5473,plain,
    ! [X31088,X31089,X31090,X31091,X31092] :
      ( ~ c_Fun_Oinj__on(X31092,X31091,X31090,hAPP(hAPP(c_Set_Oinsert(X31092),X31089),hAPP(c_List_Oset(X31092),X31088)))
      | hAPP(hAPP(c_List_Omap(X31092,X31091),X31090),hAPP(c_List_OremoveAll(X31092,X31089),X31088)) = hAPP(c_List_OremoveAll(X31091,hAPP(X31090,X31089)),hAPP(hAPP(c_List_Omap(X31092,X31091),X31090),X31088)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__removeAll__inj__on])]) ).

fof(i_0_5474,plain,
    ! [X32399,X32400,X32401] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X32401,X32401),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X32401,X32401),X32400)),c_Transitive__Closure_Ortrancl(X32401,X32400)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X32401,X32401),tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32401,X32401)),hAPP(hAPP(c_Product__Type_OPair(X32401,X32401),X32399),X32399)),c_Transitive__Closure_Otrancl(X32401,X32400))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5202])]) ).

fof(i_0_5475,plain,
    ! [X31829,X31830,X31831,X31832,X31833] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X31833),X31832),hAPP(c_List_Oset(X31833),X31831)))
      | hBOOL(hAPP(X31830,X31832))
      | c_List_OdropWhile(X31833,X31830,hAPP(hAPP(c_List_Oappend(X31833),X31831),X31829)) = hAPP(hAPP(c_List_Oappend(X31833),c_List_OdropWhile(X31833,X31830,X31831)),X31829) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5203])]) ).

fof(i_0_5476,plain,
    ! [X32065,X32066,X32067,X32068] :
      ( ( hBOOL(hAPP(hAPP(c_member(X32068),esk426_4(X32065,X32066,X32067,X32068)),hAPP(c_List_Oset(X32068),X32067)))
        | c_List_OdropWhile(X32068,X32066,hAPP(hAPP(c_List_Oappend(X32068),X32067),X32065)) = c_List_OdropWhile(X32068,X32066,X32065) )
      & ( ~ hBOOL(hAPP(X32066,esk426_4(X32065,X32066,X32067,X32068)))
        | c_List_OdropWhile(X32068,X32066,hAPP(hAPP(c_List_Oappend(X32068),X32067),X32065)) = c_List_OdropWhile(X32068,X32066,X32065) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dropWhile__append2])])])]) ).

fof(i_0_5477,plain,
    ! [X31112,X31113,X31114,X31115,X31116] :
      ( ~ c_Fun_Oinj__on(X31116,X31115,X31114,c_Orderings_Otop__class_Otop(tc_fun(X31116,tc_HOL_Obool)))
      | hAPP(hAPP(c_List_Omap(X31116,X31115),X31114),hAPP(c_List_OremoveAll(X31116,X31113),X31112)) = hAPP(c_List_OremoveAll(X31115,hAPP(X31114,X31113)),hAPP(hAPP(c_List_Omap(X31116,X31115),X31114),X31112)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__removeAll__inj])]) ).

fof(i_0_5478,plain,
    ! [X239,X18,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_OtakeWhile(X5,X18,X239))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239)))
     => ~ hBOOL(hAPP(X18,hAPP(hAPP(c_List_Onth(X5),X239),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_OtakeWhile(X5,X18,X239))))) ),
    inference(fof_simplification,[status(thm)],[fact_nth__length__takeWhile]) ).

fof(i_0_5479,plain,
    ! [X31437,X31438] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31438))),c_List_Otranspose(X31438,X31437)) = c_List_Ofoldr(tc_List_Olist(X31438),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X31438)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X31438))),X31437,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[fact_length__transpose]) ).

fof(i_0_5480,plain,
    ! [X32389,X32390,X32391,X32393,X32394,X32395,X32396] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk443_3(X32389,X32390,X32391)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32391,X32391)),X32390),c_Transitive__Closure_Otrancl(X32391,X32389))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X32391,X32391)),X32390),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X32391,X32391),tc_HOL_Obool),esk443_3(X32389,X32390,X32391)),X32389)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32391,X32391)),X32390),c_Transitive__Closure_Otrancl(X32391,X32389))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X32396))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32395,X32395)),X32394),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X32395,X32395),tc_HOL_Obool),X32396),X32393)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X32395,X32395)),X32394),c_Transitive__Closure_Otrancl(X32395,X32393))) ) ),
    inference(distribute,[status(thm)],[inference(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_5481,plain,
    ! [X31264,X31265,X31266] : c_List_Oconcat(X31266,hAPP(hAPP(c_List_Oappend(tc_List_Olist(X31266)),X31265),X31264)) = hAPP(hAPP(c_List_Oappend(X31266),c_List_Oconcat(X31266,X31265)),c_List_Oconcat(X31266,X31264)),
    inference(variable_rename,[status(thm)],[fact_concat__append]) ).

fof(i_0_5482,plain,
    ! [X82,X6,X239,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),X239))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_List_Oset(X5),X239)),hAPP(hAPP(c_Set_Oinsert(X5),hAPP(hAPP(c_List_Onth(X5),X239),X82)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))))
       => hBOOL(hAPP(c_List_Odistinct(X5),hAPP(hAPP(c_List_Olist__update(X5,X239),X82),X6))) ) ),
    inference(fof_simplification,[status(thm)],[fact_distinct__list__update]) ).

fof(i_0_5483,plain,
    ! [X21,X2,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),hAPP(c_Set_Oimage(X20,X5,X2),X21))),hAPP(c_Finite__Set_Ocard(X20),X21)))
     => ~ c_Fun_Oinj__on(X20,X5,X2,X21) ),
    inference(fof_simplification,[status(thm)],[fact_pigeonhole]) ).

fof(i_0_5484,plain,
    ! [X32306,X32307,X32308,X32309] :
      ( ( X32308 != X32307
        | X32308 = X32307
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32309,X32309)),hAPP(hAPP(c_Product__Type_OPair(X32309,X32309),X32308),X32307)),c_Transitive__Closure_Ortrancl(X32309,X32306))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X32309,X32309)),hAPP(hAPP(c_Product__Type_OPair(X32309,X32309),X32308),X32307)),c_Transitive__Closure_Otrancl(X32309,X32306)))
        | X32308 = X32307
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32309,X32309)),hAPP(hAPP(c_Product__Type_OPair(X32309,X32309),X32308),X32307)),c_Transitive__Closure_Ortrancl(X32309,X32306))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtranclD])])]) ).

fof(i_0_5485,plain,
    ! [X18,X239,X5,X50] :
      ( ! [X146] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X146),X50))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X146),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239)))
           => hBOOL(hAPP(X18,hAPP(hAPP(c_List_Onth(X5),X239),X146))) ) )
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X50),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239)))
         => ~ hBOOL(hAPP(X18,hAPP(hAPP(c_List_Onth(X5),X239),X50))) )
       => c_List_OtakeWhile(X5,X18,X239) = hAPP(hAPP(c_List_Otake(X5),X50),X239) ) ),
    inference(fof_simplification,[status(thm)],[fact_takeWhile__eq__take__P__nth]) ).

fof(i_0_5486,plain,
    ! [X32289,X32290,X32291,X32292] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32292,X32292)),hAPP(hAPP(c_Product__Type_OPair(X32292,X32292),X32291),X32290)),X32289))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X32292,X32292)),hAPP(hAPP(c_Product__Type_OPair(X32292,X32292),X32291),X32290)),c_Transitive__Closure_Otrancl(X32292,X32289))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl_Or__into__trancl])]) ).

fof(i_0_5487,plain,
    ! [X121,X23,X24,X5] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X5)
        & class_Int_Onumber(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X24),X23)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)),X23))) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)),X23)),X24)) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121))) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_divide__le__eq__number__of]) ).

fof(i_0_5488,plain,
    ! [X121,X23,X24,X5] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X5)
        & class_Int_Onumber(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X24),X23)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)),X23))) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)),X23)),X24)) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121))) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_divide__less__eq__number__of]) ).

fof(i_0_5489,plain,
    ! [X23,X24,X121,X5] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X5)
        & class_Int_Onumber(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X24),X23)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)),X23)),X24)) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)),X23))) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)),c_Groups_Ozero__class_Ozero(X5))) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_le__divide__eq__number__of]) ).

fof(i_0_5490,plain,
    ! [X23,X24,X121,X5] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X5)
        & class_Int_Onumber(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X24),X23)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)),X23)),X24)) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)),X23))) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)),c_Groups_Ozero__class_Ozero(X5))) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_less__divide__eq__number__of]) ).

fof(i_0_5491,plain,
    ! [X25,X33,X21,X2,X20,X5] :
      ( c_Fun_Oinj__on(X5,X20,X2,X21)
     => ( ~ hBOOL(hAPP(hAPP(c_member(X20),X33),hAPP(c_Set_Oimage(X5,X20,X2),X21)))
       => c_Fun_Oinj__on(X5,X20,c_Fun_Ofun__upd(X5,X20,X2,X25,X33),X21) ) ),
    inference(fof_simplification,[status(thm)],[fact_inj__on__fun__updI]) ).

fof(i_0_5492,plain,
    ! [X31929,X31930] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X31930)),esk409_2(X31929,X31930)),hAPP(c_List_Oset(tc_List_Olist(X31930)),X31929)))
        | hBOOL(hAPP(c_List_Odistinct(X31930),c_List_Oconcat(X31930,X31929)))
        | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X31930)),esk408_2(X31929,X31930)),hAPP(c_List_Oset(tc_List_Olist(X31930)),X31929)))
        | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X31930)),X31929)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X31930)),esk410_2(X31929,X31930)),hAPP(c_List_Oset(tc_List_Olist(X31930)),X31929)))
        | hBOOL(hAPP(c_List_Odistinct(X31930),c_List_Oconcat(X31930,X31929)))
        | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X31930)),esk408_2(X31929,X31930)),hAPP(c_List_Oset(tc_List_Olist(X31930)),X31929)))
        | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X31930)),X31929)) )
      & ( esk409_2(X31929,X31930) != esk410_2(X31929,X31930)
        | hBOOL(hAPP(c_List_Odistinct(X31930),c_List_Oconcat(X31930,X31929)))
        | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X31930)),esk408_2(X31929,X31930)),hAPP(c_List_Oset(tc_List_Olist(X31930)),X31929)))
        | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X31930)),X31929)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31930,tc_HOL_Obool)),hAPP(c_List_Oset(X31930),esk409_2(X31929,X31930))),hAPP(c_List_Oset(X31930),esk410_2(X31929,X31930))) != c_Orderings_Obot__class_Obot(tc_fun(X31930,tc_HOL_Obool))
        | hBOOL(hAPP(c_List_Odistinct(X31930),c_List_Oconcat(X31930,X31929)))
        | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X31930)),esk408_2(X31929,X31930)),hAPP(c_List_Oset(tc_List_Olist(X31930)),X31929)))
        | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X31930)),X31929)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X31930)),esk409_2(X31929,X31930)),hAPP(c_List_Oset(tc_List_Olist(X31930)),X31929)))
        | hBOOL(hAPP(c_List_Odistinct(X31930),c_List_Oconcat(X31930,X31929)))
        | ~ hBOOL(hAPP(c_List_Odistinct(X31930),esk408_2(X31929,X31930)))
        | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X31930)),X31929)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X31930)),esk410_2(X31929,X31930)),hAPP(c_List_Oset(tc_List_Olist(X31930)),X31929)))
        | hBOOL(hAPP(c_List_Odistinct(X31930),c_List_Oconcat(X31930,X31929)))
        | ~ hBOOL(hAPP(c_List_Odistinct(X31930),esk408_2(X31929,X31930)))
        | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X31930)),X31929)) )
      & ( esk409_2(X31929,X31930) != esk410_2(X31929,X31930)
        | hBOOL(hAPP(c_List_Odistinct(X31930),c_List_Oconcat(X31930,X31929)))
        | ~ hBOOL(hAPP(c_List_Odistinct(X31930),esk408_2(X31929,X31930)))
        | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X31930)),X31929)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31930,tc_HOL_Obool)),hAPP(c_List_Oset(X31930),esk409_2(X31929,X31930))),hAPP(c_List_Oset(X31930),esk410_2(X31929,X31930))) != c_Orderings_Obot__class_Obot(tc_fun(X31930,tc_HOL_Obool))
        | hBOOL(hAPP(c_List_Odistinct(X31930),c_List_Oconcat(X31930,X31929)))
        | ~ hBOOL(hAPP(c_List_Odistinct(X31930),esk408_2(X31929,X31930)))
        | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X31930)),X31929)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__concat])])])]) ).

fof(i_0_5493,plain,
    ! [X5,X6,X18] :
      ( ( hBOOL(hAPP(X18,X6))
       => hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(c_fequal,X6))),X18)) = hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) )
      & ( ~ hBOOL(hAPP(X18,X6))
       => hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBS(X5,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X5),c_fconj),hAPP(c_fequal,X6))),X18)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ) ),
    inference(fof_simplification,[status(thm)],[fact_Collect__conv__if2]) ).

fof(i_0_5494,plain,
    ! [X29488,X29489,X29490] : hAPP(c_List_Orotate(X29490,X29489),X29488) = hAPP(hAPP(c_List_Oappend(X29490),hAPP(hAPP(c_List_Odrop(X29490),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X29489,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29490)),X29488))),X29488)),hAPP(hAPP(c_List_Otake(X29490),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X29489,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29490)),X29488))),X29488)),
    inference(variable_rename,[status(thm)],[fact_rotate__drop__take]) ).

fof(i_0_5495,plain,
    ! [X32374,X32375,X32376,X32377,X32378] :
      ( ( ~ c_Wellfounded_Oacyclic(X32375,X32374)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32375,X32375)),hAPP(hAPP(c_Product__Type_OPair(X32375,X32375),X32376),X32376)),c_Transitive__Closure_Otrancl(X32375,X32374))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X32378,X32378)),hAPP(hAPP(c_Product__Type_OPair(X32378,X32378),esk442_2(X32377,X32378)),esk442_2(X32377,X32378))),c_Transitive__Closure_Otrancl(X32378,X32377)))
        | c_Wellfounded_Oacyclic(X32378,X32377) ) ),
    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_5204])])])])]) ).

fof(i_0_5496,plain,
    ! [X251,X239,X33,X25,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X20)),hAPP(hAPP(c_Product__Type_OPair(X5,X20),X25),X33)),hAPP(c_List_Oset(tc_prod(X5,X20)),hAPP(hAPP(c_List_Ozip(X5,X20),X239),X251))))
     => ~ ( hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X239)))
         => ~ hBOOL(hAPP(hAPP(c_member(X20),X33),hAPP(c_List_Oset(X20),X251))) ) ),
    inference(fof_simplification,[status(thm)],[fact_in__set__zipE]) ).

fof(i_0_5497,plain,
    ! [X31098,X31099,X31100,X31101] :
      ( ( X31101 != X31100
        | hAPP(c_List_OremoveAll(X31099,X31101),hAPP(hAPP(c_List_Olist_OCons(X31099),X31100),X31098)) = hAPP(c_List_OremoveAll(X31099,X31101),X31098) )
      & ( X31101 = X31100
        | hAPP(c_List_OremoveAll(X31099,X31101),hAPP(hAPP(c_List_Olist_OCons(X31099),X31100),X31098)) = hAPP(hAPP(c_List_Olist_OCons(X31099),X31100),hAPP(c_List_OremoveAll(X31099,X31101),X31098)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_removeAll_Osimps_I2_J])]) ).

fof(i_0_5498,plain,
    ! [X171,X25,X33,X5] :
      ( c_Wellfounded_Oacyclic(X5,hAPP(hAPP(c_Set_Oinsert(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X33),X25)),X171))
    <=> ( c_Wellfounded_Oacyclic(X5,X171)
        & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X33)),c_Transitive__Closure_Ortrancl(X5,X171))) ) ),
    inference(fof_simplification,[status(thm)],[fact_acyclic__insert]) ).

fof(i_0_5499,plain,
    ! [X171,X25,X33,X5] :
      ( c_Wellfounded_Owf(X5,hAPP(hAPP(c_Set_Oinsert(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X33),X25)),X171))
    <=> ( c_Wellfounded_Owf(X5,X171)
        & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X33)),c_Transitive__Closure_Ortrancl(X5,X171))) ) ),
    inference(fof_simplification,[status(thm)],[fact_wf__insert]) ).

fof(i_0_5500,plain,
    ! [X32349,X32350] : c_Transitive__Closure_Otrancl(X32350,X32349) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X32350,X32350),tc_HOL_Obool)),X32349),hAPP(hAPP(c_Relation_Orel__comp(X32350,X32350,X32350),c_Transitive__Closure_Otrancl(X32350,X32349)),X32349)),
    inference(variable_rename,[status(thm)],[fact_trancl__unfold]) ).

fof(i_0_5501,plain,
    ! [X171,X5] :
      ( c_Wellfounded_Owf(X5,X171)
    <=> ! [X296] :
          ( ? [X3] : hBOOL(hAPP(hAPP(c_member(X5),X3),X296))
         => ? [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X5),X3),X296))
              & ! [X177] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X177),X3)),X171))
                 => ~ hBOOL(hAPP(hAPP(c_member(X5),X177),X296)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_wf__eq__minimal]) ).

fof(i_0_5502,plain,
    ! [X21117,X21118] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X21118)),c_Int_OBit0(X21117)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21118),X21117)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21118),X21117))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X21118)),c_Int_OBit0(X21117))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I15_J])]) ).

fof(i_0_5503,plain,
    ! [X21115,X21116] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X21116)),c_Int_OBit0(X21115)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21116),X21115)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21116),X21115))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X21116)),c_Int_OBit0(X21115))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I33_J])]) ).

fof(i_0_5504,plain,
    ! [X21087,X21088] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X21088)),c_Int_OBit0(X21087)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21088),X21087)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21088),X21087))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X21088)),c_Int_OBit0(X21087))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I16_J])]) ).

fof(i_0_5505,plain,
    ! [X21085,X21086] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X21086)),c_Int_OBit0(X21085)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21086),X21085)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21086),X21085))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X21086)),c_Int_OBit0(X21085))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__int__code_I15_J])]) ).

fof(i_0_5506,plain,
    ! [X21677,X21678] : c_Nitpick_Oint__lcm(X21678,X21677) = 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),X21678)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X21677)))),
    inference(variable_rename,[status(thm)],[fact_Nitpick_Oint__lcm__def]) ).

fof(i_0_5507,plain,
    ! [X21683,X21684] : c_Nitpick_Onat__lcm(X21684,X21683) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21684),X21683)),c_Nitpick_Onat__gcd(X21684,X21683)),
    inference(variable_rename,[status(thm)],[fact_Nitpick_Onat__lcm__def]) ).

fof(i_0_5508,plain,
    ! [X31412,X31413,X31414,X31415,X31416,X31417] : c_List_Ofoldr(X31417,X31416,X31415,hAPP(hAPP(c_List_Olist_OCons(X31417),X31414),X31413),X31412) = hAPP(hAPP(X31415,X31414),c_List_Ofoldr(X31417,X31416,X31415,X31413,X31412)),
    inference(variable_rename,[status(thm)],[fact_foldr_Osimps_I2_J]) ).

fof(i_0_5509,plain,
    ! [X25,X6,X171,X5] :
      ( c_Wellfounded_Owf(X5,X171)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X25)),X171))
       => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X6)),X171)) ) ),
    inference(fof_simplification,[status(thm)],[fact_wf__not__sym]) ).

fof(i_0_5510,plain,
    ! [X25,X6,X171,X5] :
      ( c_Wellfounded_Owf(X5,X171)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X25)),X171))
       => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X6)),X171)) ) ),
    inference(fof_simplification,[status(thm)],[fact_wf__asym]) ).

fof(i_0_5511,plain,
    ! [X193,X50,X95] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X95,X50),X193))
    <=> ( X95 = 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),X193)),X50)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X193))
        & ( X50 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X193) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        & ( X50 != 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)),X50))
             => ( 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),X193)))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X193)),X50)) ) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X50))
             => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X50),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X193)))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X193)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_divmod__nat__rel__def]) ).

fof(i_0_5512,plain,
    ! [X6,X121,X24,X5] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X5)
        & class_Int_Onumber(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X24),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121))),X6))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)))) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121))),X24)) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),X6)) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_divide__le__eq__number__of1]) ).

fof(i_0_5513,plain,
    ! [X6,X121,X24,X5] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X5)
        & class_Int_Onumber(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X24),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121))),X6))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)))) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121))),X24)) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X6)) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_divide__less__eq__number__of1]) ).

fof(i_0_5514,plain,
    ! [X20986] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(X20986)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X20986))),
    inference(variable_rename,[status(thm)],[fact_minus__Bit1]) ).

fof(i_0_5515,plain,
    ! [X77,X60,X26,X63,X27] :
      ( c_Natural_Oevaln(c_Com_Ocom_OWhile(X27,X63),X26,X60,X77)
    <=> ( ( X77 = X26
          & ~ hBOOL(hAPP(X27,X26)) )
        | ( hBOOL(hAPP(X27,X26))
          & ? [X61] :
              ( c_Natural_Oevaln(X63,X26,X60,X61)
              & c_Natural_Oevaln(c_Com_Ocom_OWhile(X27,X63),X61,X60,X77) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_evaln_Oequations_I8_J]) ).

fof(i_0_5516,plain,
    ! [X18,X27,X191] :
      ( 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),X191),X27)))
     => ( ! [X158,X146] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X158),X146)))
           => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X158),X146))
               => hBOOL(hAPP(hAPP(X18,X158),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X146),c_Groups_Oone__class_Oone(tc_Int_Oint)))) )
             => hBOOL(hAPP(hAPP(X18,X158),X146)) ) )
       => hBOOL(hAPP(hAPP(X18,X191),X27)) ) ),
    inference(fof_simplification,[status(thm)],[fact_small__lazy_H_Opinduct]) ).

fof(i_0_5517,plain,
    ! [X54,X57,X48,X64,X52] :
      ( c_Natural_Oevaln(c_Com_Ocom_OSemi(X52,X64),X48,X57,X54)
     => ~ ! [X61] :
            ( c_Natural_Oevaln(X52,X48,X57,X61)
           => ~ c_Natural_Oevaln(X64,X61,X57,X54) ) ),
    inference(fof_simplification,[status(thm)],[fact_evaln__elim__cases_I4_J]) ).

fof(i_0_5518,plain,
    ! [X32397,X32398] :
      ( ( ~ 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),X32398),X32397)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32398),X32397)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32398),X32397))
        | 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),X32398),X32397)),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_5519,plain,
    ! [X171,X21,X194,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X194),hAPP(hAPP(c_Equiv__Relations_Oquotient(X5),X21),X171)))
     => ~ ! [X3] :
            ( X194 = hAPP(c_Relation_OImage(X5,X5,X171),hAPP(hAPP(c_Set_Oinsert(X5),X3),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))
           => ~ hBOOL(hAPP(hAPP(c_member(X5),X3),X21)) ) ),
    inference(fof_simplification,[status(thm)],[fact_quotientE]) ).

fof(i_0_5520,plain,
    ! [X22119,X22120] :
      ( ( X22120 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Divides_Odivmod__nat(X22119,X22120) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22119) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22119),X22120))
        | c_Divides_Odivmod__nat(X22119,X22120) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22119) )
      & ( X22120 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22119),X22120))
        | c_Divides_Odivmod__nat(X22119,X22120) = 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),X22119),X22120),X22120)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__nat__if])])]) ).

fof(i_0_5521,plain,
    ! [X27038,X27039] : c_Divides_Odivmod__nat(X27039,X27038) = c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X27039,X27038)),
    inference(variable_rename,[status(thm)],[fact_divmod__nat__def]) ).

fof(i_0_5522,plain,
    ! [X20977] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X20977)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20977),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20977),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X20977)),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_5523,plain,
    ! [X264,X265,X266,X267,X5] :
      ( hAPP(hAPP(c_List_Oappend(X5),X267),X266) = hAPP(hAPP(c_List_Oappend(X5),X265),X264)
    <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X267)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X265)))
         => ( X267 = hAPP(hAPP(c_List_Otake(X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X267)),X265)
            & X266 = hAPP(hAPP(c_List_Oappend(X5),hAPP(hAPP(c_List_Odrop(X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X267)),X265)),X264) ) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X267)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X265)))
         => ( hAPP(hAPP(c_List_Otake(X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X265)),X267) = X265
            & hAPP(hAPP(c_List_Oappend(X5),hAPP(hAPP(c_List_Odrop(X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X265)),X267)),X266) = X264 ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_append__eq__append__conv__if]) ).

fof(i_0_5524,plain,
    ! [X20981] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X20981)),c_Int_OMin))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20981),c_Int_OMin)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20981),c_Int_OMin))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X20981)),c_Int_OMin)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I30_J])]) ).

fof(i_0_5525,plain,
    ! [X20997] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X20997)),c_Int_OPls))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20997),c_Int_OPls)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20997),c_Int_OPls))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X20997)),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I29_J])]) ).

fof(i_0_5526,plain,
    ! [X20979] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X20979)),c_Int_OPls))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20979),c_Int_OPls)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20979),c_Int_OPls))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X20979)),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I12_J])]) ).

fof(i_0_5527,plain,
    ! [X20984] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X20984)),c_Int_OMin))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20984),c_Int_OMin)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20984),c_Int_OMin))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X20984)),c_Int_OMin)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I13_J])]) ).

fof(i_0_5528,plain,
    ! [X20985] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X20985))))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20985))) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20985)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X20985)))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__number__of__Bit1])]) ).

fof(i_0_5529,plain,
    ! [X31443,X31444] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31444)),c_List_Oremdups(X31444,c_List_Oconcat(X31444,X31443))) = hAPP(c_Finite__Set_Ocard(X31444),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(X31444),tc_fun(X31444,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(X31444)),X31443)),c_List_Oset(X31444))),
    inference(variable_rename,[status(thm)],[fact_length__remdups__concat]) ).

fof(i_0_5530,plain,
    ! [X21014,X21015] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21015),c_Groups_Oone__class_Oone(X21015)),hAPP(c_Int_Onumber__class_Onumber__of(X21015),X21014)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X21014))
        | ~ class_Int_Onumber__ring(X21015)
        | ~ class_Rings_Olinordered__idom(X21015) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X21014))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21015),c_Groups_Oone__class_Oone(X21015)),hAPP(c_Int_Onumber__class_Onumber__of(X21015),X21014)))
        | ~ class_Int_Onumber__ring(X21015)
        | ~ class_Rings_Olinordered__idom(X21015) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__special_I2_J])])]) ).

fof(i_0_5531,plain,
    ! [X21020,X21021] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21021),c_Groups_Oone__class_Oone(X21021)),hAPP(c_Int_Onumber__class_Onumber__of(X21021),X21020)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X21020))
        | ~ class_Int_Onumber__ring(X21021)
        | ~ class_Rings_Olinordered__idom(X21021) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X21020))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21021),c_Groups_Oone__class_Oone(X21021)),hAPP(c_Int_Onumber__class_Onumber__of(X21021),X21020)))
        | ~ class_Int_Onumber__ring(X21021)
        | ~ class_Rings_Olinordered__idom(X21021) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__special_I2_J])])]) ).

fof(i_0_5532,plain,
    ! [X121,X24,X6,X5] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X5)
        & class_Int_Onumber(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X24),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121))))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121))),X24)) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)))) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),c_Groups_Ozero__class_Ozero(X5))) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_le__divide__eq__number__of1]) ).

fof(i_0_5533,plain,
    ! [X121,X24,X6,X5] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X5)
        & class_Int_Onumber(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X24),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121))))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121))),X24)) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)))) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),c_Groups_Ozero__class_Ozero(X5))) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_less__divide__eq__number__of1]) ).

fof(i_0_5534,plain,
    ! [X20,X5,X21,X33,X25,X113] :
      ( ( ~ hBOOL(hAPP(hAPP(X113,X25),X33))
       => hBOOL(hAPP(hAPP(X21,X25),X33)) )
     => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_fun(X20,tc_HOL_Obool))),X21),X113),X25),X33)) ),
    inference(fof_simplification,[status(thm)],[fact_sup2CI]) ).

fof(i_0_5535,plain,
    ! [X32,X25,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),c_Wellfounded_Oacc(X5,X32)))
     => ~ ! [X154] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X154),X25)),X32))
           => hBOOL(hAPP(hAPP(c_member(X5),X154),c_Wellfounded_Oacc(X5,X32))) ) ),
    inference(fof_simplification,[status(thm)],[fact_not__acc__down]) ).

fof(i_0_5536,plain,
    ! [X24,X21,X5] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X24),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))
       => c_Partial__Function_Oflat__lub(X5,X24,X21) = X24 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X24),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))
       => c_Partial__Function_Oflat__lub(X5,X24,X21) = c_HOL_OThe(X5,hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X24),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))))) ) ),
    inference(fof_simplification,[status(thm)],[fact_flat__lub__def]) ).

fof(i_0_5537,plain,
    ! [X59,X26,X63,X27] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X27,X63)),X26),X59))
    <=> ( ( X59 = X26
          & ~ hBOOL(hAPP(X27,X26)) )
        | ( hBOOL(hAPP(X27,X26))
          & ? [X61] :
              ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X63),X26),X61))
              & hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X27,X63)),X61),X59)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_evalc_Oequations_I8_J]) ).

fof(i_0_5538,plain,
    ! [X21218,X21219] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21219)))
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X21218))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X21219))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21218)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21219)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21219)))
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X21218))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X21219))) = 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),X21218)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21219)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5205])]) ).

fof(i_0_5539,plain,
    ! [X32402,X32403] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X32403,X32403)),hAPP(hAPP(c_Product__Type_OPair(X32403,X32403),esk444_2(X32402,X32403)),esk444_2(X32402,X32403))),c_Transitive__Closure_Otrancl(X32403,X32402)))
      | c_Wellfounded_Oacyclic(X32403,X32402) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5206])])]) ).

fof(i_0_5540,plain,
    ! [X171,X239,X5] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olist_ONil(X5)),X239)),c_List_Olistrel1(X5,X171))),
    inference(fof_simplification,[status(thm)],[fact_not__Nil__listrel1]) ).

fof(i_0_5541,plain,
    ! [X171,X251,X5] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olist_ONil(X5)),X251)),c_List_Olex(X5,X171))),
    inference(fof_simplification,[status(thm)],[fact_Nil__notin__lex]) ).

fof(i_0_5542,plain,
    ! [X171,X239,X5] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X239),c_List_Olist_ONil(X5))),c_List_Olistrel1(X5,X171))),
    inference(fof_simplification,[status(thm)],[fact_not__listrel1__Nil]) ).

fof(i_0_5543,plain,
    ! [X171,X25,X5] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X25),c_List_Olist_ONil(X5))),c_List_Olexord(X5,X171))),
    inference(fof_simplification,[status(thm)],[fact_lexord__Nil__right]) ).

fof(i_0_5544,plain,
    ! [X171,X239,X5] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X239),c_List_Olist_ONil(X5))),c_List_Olex(X5,X171))),
    inference(fof_simplification,[status(thm)],[fact_Nil2__notin__lex]) ).

fof(i_0_5545,plain,
    ! [X31434,X31435,X31436] :
      ( ~ class_Groups_Omonoid__add(X31436)
      | hAPP(c_List_Ofoldl(X31436,X31436,c_Groups_Oplus__class_Oplus(X31436),X31435),X31434) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X31436),X31435),c_List_Ofoldr(X31436,X31436,c_Groups_Oplus__class_Oplus(X31436),X31434,c_Groups_Ozero__class_Ozero(X31436))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_foldl__foldr1__lemma])]) ).

fof(i_0_5546,plain,
    ! [X23425,X23426,X23427] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X23427,X23427)),hAPP(hAPP(c_Product__Type_OPair(X23427,X23427),X23426),X23425)),c_Relation_OId(X23427)))
        | X23426 = X23425 )
      & ( X23426 != X23425
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X23427,X23427)),hAPP(hAPP(c_Product__Type_OPair(X23427,X23427),X23426),X23425)),c_Relation_OId(X23427))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pair__in__Id__conv])]) ).

fof(i_0_5547,plain,
    ! [X18,X205,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X205))
     => ( hBOOL(hAPP(X18,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))
       => ( ! [X3,X230] :
              ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X230))
             => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X3),X230))
               => ( hBOOL(hAPP(X18,X230))
                 => hBOOL(hAPP(X18,hAPP(hAPP(c_Set_Oinsert(X5),X3),X230))) ) ) )
         => hBOOL(hAPP(X18,X205)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_finite__induct]) ).

fof(i_0_5548,plain,
    ! [X21136] :
      ( ~ class_Int_Onumber__ring(X21136)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21136),c_Groups_Oone__class_Oone(X21136)),c_Groups_Oone__class_Oone(X21136)) = hAPP(c_Int_Onumber__class_Onumber__of(X21136),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_5549,plain,
    ! [X31117,X31118,X31119] : hAPP(c_List_Oset(X31119),hAPP(c_List_OremoveAll(X31119,X31118),X31117)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X31119,tc_HOL_Obool)),hAPP(c_List_Oset(X31119),X31117)),hAPP(hAPP(c_Set_Oinsert(X31119),X31118),c_Orderings_Obot__class_Obot(tc_fun(X31119,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_set__removeAll]) ).

fof(i_0_5550,plain,
    ! [X21835,X21836] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X21836))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21836),X21835))
      | c_Divides_Odivmod__nat(X21835,X21836) = 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),X21835),X21836)),X21836))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21835),X21836),X21836)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__nat__step])]) ).

fof(i_0_5551,plain,
    ! [X54,X48,X64,X52] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(X52,X64)),X48),X54))
     => ~ ! [X61] :
            ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X52),X48),X61))
           => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X64),X61),X54)) ) ),
    inference(fof_simplification,[status(thm)],[fact_evalc__elim__cases_I4_J]) ).

fof(i_0_5552,plain,
    ! [X31665,X31666,X31667,X31668,X31669] : hAPP(c_List_Ofoldl(X31669,X31668,X31667,X31666),X31665) = c_List_Ofoldr(X31668,X31669,hAPP(c_COMBC(X31669,X31668,X31669),X31667),hAPP(c_List_Orev(X31668),X31665),X31666),
    inference(variable_rename,[status(thm)],[fact_foldl__foldr]) ).

fof(i_0_5553,plain,
    ! [X31804,X31805,X31806] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X31806),X31805))
      | hBOOL(hAPP(c_List_Odistinct(X31806),c_List_OdropWhile(X31806,X31804,X31805))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__dropWhile])]) ).

fof(i_0_5554,plain,
    ! [X1,X21,X205,X120,X2,X20,X5] :
      ( c_Big__Operators_Ocomm__monoid__big(X5,X20,X2,X120,X205)
     => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X20),X21))
         => hAPP(hAPP(X205,X1),X21) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X5,X20,X2),X1),X120),X21) )
        & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20),X21))
         => hAPP(hAPP(X205,X1),X21) = X120 ) ) ),
    inference(fof_simplification,[status(thm)],[fact_comm__monoid__big_OF__eq]) ).

fof(i_0_5555,plain,
    ! [X22145,X22146,X22147,X22148] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X22148,X22148)),hAPP(hAPP(c_Product__Type_OPair(X22148,X22148),X22147),X22146)),hAPP(c_Wellfounded_Omeasure(X22148),X22145)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X22145,X22147)),hAPP(X22145,X22146))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X22145,X22147)),hAPP(X22145,X22146)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X22148,X22148)),hAPP(hAPP(c_Product__Type_OPair(X22148,X22148),X22147),X22146)),hAPP(c_Wellfounded_Omeasure(X22148),X22145))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__measure])]) ).

fof(i_0_5556,plain,
    ! [X23096] : c_Wellfounded_Omeasure(X23096) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X23096),c_Wellfounded_Oless__than),
    inference(variable_rename,[status(thm)],[fact_measure__def]) ).

fof(i_0_5557,plain,
    ! [X113,X21,X24,X6,X20,X5] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X20)),hAPP(hAPP(c_Product__Type_OPair(X5,X20),X6),X24)),hAPP(hAPP(c_Product__Type_OSigma(X5,X20),X21),X113)))
     => ~ ( hBOOL(hAPP(hAPP(c_member(X5),X6),X21))
         => ~ hBOOL(hAPP(hAPP(c_member(X20),X24),hAPP(X113,X6))) ) ),
    inference(fof_simplification,[status(thm)],[fact_SigmaE2]) ).

fof(i_0_5558,plain,
    ! [X31240,X31241,X31242,X31243] : hAPP(hAPP(c_List_Omap(X31243,X31242),X31241),c_List_Oconcat(X31243,X31240)) = c_List_Oconcat(X31242,hAPP(hAPP(c_List_Omap(tc_List_Olist(X31243),tc_List_Olist(X31242)),hAPP(c_List_Omap(X31243,X31242),X31241)),X31240)),
    inference(variable_rename,[status(thm)],[fact_map__concat]) ).

fof(i_0_5559,plain,
    ! [X21094,X21095] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(X21095)),c_Int_OBit0(X21094)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X21095),X21094)),
    inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I9_J]) ).

fof(i_0_5560,plain,
    ! [X21089,X21090] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(X21090)),c_Int_OBit0(X21089)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21090),X21089)),
    inference(variable_rename,[status(thm)],[fact_add__Bit1__Bit0]) ).

fof(i_0_5561,plain,
    ! [X239,X20,X25,X2,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( ~ hBOOL(hAPP(hAPP(c_member(X5),hAPP(X2,X25)),hAPP(c_Set_Oimage(X20,X5,X2),hAPP(c_List_Oset(X20),X239))))
       => c_List_Olinorder__class_Oinsort__insert__key(X20,X5,X2,X25,X239) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X20,X5,X2),X25),X239) ) ),
    inference(fof_simplification,[status(thm)],[fact_insort__insert__insort__key]) ).

fof(i_0_5562,plain,
    ! [X23454,X23455,X23456] :
      ( ( ~ c_Relation_Ototal__on(X23456,X23455,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X23456,X23456),tc_HOL_Obool)),X23454),c_Relation_OId(X23456)))
        | c_Relation_Ototal__on(X23456,X23455,X23454) )
      & ( ~ c_Relation_Ototal__on(X23456,X23455,X23454)
        | c_Relation_Ototal__on(X23456,X23455,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X23456,X23456),tc_HOL_Obool)),X23454),c_Relation_OId(X23456))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_total__on__diff__Id])]) ).

fof(i_0_5563,plain,
    ! [X21026,X21027] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)),X21027))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21026)),X21027) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21026),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21027),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_5564,plain,
    ! [X21119,X21120] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(X21120)),X21119) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21120),X21119))),X21119),
    inference(variable_rename,[status(thm)],[fact_mult__Bit1]) ).

fof(i_0_5565,plain,
    ! [X21131] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__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(X21131))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21131))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__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(X21131))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21131))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of1])])]) ).

fof(i_0_5566,plain,
    ! [X21127,X21128] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(X21128)),c_Int_OBit1(X21127)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21128),c_Int_Osucc(X21127))),
    inference(variable_rename,[status(thm)],[fact_add__Bit1__Bit1]) ).

fof(i_0_5567,plain,
    ! [X21081,X21082] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X21082)),c_Int_OBit1(X21081)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21082),X21081)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21082),X21081))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X21082)),c_Int_OBit1(X21081))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I14_J])]) ).

fof(i_0_5568,plain,
    ! [X21079,X21080] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X21080)),c_Int_OBit1(X21079)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21080),X21079)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21080),X21079))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X21080)),c_Int_OBit1(X21079))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I32_J])]) ).

fof(i_0_5569,plain,
    ! [X21113,X21114] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X21114)),c_Int_OBit1(X21113)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21114),X21113)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21114),X21113))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X21114)),c_Int_OBit1(X21113))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__int__code_I14_J])]) ).

fof(i_0_5570,plain,
    ! [X21111,X21112] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X21112)),c_Int_OBit1(X21111)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21112),X21111)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21112),X21111))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X21112)),c_Int_OBit1(X21111))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I15_J])]) ).

fof(i_0_5571,plain,
    ! [X33851,X33852] :
      ( ( ~ c_Relation_Oantisym(X33852,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X33852,X33852),tc_HOL_Obool)),X33851),c_Relation_OId(X33852)))
        | c_Relation_Oantisym(X33852,X33851) )
      & ( ~ c_Relation_Oantisym(X33852,X33851)
        | c_Relation_Oantisym(X33852,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X33852,X33852),tc_HOL_Obool)),X33851),c_Relation_OId(X33852))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_antisym__reflcl])]) ).

fof(i_0_5572,plain,
    ! [X31798,X31799,X31800,X31801] :
      ( ( ~ hBOOL(hAPP(X31801,X31800))
        | c_List_OdropWhile(X31799,X31801,hAPP(hAPP(c_List_Olist_OCons(X31799),X31800),X31798)) = c_List_OdropWhile(X31799,X31801,X31798) )
      & ( hBOOL(hAPP(X31801,X31800))
        | c_List_OdropWhile(X31799,X31801,hAPP(hAPP(c_List_Olist_OCons(X31799),X31800),X31798)) = hAPP(hAPP(c_List_Olist_OCons(X31799),X31800),X31798) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5207])]) ).

fof(i_0_5573,plain,
    ! [X21776] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21776)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X21776)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21776)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X21776)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21776)),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_5208])]) ).

fof(i_0_5574,plain,
    ! [X32347,X32348] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X32348,X32348)),c_Transitive__Closure_Otrancl(X32348,X32347)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X32348,X32348)),X32347)) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X32348,X32348)),X32347))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X32348,X32348)),c_Transitive__Closure_Otrancl(X32348,X32347))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__trancl])]) ).

fof(i_0_5575,plain,
    ! [X113,X6,X21,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
     => ( hBOOL(hAPP(hAPP(c_member(X5),X6),X21))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X113))
         => hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X6),X113))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),X113))),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_card__Diff__insert]) ).

fof(i_0_5576,plain,
    ! [X31638,X31639] : hAPP(c_List_Orev(X31639),c_List_Oconcat(X31639,X31638)) = c_List_Oconcat(X31639,hAPP(hAPP(c_List_Omap(tc_List_Olist(X31639),tc_List_Olist(X31639)),c_List_Orev(X31639)),hAPP(c_List_Orev(tc_List_Olist(X31639)),X31638))),
    inference(variable_rename,[status(thm)],[fact_rev__concat]) ).

fof(i_0_5577,plain,
    ! [X120,X1,X6,X21,X5,X20] :
      ( class_Groups_Oab__semigroup__mult(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X21))
         => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X20,X5,c_Groups_Otimes__class_Otimes(X20)),X1),X120),hAPP(hAPP(c_Set_Oinsert(X5),X6),X21)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20),hAPP(X1,X6)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X20,X5,c_Groups_Otimes__class_Otimes(X20)),X1),X120),X21)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_fold__image__insert]) ).

fof(i_0_5578,plain,
    ! [X31178,X31179,X31180] : hAPP(c_List_Ofilter(X31180,X31179),c_List_Oconcat(X31180,X31178)) = c_List_Oconcat(X31180,hAPP(hAPP(c_List_Omap(tc_List_Olist(X31180),tc_List_Olist(X31180)),c_List_Ofilter(X31180,X31179)),X31178)),
    inference(variable_rename,[status(thm)],[fact_filter__concat]) ).

fof(i_0_5579,plain,
    ! [X33,X25,X5] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X33)),c_List_Omeasures(X5,c_List_Olist_ONil(tc_fun(X5,tc_Nat_Onat))))),
    inference(fof_simplification,[status(thm)],[fact_in__measures_I1_J]) ).

fof(i_0_5580,plain,
    ! [X6,X23,X24,X5] :
      ( class_Fields_Olinordered__field__inverse__zero(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X24),X23)),X6))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X23))) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X23)),X24)) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),X6)) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_divide__le__eq]) ).

fof(i_0_5581,plain,
    ! [X6,X23,X24,X5] :
      ( class_Fields_Olinordered__field__inverse__zero(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X24),X23)),X6))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X23))) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X23)),X24)) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X6)) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_divide__less__eq]) ).

fof(i_0_5582,plain,
    ! [X29395,X29396,X29397] :
      ( ( ~ hBOOL(hAPP(c_List_Odistinct(X29397),hAPP(c_List_Orotate(X29397,X29396),X29395)))
        | hBOOL(hAPP(c_List_Odistinct(X29397),X29395)) )
      & ( ~ hBOOL(hAPP(c_List_Odistinct(X29397),X29395))
        | hBOOL(hAPP(c_List_Odistinct(X29397),hAPP(c_List_Orotate(X29397,X29396),X29395))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__rotate])]) ).

fof(i_0_5583,plain,
    ! [X33,X32,X25,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_Relation_ODomain(X5,X5),X32)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X25),X33)),c_Transitive__Closure_Ortrancl(X5,X32)))
      <=> X25 = X33 ) ),
    inference(fof_simplification,[status(thm)],[fact_Not__Domain__rtrancl]) ).

fof(i_0_5584,plain,
    ! [X21091,X21092] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(X21092)),c_Int_OBit1(X21091)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21092),X21091)),
    inference(variable_rename,[status(thm)],[fact_add__Bit0__Bit1]) ).

fof(i_0_5585,plain,
    ! [X1,X21,X205,X120,X2,X20,X5] :
      ( c_Big__Operators_Ocomm__monoid__big(X5,X20,X2,X120,X205)
     => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X20),X21))
       => hAPP(hAPP(X205,X1),X21) = X120 ) ),
    inference(fof_simplification,[status(thm)],[fact_comm__monoid__big_Oinfinite]) ).

fof(i_0_5586,plain,
    ! [X20959,X20960] :
      ( ~ class_Int_Onumber__ring(X20960)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20960),hAPP(c_Int_Onumber__class_Onumber__of(X20960),X20959)),c_Groups_Oone__class_Oone(X20960)) = hAPP(c_Int_Onumber__class_Onumber__of(X20960),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20959),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_5587,plain,
    ! [X239,X25,X2,X5,X20] :
      ( class_Orderings_Olinorder(X20)
     => ( hBOOL(hAPP(c_List_Odistinct(X5),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X20,X2),X25),X239)))
      <=> ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X239)))
          & hBOOL(hAPP(c_List_Odistinct(X5),X239)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_distinct__insort]) ).

fof(i_0_5588,plain,
    ! [X20957,X20958] :
      ( ~ class_Int_Onumber__ring(X20958)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20958),c_Groups_Oone__class_Oone(X20958)),hAPP(c_Int_Onumber__class_Onumber__of(X20958),X20957)) = hAPP(c_Int_Onumber__class_Onumber__of(X20958),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),X20957))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__special_I1_J])]) ).

fof(i_0_5589,plain,
    ! [X32344,X32345,X32346] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32346,X32346)),X32345),X32344))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X32346,X32346)),X32345),c_Transitive__Closure_Otrancl(X32346,X32344))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_r__into__trancl_H])]) ).

fof(i_0_5590,plain,
    ! [X31222,X31223,X31224] : c_List_Oconcat(X31224,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X31224)),X31223),X31222)) = hAPP(hAPP(c_List_Oappend(X31224),X31223),c_List_Oconcat(X31224,X31222)),
    inference(variable_rename,[status(thm)],[fact_concat_Osimps_I2_J]) ).

fof(i_0_5591,plain,
    ! [X21022,X21023] :
      ( ~ class_Int_Onumber__ring(X21023)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21023),c_Groups_Oone__class_Oone(X21023)),hAPP(c_Int_Onumber__class_Onumber__of(X21023),X21022)) = hAPP(c_Int_Onumber__class_Onumber__of(X21023),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X21022)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__special_I2_J])]) ).

fof(i_0_5592,plain,
    ! [X22,X23,X24,X6,X5] :
      ( class_Orderings_Oorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,X24)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X23,X22)))
      <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),X24))
            | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X23),X6))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X24),X22))
              & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),X6))
                | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X24),X22)) ) ) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X23),X22)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_atLeastatMost__psubset__iff]) ).

fof(i_0_5593,plain,
    ! [X31364,X31365] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X31365)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X31364)))
        | c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X31365),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X31364)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X31365)),c_List_Oupt(hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X31365)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X31364))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X31365)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X31364)))
        | c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X31365),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X31364)) = c_List_Olist_ONil(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5209])]) ).

fof(i_0_5594,plain,
    ! [X205,X25,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X25),X205))
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(tc_fun(X5,tc_HOL_Obool)),X25),X205)))
           => ! [X204] :
                ( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X204),hAPP(hAPP(c_Set_Oinsert(tc_fun(X5,tc_HOL_Obool)),X25),X205)))
               => ( X3 != X204
                 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X3),X204) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ) ) )
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X25),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X205)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ) ),
    inference(fof_simplification,[status(thm)],[fact_insert__partition]) ).

fof(i_0_5595,plain,
    ! [X32380,X32381] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X32381,X32381),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X32381,X32380)),c_Relation_OId(X32381)) = c_Transitive__Closure_Ortrancl(X32381,X32380),
    inference(variable_rename,[status(thm)],[fact_reflcl__trancl]) ).

fof(i_0_5596,plain,
    ! [X66,X241,X242,X58,X57] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X57),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242)))
       => hAPP(hAPP(c_List_Olist__update(X58,hAPP(hAPP(c_List_Oappend(X58),X242),X241)),X57),X66) = hAPP(hAPP(c_List_Oappend(X58),hAPP(hAPP(c_List_Olist__update(X58,X242),X57),X66)),X241) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X57),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242)))
       => hAPP(hAPP(c_List_Olist__update(X58,hAPP(hAPP(c_List_Oappend(X58),X242),X241)),X57),X66) = hAPP(hAPP(c_List_Oappend(X58),X242),hAPP(hAPP(c_List_Olist__update(X58,X241),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X57),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242))),X66)) ) ),
    inference(fof_simplification,[status(thm)],[fact_list__update__append]) ).

fof(i_0_5597,plain,
    ! [X23,X24,X6,X5] :
      ( class_Fields_Olinordered__field__inverse__zero(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X24),X23)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X23)),X24)) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X23))) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),c_Groups_Ozero__class_Ozero(X5))) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_le__divide__eq]) ).

fof(i_0_5598,plain,
    ! [X23,X24,X6,X5] :
      ( class_Fields_Olinordered__field__inverse__zero(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X5),X24),X23)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X23)),X24)) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X23))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),X23))) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),c_Groups_Ozero__class_Ozero(X5)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),c_Groups_Ozero__class_Ozero(X5))) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_less__divide__eq]) ).

fof(i_0_5599,plain,
    ! [X33556,X33557,X33558,X33559,X33560,X33561] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X33561,X33560,X33559,X33558,c_Lazy__Sequence_Olazy__sequence_OInsert(X33560,X33557,X33556)) = hAPP(hAPP(X33558,X33557),X33556),
    inference(variable_rename,[status(thm)],[fact_lazy__sequence_Osimps_I5_J]) ).

fof(i_0_5600,plain,
    ! [X33550,X33551,X33552,X33553,X33554] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X33554,X33553,X33552,X33551,X33550) = c_Option_Ooption_Ooption__case(X33554,tc_prod(X33553,tc_Lazy__Sequence_Olazy__sequence(X33553)),X33552,hAPP(c_Product__Type_Oprod_Oprod__case(X33553,tc_Lazy__Sequence_Olazy__sequence(X33553),X33554),X33551),hAPP(c_Lazy__Sequence_Oyield(X33553),X33550)),
    inference(variable_rename,[status(thm)],[fact_seq__case]) ).

fof(i_0_5601,plain,
    ! [X20993,X20994] :
      ( ~ class_Int_Onumber__ring(X20994)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20994),hAPP(c_Int_Onumber__class_Onumber__of(X20994),c_Int_OBit1(c_Int_OPls))),X20993) = X20993 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__numeral__1])]) ).

fof(i_0_5602,plain,
    ! [X157,X82,X18] :
      ( c_List_Olist__ex(tc_Int_Oint,X18,c_List_Oupto(X82,X157))
    <=> ~ c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint,c_fNot),X18),X82,X157) ),
    inference(fof_simplification,[status(thm)],[fact_list__ex__iff__not__all__inverval__int]) ).

fof(i_0_5603,plain,
    ! [X29418,X29419,X29420] : c_List_Orotate(X29420,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X29419),X29418)) = hAPP(c_Fun_Ocomp(tc_List_Olist(X29420),tc_List_Olist(X29420),tc_List_Olist(X29420),c_List_Orotate(X29420,X29419)),c_List_Orotate(X29420,X29418)),
    inference(variable_rename,[status(thm)],[fact_rotate__add]) ).

fof(i_0_5604,plain,
    ! [X22,X23,X24,X6,X5] :
      ( class_Orderings_Oorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,X24)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X23,X22)))
      <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),X24))
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X23),X6))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X24),X22)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_atLeastatMost__subset__iff]) ).

fof(i_0_5605,plain,
    ! [X21016,X21017] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21017),hAPP(c_Int_Onumber__class_Onumber__of(X21017),X21016)),c_Groups_Oone__class_Oone(X21017)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21016),c_Int_OBit1(c_Int_OPls)))
        | ~ class_Int_Onumber__ring(X21017)
        | ~ class_Rings_Olinordered__idom(X21017) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21016),c_Int_OBit1(c_Int_OPls)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21017),hAPP(c_Int_Onumber__class_Onumber__of(X21017),X21016)),c_Groups_Oone__class_Oone(X21017)))
        | ~ class_Int_Onumber__ring(X21017)
        | ~ class_Rings_Olinordered__idom(X21017) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__special_I4_J])])]) ).

fof(i_0_5606,plain,
    ! [X21018,X21019] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21019),hAPP(c_Int_Onumber__class_Onumber__of(X21019),X21018)),c_Groups_Oone__class_Oone(X21019)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21018),c_Int_OBit1(c_Int_OPls)))
        | ~ class_Int_Onumber__ring(X21019)
        | ~ class_Rings_Olinordered__idom(X21019) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21018),c_Int_OBit1(c_Int_OPls)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21019),hAPP(c_Int_Onumber__class_Onumber__of(X21019),X21018)),c_Groups_Oone__class_Oone(X21019)))
        | ~ class_Int_Onumber__ring(X21019)
        | ~ class_Rings_Olinordered__idom(X21019) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__special_I4_J])])]) ).

fof(i_0_5607,plain,
    ! [X32749,X32750] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32750,X32750)),X32749),c_Relation_OId(X32750)))
      | X32749 = hAPP(hAPP(c_Product__Type_OPair(X32750,X32750),esk479_2(X32749,X32750)),esk479_2(X32749,X32750)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_IdE])])]) ).

fof(i_0_5608,plain,
    ! [X60,X26,X59,X63,X27] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X27,X63,X59)),X26),X60))
    <=> ( ( hBOOL(hAPP(X27,X26))
          & hBOOL(hAPP(hAPP(c_Natural_Oevalc(X63),X26),X60)) )
        | ( ~ hBOOL(hAPP(X27,X26))
          & hBOOL(hAPP(hAPP(c_Natural_Oevalc(X59),X26),X60)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_evalc_Oequations_I5_J]) ).

fof(i_0_5609,plain,
    ! [X60,X26,X63,X59,X27] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X27,X59,X63)),X26),X60))
    <=> ( ( hBOOL(hAPP(X27,X26))
          & hBOOL(hAPP(hAPP(c_Natural_Oevalc(X59),X26),X60)) )
        | ( ~ hBOOL(hAPP(X27,X26))
          & hBOOL(hAPP(hAPP(c_Natural_Oevalc(X63),X26),X60)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_evalc_Oequations_I6_J]) ).

fof(i_0_5610,plain,
    ! [X15,X76,X106,X105,X24] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X24,X105,X106)),X76),X15))
     => ( ( hBOOL(hAPP(X24,X76))
         => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X105),X76),X15)) )
       => ~ ( ~ hBOOL(hAPP(X24,X76))
           => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X106),X76),X15)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_evalc__elim__cases_I5_J]) ).

fof(i_0_5611,plain,
    ! [X20999] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X20999)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X20999)),
    inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I4_J]) ).

fof(i_0_5612,plain,
    ! [X23368,X23369] : hBOOL(hAPP(hAPP(c_member(tc_prod(X23369,X23369)),hAPP(hAPP(c_Product__Type_OPair(X23369,X23369),X23368),X23368)),c_Relation_OId(X23369))),
    inference(variable_rename,[status(thm)],[fact_IdI]) ).

fof(i_0_5613,plain,
    ! [X31210,X31211,X31212] : hAPP(c_List_Ofoldl(tc_List_Olist(X31212),tc_List_Olist(X31212),c_List_Oappend(X31212),X31211),X31210) = hAPP(hAPP(c_List_Oappend(X31212),X31211),c_List_Oconcat(X31212,X31210)),
    inference(variable_rename,[status(thm)],[fact_foldl__conv__concat]) ).

fof(i_0_5614,plain,
    ! [X21096,X21097] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(X21097)),c_Int_OBit1(X21096)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X21097),X21096)),
    inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I10_J]) ).

fof(i_0_5615,plain,
    ! [X239,X25,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X239)))
       => c_List_Olinorder__class_Oinsort__insert__key(X5,X5,c_COMBI(X5),X25,X239) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X5,c_COMBI(X5)),X25),X239) ) ),
    inference(fof_simplification,[status(thm)],[fact_insort__insert__insort]) ).

fof(i_0_5616,plain,
    ! [X171,X5] :
      ( c_Relation_Oirrefl(X5,X171)
    <=> ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X3)),X171)) ),
    inference(fof_simplification,[status(thm)],[fact_irrefl__def]) ).

fof(i_0_5617,plain,
    ! [X6,X171,X5] :
      ( c_Wellfounded_Owf(X5,X171)
     => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X6)),X171)) ),
    inference(fof_simplification,[status(thm)],[fact_wf__not__refl]) ).

fof(i_0_5618,plain,
    ! [X6,X171,X5] :
      ( c_Wellfounded_Owf(X5,X171)
     => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X6),X6)),X171)) ),
    inference(fof_simplification,[status(thm)],[fact_wf__irrefl]) ).

fof(i_0_5619,plain,
    ! [X32226,X32227] : c_Transitive__Closure_Ortrancl(X32227,X32226) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X32227,X32227),tc_HOL_Obool)),c_Relation_OId(X32227)),hAPP(hAPP(c_Relation_Orel__comp(X32227,X32227,X32227),c_Transitive__Closure_Ortrancl(X32227,X32226)),X32226)),
    inference(variable_rename,[status(thm)],[fact_rtrancl__unfold]) ).

fof(i_0_5620,plain,
    ! [X6,X113,X21,X20,X24,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X24),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X20,tc_fun(X5,tc_HOL_Obool)),X21),X113)))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X24),hAPP(X113,X6)))
       => ~ hBOOL(hAPP(hAPP(c_member(X20),X6),X21)) ) ),
    inference(fof_simplification,[status(thm)],[fact_INT__E]) ).

fof(i_0_5621,plain,
    ! [X20978] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X20978)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X20978)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X20978))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X20978))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I22_J])]) ).

fof(i_0_5622,plain,
    ! [X20998] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X20998)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X20998)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X20998))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X20998))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I5_J])]) ).

fof(i_0_5623,plain,
    ! [X20982] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X20982)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),X20982)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),X20982))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X20982))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I26_J])]) ).

fof(i_0_5624,plain,
    ! [X20983] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X20983)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X20983)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X20983))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X20983))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I9_J])]) ).

fof(i_0_5625,plain,
    ! [X21746,X21747,X21748] :
      ( ~ class_Int_Onumber__ring(X21748)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X21748),hAPP(c_Int_Onumber__class_Onumber__of(X21748),X21747)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X21746))) = hAPP(hAPP(c_HOL_OLet(X21748,X21748),hAPP(hAPP(c_Power_Opower__class_Opower(X21748),hAPP(c_Int_Onumber__class_Onumber__of(X21748),X21747)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21746))),hAPP(hAPP(c_COMBS(X21748,X21748,X21748),c_Groups_Otimes__class_Otimes(X21748)),c_COMBI(X21748))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__number__of__even__number__of])]) ).

fof(i_0_5626,plain,
    ! [X25,X33,X23] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23),X33))
       => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X23)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X25),X33)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25),X23)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X33),X23)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23),X33))
       => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),X33))
           => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X23)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X25),X33)) = 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),X25),X33))
           => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),X23)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X25),X33)) = 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,
    ! [X31432,X31433] :
      ( ~ class_Groups_Omonoid__add(X31433)
      | hAPP(c_List_Ofoldl(X31433,X31433,c_Groups_Oplus__class_Oplus(X31433),c_Groups_Ozero__class_Ozero(X31433)),X31432) = c_List_Ofoldr(X31433,X31433,c_Groups_Oplus__class_Oplus(X31433),X31432,c_Groups_Ozero__class_Ozero(X31433)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_foldl__foldr1])]) ).

fof(i_0_5628,plain,
    ! [X31395,X31396,X31397,X31398,X31399] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31399),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X31398),X31397)))
      | hAPP(hAPP(c_List_Onth(X31396),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X31396),X31395),c_List_Oupt(X31397,X31398))),X31399) = hAPP(X31395,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31397),X31399)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__map__upt])]) ).

fof(i_0_5629,plain,
    ! [X29410,X29411,X29412,X29413] : hAPP(c_List_Orotate(X29413,X29412),hAPP(c_List_Orotate(X29413,X29411),X29410)) = hAPP(c_List_Orotate(X29413,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X29412),X29411)),X29410),
    inference(variable_rename,[status(thm)],[fact_rotate__rotate]) ).

fof(i_0_5630,plain,
    ! [X31422,X31423,X31424] :
      ( ~ class_Groups_Oab__semigroup__add(X31424)
      | c_List_Ofoldr(X31424,X31424,c_Groups_Oplus__class_Oplus(X31424),X31423,X31422) = hAPP(c_List_Ofoldl(X31424,X31424,c_Groups_Oplus__class_Oplus(X31424),X31422),X31423) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_foldr__conv__foldl])]) ).

fof(i_0_5631,plain,
    ! [X33632,X33633,X33634,X33635] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X33635,X33634,X33633,X33632,c_Lazy__Sequence_Olazy__sequence_OEmpty(X33634)) = X33633,
    inference(variable_rename,[status(thm)],[fact_lazy__sequence_Osimps_I4_J]) ).

fof(i_0_5632,plain,
    ! [X29452,X29453,X29454] : hAPP(c_List_Orotate(X29454,X29453),X29452) = hAPP(c_List_Orotate(X29454,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X29453,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29454)),X29452))),X29452),
    inference(variable_rename,[status(thm)],[fact_rotate__conv__mod]) ).

fof(i_0_5633,plain,
    ! [X20987,X20988] :
      ( ~ class_Int_Onumber__ring(X20988)
      | ~ class_Int_Oring__char__0(X20988)
      | ~ c_Int_Oiszero(X20988,hAPP(c_Int_Onumber__class_Onumber__of(X20988),c_Int_OBit1(X20987))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5210])]) ).

fof(i_0_5634,plain,
    ! [X21104] : c_Int_Opred(c_Int_OBit0(X21104)) = c_Int_OBit1(c_Int_Opred(X21104)),
    inference(variable_rename,[status(thm)],[fact_pred__Bit0]) ).

fof(i_0_5635,plain,
    ! [X6,X2,X21,X5,X20] :
      ( class_Fields_Ofield(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( hAPP(X2,X6) != c_Groups_Ozero__class_Ozero(X20)
         => ( ( hBOOL(hAPP(hAPP(c_member(X5),X6),X21))
             => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X20),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X2),X21)),hAPP(X2,X6)) )
            & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X21))
             => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X2),X21) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_setprod__diff1]) ).

fof(i_0_5636,plain,
    ! [X27640,X27641] : c_Relation_Orefl__on(X27641,c_Orderings_Otop__class_Otop(tc_fun(X27641,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X27641,X27641),tc_HOL_Obool)),X27640),c_Relation_OId(X27641))),
    inference(variable_rename,[status(thm)],[fact_refl__reflcl]) ).

fof(i_0_5637,plain,
    ! [X31818,X31819,X31820] : hAPP(hAPP(c_List_Oappend(X31820),c_List_OtakeWhile(X31820,X31819,X31818)),c_List_OdropWhile(X31820,X31819,X31818)) = X31818,
    inference(variable_rename,[status(thm)],[fact_takeWhile__dropWhile__id]) ).

fof(i_0_5638,plain,
    ! [X2,X6,X21,X5,X20] :
      ( class_Groups_Oab__group__add(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( ( hBOOL(hAPP(hAPP(c_member(X5),X6),X21))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X2),X21)),hAPP(X2,X6)) )
          & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X21))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X2),X21) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_setsum__diff1]) ).

fof(i_0_5639,plain,
    ! [X31256,X31257] : hAPP(c_List_Oset(X31257),c_List_Oconcat(X31257,X31256)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(X31257),tc_fun(X31257,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(X31257)),X31256)),c_List_Oset(X31257)),
    inference(variable_rename,[status(thm)],[fact_set__concat]) ).

fof(i_0_5640,plain,
    ! [X31244,X31245] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31245)),c_List_Oconcat(X31245,X31244)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X31245),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X31245))),X31244)),
    inference(variable_rename,[status(thm)],[fact_length__concat]) ).

fof(i_0_5641,plain,
    ! [X6,X24,X113,X21,X20,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X20,tc_HOL_Obool)),X21),X113),X24))
     => ( ~ hBOOL(hAPP(hAPP(X113,X6),X24))
       => ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X21)) ) ),
    inference(fof_simplification,[status(thm)],[fact_INF1__E]) ).

fof(i_0_5642,plain,
    ! [X33823,X33824] :
      ( ~ c_Relation_Otrans(X33824,X33823)
      | ~ c_Relation_Oantisym(X33824,X33823)
      | c_Relation_Otrans(X33824,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X33824,X33824),tc_HOL_Obool)),X33823),c_Relation_OId(X33824))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__diff__Id])]) ).

fof(i_0_5643,plain,
    ! [X31705,X31706,X31707] :
      ( ( X31706 != c_List_Olist_ONil(X31707)
        | c_List_Ofoldr(X31707,X31707,c_Orderings_Oord__class_Omax(X31707),X31706,X31705) = X31705
        | ~ c_List_Olinorder__class_Osorted(X31707,hAPP(c_List_Orev(X31707),X31706))
        | ~ class_Orderings_Olinorder(X31707) )
      & ( X31706 = c_List_Olist_ONil(X31707)
        | c_List_Ofoldr(X31707,X31707,c_Orderings_Oord__class_Omax(X31707),X31706,X31705) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X31707),hAPP(hAPP(c_List_Onth(X31707),X31706),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X31705)
        | ~ c_List_Olinorder__class_Osorted(X31707,hAPP(c_List_Orev(X31707),X31706))
        | ~ class_Orderings_Olinorder(X31707) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_foldr__max__sorted])])]) ).

fof(i_0_5644,plain,
    ! [X33783,X33784] :
      ( ~ c_Relation_Otrans(X33784,X33783)
      | c_Relation_Otrans(X33784,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X33784,X33784),tc_HOL_Obool)),X33783),c_Relation_OId(X33784))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__reflclI])]) ).

fof(i_0_5645,plain,
    ! [X18,X239,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X239)))
     => ( ~ hBOOL(hAPP(X18,X25))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),hAPP(c_List_Ofilter(X5,X18),X239))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239))) ) ),
    inference(fof_simplification,[status(thm)],[fact_length__filter__less]) ).

fof(i_0_5646,plain,
    ! [X32197,X32198] : c_Transitive__Closure_Ortrancl(X32198,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X32198,X32198),tc_HOL_Obool)),X32197),c_Relation_OId(X32198))) = c_Transitive__Closure_Ortrancl(X32198,X32197),
    inference(variable_rename,[status(thm)],[fact_rtrancl__reflcl]) ).

fof(i_0_5647,plain,
    ! [X32211,X32212] : c_Transitive__Closure_Ortrancl(X32212,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X32212,X32212),tc_HOL_Obool)),X32211),c_Relation_OId(X32212))) = c_Transitive__Closure_Ortrancl(X32212,X32211),
    inference(variable_rename,[status(thm)],[fact_rtrancl__r__diff__Id]) ).

fof(i_0_5648,plain,
    ! [X31834,X31835,X31836,X31837,X31838] :
      ( ( X31836 = hAPP(hAPP(c_List_Oappend(X31838),c_List_OtakeWhile(X31838,X31837,X31836)),hAPP(hAPP(c_List_Olist_OCons(X31838),X31835),X31834))
        | c_List_OdropWhile(X31838,X31837,X31836) != hAPP(hAPP(c_List_Olist_OCons(X31838),X31835),X31834) )
      & ( ~ hBOOL(hAPP(X31837,X31835))
        | c_List_OdropWhile(X31838,X31837,X31836) != hAPP(hAPP(c_List_Olist_OCons(X31838),X31835),X31834) )
      & ( X31836 != hAPP(hAPP(c_List_Oappend(X31838),c_List_OtakeWhile(X31838,X31837,X31836)),hAPP(hAPP(c_List_Olist_OCons(X31838),X31835),X31834))
        | hBOOL(hAPP(X31837,X31835))
        | c_List_OdropWhile(X31838,X31837,X31836) = hAPP(hAPP(c_List_Olist_OCons(X31838),X31835),X31834) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5211])])]) ).

fof(i_0_5649,plain,
    ! [X23428,X23429] : c_Relation_Oirrefl(X23429,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X23429,X23429),tc_HOL_Obool)),X23428),c_Relation_OId(X23429))),
    inference(variable_rename,[status(thm)],[fact_irrefl__diff__Id]) ).

fof(i_0_5650,plain,
    ! [X21000] :
      ( ~ class_Int_Onumber__ring(X21000)
      | ~ c_Int_Oiszero(X21000,hAPP(c_Int_Onumber__class_Onumber__of(X21000),c_Int_OBit1(c_Int_OPls))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5212])]) ).

fof(i_0_5651,plain,
    ! [X134,X140,X90,X62] :
      ( X62 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X90),X140)),X134)
     => ( ( ( 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)),X134))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X134),X90)) ) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X90))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X90),X134))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X134),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
       => hBOOL(hAPP(c_Divides_Odivmod__int__rel(X62,X90),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X140),X134))) ) ),
    inference(fof_simplification,[status(thm)],[fact_divmod__int__relI]) ).

fof(i_0_5652,plain,
    ! [X21123] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X21123)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X21123)),
    inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I5_J]) ).

fof(i_0_5653,plain,
    ! [X2,X21,X6,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X6),X21))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),X2),X21)),hAPP(X2,X6)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X21))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,tc_Nat_Onat),X2),X21) ) ),
    inference(fof_simplification,[status(thm)],[fact_setsum__diff1__nat]) ).

fof(i_0_5654,plain,
    ! [X32409,X32410] :
      ( ~ c_Wellfounded_Owf(X32410,hAPP(c_Relation_Oconverse(X32410,X32410),X32409))
      | c_Wellfounded_Owf(X32410,hAPP(c_Relation_Oconverse(X32410,X32410),c_Transitive__Closure_Otrancl(X32410,X32409))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__converse__trancl])]) ).

fof(i_0_5655,plain,
    ! [X31228,X31229,X31230,X31231,X31232] :
      ( ( c_List_Oconcat(X31229,X31228) != c_List_Olist_ONil(X31229)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X31229)),X31230),hAPP(c_List_Oset(tc_List_Olist(X31229)),X31228)))
        | X31230 = c_List_Olist_ONil(X31229) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X31232)),esk385_2(X31231,X31232)),hAPP(c_List_Oset(tc_List_Olist(X31232)),X31231)))
        | c_List_Oconcat(X31232,X31231) = c_List_Olist_ONil(X31232) )
      & ( esk385_2(X31231,X31232) != c_List_Olist_ONil(X31232)
        | c_List_Oconcat(X31232,X31231) = c_List_Olist_ONil(X31232) ) ),
    inference(distribute,[status(thm)],[inference(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,
    ! [X31234,X31235,X31236,X31237,X31238] :
      ( ( c_List_Olist_ONil(X31235) != c_List_Oconcat(X31235,X31234)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X31235)),X31236),hAPP(c_List_Oset(tc_List_Olist(X31235)),X31234)))
        | X31236 = c_List_Olist_ONil(X31235) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X31238)),esk386_2(X31237,X31238)),hAPP(c_List_Oset(tc_List_Olist(X31238)),X31237)))
        | c_List_Olist_ONil(X31238) = c_List_Oconcat(X31238,X31237) )
      & ( esk386_2(X31237,X31238) != c_List_Olist_ONil(X31238)
        | c_List_Olist_ONil(X31238) = c_List_Oconcat(X31238,X31237) ) ),
    inference(distribute,[status(thm)],[inference(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,
    ! [X31359,X31360,X31361] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31361),X31360))
      | c_List_Oupt(X31361,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31360),X31359)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X31361,X31360)),c_List_Oupt(X31360,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31360),X31359))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_upt__add__eq__append])]) ).

fof(i_0_5658,plain,
    ! [X2,X95,X50,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X50)),X95))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X95,hAPP(c_Nat_OSuc,X50))) = c_Groups_Ozero__class_Ozero(X5) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X50)),X95))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X95,hAPP(c_Nat_OSuc,X50))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X95,X50))),hAPP(X2,hAPP(c_Nat_OSuc,X50))) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_setsum__cl__ivl__Suc]) ).

fof(i_0_5659,plain,
    ! [X113,X21,X23,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X23),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113)))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X23),X21))
       => hBOOL(hAPP(hAPP(c_member(X5),X23),X113)) ) ),
    inference(fof_simplification,[status(thm)],[fact_UnE]) ).

fof(i_0_5660,plain,
    ! [X31807,X31808,X31809,X31810,X31811,X31812,X31813] :
      ( ( c_List_OdropWhile(X31809,X31808,X31807) != c_List_Olist_ONil(X31809)
        | ~ hBOOL(hAPP(hAPP(c_member(X31809),X31810),hAPP(c_List_Oset(X31809),X31807)))
        | hBOOL(hAPP(X31808,X31810)) )
      & ( hBOOL(hAPP(hAPP(c_member(X31813),esk398_3(X31811,X31812,X31813)),hAPP(c_List_Oset(X31813),X31811)))
        | c_List_OdropWhile(X31813,X31812,X31811) = c_List_Olist_ONil(X31813) )
      & ( ~ hBOOL(hAPP(X31812,esk398_3(X31811,X31812,X31813)))
        | c_List_OdropWhile(X31813,X31812,X31811) = c_List_Olist_ONil(X31813) ) ),
    inference(distribute,[status(thm)],[inference(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,
    ! [X31106,X31107,X31108] :
      ( hBOOL(hAPP(hAPP(c_member(X31108),X31107),hAPP(c_List_Oset(X31108),X31106)))
      | hAPP(c_List_OremoveAll(X31108,X31107),X31106) = X31106 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5213])]) ).

fof(i_0_5662,plain,
    ! [X25,X21,X205,X2,X20,X5] :
      ( c_Finite__Set_Ofolding(X5,X20,X2,X205)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => hAPP(X205,hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(c_Fun_Ocomp(X20,X20,X20,hAPP(X205,X21)),hAPP(X2,X25)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_folding_Oinsert]) ).

fof(i_0_5663,plain,
    ! [X31795,X31796,X31797] :
      ( ~ class_Orderings_Olinorder(X31797)
      | ~ c_List_Olinorder__class_Osorted(X31797,X31796)
      | c_List_Olinorder__class_Osorted(X31797,c_List_OdropWhile(X31797,X31795,X31796)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__dropWhile])]) ).

fof(i_0_5664,plain,
    ! [X239,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X239)))
    <=> ? [X262,X289] :
          ( X239 = hAPP(hAPP(c_List_Oappend(X5),X262),hAPP(hAPP(c_List_Olist_OCons(X5),X25),X289))
          & ~ hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X289))) ) ),
    inference(fof_simplification,[status(thm)],[fact_in__set__conv__decomp__last]) ).

fof(i_0_5665,plain,
    ! [X239,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X239)))
    <=> ? [X262] :
          ( ? [X289] : X239 = hAPP(hAPP(c_List_Oappend(X5),X262),hAPP(hAPP(c_List_Olist_OCons(X5),X25),X289))
          & ~ hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X262))) ) ),
    inference(fof_simplification,[status(thm)],[fact_in__set__conv__decomp__first]) ).

fof(i_0_5666,plain,
    ! [X21108] : c_Int_Osucc(c_Int_OBit1(X21108)) = c_Int_OBit0(c_Int_Osucc(X21108)),
    inference(variable_rename,[status(thm)],[fact_succ__Bit1]) ).

fof(i_0_5667,plain,
    ! [X45,X57,X48,X49] :
      ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X49),X48,X57,X45)
     => ~ ! [X69] :
            ( X57 = hAPP(c_Nat_OSuc,X69)
           => ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X49)),X48,X69,X45) ) ),
    inference(fof_simplification,[status(thm)],[fact_evaln__elim__cases_I6_J]) ).

fof(i_0_5668,plain,
    ! [X21741,X21742,X21743] :
      ( ~ class_Int_Onumber__ring(X21743)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X21743),X21742),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X21741))) = hAPP(hAPP(c_HOL_OLet(X21743,X21743),hAPP(hAPP(c_Power_Opower__class_Opower(X21743),X21742),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21741))),hAPP(hAPP(c_COMBS(X21743,X21743,X21743),c_Groups_Otimes__class_Otimes(X21743)),c_COMBI(X21743))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__number__of__even])]) ).

fof(i_0_5669,plain,
    ! [X113,X21,X23,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X23),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),X113)))
    <=> ( hBOOL(hAPP(hAPP(c_member(X5),X23),X21))
        & ~ hBOOL(hAPP(hAPP(c_member(X5),X23),X113)) ) ),
    inference(fof_simplification,[status(thm)],[fact_Diff__iff]) ).

fof(i_0_5670,plain,
    ! [X113,X21,X23,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X23),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),X113)))
     => ~ hBOOL(hAPP(hAPP(c_member(X5),X23),X113)) ),
    inference(fof_simplification,[status(thm)],[fact_DiffD2]) ).

fof(i_0_5671,plain,
    ! [X31215,X31216,X31217,X31218] :
      ( hBOOL(hAPP(X31218,X31217))
      | hAPP(c_List_OremoveAll(X31216,X31217),hAPP(c_List_Ofilter(X31216,X31218),X31215)) = hAPP(c_List_Ofilter(X31216,X31218),X31215) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5214])]) ).

fof(i_0_5672,plain,
    ! [X31786,X31787] : hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),X31787),X31786) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint),c_List_Oembed__list(X31787)),c_List_Oembed__list(X31786))),
    inference(variable_rename,[status(thm)],[fact_transfer__nat__int__list__functions_I1_J]) ).

fof(i_0_5673,plain,
    ! [X31765] : c_List_Oreturn__list(X31765) = hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),X31765),
    inference(variable_rename,[status(thm)],[fact_return__list__def]) ).

fof(i_0_5674,plain,
    ! [X31788] : c_List_Oembed__list(X31788) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X31788),
    inference(variable_rename,[status(thm)],[fact_embed__list__def]) ).

fof(i_0_5675,plain,
    ! [X87,X21,X5] :
      ( hAPP(c_Finite__Set_Ocard(X5),X21) = hAPP(c_Nat_OSuc,X87)
    <=> ? [X188,X211] :
          ( X21 = hAPP(hAPP(c_Set_Oinsert(X5),X188),X211)
          & ~ hBOOL(hAPP(hAPP(c_member(X5),X188),X211))
          & hAPP(c_Finite__Set_Ocard(X5),X211) = X87
          & ( X87 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
           => X211 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_card__Suc__eq]) ).

fof(i_0_5676,plain,
    ! [X31109,X31110,X31111] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X31111),X31110))
      | c_List_Oremove1(X31111,X31109,X31110) = hAPP(c_List_OremoveAll(X31111,X31109),X31110) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__remove1__removeAll])]) ).

fof(i_0_5677,plain,
    ! [X31340,X31341,X31342] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31342),X31341)),X31340))
      | hAPP(hAPP(c_List_Otake(tc_Nat_Onat),X31341),c_List_Oupt(X31342,X31340)) = c_List_Oupt(X31342,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31342),X31341)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__upt])]) ).

fof(i_0_5678,plain,
    ! [X30076,X30077,X30078,X30079,X30080] : hAPP(c_List_Orotate(X30080,X30079),hAPP(hAPP(c_List_Omap(X30078,X30080),X30077),X30076)) = hAPP(hAPP(c_List_Omap(X30078,X30080),X30077),hAPP(c_List_Orotate(X30078,X30079),X30076)),
    inference(variable_rename,[status(thm)],[fact_rotate__map]) ).

fof(i_0_5679,plain,
    ! [X32407,X32408] : c_Transitive__Closure_Otrancl(X32408,hAPP(c_Relation_Oconverse(X32408,X32408),X32407)) = hAPP(c_Relation_Oconverse(X32408,X32408),c_Transitive__Closure_Otrancl(X32408,X32407)),
    inference(variable_rename,[status(thm)],[fact_trancl__converse]) ).

fof(i_0_5680,plain,
    ! [X251,X20,X33,X25,X2,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(X2,X25)),hAPP(X2,X33)))
         => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X20,X5,X2),X25),hAPP(hAPP(c_List_Olist_OCons(X20),X33),X251)) = hAPP(hAPP(c_List_Olist_OCons(X20),X25),hAPP(hAPP(c_List_Olist_OCons(X20),X33),X251)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(X2,X25)),hAPP(X2,X33)))
         => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X20,X5,X2),X25),hAPP(hAPP(c_List_Olist_OCons(X20),X33),X251)) = hAPP(hAPP(c_List_Olist_OCons(X20),X33),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X20,X5,X2),X25),X251)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_insort__key_Osimps_I2_J]) ).

fof(i_0_5681,plain,
    ! [X57,X72] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X72)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X57)))
       => c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X72),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X57)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X72)),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X72)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X57))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X72)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X57)))
       => c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X72),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X57)) = c_List_Olist_ONil(tc_Int_Oint) ) ),
    inference(fof_simplification,[status(thm)],[fact_upto__rec__number__of]) ).

fof(i_0_5682,plain,
    ! [X113,X21,X25,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),X113)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),X113)) ) ),
    inference(fof_simplification,[status(thm)],[fact_subset__insert]) ).

fof(i_0_5683,plain,
    ! [X113,X21,X23,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X23),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113)))
     => ~ ( hBOOL(hAPP(hAPP(c_member(X5),X23),X21))
         => ~ hBOOL(hAPP(hAPP(c_member(X5),X23),X113)) ) ),
    inference(fof_simplification,[status(thm)],[fact_IntE]) ).

fof(i_0_5684,plain,
    ! [X157,X82] :
      ( 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),X82),X157)))
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X82),X157))
         => c_List_Oupto(X82,X157) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),X82),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X82),c_Groups_Oone__class_Oone(tc_Int_Oint)),X157)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X82),X157))
         => c_List_Oupto(X82,X157) = c_List_Olist_ONil(tc_Int_Oint) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_upto_Opsimps]) ).

fof(i_0_5685,plain,
    ! [X120,X25,X21,X2,X20,X5] :
      ( c_Finite__Set_Ofun__left__comm(X5,X20,X2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => hAPP(hAPP(c_Finite__Set_Ofold(X5,X20,X2),X120),hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(hAPP(X2,X25),hAPP(hAPP(c_Finite__Set_Ofold(X5,X20,X2),X120),X21)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_fun__left__comm_Ofold__insert]) ).

fof(i_0_5686,plain,
    ! [X103,X104,X105,X76,X24] :
      ( ~ hBOOL(hAPP(X24,X76))
     => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X105),X76),X104))
       => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X24,X103,X105)),X76),X104)) ) ),
    inference(fof_simplification,[status(thm)],[fact_evalc_OIfFalse]) ).

fof(i_0_5687,plain,
    ! [X82,X22] :
      ( 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),X22),X82)))
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22),X82))
         => c_Lazy__Sequence_Osmall__lazy_H(X22,X82) = c_Lazy__Sequence_Oempty(tc_Int_Oint) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22),X82))
         => c_Lazy__Sequence_Osmall__lazy_H(X22,X82) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),X82),c_Lazy__Sequence_Osmall__lazy_H(X22,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X82),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_small__lazy_H_Opsimps]) ).

fof(i_0_5688,plain,
    ! [X33,X239,X25,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X239)))
     => ~ hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),c_List_Oremove1(X5,X33,X239)))) ),
    inference(fof_simplification,[status(thm)],[fact_notin__set__remove1]) ).

fof(i_0_5689,plain,
    ! [X221,X239,X25,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X239)))
     => ~ hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),c_List_Osublist(X5,X239,X221)))) ),
    inference(fof_simplification,[status(thm)],[fact_notin__set__sublistI]) ).

fof(i_0_5690,plain,
    ! [X31377,X31378,X31379] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31379),X31378)),X31377))
      | hAPP(hAPP(c_List_Onth(tc_Nat_Onat),c_List_Oupt(X31379,X31377)),X31378) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31379),X31378) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__upt])]) ).

fof(i_0_5691,plain,
    ! [X21744,X21745] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X21745),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X21744))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X21745),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21744))),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_5692,plain,
    ! [X1,X2,X5,X20] :
      ( class_Orderings_Oord(X20)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,X20)),X2),X1))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X20)),X2),X1))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X20)),X1),X2)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_less__fun__def]) ).

fof(i_0_5693,plain,
    ! [X242,X66,X58,X98] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X98),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X58),X66)))
       => hAPP(c_Random_Opick(X58,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X58)),X66),X242)),X98) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X58),X66) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X98),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X58),X66)))
       => hAPP(c_Random_Opick(X58,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X58)),X66),X242)),X98) = hAPP(c_Random_Opick(X58,X242),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X98),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X58),X66))) ) ),
    inference(fof_simplification,[status(thm)],[fact_pick_Osimps]) ).

fof(i_0_5694,plain,
    ! [X112,X21,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X21),c_Complete__Lattice_OSup__class_OSup(tc_fun(X5,tc_HOL_Obool),X112)))
     => ~ ! [X291] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X21),X291))
           => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X5,tc_HOL_Obool)),X291),X112)) ) ),
    inference(fof_simplification,[status(thm)],[fact_UnionE]) ).

fof(i_0_5695,plain,
    ! [X21054,X21055] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X21055)),c_Int_OBit0(X21054)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21055),X21054)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21055),X21054))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X21055)),c_Int_OBit0(X21054))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I31_J])]) ).

fof(i_0_5696,plain,
    ! [X21052,X21053] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X21053)),c_Int_OBit0(X21052)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21053),X21052)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21053),X21052))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X21053)),c_Int_OBit0(X21052))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I13_J])]) ).

fof(i_0_5697,plain,
    ! [X21058,X21059] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X21059)),c_Int_OBit0(X21058)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21059),X21058)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21059),X21058))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X21059)),c_Int_OBit0(X21058))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I14_J])]) ).

fof(i_0_5698,plain,
    ! [X21056,X21057] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X21057)),c_Int_OBit0(X21056)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21057),X21056)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21057),X21056))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X21057)),c_Int_OBit0(X21056))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__int__code_I13_J])]) ).

fof(i_0_5699,plain,
    ! [X31096,X31097] : hAPP(c_List_OremoveAll(X31097,X31096),c_List_Olist_ONil(X31097)) = c_List_Olist_ONil(X31097),
    inference(variable_rename,[status(thm)],[fact_removeAll_Osimps_I1_J]) ).

fof(i_0_5700,plain,
    ! [X25,X21,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
     => ( ( hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X5),X21)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
        & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(X5),X21) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_card__Diff__singleton__if]) ).

fof(i_0_5701,plain,
    ! [X21024,X21025] :
      ( ~ class_Int_Onumber__ring(X21025)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21025),hAPP(c_Int_Onumber__class_Onumber__of(X21025),X21024)),c_Groups_Oone__class_Oone(X21025)) = hAPP(c_Int_Onumber__class_Onumber__of(X21025),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21024),c_Int_OBit1(c_Int_OPls))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__special_I3_J])]) ).

fof(i_0_5702,plain,
    ! [X121,X123,X5] :
      ( ( class_Int_Onumber(X5)
        & class_Orderings_Olinorder(X5) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X123)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)))
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X121)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X123))) ) ),
    inference(fof_simplification,[status(thm)],[fact_le__number__of__eq__not__less]) ).

fof(i_0_5703,plain,
    ! [X33,X25,X20,X5] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_fun(X20,tc_HOL_Obool))),X25),X33)),
    inference(fof_simplification,[status(thm)],[fact_bot2E]) ).

fof(i_0_5704,plain,
    ! [X59,X60,X26,X63,X77,X27] :
      ( c_Natural_Oevaln(c_Com_Ocom_OCond(X27,X77,X63),X26,X60,X59)
    <=> ( ( hBOOL(hAPP(X27,X26))
          & c_Natural_Oevaln(X77,X26,X60,X59) )
        | ( ~ hBOOL(hAPP(X27,X26))
          & c_Natural_Oevaln(X63,X26,X60,X59) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_evaln_Oequations_I6_J]) ).

fof(i_0_5705,plain,
    ! [X59,X60,X26,X77,X63,X27] :
      ( c_Natural_Oevaln(c_Com_Ocom_OCond(X27,X63,X77),X26,X60,X59)
    <=> ( ( hBOOL(hAPP(X27,X26))
          & c_Natural_Oevaln(X63,X26,X60,X59) )
        | ( ~ hBOOL(hAPP(X27,X26))
          & c_Natural_Oevaln(X77,X26,X60,X59) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_evaln_Oequations_I5_J]) ).

fof(i_0_5706,plain,
    ! [X15,X50,X76,X106,X105,X24] :
      ( c_Natural_Oevaln(c_Com_Ocom_OCond(X24,X105,X106),X76,X50,X15)
     => ( ( hBOOL(hAPP(X24,X76))
         => ~ c_Natural_Oevaln(X105,X76,X50,X15) )
       => ~ ( ~ hBOOL(hAPP(X24,X76))
           => ~ c_Natural_Oevaln(X106,X76,X50,X15) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_evaln__elim__cases_I5_J]) ).

fof(i_0_5707,plain,
    ! [X65,X147,X148,X149] :
      ( X149 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X148),X147)),X65)
     => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X148))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X65))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X65),X148)) ) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X148))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X148),X65))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X65),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
       => ( X148 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => c_Divides_Odiv__class_Omod(tc_Int_Oint,X149,X148) = X65 ) ) ),
    inference(fof_simplification,[status(thm)],[fact_divmod__int__rel__mod__eq]) ).

fof(i_0_5708,plain,
    ! [X31418,X31419,X31420,X31421] : c_List_Ofoldr(X31421,X31420,X31419,c_List_Olist_ONil(X31421),X31418) = X31418,
    inference(variable_rename,[status(thm)],[fact_foldr_Osimps_I1_J]) ).

fof(i_0_5709,plain,
    ! [X31925,X31926,X31927,X31928] : c_List_Oconcat(X31928,hAPP(hAPP(c_List_Omap(X31927,tc_List_Olist(X31928)),X31926),X31925)) = c_List_Omaps(X31927,X31928,X31926,X31925),
    inference(variable_rename,[status(thm)],[fact_concat__map__maps]) ).

fof(i_0_5710,plain,
    ! [X31913,X31914,X31915,X31916] : c_List_Omaps(X31916,X31915,X31914,X31913) = c_List_Oconcat(X31915,hAPP(hAPP(c_List_Omap(X31916,tc_List_Olist(X31915)),X31914),X31913)),
    inference(variable_rename,[status(thm)],[fact_maps__def]) ).

fof(i_0_5711,plain,
    ! [X152,X65,X148,X149] :
      ( X149 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X148),X65)),X152)
     => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X148))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X152))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X152),X148)) ) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X148))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X148),X152))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X152),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
       => ( X148 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X149),X148) = X65 ) ) ),
    inference(fof_simplification,[status(thm)],[fact_divmod__int__rel__div__eq]) ).

fof(i_0_5712,plain,
    ! [X29455,X29456,X29457] : hAPP(c_List_Orotate(X29457,hAPP(c_Nat_OSuc,X29456)),X29455) = hAPP(c_List_Orotate1(X29457),hAPP(c_List_Orotate(X29457,X29456),X29455)),
    inference(variable_rename,[status(thm)],[fact_rotate__Suc]) ).

fof(i_0_5713,plain,
    ! [X120,X25,X21,X2,X20,X5] :
      ( c_Finite__Set_Ofun__left__comm(X5,X20,X2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => hAPP(hAPP(c_Finite__Set_Ofold(X5,X20,X2),X120),hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X20,X2),hAPP(hAPP(X2,X25),X120)),X21) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_fun__left__comm_Ofold__insert2]) ).

fof(i_0_5714,plain,
    ! [X31366,X31367,X31368,X31369] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31369),X31368))
        | c_List_Oupt(X31369,X31368) != hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X31367),X31366) )
      & ( X31369 = X31367
        | c_List_Oupt(X31369,X31368) != hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X31367),X31366) )
      & ( c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31369),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X31368) = X31366
        | c_List_Oupt(X31369,X31368) != hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X31367),X31366) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31369),X31368))
        | X31369 != X31367
        | c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31369),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X31368) != X31366
        | c_List_Oupt(X31369,X31368) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X31367),X31366) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_upt__eq__Cons__conv])])]) ).

fof(i_0_5715,plain,
    ! [X2,X95,X50,X5] :
      ( class_Groups_Ocomm__monoid__add(X5)
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X50),X95))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X95),hAPP(c_Nat_OSuc,X50))) = c_Groups_Ozero__class_Ozero(X5) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X50),X95))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X95),hAPP(c_Nat_OSuc,X50))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X95),X50))),hAPP(X2,X50)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_setsum__op__ivl__Suc]) ).

fof(i_0_5716,plain,
    ! [X25,X113,X21,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113),X25))
     => ( ~ hBOOL(hAPP(X21,X25))
       => hBOOL(hAPP(X113,X25)) ) ),
    inference(fof_simplification,[status(thm)],[fact_sup1E]) ).

fof(i_0_5717,plain,
    ! [X21103] : c_Int_Opred(c_Int_OBit1(X21103)) = c_Int_OBit0(X21103),
    inference(variable_rename,[status(thm)],[fact_pred__Bit1]) ).

fof(i_0_5718,plain,
    ! [X96,X164,X136] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X164)),X96)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X164)),X96) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)))
       => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X164)))
           => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X164)),X96)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)),X96) )
          & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X164)))
           => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X164)),X96)) = 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),X136),X164))),X96) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_nat__number__of__add__left]) ).

fof(i_0_5719,plain,
    ! [X32339] : c_Transitive__Closure_Otrancl(X32339,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X32339,X32339),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X32339,X32339),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_trancl__empty]) ).

fof(i_0_5720,plain,
    ! [X31391,X31392,X31393,X31394] :
      ( ~ class_Groups_Ocomm__monoid__add(X31394)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X31394),X31393),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X31392,X31391))) = hAPP(c_List_Omonoid__add__class_Olistsum(X31394),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X31394),X31393),c_List_Oupt(X31392,X31391))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__set__upt__conv__listsum__nat])]) ).

fof(i_0_5721,plain,
    ! [X31387,X31388,X31389,X31390] :
      ( ~ class_Groups_Ocomm__monoid__add(X31390)
      | hAPP(c_List_Omonoid__add__class_Olistsum(X31390),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X31390),X31389),c_List_Oupt(X31388,X31387))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X31390),X31389),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X31388,X31387))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_interv__listsum__conv__setsum__set__nat])]) ).

fof(i_0_5722,plain,
    ! [X25,X113,X21,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113),X25))
     => ~ ( hBOOL(hAPP(X21,X25))
         => ~ hBOOL(hAPP(X113,X25)) ) ),
    inference(fof_simplification,[status(thm)],[fact_inf1E]) ).

fof(i_0_5723,plain,
    ! [X29447,X29448,X29449] : hAPP(c_List_Orotate1(X29449),hAPP(c_List_Orotate(X29449,X29448),X29447)) = hAPP(c_List_Orotate(X29449,X29448),hAPP(c_List_Orotate1(X29449),X29447)),
    inference(variable_rename,[status(thm)],[fact_rotate1__rotate__swap]) ).

fof(i_0_5724,plain,
    ! [X20989,X20990] :
      ( ~ class_Int_Onumber__ring(X20990)
      | hAPP(c_Int_Onumber__class_Onumber__of(X20990),c_Int_OBit1(X20989)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20990),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20990),c_Groups_Oone__class_Oone(X20990)),hAPP(c_Int_Onumber__class_Onumber__of(X20990),X20989))),hAPP(c_Int_Onumber__class_Onumber__of(X20990),X20989)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__Bit1])]) ).

fof(i_0_5725,plain,
    ! [X113,X21,X23,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X23),X21))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X23),X113))
       => hBOOL(hAPP(hAPP(c_member(X5),X23),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),X113))) ) ),
    inference(fof_simplification,[status(thm)],[fact_DiffI]) ).

fof(i_0_5726,plain,
    ! [X21696,X21697,X21698,X21699] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X21699,X21698,X21697,c_Code__Numeral_OSuc__code__numeral(X21696)) = hAPP(hAPP(X21697,X21696),c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X21699,X21698,X21697,X21696)),
    inference(variable_rename,[status(thm)],[fact_code__numeral_Orecs_I2_J]) ).

fof(i_0_5727,plain,
    ! [X30392] : c_Code__Numeral_OSuc__code__numeral(X30392) = hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X30392))),
    inference(variable_rename,[status(thm)],[fact_Suc__code__numeral__def]) ).

fof(i_0_5728,plain,
    ! [X21,X5] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => hAPP(c_Finite__Set_Ocard(X5),X21) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,X5,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,X5),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X21) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => hAPP(c_Finite__Set_Ocard(X5),X21) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_simplification,[status(thm)],[fact_card__def]) ).

fof(i_0_5729,plain,
    ! [X28018,X28019,X28020] : hAPP(hAPP(c_Relation_Orel__comp(X28020,X28020,X28019),c_Relation_OId(X28020)),X28018) = X28018,
    inference(variable_rename,[status(thm)],[fact_Id__O__R]) ).

fof(i_0_5730,plain,
    ! [X21532,X21533] :
      ( ~ class_Fields_Ofield(X21533)
      | ~ class_Int_Onumber__ring(X21533)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21533),X21532),hAPP(c_Int_Onumber__class_Onumber__of(X21533),c_Int_OBit1(c_Int_OPls))) = X21532 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__Numeral1])]) ).

fof(i_0_5731,plain,
    ! [X21530,X21531] :
      ( ~ class_Fields_Ofield(X21531)
      | ~ class_Int_Onumber__ring(X21531)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21531),X21530),hAPP(c_Int_Onumber__class_Onumber__of(X21531),c_Int_OBit1(c_Int_OPls))) = X21530 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__numeral__1])]) ).

fof(i_0_5732,plain,
    ! [X66,X90,X62,X58] :
      ( class_Lattices_Osemilattice__sup(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X58),X62),X90)),X66))
       => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X62),X66))
           => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X90),X66)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_le__supE]) ).

fof(i_0_5733,plain,
    ! [X66,X90,X62,X58] :
      ( class_Orderings_Olinorder(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),hAPP(hAPP(c_Orderings_Oord__class_Omax(X58),X62),X90)),X66))
       => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X62),X66))
           => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X90),X66)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_min__max_Ole__supE]) ).

fof(i_0_5734,plain,
    ! [X20991,X20992] :
      ( ~ class_Int_Onumber__ring(X20992)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20992),X20991),hAPP(c_Int_Onumber__class_Onumber__of(X20992),c_Int_OBit1(c_Int_OPls))) = X20991 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__numeral__1__right])]) ).

fof(i_0_5735,plain,
    ! [X33571,X33572,X33573,X33574] :
      ( ( ~ hBOOL(hAPP(hAPP(c_List_Omember(X33574),hAPP(hAPP(c_List_Olist_OCons(X33574),X33573),X33572)),X33571))
        | X33573 = X33571
        | hBOOL(hAPP(hAPP(c_List_Omember(X33574),X33572),X33571)) )
      & ( X33573 != X33571
        | hBOOL(hAPP(hAPP(c_List_Omember(X33574),hAPP(hAPP(c_List_Olist_OCons(X33574),X33573),X33572)),X33571)) )
      & ( ~ hBOOL(hAPP(hAPP(c_List_Omember(X33574),X33572),X33571))
        | hBOOL(hAPP(hAPP(c_List_Omember(X33574),hAPP(hAPP(c_List_Olist_OCons(X33574),X33573),X33572)),X33571)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_member__rec_I1_J])])]) ).

fof(i_0_5736,plain,
    ! [X33575] : c_List_Omember(X33575) = c_List_Oset(X33575),
    inference(variable_rename,[status(thm)],[fact_member__set]) ).

fof(i_0_5737,plain,
    ! [X29392,X29393,X29394] :
      ( X29394 = c_List_Olist_ONil(X29393)
      | hAPP(c_List_Ohd(X29393),hAPP(c_List_Orotate(X29393,X29392),X29394)) = hAPP(hAPP(c_List_Onth(X29393),X29394),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X29392,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29393)),X29394))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hd__rotate__conv__nth])]) ).

fof(i_0_5738,plain,
    ! [X96,X164,X136] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X136),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X164)),X96)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X136),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X164)),X96)) = 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),X136),X164))),X96) ) ),
    inference(fof_simplification,[status(thm)],[fact_nat__number__of__mult__left]) ).

fof(i_0_5739,plain,
    ! [X29461,X29462,X29463] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29463)),X29462)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
      | hAPP(c_List_Orotate(X29463,X29461),X29462) = X29462 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rotate__length01])]) ).

fof(i_0_5740,plain,
    ! [X113,X112,X6,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X6),X112))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X6),X113)),X112) = hAPP(hAPP(c_Set_Oinsert(X5),X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X113),X112)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X112))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X6),X113)),X112) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X113),X112) ) ),
    inference(fof_simplification,[status(thm)],[fact_Int__insert__left]) ).

fof(i_0_5741,plain,
    ! [X21,X113,X23,X5] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X5),X23),X113))
       => hBOOL(hAPP(hAPP(c_member(X5),X23),X21)) )
     => hBOOL(hAPP(hAPP(c_member(X5),X23),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113))) ),
    inference(fof_simplification,[status(thm)],[fact_UnCI]) ).

fof(i_0_5742,plain,
    ! [X62,X58] :
      ( class_Rings_Olinordered__ring(X58)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X58),X62),X62)),c_Groups_Ozero__class_Ozero(X58))) ),
    inference(fof_simplification,[status(thm)],[fact_not__square__less__zero]) ).

fof(i_0_5743,plain,
    ! [X21076] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X21076)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21076),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21076),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X21076)),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_5744,plain,
    ! [X21100,X21101] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X21101))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X21100))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21101)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21100)),
    inference(variable_rename,[status(thm)],[fact_zdiv__number__of__Bit0]) ).

fof(i_0_5745,plain,
    ! [X57,X96,X72] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X72),X96)),X57))
     => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X72),X57))
         => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X96),X57)) ) ),
    inference(fof_simplification,[status(thm)],[fact_add__leE]) ).

fof(i_0_5746,plain,
    ! [X21078] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X21078)),c_Int_OPls))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21078),c_Int_OPls)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21078),c_Int_OPls))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X21078)),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I27_J])]) ).

fof(i_0_5747,plain,
    ! [X21098] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X21098)),c_Int_OMin))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21098),c_Int_OMin)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21098),c_Int_OMin))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X21098)),c_Int_OMin)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I28_J])]) ).

fof(i_0_5748,plain,
    ! [X21122] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X21122)),c_Int_OMin))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21122),c_Int_OMin)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21122),c_Int_OMin))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X21122)),c_Int_OMin)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I11_J])]) ).

fof(i_0_5749,plain,
    ! [X21083] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X21083)),c_Int_OPls))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21083),c_Int_OPls)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21083),c_Int_OPls))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X21083)),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I10_J])]) ).

fof(i_0_5750,plain,
    ! [X21102] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X21102))))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21102))) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21102)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X21102)))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__number__of__Bit0])]) ).

fof(i_0_5751,plain,
    ! [X23423,X23424] : hAPP(c_Relation_OImage(X23424,X23424,c_Relation_OId(X23424)),X23423) = X23423,
    inference(variable_rename,[status(thm)],[fact_Image__Id]) ).

fof(i_0_5752,plain,
    ! [X21,X113,X25,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X25),X113))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)),X113) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),X113) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X113))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)),X113) = hAPP(hAPP(c_Set_Oinsert(X5),X25),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X21),X113)) ) ),
    inference(fof_simplification,[status(thm)],[fact_insert__Diff__if]) ).

fof(i_0_5753,plain,
    ! [X20855,X20856] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20856),X20855))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(X20856)),X20855)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(X20856)),X20855))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20856),X20855)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__iff__pred__less])]) ).

fof(i_0_5754,plain,
    ! [X21124] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X21124)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X21124)),
    inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I6_J]) ).

fof(i_0_5755,plain,
    ! [X20691,X20692] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20692)))
        | hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20692)),X20691)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X20691) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20692)))
        | hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20692)),X20691)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X20692))),X20691) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5215])]) ).

fof(i_0_5756,plain,
    ! [X103,X104,X50,X105,X76,X24] :
      ( ~ hBOOL(hAPP(X24,X76))
     => ( c_Natural_Oevaln(X105,X76,X50,X104)
       => c_Natural_Oevaln(c_Com_Ocom_OCond(X24,X103,X105),X76,X50,X104) ) ),
    inference(fof_simplification,[status(thm)],[fact_evaln_OIfFalse]) ).

fof(i_0_5757,plain,
    ! [X72,X57] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X57))
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X72),X57))
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X72),X57) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X72),X57))
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X72),X57) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X72),X57)),X57)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_div__if]) ).

fof(i_0_5758,plain,
    ! [X72,X57] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X57))
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X72),X57))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X72),X57) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X72),X57)),X57)) ) ),
    inference(fof_simplification,[status(thm)],[fact_div__geq]) ).

fof(i_0_5759,plain,
    ! [X57] : ~ 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,X57))))),
    inference(fof_simplification,[status(thm)],[fact_not__zle__0__negative]) ).

fof(i_0_5760,plain,
    ! [X32195,X32196] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X32196,X32196),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X32196,X32195)),c_Relation_OId(X32196)) = c_Transitive__Closure_Ortrancl(X32196,X32195),
    inference(variable_rename,[status(thm)],[fact_rtrancl__reflcl__absorb]) ).

fof(i_0_5761,plain,
    ! [X31354,X31355] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31355),X31354))
        | c_List_Oupt(X31355,hAPP(c_Nat_OSuc,X31354)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X31355,X31354)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X31354),c_List_Olist_ONil(tc_Nat_Onat))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31355),X31354))
        | c_List_Oupt(X31355,hAPP(c_Nat_OSuc,X31354)) = c_List_Olist_ONil(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5216])]) ).

fof(i_0_5762,plain,
    ! [X31352,X31353] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31353),X31352))
      | c_List_Oupt(X31353,hAPP(c_Nat_OSuc,X31352)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X31353,X31352)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X31352),c_List_Olist_ONil(tc_Nat_Onat))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_upt__Suc__append])]) ).

fof(i_0_5763,plain,
    ! [X113,X21,X6,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X6),X21))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X6),X113)) = hAPP(hAPP(c_Set_Oinsert(X5),X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X21))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X6),X113)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113) ) ),
    inference(fof_simplification,[status(thm)],[fact_Int__insert__right]) ).

fof(i_0_5764,plain,
    ! [X1,X21,X5,X20] :
      ( class_Groups_Ocomm__monoid__add(X20)
     => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X1),X21) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X20,X5,c_Groups_Oplus__class_Oplus(X20)),X1),c_Groups_Ozero__class_Ozero(X20)),X21) )
        & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X1),X21) = c_Groups_Ozero__class_Ozero(X20) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_setsum_OF__eq]) ).

fof(i_0_5765,plain,
    ! [X1,X21,X5,X20] :
      ( class_Groups_Ocomm__monoid__mult(X20)
     => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X1),X21) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X20,X5,c_Groups_Otimes__class_Otimes(X20)),X1),c_Groups_Oone__class_Oone(X20)),X21) )
        & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X1),X21) = c_Groups_Oone__class_Oone(X20) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_setprod_OF__eq]) ).

fof(i_0_5766,plain,
    ! [X241,X242,X58,X57] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X57),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242)))
       => hAPP(hAPP(c_List_Onth(X58),hAPP(hAPP(c_List_Oappend(X58),X242),X241)),X57) = hAPP(hAPP(c_List_Onth(X58),X242),X57) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X57),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242)))
       => hAPP(hAPP(c_List_Onth(X58),hAPP(hAPP(c_List_Oappend(X58),X242),X241)),X57) = hAPP(hAPP(c_List_Onth(X58),X241),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X57),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X58)),X242))) ) ),
    inference(fof_simplification,[status(thm)],[fact_nth__append]) ).

fof(i_0_5767,plain,
    ! [X21,X23,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X23),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X21)))
     => ~ hBOOL(hAPP(hAPP(c_member(X5),X23),X21)) ),
    inference(fof_simplification,[status(thm)],[fact_ComplE]) ).

fof(i_0_5768,plain,
    ! [X21,X23,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X23),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X21)))
     => ~ hBOOL(hAPP(hAPP(c_member(X5),X23),X21)) ),
    inference(fof_simplification,[status(thm)],[fact_ComplD]) ).

fof(i_0_5769,plain,
    ! [X21,X23,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X23),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X21)))
    <=> ~ hBOOL(hAPP(hAPP(c_member(X5),X23),X21)) ),
    inference(fof_simplification,[status(thm)],[fact_Compl__iff]) ).

fof(i_0_5770,plain,
    ! [X21740] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X21740)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21740)),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_5771,plain,
    ! [X136,X55,X5] :
      ( ( class_Int_Onumber(X5)
        & class_Orderings_Oord(X5) )
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X55)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X136)))
         => hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X55)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X136)) = hAPP(c_Int_Onumber__class_Onumber__of(X5),X136) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X55)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X136)))
         => hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X55)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X136)) = hAPP(c_Int_Onumber__class_Onumber__of(X5),X55) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_max__number__of]) ).

fof(i_0_5772,plain,
    ! [X136,X55,X5] :
      ( ( class_Int_Onumber(X5)
        & class_Orderings_Oord(X5) )
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X55)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X136)))
         => hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X55)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X136)) = hAPP(c_Int_Onumber__class_Onumber__of(X5),X55) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X55)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X136)))
         => hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),X55)),hAPP(c_Int_Onumber__class_Onumber__of(X5),X136)) = hAPP(c_Int_Onumber__class_Onumber__of(X5),X136) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_min__number__of]) ).

fof(i_0_5773,plain,
    ! [X97,X98] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X98),X97)),X98)),
    inference(fof_simplification,[status(thm)],[fact_not__add__less1]) ).

fof(i_0_5774,plain,
    ! [X98,X97] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X97),X98)),X98)),
    inference(fof_simplification,[status(thm)],[fact_not__add__less2]) ).

fof(i_0_5775,plain,
    ! [X251,X239,X25,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X239)))
       => c_List_Oremove1(X5,X25,hAPP(hAPP(c_List_Oappend(X5),X239),X251)) = hAPP(hAPP(c_List_Oappend(X5),c_List_Oremove1(X5,X25,X239)),X251) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X239)))
       => c_List_Oremove1(X5,X25,hAPP(hAPP(c_List_Oappend(X5),X239),X251)) = hAPP(hAPP(c_List_Oappend(X5),X239),c_List_Oremove1(X5,X25,X251)) ) ),
    inference(fof_simplification,[status(thm)],[fact_remove1__append]) ).

fof(i_0_5776,plain,
    ! [X20711] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X20711))))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20711) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20711) != 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(X20711)))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__number__of__pred__iff__0])]) ).

fof(i_0_5777,plain,
    ! [X25,X2,X5] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X5,X2,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),X25)),
    inference(fof_simplification,[status(thm)],[fact_empty__fold1SetE]) ).

fof(i_0_5778,plain,
    ! [X20963,X20964] :
      ( ( c_Int_OBit1(X20964) != c_Int_OBit1(X20963)
        | X20964 = X20963 )
      & ( X20964 != X20963
        | c_Int_OBit1(X20964) = c_Int_OBit1(X20963) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I51_J])]) ).

fof(i_0_5779,plain,
    ! [X33395,X33396] : c_List_Oconcat(X33396,c_List_Oreplicate(tc_List_Olist(X33396),X33395,c_List_Olist_ONil(X33396))) = c_List_Olist_ONil(X33396),
    inference(variable_rename,[status(thm)],[fact_concat__replicate__trivial]) ).

fof(i_0_5780,plain,
    ! [X24,X6,X18] :
      ( hBOOL(hAPP(X18,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X6),X24)))
    <=> ~ ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),X24))
            & ~ hBOOL(hAPP(X18,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
          | ? [X158] :
              ( X6 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),X158)
              & ~ hBOOL(hAPP(X18,X158)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_nat__diff__split__asm]) ).

fof(i_0_5781,plain,
    ! [X239,X25,X5] :
      ( hBOOL(hAPP(c_List_Odistinct(X5),hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239)))
    <=> ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X239)))
        & hBOOL(hAPP(c_List_Odistinct(X5),X239)) ) ),
    inference(fof_simplification,[status(thm)],[fact_distinct_Osimps_I2_J]) ).

fof(i_0_5782,plain,
    ! [X29432,X29433,X29434] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29434)),hAPP(c_List_Orotate(X29434,X29433),X29432)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29434)),X29432),
    inference(variable_rename,[status(thm)],[fact_length__rotate]) ).

fof(i_0_5783,plain,
    ! [X31802,X31803] : c_List_OdropWhile(X31803,X31802,c_List_Olist_ONil(X31803)) = c_List_Olist_ONil(X31803),
    inference(variable_rename,[status(thm)],[fact_dropWhile_Osimps_I1_J]) ).

fof(i_0_5784,plain,
    ! [X21,X25,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)),hAPP(hAPP(c_Set_Oinsert(X5),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = X21 ),
    inference(fof_simplification,[status(thm)],[fact_Diff__insert__absorb]) ).

fof(i_0_5785,plain,
    ! [X2,X6,X205,X5,X20] :
      ( class_Groups_Ocomm__monoid__add(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X205))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X205))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X2),hAPP(hAPP(c_Set_Oinsert(X5),X6),X205)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20),hAPP(X2,X6)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X2),X205)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_setsum__insert]) ).

fof(i_0_5786,plain,
    ! [X1,X25,X21,X5,X20] :
      ( class_Groups_Ocomm__monoid__add(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X1),hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20),hAPP(X1,X25)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X1),X21)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_setsum_Oinsert]) ).

fof(i_0_5787,plain,
    ! [X1,X25,X21,X5,X20] :
      ( class_Groups_Ocomm__monoid__mult(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X1),hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20),hAPP(X1,X25)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X1),X21)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_setprod_Oinsert]) ).

fof(i_0_5788,plain,
    ! [X2,X6,X21,X5,X20] :
      ( class_Groups_Ocomm__monoid__mult(X20)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X21))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X2),hAPP(hAPP(c_Set_Oinsert(X5),X6),X21)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20),hAPP(X2,X6)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X2),X21)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_setprod__insert]) ).

fof(i_0_5789,plain,
    ! [X31343,X31344,X31345] : hAPP(hAPP(c_List_Odrop(tc_Nat_Onat),X31345),c_List_Oupt(X31344,X31343)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31344),X31345),X31343),
    inference(variable_rename,[status(thm)],[fact_drop__upt]) ).

fof(i_0_5790,plain,
    ! [X239,X18,X5] :
      ( hAPP(c_List_Ofilter(X5,X18),X239) = c_List_Olist_ONil(X5)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X239)))
         => ~ hBOOL(hAPP(X18,X3)) ) ),
    inference(fof_simplification,[status(thm)],[fact_filter__empty__conv]) ).

fof(i_0_5791,plain,
    ! [X72,X57] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X57)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X72)))),
    inference(fof_simplification,[status(thm)],[fact_not__int__zless__negative]) ).

fof(i_0_5792,plain,
    ! [X29404,X29405,X29406] : hAPP(c_List_Oset(X29406),hAPP(c_List_Orotate(X29406,X29405),X29404)) = hAPP(c_List_Oset(X29406),X29404),
    inference(variable_rename,[status(thm)],[fact_set__rotate]) ).

fof(i_0_5793,plain,
    ! [X5,X21,X25,X113] :
      ( ( ~ hBOOL(hAPP(X113,X25))
       => hBOOL(hAPP(X21,X25)) )
     => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X21),X113),X25)) ),
    inference(fof_simplification,[status(thm)],[fact_sup1CI]) ).

fof(i_0_5794,plain,
    ! [X278,X279,X239,X18,X5] :
      ( c_List_Opartition(X5,X18,X239) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X279),X278)
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X279)))
           => hBOOL(hAPP(X18,X3)) )
        & ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_List_Oset(X5),X278)))
           => ~ hBOOL(hAPP(X18,X3)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_partition__P]) ).

fof(i_0_5795,plain,
    ! [X32333,X32334] : hAPP(c_Relation_ODomain(X32334,X32334),c_Transitive__Closure_Otrancl(X32334,X32333)) = hAPP(c_Relation_ODomain(X32334,X32334),X32333),
    inference(variable_rename,[status(thm)],[fact_trancl__domain]) ).

fof(i_0_5796,plain,
    ! [X32340,X32341] : hAPP(c_Relation_ORange(X32341,X32341),c_Transitive__Closure_Otrancl(X32341,X32340)) = hAPP(c_Relation_ORange(X32341,X32341),X32340),
    inference(variable_rename,[status(thm)],[fact_trancl__range]) ).

fof(i_0_5797,plain,
    ! [X168,X123] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X123)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X168)))
    <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X123),X168))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X123),c_Int_OPls)) ) ),
    inference(fof_simplification,[status(thm)],[fact_le__nat__number__of]) ).

fof(i_0_5798,plain,
    ! [X21071,X21072] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(X21072)),c_Int_OBit0(X21071)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X21072),X21071)),
    inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I7_J]) ).

fof(i_0_5799,plain,
    ! [X21067,X21068] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(X21068)),c_Int_OBit0(X21067)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21068),X21067)),
    inference(variable_rename,[status(thm)],[fact_add__Bit0__Bit0]) ).

fof(i_0_5800,plain,
    ! [X25,X21,X205,X2,X5] :
      ( c_Finite__Set_Ofolding__one(X5,X2,X205)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => hAPP(X205,hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,X2),X25),X21) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_folding__one_Oeq__fold_H]) ).

fof(i_0_5801,plain,
    ! [X25] :
      ~ ! [X177] :
          ( X25 = hAPP(c_Int_OAbs__Integ,X177)
         => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X177),c_Int_OInteg)) ),
    inference(fof_simplification,[status(thm)],[fact_Abs__Integ__cases]) ).

fof(i_0_5802,plain,
    ! [X31348,X31349] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31349),X31348))
      | c_List_Oupt(X31349,X31348) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X31349),c_List_Oupt(hAPP(c_Nat_OSuc,X31349),X31348)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_upt__conv__Cons])]) ).

fof(i_0_5803,plain,
    ! [X31346,X31347] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31347),X31346))
        | c_List_Oupt(X31347,X31346) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X31347),c_List_Oupt(hAPP(c_Nat_OSuc,X31347),X31346)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31347),X31346))
        | c_List_Oupt(X31347,X31346) = c_List_Olist_ONil(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5217])]) ).

fof(i_0_5804,plain,
    ! [X239,X2,X5,X25,X18,X20] :
      ( class_Orderings_Olinorder(X20)
     => ( ~ hBOOL(hAPP(X18,X25))
       => hAPP(c_List_Ofilter(X5,X18),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X5,X20,X2),X25),X239)) = hAPP(c_List_Ofilter(X5,X18),X239) ) ),
    inference(fof_simplification,[status(thm)],[fact_filter__insort__triv]) ).

fof(i_0_5805,plain,
    ! [X25,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omin(X5)),X25),X21) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_min__max_OInf__fin_Oeq__fold_H]) ).

fof(i_0_5806,plain,
    ! [X25,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omax(X5)),X25),X21) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_min__max_OSup__fin_Oeq__fold_H]) ).

fof(i_0_5807,plain,
    ! [X21,X5] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X21),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),
    inference(fof_simplification,[status(thm)],[fact_not__psubset__empty]) ).

fof(i_0_5808,plain,
    ! [X6,X21,X5] :
      ( class_Groups_Oab__semigroup__mult(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X21))
         => hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),hAPP(hAPP(c_Set_Oinsert(X5),X6),X21)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Groups_Otimes__class_Otimes(X5)),X6),X21) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_fold1__eq__fold]) ).

fof(i_0_5809,plain,
    ! [X21109,X21110] :
      ( ~ class_Int_Onumber__ring(X21110)
      | hAPP(c_Int_Onumber__class_Onumber__of(X21110),c_Int_OBit0(X21109)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21110),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21110),c_Groups_Ozero__class_Ozero(X21110)),hAPP(c_Int_Onumber__class_Onumber__of(X21110),X21109))),hAPP(c_Int_Onumber__class_Onumber__of(X21110),X21109)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__Bit0])]) ).

fof(i_0_5810,plain,
    ! [X31385,X31386] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X31386),hAPP(c_List_Onth(X31386),X31385)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31386)),X31385))) = X31385,
    inference(variable_rename,[status(thm)],[fact_map__nth]) ).

fof(i_0_5811,plain,
    ! [X90,X62,X66,X58] :
      ( class_Lattices_Osemilattice__inf(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X66),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X58),X62),X90)))
       => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X66),X62))
           => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X66),X90)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_le__infE]) ).

fof(i_0_5812,plain,
    ! [X90,X62,X66,X58] :
      ( class_Orderings_Olinorder(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X66),hAPP(hAPP(c_Orderings_Oord__class_Omin(X58),X62),X90)))
       => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X66),X62))
           => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X66),X90)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_min__max_Ole__infE]) ).

fof(i_0_5813,plain,
    ! [X239,X25,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X239)))
       => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_Oremove1(X5,X25,X239)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X239)))
       => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_Oremove1(X5,X25,X239)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X239) ) ),
    inference(fof_simplification,[status(thm)],[fact_length__remove1]) ).

fof(i_0_5814,plain,
    ! [X113,X112,X6,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X112))
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X5),X6),X113)),X112) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X113),X112) ),
    inference(fof_simplification,[status(thm)],[fact_Int__insert__left__if0]) ).

fof(i_0_5815,plain,
    ! [X21614,X21615] :
      ( ( X21615 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
        | c_Code__Numeral_Onat__of__aux(X21615,X21614) = X21614 )
      & ( X21615 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
        | c_Code__Numeral_Onat__of__aux(X21615,X21614) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X21615),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,X21614)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__of__aux__code])]) ).

fof(i_0_5816,plain,
    ! [X30390,X30391] : c_Code__Numeral_Onat__of__aux(X30391,X30390) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X30391)),X30390),
    inference(variable_rename,[status(thm)],[fact_nat__of__aux__def]) ).

fof(i_0_5817,plain,
    ! [X33928,X33929] :
      ( ~ c_Relation_Osym(X33929,X33928)
      | c_Relation_Osym(X33929,c_Transitive__Closure_Otrancl(X33929,X33928)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sym__trancl])]) ).

fof(i_0_5818,plain,
    ! [X32342,X32343] :
      ( ~ c_Wellfounded_Owf(X32343,X32342)
      | c_Wellfounded_Owf(X32343,c_Transitive__Closure_Otrancl(X32343,X32342)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__trancl])]) ).

fof(i_0_5819,plain,
    ! [X28015,X28016,X28017] : hAPP(hAPP(c_Relation_Orel__comp(X28017,X28016,X28016),X28015),c_Relation_OId(X28016)) = X28015,
    inference(variable_rename,[status(thm)],[fact_R__O__Id]) ).

fof(i_0_5820,plain,
    ! [X32329,X32330] : c_Transitive__Closure_Otrancl(X32330,X32329) = hAPP(hAPP(c_Relation_Orel__comp(X32330,X32330,X32330),c_Transitive__Closure_Ortrancl(X32330,X32329)),X32329),
    inference(variable_rename,[status(thm)],[fact_trancl__unfold__right]) ).

fof(i_0_5821,plain,
    ! [X32325,X32326] : c_Transitive__Closure_Ortrancl(X32326,c_Transitive__Closure_Otrancl(X32326,X32325)) = c_Transitive__Closure_Ortrancl(X32326,X32325),
    inference(variable_rename,[status(thm)],[fact_trancl__rtrancl__absorb]) ).

fof(i_0_5822,plain,
    ! [X31221] : c_List_Oconcat(X31221,c_List_Olist_ONil(tc_List_Olist(X31221))) = c_List_Olist_ONil(X31221),
    inference(variable_rename,[status(thm)],[fact_concat_Osimps_I1_J]) ).

fof(i_0_5823,plain,
    ! [X25,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => c_Big__Operators_Olinorder__class_OMin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omin(X5)),X25),X21) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_Min_Oeq__fold_H]) ).

fof(i_0_5824,plain,
    ! [X25,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => c_Big__Operators_Olinorder__class_OMax(X5,hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Orderings_Oord__class_Omax(X5)),X25),X21) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_Max_Oeq__fold_H]) ).

fof(i_0_5825,plain,
    ! [X25,X21,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => c_Big__Operators_Olattice__class_OSup__fin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Lattices_Osemilattice__sup__class_Osup(X5)),X25),X21) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_Sup__fin_Oeq__fold_H]) ).

fof(i_0_5826,plain,
    ! [X25,X21,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => c_Big__Operators_Olattice__class_OInf__fin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(hAPP(c_Finite__Set_Ofold(X5,X5,c_Lattices_Osemilattice__inf__class_Oinf(X5)),X25),X21) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_Inf__fin_Oeq__fold_H]) ).

fof(i_0_5827,plain,
    ! [X33779,X33780] : c_Relation_Otrans(X33780,c_Transitive__Closure_Otrancl(X33780,X33779)),
    inference(variable_rename,[status(thm)],[fact_trans__trancl]) ).

fof(i_0_5828,plain,
    ! [X168,X123] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X123) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X168)
    <=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X123)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X168)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X123)))
         => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X168)))
             => hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X123) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
            & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X168)))
             => X123 = X168 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_eq__nat__number__of]) ).

fof(i_0_5829,plain,
    ! [X66,X58] :
      ( ( class_Int_Onumber__ring(X58)
        & class_Rings_Olinordered__idom(X58) )
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(c_Int_Onumber__class_Onumber__of(X58),X66)),c_Groups_Ozero__class_Ozero(X58)))
         => hAPP(c_Groups_Oabs__class_Oabs(X58),hAPP(c_Int_Onumber__class_Onumber__of(X58),X66)) = hAPP(c_Groups_Ouminus__class_Ouminus(X58),hAPP(c_Int_Onumber__class_Onumber__of(X58),X66)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(c_Int_Onumber__class_Onumber__of(X58),X66)),c_Groups_Ozero__class_Ozero(X58)))
         => hAPP(c_Groups_Oabs__class_Oabs(X58),hAPP(c_Int_Onumber__class_Onumber__of(X58),X66)) = hAPP(c_Int_Onumber__class_Onumber__of(X58),X66) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_abs__number__of]) ).

fof(i_0_5830,plain,
    ! [X32452] : hAPP(c_Relation_Oconverse(X32452,X32452),c_Relation_OId(X32452)) = c_Relation_OId(X32452),
    inference(variable_rename,[status(thm)],[fact_converse__Id]) ).

fof(i_0_5831,plain,
    ! [X164,X136] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)))
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X164)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)))
       => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X164)))
           => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X164)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136) )
          & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X164)))
           => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X164)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X164))) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_mod__nat__number__of]) ).

fof(i_0_5832,plain,
    ! [X25,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X25),c_Big__Operators_Olattice_OInf__fin(X5,c_Orderings_Oord__class_Omin(X5),X21)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_min__max_OInf__fin_Oinsert]) ).

fof(i_0_5833,plain,
    ! [X25,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X25),c_Big__Operators_Olattice_OSup__fin(X5,c_Orderings_Oord__class_Omax(X5),X21)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_min__max_OSup__fin_Oinsert]) ).

fof(i_0_5834,plain,
    ! [X21069,X21070] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(X21070)),X21069) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21070),X21069)),
    inference(variable_rename,[status(thm)],[fact_mult__Bit0]) ).

fof(i_0_5835,plain,
    ! [X251,X18,X239,X25,X5] :
      ( hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X239)))
     => ( ~ hBOOL(hAPP(X18,X25))
       => c_List_OtakeWhile(X5,X18,hAPP(hAPP(c_List_Oappend(X5),X239),X251)) = c_List_OtakeWhile(X5,X18,X239) ) ),
    inference(fof_simplification,[status(thm)],[fact_takeWhile__append1]) ).

fof(i_0_5836,plain,
    ! [X128,X136] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)))
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X128)) = 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),X128)) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)))
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X128)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X128))) ) ),
    inference(fof_simplification,[status(thm)],[fact_power__nat__number__of__number__of]) ).

fof(i_0_5837,plain,
    ! [X164,X136] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X164)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X164)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X164))) ) ),
    inference(fof_simplification,[status(thm)],[fact_div__nat__number__of]) ).

fof(i_0_5838,plain,
    ! [X25,X21,X5] :
      ( class_Groups_Oab__semigroup__mult(X5)
     => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
         => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
           => hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X25),hAPP(c_Finite__Set_Ofold1(X5,c_Groups_Otimes__class_Otimes(X5)),X21)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_fold1__insert]) ).

fof(i_0_5839,plain,
    ! [X20949,X20950] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X20950))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X20949)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20950)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20949),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(X20950))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__diff__number__of])]) ).

fof(i_0_5840,plain,
    ! [X50,X18] :
      ( ~ hBOOL(hAPP(X18,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
     => ( hBOOL(hAPP(X18,X50))
       => ? [X100] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X100),X50))
            & ! [X146] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X146),X100))
               => ~ hBOOL(hAPP(X18,X146)) )
            & hBOOL(hAPP(X18,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X100),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_ex__least__nat__less]) ).

fof(i_0_5841,plain,
    ! [X31380,X31381] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X31381,X31380) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,X31381),hAPP(c_Nat_OSuc,X31380))),
    inference(variable_rename,[status(thm)],[fact_greaterThanAtMost__upt]) ).

fof(i_0_5842,plain,
    ! [X21077] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X21077)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X21077)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X21077))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X21077))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I21_J])]) ).

fof(i_0_5843,plain,
    ! [X21084] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X21084)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X21084)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X21084))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X21084))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I4_J])]) ).

fof(i_0_5844,plain,
    ! [X21121] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X21121)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X21121)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X21121))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X21121))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I25_J])]) ).

fof(i_0_5845,plain,
    ! [X21099] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X21099)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X21099)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X21099))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X21099))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I8_J])]) ).

fof(i_0_5846,plain,
    ! [X113,X21,X6,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X21))
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X5),X6),X113)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X5,tc_HOL_Obool)),X21),X113) ),
    inference(fof_simplification,[status(thm)],[fact_Int__insert__right__if0]) ).

fof(i_0_5847,plain,
    ! [X29458,X29459,X29460] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X29460,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29459)),X29458)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | hAPP(c_List_Orotate(X29459,X29460),X29458) = X29458 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rotate__id])]) ).

fof(i_0_5848,plain,
    ! [X29429,X29430,X29431] :
      ( ( hAPP(c_List_Orotate(X29431,X29430),X29429) != c_List_Olist_ONil(X29431)
        | X29429 = c_List_Olist_ONil(X29431) )
      & ( X29429 != c_List_Olist_ONil(X29431)
        | hAPP(c_List_Orotate(X29431,X29430),X29429) = c_List_Olist_ONil(X29431) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rotate__is__Nil__conv])]) ).

fof(i_0_5849,plain,
    ! [X82,X157] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X157),X82))
       => c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X82,X157) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X157),X82))
       => c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X82,X157) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),X82),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X82),c_Groups_Oone__class_Oone(tc_Int_Oint)),X157)) ) ),
    inference(fof_simplification,[status(thm)],[fact_simp__from__to]) ).

fof(i_0_5850,plain,
    ! [X21129,X21130] :
      ( ~ class_Int_Onumber__ring(X21130)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21130),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21130),c_Groups_Oone__class_Oone(X21130)),c_Groups_Oone__class_Oone(X21130))),hAPP(c_Int_Onumber__class_Onumber__of(X21130),X21129)) = hAPP(c_Int_Onumber__class_Onumber__of(X21130),c_Int_OBit0(X21129)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__number__of__Bit0])]) ).

fof(i_0_5851,plain,
    ! [X24,X113,X6,X5] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X113))
       => X6 = X24 )
     => hBOOL(hAPP(hAPP(c_member(X5),X6),hAPP(hAPP(c_Set_Oinsert(X5),X24),X113))) ),
    inference(fof_simplification,[status(thm)],[fact_insertCI]) ).

fof(i_0_5852,plain,
    ! [X20980] : c_Int_OBit1(X20980) = 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)),X20980)),X20980),
    inference(variable_rename,[status(thm)],[fact_Bit1__def]) ).

fof(i_0_5853,plain,
    ! [X33211,X33212,X33213,X33214,X33215,X33216] : hAPP(hAPP(c_Product__Type_Ointernal__split(X33216,X33215,X33214),X33213),hAPP(hAPP(c_Product__Type_OPair(X33216,X33215),X33212),X33211)) = hAPP(hAPP(X33213,X33212),X33211),
    inference(variable_rename,[status(thm)],[fact_internal__split__conv]) ).

fof(i_0_5854,plain,
    ! [X33206,X33207,X33208] : c_Product__Type_Ointernal__split(X33208,X33207,X33206) = c_Product__Type_Oprod_Oprod__case(X33208,X33207,X33206),
    inference(variable_rename,[status(thm)],[fact_internal__split__def]) ).

fof(i_0_5855,plain,
    ! [X33490,X33491,X33492] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X33492),hAPP(c_COMBK(X33492,tc_Nat_Onat),X33491)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X33490)) = c_List_Oreplicate(X33492,X33490,X33491),
    inference(variable_rename,[status(thm)],[fact_map__replicate__trivial]) ).

fof(i_0_5856,plain,
    ! [X21,X23,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X23),X21))
     => hBOOL(hAPP(hAPP(c_member(X5),X23),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X21))) ),
    inference(fof_simplification,[status(thm)],[fact_ComplI]) ).

fof(i_0_5857,plain,
    ! [X20,X21,X23,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X23),X21))
       => hAPP(c_Set_Ovimage(X20,X5,hAPP(c_COMBK(X5,X20),X23)),X21) = c_Orderings_Otop__class_Otop(tc_fun(X20,tc_HOL_Obool)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X23),X21))
       => hAPP(c_Set_Ovimage(X20,X5,hAPP(c_COMBK(X5,X20),X23)),X21) = c_Orderings_Obot__class_Obot(tc_fun(X20,tc_HOL_Obool)) ) ),
    inference(fof_simplification,[status(thm)],[fact_vimage__const]) ).

fof(i_0_5858,plain,
    ! [X25,X21,X205,X2,X5] :
      ( c_Finite__Set_Ofolding__one(X5,X2,X205)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => hAPP(X205,hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(hAPP(X2,X25),hAPP(X205,X21)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_folding__one_Oinsert]) ).

fof(i_0_5859,plain,
    ! [X31372,X31373] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),c_List_Oupt(X31373,X31372)) = c_List_Oupt(hAPP(c_Nat_OSuc,X31373),hAPP(c_Nat_OSuc,X31372)),
    inference(variable_rename,[status(thm)],[fact_map__Suc__upt]) ).

fof(i_0_5860,plain,
    ! [X90,X62] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X62))
       => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X90))
           => c_Divides_Odivmod__int(X62,X90) = c_Divides_OposDivAlg(X62,X90) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X90))
           => ( ( X62 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
               => c_Divides_Odivmod__int(X62,X90) = 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)) )
              & ( X62 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
               => c_Divides_Odivmod__int(X62,X90) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X62),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X90))) ) ) ) ) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X62))
       => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X90))
           => c_Divides_Odivmod__int(X62,X90) = c_Divides_OnegDivAlg(X62,X90) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X90))
           => c_Divides_Odivmod__int(X62,X90) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X62),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X90))) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_divmod__int__def]) ).

fof(i_0_5861,plain,
    ! [X156,X239,X5,X25,X18] :
      ( ~ hBOOL(hAPP(X18,X25))
     => c_List_OtakeWhile(X5,X18,hAPP(hAPP(c_List_Oappend(X5),X239),hAPP(hAPP(c_List_Olist_OCons(X5),X25),X156))) = c_List_OtakeWhile(X5,X18,X239) ),
    inference(fof_simplification,[status(thm)],[fact_takeWhile__tail]) ).

fof(i_0_5862,plain,
    ! [X27620] : c_Relation_Orefl__on(X27620,c_Orderings_Otop__class_Otop(tc_fun(X27620,tc_HOL_Obool)),c_Relation_OId(X27620)),
    inference(variable_rename,[status(thm)],[fact_refl__Id]) ).

fof(i_0_5863,plain,
    ! [X20996] :
      ( ~ class_Int_Onumber__ring(X20996)
      | hAPP(c_Int_Onumber__class_Onumber__of(X20996),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(X20996) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_numeral__1__eq__1])]) ).

fof(i_0_5864,plain,
    ! [X20995] :
      ( ~ class_Int_Onumber__ring(X20995)
      | c_Groups_Oone__class_Oone(X20995) = hAPP(c_Int_Onumber__class_Onumber__of(X20995),c_Int_OBit1(c_Int_OPls)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_semiring__norm_I110_J])]) ).

fof(i_0_5865,plain,
    ! [X50,X95] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X50))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X50)),X95)) ),
    inference(fof_simplification,[status(thm)],[fact_not__less__eq__eq]) ).

fof(i_0_5866,plain,
    ! [X62,X58] :
      ( class_Groups_Oordered__ab__group__add__abs(X58)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(c_Groups_Oabs__class_Oabs(X58),X62)),c_Groups_Ozero__class_Ozero(X58))) ),
    inference(fof_simplification,[status(thm)],[fact_abs__not__less__zero]) ).

fof(i_0_5867,plain,
    ! [X72,X58] :
      ( class_Rings_Olinordered__semidom(X58)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X58),X72)),c_Groups_Ozero__class_Ozero(X58))) ),
    inference(fof_simplification,[status(thm)],[fact_of__nat__less__0__iff]) ).

fof(i_0_5868,plain,
    ! [X21105,X21106] :
      ( ( ~ c_Int_Oiszero(X21106,hAPP(c_Int_Onumber__class_Onumber__of(X21106),c_Int_OBit0(X21105)))
        | c_Int_Oiszero(X21106,hAPP(c_Int_Onumber__class_Onumber__of(X21106),X21105))
        | ~ class_Int_Onumber__ring(X21106)
        | ~ class_Int_Oring__char__0(X21106) )
      & ( ~ c_Int_Oiszero(X21106,hAPP(c_Int_Onumber__class_Onumber__of(X21106),X21105))
        | c_Int_Oiszero(X21106,hAPP(c_Int_Onumber__class_Onumber__of(X21106),c_Int_OBit0(X21105)))
        | ~ class_Int_Onumber__ring(X21106)
        | ~ class_Int_Oring__char__0(X21106) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_iszero__number__of__Bit0])])]) ).

fof(i_0_5869,plain,
    ! [X164,X136] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X136),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X164)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X164) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X136),c_Int_OPls))
       => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X164),c_Int_OPls))
           => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X164)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X164),c_Int_OPls))
           => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X164)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X136),X164)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_add__nat__number__of]) ).

fof(i_0_5870,plain,
    ! [X57,X136] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)))
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)),X57) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X57) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)))
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)),X57) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)),X57)) ) ),
    inference(fof_simplification,[status(thm)],[fact_power__nat__number__of]) ).

fof(i_0_5871,plain,
    ! [X21093] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X21093)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),X21093)),
    inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I3_J]) ).

fof(i_0_5872,plain,
    ! [X134,X99,X96] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X96),X99))
       => c_Random_Ominus__shift(X134,X96,X99) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X134),X96)),X99) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X96),X99))
       => c_Random_Ominus__shift(X134,X96,X99) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X96),X99) ) ),
    inference(fof_simplification,[status(thm)],[fact_minus__shift__def]) ).

fof(i_0_5873,axiom,
    ! [X87,X50,X18] :
      ( hBOOL(hAPP(X18,c_Divides_Odiv__class_Omod(tc_Int_Oint,X50,X87)))
    <=> epred1_3(X18,X50,X87) ),
    inference(apply_def,[status(thm)],[fact_split__zmod,c_0_5218]) ).

fof(i_0_5874,plain,
    ! [X97,X98] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X98),X97))
       => c_List_Oupto(X98,X97) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),X98),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X98),c_Groups_Oone__class_Oone(tc_Int_Oint)),X97)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X98),X97))
       => c_List_Oupto(X98,X97) = c_List_Olist_ONil(tc_Int_Oint) ) ),
    inference(fof_simplification,[status(thm)],[fact_upto_Osimps]) ).

fof(i_0_5875,plain,
    ! [X21064,X21065] : c_Int_OBit0(X21065) != c_Int_OBit1(X21064),
    inference(variable_rename,[status(thm)],[fact_rel__simps_I49_J]) ).

fof(i_0_5876,plain,
    ! [X21062,X21063] : c_Int_OBit1(X21063) != c_Int_OBit0(X21062),
    inference(variable_rename,[status(thm)],[fact_rel__simps_I50_J]) ).

fof(i_0_5877,plain,
    ! [X21852,X21853] : c_Divides_Odivmod__nat(X21853,X21852) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X21853),X21852)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21853,X21852)),
    inference(variable_rename,[status(thm)],[fact_divmod__nat__div__mod]) ).

fof(i_0_5878,plain,
    ! [X21654,X21655,X21656,X21657] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X21657,X21656,X21655,c_Code__Numeral_OSuc__code__numeral(X21654)) = hAPP(X21655,X21654),
    inference(variable_rename,[status(thm)],[fact_code__numeral_Osimps_I5_J]) ).

fof(i_0_5879,plain,
    ! [X31382,X31383] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X31383,X31382) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,X31383),X31382)),
    inference(variable_rename,[status(thm)],[fact_greaterThanLessThan__upt]) ).

fof(i_0_5880,plain,
    ! [X239,X25,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X239)))
       => c_List_Oremdups(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239)) = c_List_Oremdups(X5,X239) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X239)))
       => c_List_Oremdups(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239)) = hAPP(hAPP(c_List_Olist_OCons(X5),X25),c_List_Oremdups(X5,X239)) ) ),
    inference(fof_simplification,[status(thm)],[fact_remdups_Osimps_I2_J]) ).

fof(i_0_5881,plain,
    ! [X96,X58] :
      ( class_Rings_Oring__1(X58)
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X96),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => hAPP(c_Int_Oring__1__class_Oof__int(X58),X96) = hAPP(c_Groups_Ouminus__class_Ouminus(X58),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X58),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X96)))) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X96),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => hAPP(c_Int_Oring__1__class_Oof__int(X58),X96) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X58),hAPP(c_Int_Onat,X96)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_of__int__of__nat]) ).

fof(i_0_5882,plain,
    ! [X98,X91] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X91),X98))
       => c_Lazy__Sequence_Osmall__lazy_H(X91,X98) = c_Lazy__Sequence_Oempty(tc_Int_Oint) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X91),X98))
       => c_Lazy__Sequence_Osmall__lazy_H(X91,X98) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),X98),c_Lazy__Sequence_Osmall__lazy_H(X91,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X98),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    inference(fof_simplification,[status(thm)],[fact_small__lazy_H_Osimps]) ).

fof(i_0_5883,plain,
    ! [X30887] : hAPP(c_Relation_ODomain(X30887,X30887),c_Relation_OId(X30887)) = c_Orderings_Otop__class_Otop(tc_fun(X30887,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Domain__Id]) ).

fof(i_0_5884,plain,
    ! [X28271] : hAPP(c_Relation_ORange(X28271,X28271),c_Relation_OId(X28271)) = c_Orderings_Otop__class_Otop(tc_fun(X28271,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Range__Id]) ).

fof(i_0_5885,plain,
    ! [X25,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => c_Big__Operators_Olinorder__class_OMin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X25),c_Big__Operators_Olinorder__class_OMin(X5,X21)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_Min_Oinsert]) ).

fof(i_0_5886,plain,
    ! [X25,X21,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => c_Big__Operators_Olinorder__class_OMax(X5,hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X25),c_Big__Operators_Olinorder__class_OMax(X5,X21)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_Max_Oinsert]) ).

fof(i_0_5887,plain,
    ! [X25,X21,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => c_Big__Operators_Olattice__class_OSup__fin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X25),c_Big__Operators_Olattice__class_OSup__fin(X5,X21)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_Sup__fin_Oinsert]) ).

fof(i_0_5888,plain,
    ! [X25,X21,X5] :
      ( class_Lattices_Olattice(X5)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => ( X21 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
           => c_Big__Operators_Olattice__class_OInf__fin(X5,hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X25),c_Big__Operators_Olattice__class_OInf__fin(X5,X21)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_Inf__fin_Oinsert]) ).

fof(i_0_5889,plain,
    ! [X32327,X32328] : c_Transitive__Closure_Otrancl(X32328,c_Transitive__Closure_Ortrancl(X32328,X32327)) = c_Transitive__Closure_Ortrancl(X32328,X32327),
    inference(variable_rename,[status(thm)],[fact_rtrancl__trancl__absorb]) ).

fof(i_0_5890,plain,
    ! [X25,X5,X21] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X21))
       => c_List_Osublist(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X25),c_List_Olist_ONil(X5)),X21) = hAPP(hAPP(c_List_Olist_OCons(X5),X25),c_List_Olist_ONil(X5)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X21))
       => c_List_Osublist(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X25),c_List_Olist_ONil(X5)),X21) = c_List_Olist_ONil(X5) ) ),
    inference(fof_simplification,[status(thm)],[fact_sublist__singleton]) ).

fof(i_0_5891,plain,
    ! [X33578,X33579,X33580] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X33580),X33579),hAPP(c_List_Oset(X33580),X33578)))
        | hBOOL(hAPP(hAPP(c_List_Omember(X33580),X33578),X33579)) )
      & ( ~ hBOOL(hAPP(hAPP(c_List_Omember(X33580),X33578),X33579))
        | hBOOL(hAPP(hAPP(c_member(X33580),X33579),hAPP(c_List_Oset(X33580),X33578))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__set__member])]) ).

fof(i_0_5892,plain,
    ! [X33568,X33569,X33570] :
      ( ( ~ hBOOL(hAPP(hAPP(c_List_Omember(X33570),X33569),X33568))
        | hBOOL(hAPP(hAPP(c_member(X33570),X33568),hAPP(c_List_Oset(X33570),X33569))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X33570),X33568),hAPP(c_List_Oset(X33570),X33569)))
        | hBOOL(hAPP(hAPP(c_List_Omember(X33570),X33569),X33568)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_List_Omember__def])]) ).

fof(i_0_5893,plain,
    ! [X164] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X164)))
       => 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),X164)) = 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),X164)))
       => 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),X164)) = 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),X164))) ) ),
    inference(fof_simplification,[status(thm)],[fact_one__mod__nat__number__of]) ).

fof(i_0_5894,plain,
    ! [X32547] : c_Relation_Osingle__valued(X32547,X32547,c_Relation_OId(X32547)),
    inference(variable_rename,[status(thm)],[fact_single__valued__Id]) ).

fof(i_0_5895,plain,
    ! [X33,X25,X5] :
      ( class_Orderings_Opreorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X25),X33))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X25),X33))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X33),X25)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_less__le__not__le]) ).

fof(i_0_5896,plain,
    ! [X25,X21,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
       => hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X5),X21)) ) ),
    inference(fof_simplification,[status(thm)],[fact_card_Oinsert]) ).

fof(i_0_5897,axiom,
    ! [X87,X50,X18] :
      ( hBOOL(hAPP(X18,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X50),X87)))
    <=> epred2_3(X18,X50,X87) ),
    inference(apply_def,[status(thm)],[fact_split__zdiv,c_0_5219]) ).

fof(i_0_5898,plain,
    ! [X113,X21,X25,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X113))
       => ( hAPP(hAPP(c_Set_Oinsert(X5),X25),X21) = hAPP(hAPP(c_Set_Oinsert(X5),X25),X113)
        <=> X21 = X113 ) ) ),
    inference(fof_simplification,[status(thm)],[fact_insert__ident]) ).

fof(i_0_5899,plain,
    ! [X25,X21,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
     => ( ( hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(c_Finite__Set_Ocard(X5),X21) )
        & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
         => hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X5),X21)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_card__insert__if]) ).

fof(i_0_5900,plain,
    ! [X31370,X31371] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31371),X31370))
      | c_List_Olast(tc_Nat_Onat,c_List_Oupt(X31371,X31370)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X31370),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__upt])]) ).

fof(i_0_5901,plain,
    ! [X21658] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(X21658)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = X21658,
    inference(variable_rename,[status(thm)],[fact_Suc__code__numeral__minus__one]) ).

fof(i_0_5902,plain,
    ! [X50,X95] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X95),X50))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X50),hAPP(c_Nat_OSuc,X95))) ),
    inference(fof_simplification,[status(thm)],[fact_not__less__eq]) ).

fof(i_0_5903,plain,
    ! [X31334,X31335] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(X31335,X31334))),
    inference(variable_rename,[status(thm)],[fact_distinct__upt]) ).

fof(i_0_5904,plain,
    ! [X23430,X23431] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(X23431,X23431),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X23430) = c_Relation_OId(X23431),
    inference(variable_rename,[status(thm)],[fact_relpow_Osimps_I1_J]) ).

fof(i_0_5905,plain,
    ! [X239,X5,X25,X18] :
      ( ( hBOOL(hAPP(X18,X25))
       => c_List_OtakeWhile(X5,X18,hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239)) = hAPP(hAPP(c_List_Olist_OCons(X5),X25),c_List_OtakeWhile(X5,X18,X239)) )
      & ( ~ hBOOL(hAPP(X18,X25))
       => c_List_OtakeWhile(X5,X18,hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239)) = c_List_Olist_ONil(X5) ) ),
    inference(fof_simplification,[status(thm)],[fact_takeWhile_Osimps_I2_J]) ).

fof(i_0_5906,plain,
    ! [X96] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X96)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(fof_simplification,[status(thm)],[fact_int__less__0__conv]) ).

fof(i_0_5907,plain,
    ! [X20975] :
      ( ( c_Int_OMin != c_Int_OBit1(X20975)
        | c_Int_OMin = X20975 )
      & ( c_Int_OMin != X20975
        | c_Int_OMin = c_Int_OBit1(X20975) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I43_J])]) ).

fof(i_0_5908,plain,
    ! [X20976] :
      ( ( c_Int_OBit1(X20976) != c_Int_OMin
        | X20976 = c_Int_OMin )
      & ( X20976 != c_Int_OMin
        | c_Int_OBit1(X20976) = c_Int_OMin ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I47_J])]) ).

fof(i_0_5909,plain,
    ! [X20974] : c_Int_OBit1(X20974) != c_Int_OPls,
    inference(variable_rename,[status(thm)],[fact_rel__simps_I46_J]) ).

fof(i_0_5910,plain,
    ! [X20973] : c_Int_OPls != c_Int_OBit1(X20973),
    inference(variable_rename,[status(thm)],[fact_rel__simps_I39_J]) ).

fof(i_0_5911,plain,
    ! [X33896] : c_Relation_Osym(X33896,c_Relation_OId(X33896)),
    inference(variable_rename,[status(thm)],[fact_sym__Id]) ).

fof(i_0_5912,plain,
    ! [X33829] : c_Relation_Oantisym(X33829,c_Relation_OId(X33829)),
    inference(variable_rename,[status(thm)],[fact_antisym__Id]) ).

fof(i_0_5913,plain,
    ! [X33795] : c_Relation_Otrans(X33795,c_Relation_OId(X33795)),
    inference(variable_rename,[status(thm)],[fact_trans__Id]) ).

fof(i_0_5914,plain,
    ! [X136,X58] :
      ( class_Int_Onumber__ring(X58)
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)))
         => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X58),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)) = hAPP(c_Int_Onumber__class_Onumber__of(X58),X136) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)))
         => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X58),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)) = c_Groups_Ozero__class_Ozero(X58) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_of__nat__number__of__lemma]) ).

fof(i_0_5915,plain,
    ! [X25,X21,X5] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),X21))
       => hAPP(c_Finite__Set_Ocard(X5),hAPP(hAPP(c_Set_Oinsert(X5),X25),X21)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X5),X21)) ) ),
    inference(fof_simplification,[status(thm)],[fact_card__insert__disjoint]) ).

fof(i_0_5916,plain,
    ! [X33,X25,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X25),X33))
       => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X25),X33))
        <=> X25 = X33 ) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv2]) ).

fof(i_0_5917,plain,
    ! [X5] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X5)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X5),tc_HOL_Obool)))),
    inference(fof_simplification,[status(thm)],[fact_infinite__UNIV__listI]) ).

fof(i_0_5918,plain,
    ! [X23,X76,X24] :
      ( ~ hBOOL(hAPP(X24,X76))
     => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X24,X23)),X76),X76)) ),
    inference(fof_simplification,[status(thm)],[fact_evalc_OWhileFalse]) ).

fof(i_0_5919,plain,
    ! [X239,X25,X5] :
      ( ( hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X239)))
       => c_List_Oinsert(X5,X25,X239) = X239 )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X239)))
       => c_List_Oinsert(X5,X25,X239) = hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239) ) ),
    inference(fof_simplification,[status(thm)],[fact_List_Oinsert__def]) ).

fof(i_0_5920,plain,
    ! [X62,X90,X58] :
      ( class_Orderings_Oorder(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X90),X62))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X62),X90)) ) ),
    inference(fof_simplification,[status(thm)],[fact_xt1_I9_J]) ).

fof(i_0_5921,plain,
    ! [X65,X66,X58] :
      ( class_Orderings_Opreorder(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X66),X65))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X65),X66)) ) ),
    inference(fof_simplification,[status(thm)],[fact_order__less__not__sym]) ).

fof(i_0_5922,plain,
    ! [X65,X66,X58] :
      ( class_Orderings_Opreorder(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X66),X65))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X65),X66)) ) ),
    inference(fof_simplification,[status(thm)],[fact_order__less__imp__not__less]) ).

fof(i_0_5923,plain,
    ! [X90,X62,X58] :
      ( class_Orderings_Opreorder(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X62),X90))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X90),X62)) ) ),
    inference(fof_simplification,[status(thm)],[fact_order__less__asym_H]) ).

fof(i_0_5924,plain,
    ! [X65,X66,X58] :
      ( class_Orderings_Opreorder(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X66),X65))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X65),X66)) ) ),
    inference(fof_simplification,[status(thm)],[fact_order__less__asym]) ).

fof(i_0_5925,plain,
    ! [X33,X25,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X25),X33))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X33),X25)) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__not__le]) ).

fof(i_0_5926,plain,
    ! [X66,X65,X58] :
      ( class_Orderings_Olinorder(X58)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X65),X66))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X66),X65)) ) ),
    inference(fof_simplification,[status(thm)],[fact_leD]) ).

fof(i_0_5927,plain,
    ! [X33,X25,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X25),X33))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X33),X25)) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__not__less]) ).

fof(i_0_5928,plain,
    ! [X33,X25,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X25),X33))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X33),X25))
          | X25 = X33 ) ) ),
    inference(fof_simplification,[status(thm)],[fact_not__less__iff__gr__or__eq]) ).

fof(i_0_5929,plain,
    ! [X164,X136] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X136),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X164)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X136),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X164)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X136),X164)) ) ),
    inference(fof_simplification,[status(thm)],[fact_mult__nat__number__of]) ).

fof(i_0_5930,plain,
    ! [X31338,X31339] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31339),X31338))
      | hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(X31339,X31338)) = X31339 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hd__upt])]) ).

fof(i_0_5931,plain,
    ! [X23,X5] : ~ hBOOL(hAPP(hAPP(c_member(X5),X23),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),
    inference(fof_simplification,[status(thm)],[fact_empty__iff]) ).

fof(i_0_5932,plain,
    ! [X6,X5] : ~ hBOOL(hAPP(hAPP(c_member(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),
    inference(fof_simplification,[status(thm)],[fact_emptyE]) ).

fof(i_0_5933,plain,
    ! [X57,X72] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X72),hAPP(c_Nat_OSuc,X57)))
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X72),X57))
       => X72 = hAPP(c_Nat_OSuc,X57) ) ),
    inference(fof_simplification,[status(thm)],[fact_le__SucE]) ).

fof(i_0_5934,plain,
    ! [X31374,X31375] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X31375,X31374) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X31375,hAPP(c_Nat_OSuc,X31374))),
    inference(variable_rename,[status(thm)],[fact_atLeastAtMost__upt]) ).

fof(i_0_5935,plain,
    ! [X50,X95] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X50))
       => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X95),hAPP(c_Nat_OSuc,X50)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X50),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X95),X50)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X95),X50))
       => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X95),hAPP(c_Nat_OSuc,X50)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
    inference(fof_simplification,[status(thm)],[fact_atLeastLessThanSuc]) ).

fof(i_0_5936,plain,
    ! [X239,X5,X25,X18] :
      ( ( hBOOL(hAPP(X18,X25))
       => hAPP(c_List_Ofilter(X5,X18),hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239)) = hAPP(hAPP(c_List_Olist_OCons(X5),X25),hAPP(c_List_Ofilter(X5,X18),X239)) )
      & ( ~ hBOOL(hAPP(X18,X25))
       => hAPP(c_List_Ofilter(X5,X18),hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239)) = hAPP(c_List_Ofilter(X5,X18),X239) ) ),
    inference(fof_simplification,[status(thm)],[fact_filter_Osimps_I2_J]) ).

fof(i_0_5937,plain,
    ! [X57,X72] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X72),hAPP(c_Nat_OSuc,X57)))
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X72),X57))
       => X72 = X57 ) ),
    inference(fof_simplification,[status(thm)],[fact_less__SucE]) ).

fof(i_0_5938,plain,
    ! [X72,X57] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X57),X72))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X57),hAPP(c_Nat_OSuc,X72)))
       => X72 = X57 ) ),
    inference(fof_simplification,[status(thm)],[fact_less__antisym]) ).

fof(i_0_5939,plain,
    ! [X95,X50] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X50),X95))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X50),hAPP(c_Nat_OSuc,X95)))
      <=> X50 = X95 ) ),
    inference(fof_simplification,[status(thm)],[fact_not__less__less__Suc__eq]) ).

fof(i_0_5940,plain,
    ! [X21877,X21878] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X21878,X21877),c_Divides_Odivmod__nat(X21878,X21877))),
    inference(variable_rename,[status(thm)],[fact_divmod__nat__rel__divmod__nat]) ).

fof(i_0_5941,plain,
    ! [X21633] : hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(X21633)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),X21633)),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_5942,plain,
    ! [X31384] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X31384) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,X31384))),
    inference(variable_rename,[status(thm)],[fact_atMost__upto]) ).

fof(i_0_5943,plain,
    ! [X20883] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20883),c_Int_OPls))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20883)),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),X20883),c_Int_OPls))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20883)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(X20883)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5220])]) ).

fof(i_0_5944,plain,
    ! [X20886] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20886),c_Int_OPls))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20886)),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),X20886),c_Int_OPls))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20886)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X20886)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5221])]) ).

fof(i_0_5945,plain,
    ! [X20879,X20880] :
      ( ~ class_Int_Onumber__ring(X20880)
      | hAPP(c_Int_Onumber__class_Onumber__of(X20880),c_Int_Opred(X20879)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20880),hAPP(c_Groups_Ouminus__class_Ouminus(X20880),c_Groups_Oone__class_Oone(X20880))),hAPP(c_Int_Onumber__class_Onumber__of(X20880),X20879)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__pred])]) ).

fof(i_0_5946,plain,
    ! [X50,X23,X76,X24] :
      ( ~ hBOOL(hAPP(X24,X76))
     => c_Natural_Oevaln(c_Com_Ocom_OWhile(X24,X23),X76,X50,X76) ),
    inference(fof_simplification,[status(thm)],[fact_evaln_OWhileFalse]) ).

fof(i_0_5947,plain,
    ! [X33781,X33782] :
      ( ~ c_Relation_Otrans(X33782,X33781)
      | c_Transitive__Closure_Otrancl(X33782,X33781) = X33781 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__id])]) ).

fof(i_0_5948,plain,
    ! [X24,X6,X5] :
      ( class_Orderings_Oorder(X5)
     => ( c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,X24)
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),X24)) ) ),
    inference(fof_simplification,[status(thm)],[fact_atLeastatMost__empty__iff2]) ).

fof(i_0_5949,plain,
    ! [X156,X87,X5] :
      ( class_Orderings_Oorder(X5)
     => ( c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X87,X156)
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X87),X156)) ) ),
    inference(fof_simplification,[status(thm)],[fact_greaterThanAtMost__empty__iff2]) ).

fof(i_0_5950,plain,
    ! [X24,X6,X5] :
      ( class_Orderings_Oorder(X5)
     => ( c_SetInterval_Oord__class_OatLeastAtMost(X5,X6,X24) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X6),X24)) ) ),
    inference(fof_simplification,[status(thm)],[fact_atLeastatMost__empty__iff]) ).

fof(i_0_5951,plain,
    ! [X156,X87,X5] :
      ( class_Orderings_Oorder(X5)
     => ( c_SetInterval_Oord__class_OgreaterThanAtMost(X5,X87,X156) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X87),X156)) ) ),
    inference(fof_simplification,[status(thm)],[fact_greaterThanAtMost__empty__iff]) ).

fof(i_0_5952,plain,
    ! [X21850,X21851] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21851),X21850))
      | c_Divides_Odivmod__nat(X21851,X21850) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X21851) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__nat__base])]) ).

fof(i_0_5953,plain,
    ! [X5,X113,X21] :
      ( X21 = X113
     => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X21),X113))
         => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X113),X21)) ) ),
    inference(fof_simplification,[status(thm)],[fact_equalityE]) ).

fof(i_0_5954,plain,
    ! [X57] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X57)),X57)),
    inference(fof_simplification,[status(thm)],[fact_Suc__n__not__le__n]) ).

fof(i_0_5955,plain,
    ! [X96,X99] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X99))
       => c_SMT_Oz3div(X96,X99) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X96),X99) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X99))
       => c_SMT_Oz3div(X96,X99) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X96),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X99))) ) ),
    inference(fof_simplification,[status(thm)],[fact_z3div__def]) ).

fof(i_0_5956,plain,
    ! [X57,X72] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X72),X57))
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,X72,X57) = X72 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X72),X57))
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,X72,X57) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X72),X57),X57) ) ),
    inference(fof_simplification,[status(thm)],[fact_mod__if]) ).

fof(i_0_5957,plain,
    ! [X57,X72] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X72),X57))
     => c_Divides_Odiv__class_Omod(tc_Nat_Onat,X72,X57) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X72),X57),X57) ),
    inference(fof_simplification,[status(thm)],[fact_mod__geq]) ).

fof(i_0_5958,plain,
    ! [X239,X25,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X239)))
     => c_List_Oinsert(X5,X25,X239) = hAPP(hAPP(c_List_Olist_OCons(X5),X25),X239) ),
    inference(fof_simplification,[status(thm)],[fact_not__in__set__insert]) ).

fof(i_0_5959,plain,
    ! [X33,X25,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X25),X33))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X25),X33))
        <=> X25 = X33 ) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv1]) ).

fof(i_0_5960,plain,
    ! [X24,X6,X5] :
      ( class_Orderings_Oorder(X5)
     => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X6),X24) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),X24)) ) ),
    inference(fof_simplification,[status(thm)],[fact_atLeastLessThan__empty__iff]) ).

fof(i_0_5961,plain,
    ! [X24,X6,X5] :
      ( class_Orderings_Oorder(X5)
     => ( c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X5,X6),X24)
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X6),X24)) ) ),
    inference(fof_simplification,[status(thm)],[fact_atLeastLessThan__empty__iff2]) ).

fof(i_0_5962,plain,
    ! [X20887] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20887),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),X20887)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20887),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),X20887)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X20887)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5222])]) ).

fof(i_0_5963,plain,
    ! [X32,X5] :
      ( c_Equiv__Relations_Opart__equivp(X5,X32)
     => ~ ( ? [X3] : hBOOL(hAPP(hAPP(X32,X3),X3))
         => ( c_Predicate_Osymp(X5,X32)
           => ~ c_Predicate_Otransp(X5,X32) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_part__equivpE]) ).

fof(i_0_5964,plain,
    ! [X21642,X21643] :
      ( ( c_Code__Numeral_OSuc__code__numeral(X21643) != c_Code__Numeral_OSuc__code__numeral(X21642)
        | X21643 = X21642 )
      & ( X21643 != X21642
        | c_Code__Numeral_OSuc__code__numeral(X21643) = c_Code__Numeral_OSuc__code__numeral(X21642) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_code__numeral_Oinject])]) ).

fof(i_0_5965,plain,
    ! [X21634] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(X21634)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(X21634)),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_5966,plain,
    ! [X21073] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(X21073)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21073)),
    inference(variable_rename,[status(thm)],[fact_minus__Bit0]) ).

fof(i_0_5967,plain,
    ! [X50,X5,X25,X18] :
      ( ( hBOOL(hAPP(X18,X25))
       => hAPP(c_List_Ofilter(X5,X18),c_List_Oreplicate(X5,X50,X25)) = c_List_Oreplicate(X5,X50,X25) )
      & ( ~ hBOOL(hAPP(X18,X25))
       => hAPP(c_List_Ofilter(X5,X18),c_List_Oreplicate(X5,X50,X25)) = c_List_Olist_ONil(X5) ) ),
    inference(fof_simplification,[status(thm)],[fact_filter__replicate]) ).

fof(i_0_5968,plain,
    ! [X31785] :
      ( ~ c_List_Onat__list(X31785)
      | c_List_Oembed__list(c_List_Oreturn__list(X31785)) = X31785 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__list__return__embed])]) ).

fof(i_0_5969,plain,
    ! [X20693] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20693)))
        | hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20693)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20693)))
        | hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20693)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X20693)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5223])]) ).

fof(i_0_5970,plain,
    ! [X21,X5] :
      ( ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(X5),X3),X21))
    <=> X21 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
    inference(fof_simplification,[status(thm)],[fact_all__not__in__conv]) ).

fof(i_0_5971,plain,
    ! [X239,X25,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X5),X25),hAPP(c_List_Oset(X5),X239)))
     => c_List_Oremove1(X5,X25,X239) = X239 ),
    inference(fof_simplification,[status(thm)],[fact_remove1__idem]) ).

fof(i_0_5972,plain,
    ! [X31362,X31363] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),c_List_Oupt(X31363,X31362)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X31362),X31363),
    inference(variable_rename,[status(thm)],[fact_length__upt]) ).

fof(i_0_5973,plain,
    ! [X66,X58] :
      ( class_Groups_Osgn__if(X58)
     => ( ( X66 = c_Groups_Ozero__class_Ozero(X58)
         => c_Groups_Osgn__class_Osgn(X58,X66) = c_Groups_Ozero__class_Ozero(X58) )
        & ( X66 != c_Groups_Ozero__class_Ozero(X58)
         => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),X66))
             => c_Groups_Osgn__class_Osgn(X58,X66) = c_Groups_Oone__class_Oone(X58) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Ozero__class_Ozero(X58)),X66))
             => c_Groups_Osgn__class_Osgn(X58,X66) = hAPP(c_Groups_Ouminus__class_Ouminus(X58),c_Groups_Oone__class_Oone(X58)) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_sgn__if]) ).

fof(i_0_5974,plain,
    ! [X31357,X31358] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31358),X31357))
      | c_List_Oupt(X31357,X31358) = c_List_Olist_ONil(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_upt__conv__Nil])]) ).

fof(i_0_5975,plain,
    ! [X31350,X31351] :
      ( ( c_List_Oupt(X31351,X31350) != c_List_Olist_ONil(tc_Nat_Onat)
        | X31350 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31350),X31351)) )
      & ( X31350 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_List_Oupt(X31351,X31350) = c_List_Olist_ONil(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31350),X31351))
        | c_List_Oupt(X31351,X31350) = 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_5976,plain,
    ! [X96,X99] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X99))
       => c_SMT_Oz3mod(X96,X99) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X96,X99) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X99))
       => c_SMT_Oz3mod(X96,X99) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X96,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X99)) ) ),
    inference(fof_simplification,[status(thm)],[fact_z3mod__def]) ).

fof(i_0_5977,plain,
    ! [X62,X58] :
      ( class_Groups_Oabs__if(X58)
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X62),c_Groups_Ozero__class_Ozero(X58)))
         => hAPP(c_Groups_Oabs__class_Oabs(X58),X62) = hAPP(c_Groups_Ouminus__class_Ouminus(X58),X62) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X62),c_Groups_Ozero__class_Ozero(X58)))
         => hAPP(c_Groups_Oabs__class_Oabs(X58),X62) = X62 ) ) ),
    inference(fof_simplification,[status(thm)],[fact_abs__if]) ).

fof(i_0_5978,plain,
    ! [X58] :
      ( class_Rings_Olinordered__semidom(X58)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),c_Groups_Oone__class_Oone(X58)),c_Groups_Ozero__class_Ozero(X58))) ),
    inference(fof_simplification,[status(thm)],[fact_not__one__le__zero]) ).

fof(i_0_5979,plain,
    ! [X58] :
      ( class_Rings_Olinordered__semidom(X58)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),c_Groups_Oone__class_Oone(X58)),c_Groups_Ozero__class_Ozero(X58))) ),
    inference(fof_simplification,[status(thm)],[fact_not__one__less__zero]) ).

fof(i_0_5980,plain,
    ! [X57,X72] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X72),X57))
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X57),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X72),X57)) = X72 ),
    inference(fof_simplification,[status(thm)],[fact_add__diff__inverse]) ).

fof(i_0_5981,plain,
    ! [X31376] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X31376) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X31376)),
    inference(variable_rename,[status(thm)],[fact_atLeast__upt]) ).

fof(i_0_5982,plain,
    ! [X65,X66,X58] :
      ( class_Rings_Olinordered__idom(X58)
     => ( X66 != X65
       => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X66),X65))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X65),X66)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__neqE__linordered__idom]) ).

fof(i_0_5983,plain,
    ! [X25,X33,X5] :
      ( class_Orderings_Olinorder(X5)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X33),X25))
       => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X25),X33))
        <=> X25 = X33 ) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv3]) ).

fof(i_0_5984,plain,
    ! [X65,X66,X58] :
      ( class_Orderings_Olinorder(X58)
     => ( X66 != X65
       => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X66),X65))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X65),X66)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__neqE]) ).

fof(i_0_5985,plain,
    ! [X65,X66,X58] :
      ( class_Orderings_Olinorder(X58)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X66),X65))
       => ( X66 != X65
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X65),X66)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__cases]) ).

fof(i_0_5986,plain,
    ! [X65,X66,X58] :
      ( class_Orderings_Olinorder(X58)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X66),X65))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X65),X66)) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__le__cases]) ).

fof(i_0_5987,plain,
    ! [X65,X66,X58] :
      ( class_Orderings_Olinorder(X58)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X66),X65))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X65),X66)) ) ),
    inference(fof_simplification,[status(thm)],[fact_leI]) ).

fof(i_0_5988,plain,
    ! [X66,X65,X58] :
      ( class_Orderings_Olinorder(X58)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X58),X65),X66))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X66),X65)) ) ),
    inference(fof_simplification,[status(thm)],[fact_not__leE]) ).

fof(i_0_5989,plain,
    ! [X31332,X31333] : hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X31333,X31332)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X31333),X31332),
    inference(variable_rename,[status(thm)],[fact_set__upt]) ).

fof(i_0_5990,plain,
    ! [X31330,X31331] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X31331),X31330) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X31331,X31330)),
    inference(variable_rename,[status(thm)],[fact_atLeastLessThan__upt]) ).

fof(i_0_5991,plain,
    ! [X20756] : c_Int_Osucc(c_Int_Opred(X20756)) = X20756,
    inference(variable_rename,[status(thm)],[fact_succ__pred]) ).

fof(i_0_5992,plain,
    ! [X20877,X20878] :
      ( ~ class_Int_Onumber__ring(X20878)
      | hAPP(c_Int_Onumber__class_Onumber__of(X20878),c_Int_Osucc(X20877)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20878),c_Groups_Oone__class_Oone(X20878)),hAPP(c_Int_Onumber__class_Onumber__of(X20878),X20877)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__succ])]) ).

fof(i_0_5993,plain,
    ! [X6,X5,X21] :
      ( X21 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
     => ~ hBOOL(hAPP(hAPP(c_member(X5),X6),X21)) ),
    inference(fof_simplification,[status(thm)],[fact_equals0D]) ).

fof(i_0_5994,plain,
    ! [X25] :
      ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X25))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25)) ),
    inference(fof_simplification,[status(thm)],[fact_not__neg__eq__ge__0]) ).

fof(i_0_5995,plain,
    ! [X25] :
      ~ ! [X177] :
          ( X25 = hAPP(c_Code__Numeral_Oof__nat,X177)
         => ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X177),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_5996,plain,
    ! [X95,X121] :
      ( hAPP(c_Int_Onat,X121) = X95
    <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X121))
         => X121 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X95) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X121))
         => X95 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_nat__eq__iff]) ).

fof(i_0_5997,plain,
    ! [X121,X95] :
      ( X95 = hAPP(c_Int_Onat,X121)
    <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X121))
         => X121 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X95) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X121))
         => X95 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_nat__eq__iff2]) ).

fof(i_0_5998,plain,
    ! [X94] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X94))
       => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X94)) = X94 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X94))
       => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X94)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(fof_simplification,[status(thm)],[fact_int__nat__eq]) ).

fof(i_0_5999,plain,
    ! [X66,X65] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X65),X66))
       => c_Nat__Transfer_Otsub(X66,X65) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X66),X65) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X65),X66))
       => c_Nat__Transfer_Otsub(X66,X65) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(fof_simplification,[status(thm)],[fact_tsub__def]) ).

fof(i_0_6000,plain,
    ! [X136,X58] :
      ( class_Int_Onumber__ring(X58)
     => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)))
         => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X58),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)) = c_Groups_Ozero__class_Ozero(X58) )
        & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)))
         => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X58),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)) = hAPP(c_Int_Onumber__class_Onumber__of(X58),X136) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_of__nat__number__of__eq]) ).

fof(i_0_6001,plain,
    ! [X33576,X33577] : ~ hBOOL(hAPP(hAPP(c_List_Omember(X33577),c_List_Olist_ONil(X33577)),X33576)),
    inference(variable_rename,[status(thm)],[i_0_5224]) ).

fof(i_0_6002,plain,
    ! [X22257,X22258] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X22258,X22257) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(X22258,X22257)),
    inference(variable_rename,[status(thm)],[fact_mod__nat__def]) ).

fof(i_0_6003,plain,
    ! [X239,X5,X25,X18] :
      ( ~ hBOOL(hAPP(X18,X25))
     => c_List_Oremove1(X5,X25,hAPP(c_List_Ofilter(X5,X18),X239)) = hAPP(c_List_Ofilter(X5,X18),X239) ),
    inference(fof_simplification,[status(thm)],[fact_remove1__filter__not]) ).

fof(i_0_6004,plain,
    ! [X22345,X22346] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X22346),X22345) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(X22346,X22345)),
    inference(variable_rename,[status(thm)],[fact_div__nat__def]) ).

fof(i_0_6005,plain,
    ! [X136] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)))
       => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)))
       => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136) ) ),
    inference(fof_simplification,[status(thm)],[fact_int__nat__number__of]) ).

fof(i_0_6006,plain,
    ! [X98] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X98),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X98) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X98) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X98),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X98) = X98 ) ),
    inference(fof_simplification,[status(thm)],[fact_zabs__def]) ).

fof(i_0_6007,plain,
    ! [X65,X66] :
      ( X66 != X65
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X66),X65))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X65),X66)) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__neqE__nat]) ).

fof(i_0_6008,plain,
    ! [X21874,X21875,X21876] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X21876,X21875),X21874))
      | c_Divides_Odivmod__nat(X21876,X21875) = X21874 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__nat__eq])]) ).

fof(i_0_6009,plain,
    ! [X98] :
      ( ( X98 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Groups_Osgn__class_Osgn(tc_Int_Oint,X98) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( X98 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X98))
           => c_Groups_Osgn__class_Osgn(tc_Int_Oint,X98) = c_Groups_Oone__class_Oone(tc_Int_Oint) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X98))
           => c_Groups_Osgn__class_Osgn(tc_Int_Oint,X98) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_zsgn__def]) ).

fof(i_0_6010,plain,
    ! [X31545,X31546] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(X31546,X31545)),
    inference(variable_rename,[status(thm)],[fact_sorted__upt]) ).

fof(i_0_6011,plain,
    ! [X28115,X28116] : c_Wellfounded_Owf(X28116,hAPP(c_Wellfounded_Omeasure(X28116),X28115)),
    inference(variable_rename,[status(thm)],[fact_wf__measure]) ).

fof(i_0_6012,plain,
    ! [X66,X58] :
      ( class_Orderings_Opreorder(X58)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X58),X66),X66)) ),
    inference(fof_simplification,[status(thm)],[fact_order__less__irrefl]) ).

fof(i_0_6013,plain,
    ! [X99,X96] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X96),X99))
       => c_Quickcheck_Obeyond(X96,X99) = X99 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X96),X99))
       => c_Quickcheck_Obeyond(X96,X99) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(fof_simplification,[status(thm)],[fact_beyond__def]) ).

fof(i_0_6014,plain,
    ! [X29421] : c_List_Orotate(X29421,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(X29421)),
    inference(variable_rename,[status(thm)],[fact_rotate0]) ).

fof(i_0_6015,plain,
    ! [X57] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X57),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_simplification,[status(thm)],[fact_less__nat__zero__code]) ).

fof(i_0_6016,plain,
    ! [X57] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X57),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_simplification,[status(thm)],[fact_not__less0]) ).

fof(i_0_6017,plain,
    ! [X57] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X57),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_simplification,[status(thm)],[fact_less__zeroE]) ).

fof(i_0_6018,plain,
    ! [X21849] : c_Divides_Odivmod__nat(X21849,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)),X21849),
    inference(variable_rename,[status(thm)],[fact_divmod__nat__zero]) ).

fof(i_0_6019,plain,
    ! [X57] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X57),X57)),
    inference(fof_simplification,[status(thm)],[fact_less__not__refl]) ).

fof(i_0_6020,plain,
    ! [X57] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X57),X57)),
    inference(fof_simplification,[status(thm)],[fact_less__irrefl__nat]) ).

fof(i_0_6021,plain,
    ! [X21050,X21051] :
      ( ( c_Int_OBit0(X21051) != c_Int_OBit0(X21050)
        | X21051 = X21050 )
      & ( X21051 != X21050
        | c_Int_OBit0(X21051) = c_Int_OBit0(X21050) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I48_J])]) ).

fof(i_0_6022,plain,
    ! [X1,X21,X5,X20] :
      ( class_Groups_Ocomm__monoid__add(X20)
     => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X1),X21) = c_Groups_Ozero__class_Ozero(X20) ) ),
    inference(fof_simplification,[status(thm)],[fact_setsum_Oinfinite]) ).

fof(i_0_6023,plain,
    ! [X2,X21,X5,X20] :
      ( class_Groups_Ocomm__monoid__add(X20)
     => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X20),X2),X21) = c_Groups_Ozero__class_Ozero(X20) ) ),
    inference(fof_simplification,[status(thm)],[fact_setsum__infinite]) ).

fof(i_0_6024,plain,
    ! [X1,X21,X5,X20] :
      ( class_Groups_Ocomm__monoid__mult(X20)
     => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X1),X21) = c_Groups_Oone__class_Oone(X20) ) ),
    inference(fof_simplification,[status(thm)],[fact_setprod_Oinfinite]) ).

fof(i_0_6025,plain,
    ! [X2,X21,X5,X20] :
      ( class_Groups_Ocomm__monoid__mult(X20)
     => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X5,X20),X2),X21) = c_Groups_Oone__class_Oone(X20) ) ),
    inference(fof_simplification,[status(thm)],[fact_setprod__infinite]) ).

fof(i_0_6026,plain,
    ! [X57] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X57))),
    inference(fof_simplification,[status(thm)],[fact_not__neg__int]) ).

fof(i_0_6027,plain,
    ! [X171,X21,X5] :
      ( c_Equiv__Relations_Oequiv(X5,X21,X171)
     => ~ ( c_Relation_Orefl__on(X5,X21,X171)
         => ( c_Relation_Osym(X5,X171)
           => ~ c_Relation_Otrans(X5,X171) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_equivE]) ).

fof(i_0_6028,plain,
    ! [X21653] : c_Code__Numeral_OSuc__code__numeral(X21653) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
    inference(variable_rename,[status(thm)],[fact_code__numeral_Osimps_I3_J]) ).

fof(i_0_6029,plain,
    ! [X21652] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(X21652),
    inference(variable_rename,[status(thm)],[fact_code__numeral_Osimps_I2_J]) ).

fof(i_0_6030,plain,
    ! [X16,X18] :
      ( ~ hBOOL(hAPP(hAPP(c_fimplies,X18),X16))
      | ~ hBOOL(X18)
      | hBOOL(X16) ),
    inference(fof_simplification,[status(thm)],[help_c__fimplies__3]) ).

fof(i_0_6031,plain,
    ! [X21,X5] :
      ( hAPP(c_Finite__Set_Ocard(X5),X21) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> ( X21 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21)) ) ),
    inference(fof_simplification,[status(thm)],[fact_card__eq__0__iff]) ).

fof(i_0_6032,plain,
    ! [X16,X18] :
      ( ~ hBOOL(hAPP(hAPP(c_fdisj,X18),X16))
      | hBOOL(X18)
      | hBOOL(X16) ),
    inference(fof_simplification,[status(thm)],[help_c__fdisj__3]) ).

fof(i_0_6033,plain,
    ! [X16,X18] :
      ( ~ hBOOL(hAPP(hAPP(c_fconj,X18),X16))
      | hBOOL(X18) ),
    inference(fof_simplification,[status(thm)],[help_c__fconj__2]) ).

fof(i_0_6034,plain,
    ! [X16,X18] :
      ( ~ hBOOL(hAPP(hAPP(c_fconj,X18),X16))
      | hBOOL(X16) ),
    inference(fof_simplification,[status(thm)],[help_c__fconj__3]) ).

fof(i_0_6035,plain,
    ! [X18,X5] :
      ( c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X5),X18)
    <=> ! [X3] : ~ hBOOL(hAPP(X18,X3)) ),
    inference(fof_simplification,[status(thm)],[fact_empty__Collect__eq]) ).

fof(i_0_6036,plain,
    ! [X18,X5] :
      ( hAPP(c_Set_OCollect(X5),X18) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
    <=> ! [X3] : ~ hBOOL(hAPP(X18,X3)) ),
    inference(fof_simplification,[status(thm)],[fact_Collect__empty__eq]) ).

fof(i_0_6037,plain,
    ! [X33,X25] :
      ( ~ hBOOL(hAPP(hAPP(c_fequal,X25),X33))
      | X25 = X33 ),
    inference(fof_simplification,[status(thm)],[help_c__fequal__1]) ).

fof(i_0_6038,plain,
    ! [X30389] : hAPP(c_Code__Numeral_Onat__of,X30389) = c_Code__Numeral_Onat__of__aux(X30389,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[fact_nat__of__code]) ).

fof(i_0_6039,plain,
    ! [X18,X5] : ~ c_List_Olist__ex1(X5,X18,c_List_Olist_ONil(X5)),
    inference(fof_simplification,[status(thm)],[fact_list__ex1__simps_I1_J]) ).

fof(i_0_6040,plain,
    ! [X18,X5] : ~ c_List_Olist__ex(X5,X18,c_List_Olist_ONil(X5)),
    inference(fof_simplification,[status(thm)],[fact_list__ex__simps_I2_J]) ).

fof(i_0_6041,plain,
    ! [X20866] : c_Int_Osucc(X20866) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20866),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(variable_rename,[status(thm)],[fact_succ__def]) ).

fof(i_0_6042,plain,
    ! [X20857] : c_Int_Opred(X20857) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20857),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(variable_rename,[status(thm)],[fact_pred__def]) ).

fof(i_0_6043,plain,
    ! [X31356] : c_List_Oupt(X31356,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_6044,plain,
    ! [X16,X18] :
      ( ~ hBOOL(X18)
      | ~ hBOOL(X16)
      | hBOOL(hAPP(hAPP(c_fconj,X18),X16)) ),
    inference(fof_simplification,[status(thm)],[help_c__fconj__1]) ).

fof(i_0_6045,plain,
    ! [X20858] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),X20858) = c_Int_Opred(X20858),
    inference(variable_rename,[status(thm)],[fact_add__Min]) ).

fof(i_0_6046,plain,
    ! [X58] :
      ( class_Int_Onumber__ring(X58)
     => ~ c_Int_Oiszero(X58,hAPP(c_Int_Onumber__class_Onumber__of(X58),c_Int_OMin)) ),
    inference(fof_simplification,[status(thm)],[fact_nonzero__number__of__Min]) ).

fof(i_0_6047,plain,
    ! [X16,X18] :
      ( ~ hBOOL(X18)
      | hBOOL(hAPP(hAPP(c_fdisj,X18),X16)) ),
    inference(fof_simplification,[status(thm)],[help_c__fdisj__1]) ).

fof(i_0_6048,plain,
    ! [X18,X16] :
      ( ~ hBOOL(X16)
      | hBOOL(hAPP(hAPP(c_fdisj,X18),X16)) ),
    inference(fof_simplification,[status(thm)],[help_c__fdisj__2]) ).

fof(i_0_6049,plain,
    ! [X18,X16] :
      ( ~ hBOOL(X16)
      | hBOOL(hAPP(hAPP(c_fimplies,X18),X16)) ),
    inference(fof_simplification,[status(thm)],[help_c__fimplies__2]) ).

fof(i_0_6050,plain,
    ! [X21061] :
      ( ( c_Int_OPls != c_Int_OBit0(X21061)
        | c_Int_OPls = X21061 )
      & ( c_Int_OPls != X21061
        | c_Int_OPls = c_Int_OBit0(X21061) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I38_J])]) ).

fof(i_0_6051,plain,
    ! [X21060] :
      ( ( c_Int_OBit0(X21060) != c_Int_OPls
        | X21060 = c_Int_OPls )
      & ( X21060 != c_Int_OPls
        | c_Int_OBit0(X21060) = c_Int_OPls ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I44_J])]) ).

fof(i_0_6052,plain,
    ! [X21074] : c_Int_OBit0(X21074) != c_Int_OMin,
    inference(variable_rename,[status(thm)],[fact_rel__simps_I45_J]) ).

fof(i_0_6053,plain,
    ! [X21075] : c_Int_OMin != c_Int_OBit0(X21075),
    inference(variable_rename,[status(thm)],[fact_rel__simps_I42_J]) ).

fof(i_0_6054,plain,
    ! [X94] :
      ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X94))
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X94)) = X94 ),
    inference(fof_simplification,[status(thm)],[fact_not__neg__nat]) ).

fof(i_0_6055,plain,
    ! [X21,X5] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X21))
     => hAPP(c_Finite__Set_Ocard(X5),X21) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(fof_simplification,[status(thm)],[fact_card__infinite]) ).

fof(i_0_6056,plain,
    ! [X18] :
      ( ~ hBOOL(hAPP(c_fNot,X18))
      | ~ hBOOL(X18) ),
    inference(fof_simplification,[status(thm)],[help_c__fNot__1]) ).

fof(i_0_6057,plain,
    ! [X58] :
      ( class_Rings_Osemiring__1(X58)
     => ~ c_Int_Oiszero(X58,c_Groups_Oone__class_Oone(X58)) ),
    inference(fof_simplification,[status(thm)],[fact_not__iszero__1]) ).

fof(i_0_6058,plain,
    ! [X32,X5] :
      ( c_Equiv__Relations_Oequivp(X5,X32)
     => ~ ( c_Predicate_Oreflp(X5,X32)
         => ( c_Predicate_Osymp(X5,X32)
           => ~ c_Predicate_Otransp(X5,X32) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_equivpE]) ).

fof(i_0_6059,plain,
    ! [X18] :
      ( hBOOL(X18)
      | hBOOL(hAPP(c_fNot,X18)) ),
    inference(fof_simplification,[status(thm)],[help_c__fNot__2]) ).

fof(i_0_6060,plain,
    ! [X25238,X25239,X25240,X25241,X25242,X25243,X25244,X25245,X25246,X25247,X25248] :
      ( ( hBOOL(hAPP(hAPP(c_member(X25248),esk161_11(X25238,X25239,X25240,X25241,X25242,X25243,X25244,X25245,X25246,X25247,X25248)),X25247))
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X25242,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25248,tc_fun(X25242,tc_HOL_Obool)),X25240),hAPP(hAPP(c_COMBB(tc_fun(X25245,tc_fun(X25242,tc_HOL_Obool)),tc_fun(X25242,tc_HOL_Obool),X25248),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25245,tc_fun(X25242,tc_HOL_Obool)),X25239)),X25241))),X25238))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X25245,tc_HOL_Obool)),X25239),hAPP(hAPP(c_Equiv__Relations_Oquotient(X25245),X25244),X25243)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X25248,tc_HOL_Obool)),X25240),hAPP(hAPP(c_Equiv__Relations_Oquotient(X25248),X25247),X25246)))
        | ~ c_Equiv__Relations_Ocongruent2(X25248,X25245,tc_fun(X25242,tc_HOL_Obool),X25246,X25243,X25241)
        | ~ c_Equiv__Relations_Oequiv(X25245,X25244,X25243)
        | ~ c_Equiv__Relations_Oequiv(X25248,X25247,X25246) )
      & ( hBOOL(hAPP(hAPP(c_member(X25245),esk162_11(X25238,X25239,X25240,X25241,X25242,X25243,X25244,X25245,X25246,X25247,X25248)),X25244))
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X25242,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25248,tc_fun(X25242,tc_HOL_Obool)),X25240),hAPP(hAPP(c_COMBB(tc_fun(X25245,tc_fun(X25242,tc_HOL_Obool)),tc_fun(X25242,tc_HOL_Obool),X25248),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25245,tc_fun(X25242,tc_HOL_Obool)),X25239)),X25241))),X25238))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X25245,tc_HOL_Obool)),X25239),hAPP(hAPP(c_Equiv__Relations_Oquotient(X25245),X25244),X25243)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X25248,tc_HOL_Obool)),X25240),hAPP(hAPP(c_Equiv__Relations_Oquotient(X25248),X25247),X25246)))
        | ~ c_Equiv__Relations_Ocongruent2(X25248,X25245,tc_fun(X25242,tc_HOL_Obool),X25246,X25243,X25241)
        | ~ c_Equiv__Relations_Oequiv(X25245,X25244,X25243)
        | ~ c_Equiv__Relations_Oequiv(X25248,X25247,X25246) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X25242,tc_HOL_Obool)),hAPP(hAPP(X25241,esk161_11(X25238,X25239,X25240,X25241,X25242,X25243,X25244,X25245,X25246,X25247,X25248)),esk162_11(X25238,X25239,X25240,X25241,X25242,X25243,X25244,X25245,X25246,X25247,X25248))),X25238))
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X25242,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25248,tc_fun(X25242,tc_HOL_Obool)),X25240),hAPP(hAPP(c_COMBB(tc_fun(X25245,tc_fun(X25242,tc_HOL_Obool)),tc_fun(X25242,tc_HOL_Obool),X25248),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25245,tc_fun(X25242,tc_HOL_Obool)),X25239)),X25241))),X25238))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X25245,tc_HOL_Obool)),X25239),hAPP(hAPP(c_Equiv__Relations_Oquotient(X25245),X25244),X25243)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X25248,tc_HOL_Obool)),X25240),hAPP(hAPP(c_Equiv__Relations_Oquotient(X25248),X25247),X25246)))
        | ~ c_Equiv__Relations_Ocongruent2(X25248,X25245,tc_fun(X25242,tc_HOL_Obool),X25246,X25243,X25241)
        | ~ c_Equiv__Relations_Oequiv(X25245,X25244,X25243)
        | ~ c_Equiv__Relations_Oequiv(X25248,X25247,X25246) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__equiv__class__type2])])])]) ).

cnf(i_0_6061,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_5225]) ).

cnf(i_0_6062,plain,
    c_Int_Osucc(c_Int_OBit0(X1)) = c_Int_OBit1(X1),
    inference(split_conjunct,[status(thm)],[i_0_5226]) ).

cnf(i_0_6063,plain,
    c_Int_OBit0(X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1),
    inference(split_conjunct,[status(thm)],[i_0_5227]) ).

cnf(i_0_6064,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_5228]) ).

fof(i_0_6065,plain,
    ! [X27898,X27899,X27900,X27901,X27902,X27903,X27904] :
      ( ~ class_Rings_Osemiring__0(X27904)
      | ~ c_Fun_Oinj__on(tc_prod(X27903,X27902),X27904,hAPP(c_Product__Type_Oprod_Oprod__case(X27903,X27902,X27904),hAPP(hAPP(c_COMBC(X27903,tc_fun(X27902,X27904),tc_fun(X27902,X27904)),hAPP(hAPP(c_COMBB(tc_fun(X27904,X27904),tc_fun(tc_fun(X27902,X27904),tc_fun(X27902,X27904)),X27903),c_COMBB(X27904,X27904,X27902)),hAPP(hAPP(c_COMBB(X27904,tc_fun(X27904,X27904),X27903),c_Groups_Otimes__class_Otimes(X27904)),X27901))),X27900)),hAPP(hAPP(c_Product__Type_OSigma(X27903,X27902),X27899),hAPP(c_COMBK(tc_fun(X27902,tc_HOL_Obool),X27903),X27898)))
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27904),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27903,X27904),X27901),X27899)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27902,X27904),X27900),X27898)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27904,X27904),c_Fun_Oid(X27904)),hAPP(c_Set_OCollect(X27904),hAPP(hAPP(c_COMBB(tc_fun(X27903,tc_HOL_Obool),tc_HOL_Obool,X27904),c_HOL_OEx(X27903)),hAPP(hAPP(c_COMBB(tc_fun(X27903,tc_fun(X27902,tc_HOL_Obool)),tc_fun(X27903,tc_HOL_Obool),X27904),hAPP(c_COMBB(tc_fun(X27902,tc_HOL_Obool),tc_HOL_Obool,X27903),c_HOL_OEx(X27902))),hAPP(hAPP(c_COMBC(X27904,tc_fun(X27903,tc_fun(X27902,tc_HOL_Obool)),tc_fun(X27903,tc_fun(X27902,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X27903,tc_fun(tc_fun(X27902,tc_HOL_Obool),tc_fun(X27902,tc_HOL_Obool))),tc_fun(tc_fun(X27903,tc_fun(X27902,tc_HOL_Obool)),tc_fun(X27903,tc_fun(X27902,tc_HOL_Obool))),X27904),c_COMBS(X27903,tc_fun(X27902,tc_HOL_Obool),tc_fun(X27902,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X27903,tc_fun(X27902,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X27903,tc_fun(tc_fun(X27902,tc_HOL_Obool),tc_fun(X27902,tc_HOL_Obool))),X27904),hAPP(c_COMBB(tc_fun(X27902,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X27902,tc_HOL_Obool),tc_fun(X27902,tc_HOL_Obool)),X27903),c_COMBS(X27902,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X27903,tc_fun(X27902,tc_HOL_Obool)),tc_fun(X27903,tc_fun(X27902,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X27904),hAPP(c_COMBB(tc_fun(X27902,tc_HOL_Obool),tc_fun(X27902,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X27903),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27902),c_fconj))),hAPP(hAPP(c_COMBC(X27904,tc_fun(X27903,tc_fun(X27902,X27904)),tc_fun(X27903,tc_fun(X27902,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X27902,X27904),tc_fun(X27902,tc_HOL_Obool)),tc_fun(tc_fun(X27903,tc_fun(X27902,X27904)),tc_fun(X27903,tc_fun(X27902,tc_HOL_Obool))),X27904),c_COMBB(tc_fun(X27902,X27904),tc_fun(X27902,tc_HOL_Obool),X27903)),hAPP(hAPP(c_COMBB(tc_fun(X27904,tc_HOL_Obool),tc_fun(tc_fun(X27902,X27904),tc_fun(X27902,tc_HOL_Obool)),X27904),c_COMBB(X27904,tc_HOL_Obool,X27902)),c_fequal))),hAPP(hAPP(c_COMBC(X27903,tc_fun(X27902,X27904),tc_fun(X27902,X27904)),hAPP(hAPP(c_COMBB(tc_fun(X27904,X27904),tc_fun(tc_fun(X27902,X27904),tc_fun(X27902,X27904)),X27903),c_COMBB(X27904,X27904,X27902)),hAPP(hAPP(c_COMBB(X27904,tc_fun(X27904,X27904),X27903),c_Groups_Otimes__class_Otimes(X27904)),X27901))),X27900)))))),hAPP(hAPP(c_COMBC(X27903,tc_fun(X27902,tc_HOL_Obool),tc_fun(X27902,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X27902,tc_HOL_Obool),tc_fun(X27902,tc_HOL_Obool)),X27903),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X27902)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27903),c_fconj),hAPP(hAPP(c_COMBC(X27903,tc_fun(X27903,tc_HOL_Obool),tc_HOL_Obool),c_member(X27903)),X27899)))),hAPP(hAPP(c_COMBC(X27902,tc_fun(X27902,tc_HOL_Obool),tc_HOL_Obool),c_member(X27902)),X27898))))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__mult__setsum__if__inj])]) ).

fof(i_0_6066,plain,
    ! [X27985,X27986,X27987,X27988,X27989] : hAPP(hAPP(c_Relation_Orel__comp(X27989,X27988,X27987),X27986),X27985) = hAPP(c_Set_OCollect(tc_prod(X27989,X27987)),hAPP(c_Product__Type_Oprod_Oprod__case(X27989,X27987,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X27987,tc_fun(X27988,tc_HOL_Obool)),tc_fun(X27987,tc_HOL_Obool),X27989),hAPP(c_COMBB(tc_fun(X27988,tc_HOL_Obool),tc_HOL_Obool,X27987),c_HOL_OEx(X27988))),hAPP(hAPP(c_COMBC(X27989,tc_fun(X27987,tc_fun(X27988,tc_HOL_Obool)),tc_fun(X27987,tc_fun(X27988,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X27988,tc_HOL_Obool),tc_fun(X27988,tc_HOL_Obool)),tc_fun(tc_fun(X27987,tc_fun(X27988,tc_HOL_Obool)),tc_fun(X27987,tc_fun(X27988,tc_HOL_Obool))),X27989),c_COMBB(tc_fun(X27988,tc_HOL_Obool),tc_fun(X27988,tc_HOL_Obool),X27987)),hAPP(hAPP(c_COMBB(tc_fun(X27988,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X27988,tc_HOL_Obool),tc_fun(X27988,tc_HOL_Obool)),X27989),c_COMBS(X27988,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27988,tc_HOL_Obool),tc_fun(X27988,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X27989),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27988),c_fconj)),hAPP(hAPP(c_COMBC(X27989,tc_fun(tc_prod(X27989,X27988),tc_HOL_Obool),tc_fun(X27988,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27988,tc_fun(tc_fun(tc_prod(X27989,X27988),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X27989,X27988),tc_HOL_Obool),tc_fun(X27988,tc_HOL_Obool)),X27989),c_COMBC(X27988,tc_fun(tc_prod(X27989,X27988),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27988,tc_prod(X27989,X27988)),tc_fun(X27988,tc_fun(tc_fun(tc_prod(X27989,X27988),tc_HOL_Obool),tc_HOL_Obool)),X27989),hAPP(c_COMBB(tc_prod(X27989,X27988),tc_fun(tc_fun(tc_prod(X27989,X27988),tc_HOL_Obool),tc_HOL_Obool),X27988),c_member(tc_prod(X27989,X27988)))),c_Product__Type_OPair(X27989,X27988)))),X27986))))),hAPP(hAPP(c_COMBC(X27987,tc_fun(tc_prod(X27988,X27987),tc_HOL_Obool),tc_fun(X27988,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27988,tc_fun(tc_fun(tc_prod(X27988,X27987),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X27988,X27987),tc_HOL_Obool),tc_fun(X27988,tc_HOL_Obool)),X27987),c_COMBC(X27988,tc_fun(tc_prod(X27988,X27987),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27988,tc_prod(X27988,X27987)),tc_fun(X27988,tc_fun(tc_fun(tc_prod(X27988,X27987),tc_HOL_Obool),tc_HOL_Obool)),X27987),hAPP(c_COMBB(tc_prod(X27988,X27987),tc_fun(tc_fun(tc_prod(X27988,X27987),tc_HOL_Obool),tc_HOL_Obool),X27988),c_member(tc_prod(X27988,X27987)))),hAPP(c_COMBC(X27988,X27987,tc_prod(X27988,X27987)),c_Product__Type_OPair(X27988,X27987))))),X27985))))),
    inference(variable_rename,[status(thm)],[fact_rel__comp__def]) ).

fof(i_0_6067,plain,
    ! [X27884,X27885,X27886] :
      ( ~ class_Orderings_Olinorder(X27886)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27886),X27885))
      | X27885 = c_Orderings_Obot__class_Obot(tc_fun(X27886,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27886),X27884))
      | X27884 = c_Orderings_Obot__class_Obot(tc_fun(X27886,tc_HOL_Obool))
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X27886),c_Big__Operators_Olattice_OInf__fin(X27886,c_Orderings_Oord__class_Omin(X27886),X27885)),c_Big__Operators_Olattice_OInf__fin(X27886,c_Orderings_Oord__class_Omin(X27886),X27884)) = c_Big__Operators_Olattice_OInf__fin(X27886,c_Orderings_Oord__class_Omin(X27886),hAPP(c_Set_OCollect(X27886),hAPP(hAPP(c_COMBB(tc_fun(X27886,tc_HOL_Obool),tc_HOL_Obool,X27886),c_HOL_OEx(X27886)),hAPP(hAPP(c_COMBB(tc_fun(X27886,tc_fun(X27886,tc_HOL_Obool)),tc_fun(X27886,tc_HOL_Obool),X27886),hAPP(c_COMBB(tc_fun(X27886,tc_HOL_Obool),tc_HOL_Obool,X27886),c_HOL_OEx(X27886))),hAPP(hAPP(c_COMBC(X27886,tc_fun(X27886,tc_fun(X27886,tc_HOL_Obool)),tc_fun(X27886,tc_fun(X27886,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X27886,tc_fun(tc_fun(X27886,tc_HOL_Obool),tc_fun(X27886,tc_HOL_Obool))),tc_fun(tc_fun(X27886,tc_fun(X27886,tc_HOL_Obool)),tc_fun(X27886,tc_fun(X27886,tc_HOL_Obool))),X27886),c_COMBS(X27886,tc_fun(X27886,tc_HOL_Obool),tc_fun(X27886,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X27886,tc_fun(X27886,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X27886,tc_fun(tc_fun(X27886,tc_HOL_Obool),tc_fun(X27886,tc_HOL_Obool))),X27886),hAPP(c_COMBB(tc_fun(X27886,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X27886,tc_HOL_Obool),tc_fun(X27886,tc_HOL_Obool)),X27886),c_COMBS(X27886,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X27886,tc_fun(X27886,tc_HOL_Obool)),tc_fun(X27886,tc_fun(X27886,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X27886),hAPP(c_COMBB(tc_fun(X27886,tc_HOL_Obool),tc_fun(X27886,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X27886),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27886),c_fconj))),hAPP(hAPP(c_COMBC(X27886,tc_fun(X27886,tc_fun(X27886,X27886)),tc_fun(X27886,tc_fun(X27886,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X27886,X27886),tc_fun(X27886,tc_HOL_Obool)),tc_fun(tc_fun(X27886,tc_fun(X27886,X27886)),tc_fun(X27886,tc_fun(X27886,tc_HOL_Obool))),X27886),c_COMBB(tc_fun(X27886,X27886),tc_fun(X27886,tc_HOL_Obool),X27886)),hAPP(hAPP(c_COMBB(tc_fun(X27886,tc_HOL_Obool),tc_fun(tc_fun(X27886,X27886),tc_fun(X27886,tc_HOL_Obool)),X27886),c_COMBB(X27886,tc_HOL_Obool,X27886)),c_fequal))),c_Orderings_Oord__class_Omax(X27886)))))),hAPP(hAPP(c_COMBC(X27886,tc_fun(X27886,tc_HOL_Obool),tc_fun(X27886,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X27886,tc_HOL_Obool),tc_fun(X27886,tc_HOL_Obool)),X27886),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X27886)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27886),c_fconj),hAPP(hAPP(c_COMBC(X27886,tc_fun(X27886,tc_HOL_Obool),tc_HOL_Obool),c_member(X27886)),X27885)))),hAPP(hAPP(c_COMBC(X27886,tc_fun(X27886,tc_HOL_Obool),tc_HOL_Obool),c_member(X27886)),X27884))))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__Inf2__distrib])]) ).

fof(i_0_6068,plain,
    ! [X27836,X27837,X27838] :
      ( ~ class_Orderings_Olinorder(X27838)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27838),X27837))
      | X27837 = c_Orderings_Obot__class_Obot(tc_fun(X27838,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27838),X27836))
      | X27836 = c_Orderings_Obot__class_Obot(tc_fun(X27838,tc_HOL_Obool))
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X27838),c_Big__Operators_Olattice_OSup__fin(X27838,c_Orderings_Oord__class_Omax(X27838),X27837)),c_Big__Operators_Olattice_OSup__fin(X27838,c_Orderings_Oord__class_Omax(X27838),X27836)) = c_Big__Operators_Olattice_OSup__fin(X27838,c_Orderings_Oord__class_Omax(X27838),hAPP(c_Set_OCollect(X27838),hAPP(hAPP(c_COMBB(tc_fun(X27838,tc_HOL_Obool),tc_HOL_Obool,X27838),c_HOL_OEx(X27838)),hAPP(hAPP(c_COMBB(tc_fun(X27838,tc_fun(X27838,tc_HOL_Obool)),tc_fun(X27838,tc_HOL_Obool),X27838),hAPP(c_COMBB(tc_fun(X27838,tc_HOL_Obool),tc_HOL_Obool,X27838),c_HOL_OEx(X27838))),hAPP(hAPP(c_COMBC(X27838,tc_fun(X27838,tc_fun(X27838,tc_HOL_Obool)),tc_fun(X27838,tc_fun(X27838,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X27838,tc_fun(tc_fun(X27838,tc_HOL_Obool),tc_fun(X27838,tc_HOL_Obool))),tc_fun(tc_fun(X27838,tc_fun(X27838,tc_HOL_Obool)),tc_fun(X27838,tc_fun(X27838,tc_HOL_Obool))),X27838),c_COMBS(X27838,tc_fun(X27838,tc_HOL_Obool),tc_fun(X27838,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X27838,tc_fun(X27838,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X27838,tc_fun(tc_fun(X27838,tc_HOL_Obool),tc_fun(X27838,tc_HOL_Obool))),X27838),hAPP(c_COMBB(tc_fun(X27838,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X27838,tc_HOL_Obool),tc_fun(X27838,tc_HOL_Obool)),X27838),c_COMBS(X27838,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X27838,tc_fun(X27838,tc_HOL_Obool)),tc_fun(X27838,tc_fun(X27838,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X27838),hAPP(c_COMBB(tc_fun(X27838,tc_HOL_Obool),tc_fun(X27838,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X27838),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27838),c_fconj))),hAPP(hAPP(c_COMBC(X27838,tc_fun(X27838,tc_fun(X27838,X27838)),tc_fun(X27838,tc_fun(X27838,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X27838,X27838),tc_fun(X27838,tc_HOL_Obool)),tc_fun(tc_fun(X27838,tc_fun(X27838,X27838)),tc_fun(X27838,tc_fun(X27838,tc_HOL_Obool))),X27838),c_COMBB(tc_fun(X27838,X27838),tc_fun(X27838,tc_HOL_Obool),X27838)),hAPP(hAPP(c_COMBB(tc_fun(X27838,tc_HOL_Obool),tc_fun(tc_fun(X27838,X27838),tc_fun(X27838,tc_HOL_Obool)),X27838),c_COMBB(X27838,tc_HOL_Obool,X27838)),c_fequal))),c_Orderings_Oord__class_Omin(X27838)))))),hAPP(hAPP(c_COMBC(X27838,tc_fun(X27838,tc_HOL_Obool),tc_fun(X27838,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X27838,tc_HOL_Obool),tc_fun(X27838,tc_HOL_Obool)),X27838),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X27838)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27838),c_fconj),hAPP(hAPP(c_COMBC(X27838,tc_fun(X27838,tc_HOL_Obool),tc_HOL_Obool),c_member(X27838)),X27837)))),hAPP(hAPP(c_COMBC(X27838,tc_fun(X27838,tc_HOL_Obool),tc_HOL_Obool),c_member(X27838)),X27836))))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__Sup2__distrib])]) ).

fof(i_0_6069,plain,
    ! [X27878,X27879,X27880] :
      ( ~ class_Lattices_Odistrib__lattice(X27880)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27880),X27879))
      | X27879 = c_Orderings_Obot__class_Obot(tc_fun(X27880,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27880),X27878))
      | X27878 = c_Orderings_Obot__class_Obot(tc_fun(X27880,tc_HOL_Obool))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27880),c_Big__Operators_Olattice__class_OSup__fin(X27880,X27879)),c_Big__Operators_Olattice__class_OSup__fin(X27880,X27878)) = c_Big__Operators_Olattice__class_OSup__fin(X27880,hAPP(c_Set_OCollect(X27880),hAPP(hAPP(c_COMBB(tc_fun(X27880,tc_HOL_Obool),tc_HOL_Obool,X27880),c_HOL_OEx(X27880)),hAPP(hAPP(c_COMBB(tc_fun(X27880,tc_fun(X27880,tc_HOL_Obool)),tc_fun(X27880,tc_HOL_Obool),X27880),hAPP(c_COMBB(tc_fun(X27880,tc_HOL_Obool),tc_HOL_Obool,X27880),c_HOL_OEx(X27880))),hAPP(hAPP(c_COMBC(X27880,tc_fun(X27880,tc_fun(X27880,tc_HOL_Obool)),tc_fun(X27880,tc_fun(X27880,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X27880,tc_fun(tc_fun(X27880,tc_HOL_Obool),tc_fun(X27880,tc_HOL_Obool))),tc_fun(tc_fun(X27880,tc_fun(X27880,tc_HOL_Obool)),tc_fun(X27880,tc_fun(X27880,tc_HOL_Obool))),X27880),c_COMBS(X27880,tc_fun(X27880,tc_HOL_Obool),tc_fun(X27880,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X27880,tc_fun(X27880,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X27880,tc_fun(tc_fun(X27880,tc_HOL_Obool),tc_fun(X27880,tc_HOL_Obool))),X27880),hAPP(c_COMBB(tc_fun(X27880,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X27880,tc_HOL_Obool),tc_fun(X27880,tc_HOL_Obool)),X27880),c_COMBS(X27880,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X27880,tc_fun(X27880,tc_HOL_Obool)),tc_fun(X27880,tc_fun(X27880,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X27880),hAPP(c_COMBB(tc_fun(X27880,tc_HOL_Obool),tc_fun(X27880,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X27880),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27880),c_fconj))),hAPP(hAPP(c_COMBC(X27880,tc_fun(X27880,tc_fun(X27880,X27880)),tc_fun(X27880,tc_fun(X27880,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X27880,X27880),tc_fun(X27880,tc_HOL_Obool)),tc_fun(tc_fun(X27880,tc_fun(X27880,X27880)),tc_fun(X27880,tc_fun(X27880,tc_HOL_Obool))),X27880),c_COMBB(tc_fun(X27880,X27880),tc_fun(X27880,tc_HOL_Obool),X27880)),hAPP(hAPP(c_COMBB(tc_fun(X27880,tc_HOL_Obool),tc_fun(tc_fun(X27880,X27880),tc_fun(X27880,tc_HOL_Obool)),X27880),c_COMBB(X27880,tc_HOL_Obool,X27880)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(X27880)))))),hAPP(hAPP(c_COMBC(X27880,tc_fun(X27880,tc_HOL_Obool),tc_fun(X27880,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X27880,tc_HOL_Obool),tc_fun(X27880,tc_HOL_Obool)),X27880),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X27880)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27880),c_fconj),hAPP(hAPP(c_COMBC(X27880,tc_fun(X27880,tc_HOL_Obool),tc_HOL_Obool),c_member(X27880)),X27879)))),hAPP(hAPP(c_COMBC(X27880,tc_fun(X27880,tc_HOL_Obool),tc_HOL_Obool),c_member(X27880)),X27878))))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__Sup2__distrib])]) ).

fof(i_0_6070,plain,
    ! [X27875,X27876,X27877] :
      ( ~ class_Lattices_Odistrib__lattice(X27877)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27877),X27876))
      | X27876 = c_Orderings_Obot__class_Obot(tc_fun(X27877,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27877),X27875))
      | X27875 = c_Orderings_Obot__class_Obot(tc_fun(X27877,tc_HOL_Obool))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27877),c_Big__Operators_Olattice__class_OInf__fin(X27877,X27876)),c_Big__Operators_Olattice__class_OInf__fin(X27877,X27875)) = c_Big__Operators_Olattice__class_OInf__fin(X27877,hAPP(c_Set_OCollect(X27877),hAPP(hAPP(c_COMBB(tc_fun(X27877,tc_HOL_Obool),tc_HOL_Obool,X27877),c_HOL_OEx(X27877)),hAPP(hAPP(c_COMBB(tc_fun(X27877,tc_fun(X27877,tc_HOL_Obool)),tc_fun(X27877,tc_HOL_Obool),X27877),hAPP(c_COMBB(tc_fun(X27877,tc_HOL_Obool),tc_HOL_Obool,X27877),c_HOL_OEx(X27877))),hAPP(hAPP(c_COMBC(X27877,tc_fun(X27877,tc_fun(X27877,tc_HOL_Obool)),tc_fun(X27877,tc_fun(X27877,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X27877,tc_fun(tc_fun(X27877,tc_HOL_Obool),tc_fun(X27877,tc_HOL_Obool))),tc_fun(tc_fun(X27877,tc_fun(X27877,tc_HOL_Obool)),tc_fun(X27877,tc_fun(X27877,tc_HOL_Obool))),X27877),c_COMBS(X27877,tc_fun(X27877,tc_HOL_Obool),tc_fun(X27877,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X27877,tc_fun(X27877,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X27877,tc_fun(tc_fun(X27877,tc_HOL_Obool),tc_fun(X27877,tc_HOL_Obool))),X27877),hAPP(c_COMBB(tc_fun(X27877,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X27877,tc_HOL_Obool),tc_fun(X27877,tc_HOL_Obool)),X27877),c_COMBS(X27877,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X27877,tc_fun(X27877,tc_HOL_Obool)),tc_fun(X27877,tc_fun(X27877,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X27877),hAPP(c_COMBB(tc_fun(X27877,tc_HOL_Obool),tc_fun(X27877,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X27877),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27877),c_fconj))),hAPP(hAPP(c_COMBC(X27877,tc_fun(X27877,tc_fun(X27877,X27877)),tc_fun(X27877,tc_fun(X27877,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X27877,X27877),tc_fun(X27877,tc_HOL_Obool)),tc_fun(tc_fun(X27877,tc_fun(X27877,X27877)),tc_fun(X27877,tc_fun(X27877,tc_HOL_Obool))),X27877),c_COMBB(tc_fun(X27877,X27877),tc_fun(X27877,tc_HOL_Obool),X27877)),hAPP(hAPP(c_COMBB(tc_fun(X27877,tc_HOL_Obool),tc_fun(tc_fun(X27877,X27877),tc_fun(X27877,tc_HOL_Obool)),X27877),c_COMBB(X27877,tc_HOL_Obool,X27877)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(X27877)))))),hAPP(hAPP(c_COMBC(X27877,tc_fun(X27877,tc_HOL_Obool),tc_fun(X27877,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X27877,tc_HOL_Obool),tc_fun(X27877,tc_HOL_Obool)),X27877),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X27877)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27877),c_fconj),hAPP(hAPP(c_COMBC(X27877,tc_fun(X27877,tc_HOL_Obool),tc_HOL_Obool),c_member(X27877)),X27876)))),hAPP(hAPP(c_COMBC(X27877,tc_fun(X27877,tc_HOL_Obool),tc_HOL_Obool),c_member(X27877)),X27875))))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__Inf2__distrib])]) ).

fof(i_0_6071,plain,
    ! [X28402,X28403,X28404] : c_List_Oset__Cons(X28404,X28403,X28402) = hAPP(c_Set_OCollect(tc_List_Olist(X28404)),hAPP(hAPP(c_COMBB(tc_fun(X28404,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(X28404)),c_HOL_OEx(X28404)),hAPP(hAPP(c_COMBB(tc_fun(X28404,tc_fun(tc_List_Olist(X28404),tc_HOL_Obool)),tc_fun(X28404,tc_HOL_Obool),tc_List_Olist(X28404)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X28404),tc_HOL_Obool),tc_HOL_Obool,X28404),c_HOL_OEx(tc_List_Olist(X28404)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X28404),tc_fun(X28404,tc_fun(tc_List_Olist(X28404),tc_HOL_Obool)),tc_fun(X28404,tc_fun(tc_List_Olist(X28404),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X28404,tc_fun(tc_fun(tc_List_Olist(X28404),tc_HOL_Obool),tc_fun(tc_List_Olist(X28404),tc_HOL_Obool))),tc_fun(tc_fun(X28404,tc_fun(tc_List_Olist(X28404),tc_HOL_Obool)),tc_fun(X28404,tc_fun(tc_List_Olist(X28404),tc_HOL_Obool))),tc_List_Olist(X28404)),c_COMBS(X28404,tc_fun(tc_List_Olist(X28404),tc_HOL_Obool),tc_fun(tc_List_Olist(X28404),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X28404,tc_fun(tc_List_Olist(X28404),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X28404,tc_fun(tc_fun(tc_List_Olist(X28404),tc_HOL_Obool),tc_fun(tc_List_Olist(X28404),tc_HOL_Obool))),tc_List_Olist(X28404)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X28404),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X28404),tc_HOL_Obool),tc_fun(tc_List_Olist(X28404),tc_HOL_Obool)),X28404),c_COMBS(tc_List_Olist(X28404),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X28404,tc_fun(tc_List_Olist(X28404),tc_HOL_Obool)),tc_fun(X28404,tc_fun(tc_List_Olist(X28404),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(X28404)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X28404),tc_HOL_Obool),tc_fun(tc_List_Olist(X28404),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X28404),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X28404)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(X28404),tc_fun(X28404,tc_fun(tc_List_Olist(X28404),tc_List_Olist(X28404))),tc_fun(X28404,tc_fun(tc_List_Olist(X28404),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(X28404),tc_List_Olist(X28404)),tc_fun(tc_List_Olist(X28404),tc_HOL_Obool)),tc_fun(tc_fun(X28404,tc_fun(tc_List_Olist(X28404),tc_List_Olist(X28404))),tc_fun(X28404,tc_fun(tc_List_Olist(X28404),tc_HOL_Obool))),tc_List_Olist(X28404)),c_COMBB(tc_fun(tc_List_Olist(X28404),tc_List_Olist(X28404)),tc_fun(tc_List_Olist(X28404),tc_HOL_Obool),X28404)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X28404),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X28404),tc_List_Olist(X28404)),tc_fun(tc_List_Olist(X28404),tc_HOL_Obool)),tc_List_Olist(X28404)),c_COMBB(tc_List_Olist(X28404),tc_HOL_Obool,tc_List_Olist(X28404))),c_fequal))),c_List_Olist_OCons(X28404)))))),hAPP(hAPP(c_COMBC(X28404,tc_fun(tc_List_Olist(X28404),tc_HOL_Obool),tc_fun(tc_List_Olist(X28404),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X28404),tc_HOL_Obool),tc_fun(tc_List_Olist(X28404),tc_HOL_Obool)),X28404),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X28404))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X28404),c_fconj),hAPP(hAPP(c_COMBC(X28404,tc_fun(X28404,tc_HOL_Obool),tc_HOL_Obool),c_member(X28404)),X28403)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X28404),tc_fun(tc_List_Olist(X28404),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(X28404))),X28402)))))),
    inference(variable_rename,[status(thm)],[fact_set__Cons__def]) ).

fof(i_0_6072,plain,
    ! [X27592,X27593,X27594,X27595,X27596,X27597,X27598,X27599] :
      ( ( X27597 = hAPP(hAPP(c_Product__Type_OPair(X27599,X27598),hAPP(X27594,esk283_8(X27592,X27593,X27594,X27595,X27596,X27597,X27598,X27599))),hAPP(X27593,esk284_8(X27592,X27593,X27594,X27595,X27596,X27597,X27598,X27599)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27599,X27598)),X27597),hAPP(c_Set_Oimage(tc_prod(X27596,X27595),tc_prod(X27599,X27598),c_Product__Type_Omap__pair(X27596,X27599,X27595,X27598,X27594,X27593)),X27592))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X27596,X27595)),hAPP(hAPP(c_Product__Type_OPair(X27596,X27595),esk283_8(X27592,X27593,X27594,X27595,X27596,X27597,X27598,X27599)),esk284_8(X27592,X27593,X27594,X27595,X27596,X27597,X27598,X27599))),X27592))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27599,X27598)),X27597),hAPP(c_Set_Oimage(tc_prod(X27596,X27595),tc_prod(X27599,X27598),c_Product__Type_Omap__pair(X27596,X27599,X27595,X27598,X27594,X27593)),X27592))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5229])])])]) ).

cnf(i_0_6073,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_5230]) ).

cnf(i_0_6074,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_5231]) ).

cnf(i_0_6075,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_5232]) ).

fof(i_0_6076,plain,
    ! [X30411,X30412,X30413,X30414,X30415,X30416,X30417,X30418] :
      ( ( hBOOL(hAPP(hAPP(c_member(X30414),esk361_8(X30411,X30412,X30413,X30414,X30415,X30416,X30417,X30418)),X30413))
        | ~ hBOOL(hAPP(hAPP(c_member(X30414),X30411),X30413))
        | hAPP(c_Set_Oimage(X30418,X30417,X30416),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30414,tc_fun(X30418,tc_HOL_Obool)),X30413),X30412)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30414,tc_fun(X30417,tc_HOL_Obool)),X30413),hAPP(hAPP(c_COMBB(tc_fun(X30418,tc_HOL_Obool),tc_fun(X30417,tc_HOL_Obool),X30414),c_Set_Oimage(X30418,X30417,X30416)),X30412))
        | ~ c_Fun_Oinj__on(X30418,X30417,X30416,X30415) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X30418,tc_HOL_Obool)),hAPP(X30412,esk361_8(X30411,X30412,X30413,X30414,X30415,X30416,X30417,X30418))),X30415))
        | ~ hBOOL(hAPP(hAPP(c_member(X30414),X30411),X30413))
        | hAPP(c_Set_Oimage(X30418,X30417,X30416),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30414,tc_fun(X30418,tc_HOL_Obool)),X30413),X30412)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30414,tc_fun(X30417,tc_HOL_Obool)),X30413),hAPP(hAPP(c_COMBB(tc_fun(X30418,tc_HOL_Obool),tc_fun(X30417,tc_HOL_Obool),X30414),c_Set_Oimage(X30418,X30417,X30416)),X30412))
        | ~ c_Fun_Oinj__on(X30418,X30417,X30416,X30415) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__INT])])])]) ).

fof(i_0_6077,plain,
    ! [X24182,X24183,X24184,X24185,X24186,X24187] :
      ( ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24187,tc_fun(X24186,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X24187,tc_fun(tc_prod(X24187,X24186),tc_HOL_Obool),tc_fun(X24186,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X24186,tc_fun(tc_fun(tc_prod(X24187,X24186),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X24187,X24186),tc_HOL_Obool),tc_fun(X24186,tc_HOL_Obool)),X24187),c_COMBC(X24186,tc_fun(tc_prod(X24187,X24186),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X24186,tc_prod(X24187,X24186)),tc_fun(X24186,tc_fun(tc_fun(tc_prod(X24187,X24186),tc_HOL_Obool),tc_HOL_Obool)),X24187),hAPP(c_COMBB(tc_prod(X24187,X24186),tc_fun(tc_fun(tc_prod(X24187,X24186),tc_HOL_Obool),tc_HOL_Obool),X24186),c_member(tc_prod(X24187,X24186)))),c_Product__Type_OPair(X24187,X24186)))),X24185)),hAPP(hAPP(c_COMBC(X24187,tc_fun(tc_prod(X24187,X24186),tc_HOL_Obool),tc_fun(X24186,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X24186,tc_fun(tc_fun(tc_prod(X24187,X24186),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X24187,X24186),tc_HOL_Obool),tc_fun(X24186,tc_HOL_Obool)),X24187),c_COMBC(X24186,tc_fun(tc_prod(X24187,X24186),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X24186,tc_prod(X24187,X24186)),tc_fun(X24186,tc_fun(tc_fun(tc_prod(X24187,X24186),tc_HOL_Obool),tc_HOL_Obool)),X24187),hAPP(c_COMBB(tc_prod(X24187,X24186),tc_fun(tc_fun(tc_prod(X24187,X24186),tc_HOL_Obool),tc_HOL_Obool),X24186),c_member(tc_prod(X24187,X24186)))),c_Product__Type_OPair(X24187,X24186)))),X24184)),X24183),X24182))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X24187,X24186)),hAPP(hAPP(c_Product__Type_OPair(X24187,X24186),X24183),X24182)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X24187,X24186),tc_HOL_Obool)),X24185),X24184))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X24187,X24186)),hAPP(hAPP(c_Product__Type_OPair(X24187,X24186),X24183),X24182)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X24187,X24186),tc_HOL_Obool)),X24185),X24184)))
        | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24187,tc_fun(X24186,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X24187,tc_fun(tc_prod(X24187,X24186),tc_HOL_Obool),tc_fun(X24186,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X24186,tc_fun(tc_fun(tc_prod(X24187,X24186),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X24187,X24186),tc_HOL_Obool),tc_fun(X24186,tc_HOL_Obool)),X24187),c_COMBC(X24186,tc_fun(tc_prod(X24187,X24186),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X24186,tc_prod(X24187,X24186)),tc_fun(X24186,tc_fun(tc_fun(tc_prod(X24187,X24186),tc_HOL_Obool),tc_HOL_Obool)),X24187),hAPP(c_COMBB(tc_prod(X24187,X24186),tc_fun(tc_fun(tc_prod(X24187,X24186),tc_HOL_Obool),tc_HOL_Obool),X24186),c_member(tc_prod(X24187,X24186)))),c_Product__Type_OPair(X24187,X24186)))),X24185)),hAPP(hAPP(c_COMBC(X24187,tc_fun(tc_prod(X24187,X24186),tc_HOL_Obool),tc_fun(X24186,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X24186,tc_fun(tc_fun(tc_prod(X24187,X24186),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X24187,X24186),tc_HOL_Obool),tc_fun(X24186,tc_HOL_Obool)),X24187),c_COMBC(X24186,tc_fun(tc_prod(X24187,X24186),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X24186,tc_prod(X24187,X24186)),tc_fun(X24186,tc_fun(tc_fun(tc_prod(X24187,X24186),tc_HOL_Obool),tc_HOL_Obool)),X24187),hAPP(c_COMBB(tc_prod(X24187,X24186),tc_fun(tc_fun(tc_prod(X24187,X24186),tc_HOL_Obool),tc_HOL_Obool),X24186),c_member(tc_prod(X24187,X24186)))),c_Product__Type_OPair(X24187,X24186)))),X24184)),X24183),X24182)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__Int__eq2])]) ).

fof(i_0_6078,plain,
    ! [X23090,X23091,X23092,X23093,X23094,X23095] :
      ( ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23095,tc_fun(X23094,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X23095,tc_fun(tc_prod(X23095,X23094),tc_HOL_Obool),tc_fun(X23094,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X23094,tc_fun(tc_fun(tc_prod(X23095,X23094),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X23095,X23094),tc_HOL_Obool),tc_fun(X23094,tc_HOL_Obool)),X23095),c_COMBC(X23094,tc_fun(tc_prod(X23095,X23094),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X23094,tc_prod(X23095,X23094)),tc_fun(X23094,tc_fun(tc_fun(tc_prod(X23095,X23094),tc_HOL_Obool),tc_HOL_Obool)),X23095),hAPP(c_COMBB(tc_prod(X23095,X23094),tc_fun(tc_fun(tc_prod(X23095,X23094),tc_HOL_Obool),tc_HOL_Obool),X23094),c_member(tc_prod(X23095,X23094)))),c_Product__Type_OPair(X23095,X23094)))),X23093)),hAPP(hAPP(c_COMBC(X23095,tc_fun(tc_prod(X23095,X23094),tc_HOL_Obool),tc_fun(X23094,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X23094,tc_fun(tc_fun(tc_prod(X23095,X23094),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X23095,X23094),tc_HOL_Obool),tc_fun(X23094,tc_HOL_Obool)),X23095),c_COMBC(X23094,tc_fun(tc_prod(X23095,X23094),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X23094,tc_prod(X23095,X23094)),tc_fun(X23094,tc_fun(tc_fun(tc_prod(X23095,X23094),tc_HOL_Obool),tc_HOL_Obool)),X23095),hAPP(c_COMBB(tc_prod(X23095,X23094),tc_fun(tc_fun(tc_prod(X23095,X23094),tc_HOL_Obool),tc_HOL_Obool),X23094),c_member(tc_prod(X23095,X23094)))),c_Product__Type_OPair(X23095,X23094)))),X23092)),X23091),X23090))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X23095,X23094)),hAPP(hAPP(c_Product__Type_OPair(X23095,X23094),X23091),X23090)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X23095,X23094),tc_HOL_Obool)),X23093),X23092))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X23095,X23094)),hAPP(hAPP(c_Product__Type_OPair(X23095,X23094),X23091),X23090)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X23095,X23094),tc_HOL_Obool)),X23093),X23092)))
        | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23095,tc_fun(X23094,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X23095,tc_fun(tc_prod(X23095,X23094),tc_HOL_Obool),tc_fun(X23094,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X23094,tc_fun(tc_fun(tc_prod(X23095,X23094),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X23095,X23094),tc_HOL_Obool),tc_fun(X23094,tc_HOL_Obool)),X23095),c_COMBC(X23094,tc_fun(tc_prod(X23095,X23094),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X23094,tc_prod(X23095,X23094)),tc_fun(X23094,tc_fun(tc_fun(tc_prod(X23095,X23094),tc_HOL_Obool),tc_HOL_Obool)),X23095),hAPP(c_COMBB(tc_prod(X23095,X23094),tc_fun(tc_fun(tc_prod(X23095,X23094),tc_HOL_Obool),tc_HOL_Obool),X23094),c_member(tc_prod(X23095,X23094)))),c_Product__Type_OPair(X23095,X23094)))),X23093)),hAPP(hAPP(c_COMBC(X23095,tc_fun(tc_prod(X23095,X23094),tc_HOL_Obool),tc_fun(X23094,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X23094,tc_fun(tc_fun(tc_prod(X23095,X23094),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X23095,X23094),tc_HOL_Obool),tc_fun(X23094,tc_HOL_Obool)),X23095),c_COMBC(X23094,tc_fun(tc_prod(X23095,X23094),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X23094,tc_prod(X23095,X23094)),tc_fun(X23094,tc_fun(tc_fun(tc_prod(X23095,X23094),tc_HOL_Obool),tc_HOL_Obool)),X23095),hAPP(c_COMBB(tc_prod(X23095,X23094),tc_fun(tc_fun(tc_prod(X23095,X23094),tc_HOL_Obool),tc_HOL_Obool),X23094),c_member(tc_prod(X23095,X23094)))),c_Product__Type_OPair(X23095,X23094)))),X23092)),X23091),X23090)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__Un__eq2])]) ).

fof(i_0_6079,plain,
    ! [X28324,X28325] : c_List_Olenlex(X28325,X28324) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(X28325),tc_List_Olist(X28325))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X28325),tc_List_Olist(X28325),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(X28325),tc_fun(tc_List_Olist(X28325),tc_HOL_Obool),tc_fun(tc_List_Olist(X28325),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X28325),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X28325),tc_HOL_Obool),tc_fun(tc_List_Olist(X28325),tc_HOL_Obool)),tc_List_Olist(X28325)),c_COMBS(tc_List_Olist(X28325),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X28325),tc_HOL_Obool),tc_fun(tc_List_Olist(X28325),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(X28325)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X28325)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(X28325),tc_fun(tc_List_Olist(X28325),tc_Nat_Onat),tc_fun(tc_List_Olist(X28325),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X28325),tc_Nat_Onat),tc_fun(tc_List_Olist(X28325),tc_HOL_Obool)),tc_List_Olist(X28325)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X28325))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X28325)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X28325))))),c_Nat_Osize__class_Osize(tc_List_Olist(X28325)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(X28325),tc_fun(tc_List_Olist(X28325),tc_HOL_Obool),tc_fun(tc_List_Olist(X28325),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X28325),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X28325),tc_HOL_Obool),tc_fun(tc_List_Olist(X28325),tc_HOL_Obool)),tc_List_Olist(X28325)),c_COMBS(tc_List_Olist(X28325),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X28325),tc_HOL_Obool),tc_fun(tc_List_Olist(X28325),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(X28325)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X28325)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(X28325),tc_fun(tc_List_Olist(X28325),tc_Nat_Onat),tc_fun(tc_List_Olist(X28325),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X28325),tc_Nat_Onat),tc_fun(tc_List_Olist(X28325),tc_HOL_Obool)),tc_List_Olist(X28325)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X28325))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X28325)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X28325))))),c_Nat_Osize__class_Osize(tc_List_Olist(X28325)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X28325),tc_fun(tc_prod(tc_List_Olist(X28325),tc_List_Olist(X28325)),tc_HOL_Obool),tc_fun(tc_List_Olist(X28325),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X28325),tc_fun(tc_fun(tc_prod(tc_List_Olist(X28325),tc_List_Olist(X28325)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(X28325),tc_List_Olist(X28325)),tc_HOL_Obool),tc_fun(tc_List_Olist(X28325),tc_HOL_Obool)),tc_List_Olist(X28325)),c_COMBC(tc_List_Olist(X28325),tc_fun(tc_prod(tc_List_Olist(X28325),tc_List_Olist(X28325)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X28325),tc_prod(tc_List_Olist(X28325),tc_List_Olist(X28325))),tc_fun(tc_List_Olist(X28325),tc_fun(tc_fun(tc_prod(tc_List_Olist(X28325),tc_List_Olist(X28325)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(X28325)),hAPP(c_COMBB(tc_prod(tc_List_Olist(X28325),tc_List_Olist(X28325)),tc_fun(tc_fun(tc_prod(tc_List_Olist(X28325),tc_List_Olist(X28325)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X28325)),c_member(tc_prod(tc_List_Olist(X28325),tc_List_Olist(X28325))))),c_Product__Type_OPair(tc_List_Olist(X28325),tc_List_Olist(X28325))))),c_List_Olex(X28325,X28324)))))),
    inference(variable_rename,[status(thm)],[fact_lenlex__conv]) ).

fof(i_0_6080,plain,
    ! [X31965,X31966,X31967,X31968,X31969,X31970,X31971,X31972] :
      ( ( hBOOL(hAPP(hAPP(c_member(X31972),esk413_8(X31965,X31966,X31967,X31968,X31969,X31970,X31971,X31972)),hAPP(c_List_Oset(X31972),X31971)))
        | hAPP(c_List_Ofoldl(X31970,X31972,hAPP(c_COMBC(X31972,X31970,X31970),X31968),hAPP(X31967,X31965)),X31971) = hAPP(X31967,hAPP(c_List_Ofoldl(X31969,X31972,hAPP(c_COMBC(X31972,X31969,X31969),X31966),X31965),X31971)) )
      & ( hAPP(c_Fun_Ocomp(X31970,X31970,X31969,hAPP(X31968,esk413_8(X31965,X31966,X31967,X31968,X31969,X31970,X31971,X31972))),X31967) != hAPP(c_Fun_Ocomp(X31969,X31970,X31969,X31967),hAPP(X31966,esk413_8(X31965,X31966,X31967,X31968,X31969,X31970,X31971,X31972)))
        | hAPP(c_List_Ofoldl(X31970,X31972,hAPP(c_COMBC(X31972,X31970,X31970),X31968),hAPP(X31967,X31965)),X31971) = hAPP(X31967,hAPP(c_List_Ofoldl(X31969,X31972,hAPP(c_COMBC(X31972,X31969,X31969),X31966),X31965),X31971)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_foldl__apply])])])]) ).

cnf(i_0_6081,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_5233]) ).

cnf(i_0_6082,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_5234]) ).

cnf(i_0_6083,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_5235]) ).

fof(i_0_6084,plain,
    ! [X29812,X29813,X29814,X29815,X29816,X29817] :
      ( ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29817,tc_fun(X29816,tc_fun(X29815,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X29817,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X29816,X29815),tc_HOL_Obool),tc_fun(X29816,tc_fun(X29815,tc_HOL_Obool)),X29817),hAPP(c_COMBC(X29816,tc_fun(tc_prod(X29816,X29815),tc_HOL_Obool),tc_fun(X29815,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29815,tc_fun(tc_fun(tc_prod(X29816,X29815),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X29816,X29815),tc_HOL_Obool),tc_fun(X29815,tc_HOL_Obool)),X29816),c_COMBC(X29815,tc_fun(tc_prod(X29816,X29815),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29815,tc_prod(X29816,X29815)),tc_fun(X29815,tc_fun(tc_fun(tc_prod(X29816,X29815),tc_HOL_Obool),tc_HOL_Obool)),X29816),hAPP(c_COMBB(tc_prod(X29816,X29815),tc_fun(tc_fun(tc_prod(X29816,X29815),tc_HOL_Obool),tc_HOL_Obool),X29815),c_member(tc_prod(X29816,X29815)))),c_Product__Type_OPair(X29816,X29815))))),X29814)),X29813),X29812))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X29816,X29815)),hAPP(hAPP(c_Product__Type_OPair(X29816,X29815),X29813),X29812)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29817,tc_fun(tc_prod(X29816,X29815),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X29817,tc_HOL_Obool))),X29814))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29816,X29815)),hAPP(hAPP(c_Product__Type_OPair(X29816,X29815),X29813),X29812)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29817,tc_fun(tc_prod(X29816,X29815),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X29817,tc_HOL_Obool))),X29814)))
        | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29817,tc_fun(X29816,tc_fun(X29815,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X29817,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X29816,X29815),tc_HOL_Obool),tc_fun(X29816,tc_fun(X29815,tc_HOL_Obool)),X29817),hAPP(c_COMBC(X29816,tc_fun(tc_prod(X29816,X29815),tc_HOL_Obool),tc_fun(X29815,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29815,tc_fun(tc_fun(tc_prod(X29816,X29815),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X29816,X29815),tc_HOL_Obool),tc_fun(X29815,tc_HOL_Obool)),X29816),c_COMBC(X29815,tc_fun(tc_prod(X29816,X29815),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29815,tc_prod(X29816,X29815)),tc_fun(X29815,tc_fun(tc_fun(tc_prod(X29816,X29815),tc_HOL_Obool),tc_HOL_Obool)),X29816),hAPP(c_COMBB(tc_prod(X29816,X29815),tc_fun(tc_fun(tc_prod(X29816,X29815),tc_HOL_Obool),tc_HOL_Obool),X29815),c_member(tc_prod(X29816,X29815)))),c_Product__Type_OPair(X29816,X29815))))),X29814)),X29813),X29812)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF__INT__eq2])]) ).

fof(i_0_6085,plain,
    ! [X26840,X26841,X26842,X26843,X26844,X26845] :
      ( ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26845,tc_fun(X26844,tc_fun(X26843,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X26845,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X26844,X26843),tc_HOL_Obool),tc_fun(X26844,tc_fun(X26843,tc_HOL_Obool)),X26845),hAPP(c_COMBC(X26844,tc_fun(tc_prod(X26844,X26843),tc_HOL_Obool),tc_fun(X26843,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26843,tc_fun(tc_fun(tc_prod(X26844,X26843),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X26844,X26843),tc_HOL_Obool),tc_fun(X26843,tc_HOL_Obool)),X26844),c_COMBC(X26843,tc_fun(tc_prod(X26844,X26843),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26843,tc_prod(X26844,X26843)),tc_fun(X26843,tc_fun(tc_fun(tc_prod(X26844,X26843),tc_HOL_Obool),tc_HOL_Obool)),X26844),hAPP(c_COMBB(tc_prod(X26844,X26843),tc_fun(tc_fun(tc_prod(X26844,X26843),tc_HOL_Obool),tc_HOL_Obool),X26843),c_member(tc_prod(X26844,X26843)))),c_Product__Type_OPair(X26844,X26843))))),X26842)),X26841),X26840))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X26844,X26843)),hAPP(hAPP(c_Product__Type_OPair(X26844,X26843),X26841),X26840)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26845,tc_fun(tc_prod(X26844,X26843),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X26845,tc_HOL_Obool))),X26842))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X26844,X26843)),hAPP(hAPP(c_Product__Type_OPair(X26844,X26843),X26841),X26840)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26845,tc_fun(tc_prod(X26844,X26843),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X26845,tc_HOL_Obool))),X26842)))
        | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26845,tc_fun(X26844,tc_fun(X26843,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X26845,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X26844,X26843),tc_HOL_Obool),tc_fun(X26844,tc_fun(X26843,tc_HOL_Obool)),X26845),hAPP(c_COMBC(X26844,tc_fun(tc_prod(X26844,X26843),tc_HOL_Obool),tc_fun(X26843,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26843,tc_fun(tc_fun(tc_prod(X26844,X26843),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X26844,X26843),tc_HOL_Obool),tc_fun(X26843,tc_HOL_Obool)),X26844),c_COMBC(X26843,tc_fun(tc_prod(X26844,X26843),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26843,tc_prod(X26844,X26843)),tc_fun(X26843,tc_fun(tc_fun(tc_prod(X26844,X26843),tc_HOL_Obool),tc_HOL_Obool)),X26844),hAPP(c_COMBB(tc_prod(X26844,X26843),tc_fun(tc_fun(tc_prod(X26844,X26843),tc_HOL_Obool),tc_HOL_Obool),X26843),c_member(tc_prod(X26844,X26843)))),c_Product__Type_OPair(X26844,X26843))))),X26842)),X26841),X26840)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUP__UN__eq2])]) ).

fof(i_0_6086,plain,
    ! [X28084,X28085,X28086,X28087,X28088,X28089,X28090] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X28090,X28089,X28088,hAPP(hAPP(c_COMBC(X28090,tc_fun(tc_prod(X28090,X28089),tc_HOL_Obool),tc_fun(X28089,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28089,tc_fun(tc_fun(tc_prod(X28090,X28089),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X28090,X28089),tc_HOL_Obool),tc_fun(X28089,tc_HOL_Obool)),X28090),c_COMBC(X28089,tc_fun(tc_prod(X28090,X28089),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28089,tc_prod(X28090,X28089)),tc_fun(X28089,tc_fun(tc_fun(tc_prod(X28090,X28089),tc_HOL_Obool),tc_HOL_Obool)),X28090),hAPP(c_COMBB(tc_prod(X28090,X28089),tc_fun(tc_fun(tc_prod(X28090,X28089),tc_HOL_Obool),tc_HOL_Obool),X28089),c_member(tc_prod(X28090,X28089)))),c_Product__Type_OPair(X28090,X28089)))),X28087),hAPP(hAPP(c_COMBC(X28089,tc_fun(tc_prod(X28089,X28088),tc_HOL_Obool),tc_fun(X28088,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28088,tc_fun(tc_fun(tc_prod(X28089,X28088),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X28089,X28088),tc_HOL_Obool),tc_fun(X28088,tc_HOL_Obool)),X28089),c_COMBC(X28088,tc_fun(tc_prod(X28089,X28088),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28088,tc_prod(X28089,X28088)),tc_fun(X28088,tc_fun(tc_fun(tc_prod(X28089,X28088),tc_HOL_Obool),tc_HOL_Obool)),X28089),hAPP(c_COMBB(tc_prod(X28089,X28088),tc_fun(tc_fun(tc_prod(X28089,X28088),tc_HOL_Obool),tc_HOL_Obool),X28088),c_member(tc_prod(X28089,X28088)))),c_Product__Type_OPair(X28089,X28088)))),X28086)),X28085),X28084))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X28090,X28088)),hAPP(hAPP(c_Product__Type_OPair(X28090,X28088),X28085),X28084)),hAPP(hAPP(c_Relation_Orel__comp(X28090,X28089,X28088),X28087),X28086))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28090,X28088)),hAPP(hAPP(c_Product__Type_OPair(X28090,X28088),X28085),X28084)),hAPP(hAPP(c_Relation_Orel__comp(X28090,X28089,X28088),X28087),X28086)))
        | hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X28090,X28089,X28088,hAPP(hAPP(c_COMBC(X28090,tc_fun(tc_prod(X28090,X28089),tc_HOL_Obool),tc_fun(X28089,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28089,tc_fun(tc_fun(tc_prod(X28090,X28089),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X28090,X28089),tc_HOL_Obool),tc_fun(X28089,tc_HOL_Obool)),X28090),c_COMBC(X28089,tc_fun(tc_prod(X28090,X28089),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28089,tc_prod(X28090,X28089)),tc_fun(X28089,tc_fun(tc_fun(tc_prod(X28090,X28089),tc_HOL_Obool),tc_HOL_Obool)),X28090),hAPP(c_COMBB(tc_prod(X28090,X28089),tc_fun(tc_fun(tc_prod(X28090,X28089),tc_HOL_Obool),tc_HOL_Obool),X28089),c_member(tc_prod(X28090,X28089)))),c_Product__Type_OPair(X28090,X28089)))),X28087),hAPP(hAPP(c_COMBC(X28089,tc_fun(tc_prod(X28089,X28088),tc_HOL_Obool),tc_fun(X28088,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28088,tc_fun(tc_fun(tc_prod(X28089,X28088),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X28089,X28088),tc_HOL_Obool),tc_fun(X28088,tc_HOL_Obool)),X28089),c_COMBC(X28088,tc_fun(tc_prod(X28089,X28088),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28088,tc_prod(X28089,X28088)),tc_fun(X28088,tc_fun(tc_fun(tc_prod(X28089,X28088),tc_HOL_Obool),tc_HOL_Obool)),X28089),hAPP(c_COMBB(tc_prod(X28089,X28088),tc_fun(tc_fun(tc_prod(X28089,X28088),tc_HOL_Obool),tc_HOL_Obool),X28088),c_member(tc_prod(X28089,X28088)))),c_Product__Type_OPair(X28089,X28088)))),X28086)),X28085),X28084)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__comp__rel__comp__eq])]) ).

cnf(i_0_6087,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_5236]) ).

cnf(i_0_6088,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_5237]) ).

fof(i_0_6089,plain,
    ! [X25229,X25230,X25231,X25232,X25233,X25234,X25235] :
      ( ( hBOOL(hAPP(hAPP(c_member(X25235),esk159_7(X25229,X25230,X25231,X25232,X25233,X25234,X25235)),X25234))
        | X25230 = X25229
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X25235,tc_HOL_Obool)),X25229),hAPP(hAPP(c_Equiv__Relations_Oquotient(X25235),X25234),X25233)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X25235,tc_HOL_Obool)),X25230),hAPP(hAPP(c_Equiv__Relations_Oquotient(X25235),X25234),X25233)))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25235,tc_fun(X25232,tc_HOL_Obool)),X25230),X25231) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25235,tc_fun(X25232,tc_HOL_Obool)),X25229),X25231)
        | ~ c_Equiv__Relations_Ocongruent(X25235,tc_fun(X25232,tc_HOL_Obool),X25233,X25231)
        | ~ c_Equiv__Relations_Oequiv(X25235,X25234,X25233) )
      & ( hBOOL(hAPP(hAPP(c_member(X25235),esk160_7(X25229,X25230,X25231,X25232,X25233,X25234,X25235)),X25234))
        | X25230 = X25229
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X25235,tc_HOL_Obool)),X25229),hAPP(hAPP(c_Equiv__Relations_Oquotient(X25235),X25234),X25233)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X25235,tc_HOL_Obool)),X25230),hAPP(hAPP(c_Equiv__Relations_Oquotient(X25235),X25234),X25233)))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25235,tc_fun(X25232,tc_HOL_Obool)),X25230),X25231) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25235,tc_fun(X25232,tc_HOL_Obool)),X25229),X25231)
        | ~ c_Equiv__Relations_Ocongruent(X25235,tc_fun(X25232,tc_HOL_Obool),X25233,X25231)
        | ~ c_Equiv__Relations_Oequiv(X25235,X25234,X25233) )
      & ( hAPP(X25231,esk159_7(X25229,X25230,X25231,X25232,X25233,X25234,X25235)) = hAPP(X25231,esk160_7(X25229,X25230,X25231,X25232,X25233,X25234,X25235))
        | X25230 = X25229
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X25235,tc_HOL_Obool)),X25229),hAPP(hAPP(c_Equiv__Relations_Oquotient(X25235),X25234),X25233)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X25235,tc_HOL_Obool)),X25230),hAPP(hAPP(c_Equiv__Relations_Oquotient(X25235),X25234),X25233)))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25235,tc_fun(X25232,tc_HOL_Obool)),X25230),X25231) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25235,tc_fun(X25232,tc_HOL_Obool)),X25229),X25231)
        | ~ c_Equiv__Relations_Ocongruent(X25235,tc_fun(X25232,tc_HOL_Obool),X25233,X25231)
        | ~ c_Equiv__Relations_Oequiv(X25235,X25234,X25233) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X25235,X25235)),hAPP(hAPP(c_Product__Type_OPair(X25235,X25235),esk159_7(X25229,X25230,X25231,X25232,X25233,X25234,X25235)),esk160_7(X25229,X25230,X25231,X25232,X25233,X25234,X25235))),X25233))
        | X25230 = X25229
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X25235,tc_HOL_Obool)),X25229),hAPP(hAPP(c_Equiv__Relations_Oquotient(X25235),X25234),X25233)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X25235,tc_HOL_Obool)),X25230),hAPP(hAPP(c_Equiv__Relations_Oquotient(X25235),X25234),X25233)))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25235,tc_fun(X25232,tc_HOL_Obool)),X25230),X25231) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25235,tc_fun(X25232,tc_HOL_Obool)),X25229),X25231)
        | ~ c_Equiv__Relations_Ocongruent(X25235,tc_fun(X25232,tc_HOL_Obool),X25233,X25231)
        | ~ c_Equiv__Relations_Oequiv(X25235,X25234,X25233) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__equiv__class__inject])])])]) ).

fof(i_0_6090,plain,
    ! [X23298,X23299,X23300,X23301,X23302] :
      ( ~ c_Hoare__Mirabelle_Ohoare__derivs(X23302,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(X23302),tc_HOL_Obool)),X23301),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X23302),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(X23302,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X23302)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X23302,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X23302))),hAPP(hAPP(c_COMBB(tc_fun(X23302,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X23302,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X23302))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(X23302)),X23300)),c_Com_Ocom_OBODY)),X23299)),X23298)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X23302),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(X23302,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X23302)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X23302,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X23302))),hAPP(hAPP(c_COMBB(tc_fun(X23302,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X23302,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X23302))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(X23302)),X23300)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),X23299)),X23298))
      | c_Hoare__Mirabelle_Ohoare__derivs(X23302,X23301,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X23302),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(X23302,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X23302)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X23302,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X23302))),hAPP(hAPP(c_COMBB(tc_fun(X23302,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X23302,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X23302))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(X23302)),X23300)),c_Com_Ocom_OBODY)),X23299)),X23298)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hoare__derivs_OBody])]) ).

cnf(i_0_6091,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_5236]) ).

cnf(i_0_6092,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_5238]) ).

fof(i_0_6093,plain,
    ! [X27846,X27847,X27848,X27849] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27849),hAPP(c_Set_OCollect(X27849),X27848)))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X27847),hAPP(c_Set_OCollect(X27847),hAPP(hAPP(c_COMBB(tc_fun(X27849,tc_HOL_Obool),tc_HOL_Obool,X27847),c_HOL_OEx(X27849)),hAPP(hAPP(c_COMBC(X27847,tc_fun(X27849,tc_HOL_Obool),tc_fun(X27849,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27849,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X27849,tc_HOL_Obool),tc_fun(X27849,tc_HOL_Obool)),X27847),c_COMBS(X27849,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27849,tc_HOL_Obool),tc_fun(X27849,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X27847),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27849),c_fconj)),hAPP(hAPP(c_COMBC(X27847,tc_fun(X27849,X27847),tc_fun(X27849,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27847,tc_HOL_Obool),tc_fun(tc_fun(X27849,X27847),tc_fun(X27849,tc_HOL_Obool)),X27847),c_COMBB(X27847,tc_HOL_Obool,X27849)),c_fequal)),X27846)))),X27848))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__image__set])]) ).

fof(i_0_6094,plain,
    ! [X32719,X32720,X32721,X32722,X32723,X32724,X32725,X32726] :
      ( ( hBOOL(hAPP(hAPP(c_member(X32725),esk477_8(X32719,X32720,X32721,X32722,X32723,X32724,X32725,X32726)),X32722))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X32724,X32726),X32719),X32721) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X32725,X32726),X32720),X32722)
        | X32721 != hAPP(c_Set_Oimage(X32725,X32724,X32723),X32722)
        | ~ c_Fun_Oinj__on(X32725,X32724,X32723,X32722)
        | ~ class_Groups_Ocomm__monoid__add(X32726) )
      & ( hAPP(X32720,esk477_8(X32719,X32720,X32721,X32722,X32723,X32724,X32725,X32726)) != hAPP(X32719,hAPP(X32723,esk477_8(X32719,X32720,X32721,X32722,X32723,X32724,X32725,X32726)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X32724,X32726),X32719),X32721) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X32725,X32726),X32720),X32722)
        | X32721 != hAPP(c_Set_Oimage(X32725,X32724,X32723),X32722)
        | ~ c_Fun_Oinj__on(X32725,X32724,X32723,X32722)
        | ~ class_Groups_Ocomm__monoid__add(X32726) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__reindex__cong])])])]) ).

fof(i_0_6095,plain,
    ! [X23113,X23114,X23115,X23116,X23117,X23118] :
      ( ~ c_Hoare__Mirabelle_Ohoare__derivs(X23118,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(X23118),tc_HOL_Obool)),X23117),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X23118),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(X23118,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X23118)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X23118,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X23118))),hAPP(hAPP(c_COMBB(tc_fun(X23118,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X23118,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X23118))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(X23118)),X23116)),c_Com_Ocom_OBODY)),X23115)),X23114)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X23118),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(X23118,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X23118)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X23118,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X23118))),hAPP(hAPP(c_COMBB(tc_fun(X23118,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X23118,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X23118))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(X23118)),X23116)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),X23115)),X23114))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X23113),X23114))
      | c_Hoare__Mirabelle_Ohoare__derivs(X23118,X23117,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X23118)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X23118),hAPP(X23116,X23113)),hAPP(c_Com_Ocom_OBODY,X23113)),hAPP(X23115,X23113))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X23118),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Body1])]) ).

cnf(i_0_6096,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_5239]) ).

cnf(i_0_6097,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_5240]) ).

cnf(i_0_6098,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_5241]) ).

fof(i_0_6099,plain,
    ! [X33375,X33376,X33377,X33378,X33379] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X33379,X33378,hAPP(hAPP(c_COMBC(X33379,tc_fun(tc_prod(X33379,X33378),tc_HOL_Obool),tc_fun(X33378,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X33378,tc_fun(tc_fun(tc_prod(X33379,X33378),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X33379,X33378),tc_HOL_Obool),tc_fun(X33378,tc_HOL_Obool)),X33379),c_COMBC(X33378,tc_fun(tc_prod(X33379,X33378),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X33378,tc_prod(X33379,X33378)),tc_fun(X33378,tc_fun(tc_fun(tc_prod(X33379,X33378),tc_HOL_Obool),tc_HOL_Obool)),X33379),hAPP(c_COMBB(tc_prod(X33379,X33378),tc_fun(tc_fun(tc_prod(X33379,X33378),tc_HOL_Obool),tc_HOL_Obool),X33378),c_member(tc_prod(X33379,X33378)))),c_Product__Type_OPair(X33379,X33378)))),X33377)),X33376),X33375))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X33378,X33379)),hAPP(hAPP(c_Product__Type_OPair(X33378,X33379),X33376),X33375)),hAPP(c_Relation_Oconverse(X33379,X33378),X33377))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X33378,X33379)),hAPP(hAPP(c_Product__Type_OPair(X33378,X33379),X33376),X33375)),hAPP(c_Relation_Oconverse(X33379,X33378),X33377)))
        | hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X33379,X33378,hAPP(hAPP(c_COMBC(X33379,tc_fun(tc_prod(X33379,X33378),tc_HOL_Obool),tc_fun(X33378,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X33378,tc_fun(tc_fun(tc_prod(X33379,X33378),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X33379,X33378),tc_HOL_Obool),tc_fun(X33378,tc_HOL_Obool)),X33379),c_COMBC(X33378,tc_fun(tc_prod(X33379,X33378),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X33378,tc_prod(X33379,X33378)),tc_fun(X33378,tc_fun(tc_fun(tc_prod(X33379,X33378),tc_HOL_Obool),tc_HOL_Obool)),X33379),hAPP(c_COMBB(tc_prod(X33379,X33378),tc_fun(tc_fun(tc_prod(X33379,X33378),tc_HOL_Obool),tc_HOL_Obool),X33378),c_member(tc_prod(X33379,X33378)))),c_Product__Type_OPair(X33379,X33378)))),X33377)),X33376),X33375)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_conversep__converse__eq])]) ).

fof(i_0_6100,plain,
    ! [X26085,X26086,X26087,X26088,X26089,X26090,X26091,X26092] :
      ( ( hBOOL(hAPP(hAPP(c_member(X26091),esk224_8(X26085,X26086,X26087,X26088,X26089,X26090,X26091,X26092)),X26088))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26090,X26092),X26085),X26087) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26091,X26092),X26086),X26088)
        | X26087 != hAPP(c_Set_Oimage(X26091,X26090,X26089),X26088)
        | ~ c_Fun_Oinj__on(X26091,X26090,X26089,X26088)
        | ~ class_Groups_Ocomm__monoid__mult(X26092) )
      & ( hAPP(X26086,esk224_8(X26085,X26086,X26087,X26088,X26089,X26090,X26091,X26092)) != hAPP(hAPP(c_Fun_Ocomp(X26090,X26092,X26091,X26085),X26089),esk224_8(X26085,X26086,X26087,X26088,X26089,X26090,X26091,X26092))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26090,X26092),X26085),X26087) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X26091,X26092),X26086),X26088)
        | X26087 != hAPP(c_Set_Oimage(X26091,X26090,X26089),X26088)
        | ~ c_Fun_Oinj__on(X26091,X26090,X26089,X26088)
        | ~ class_Groups_Ocomm__monoid__mult(X26092) ) ),
    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_6101,plain,
    ! [X32752,X32753,X32754,X32755,X32756,X32757,X32758,X32759] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X32758),X32756),esk480_8(X32752,X32753,X32754,X32755,X32756,X32757,X32758,X32759)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X32758,X32759),X32753),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X32758,X32757),X32755)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X32758,X32759),X32752),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X32758,X32756),X32754))
        | X32755 != X32754
        | X32757 != X32756
        | ~ class_Groups_Ocomm__monoid__add(X32759)
        | ~ class_Orderings_Oord(X32758) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X32758),esk480_8(X32752,X32753,X32754,X32755,X32756,X32757,X32758,X32759)),X32754))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X32758,X32759),X32753),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X32758,X32757),X32755)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X32758,X32759),X32752),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X32758,X32756),X32754))
        | X32755 != X32754
        | X32757 != X32756
        | ~ class_Groups_Ocomm__monoid__add(X32759)
        | ~ class_Orderings_Oord(X32758) )
      & ( hAPP(X32753,esk480_8(X32752,X32753,X32754,X32755,X32756,X32757,X32758,X32759)) != hAPP(X32752,esk480_8(X32752,X32753,X32754,X32755,X32756,X32757,X32758,X32759))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X32758,X32759),X32753),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X32758,X32757),X32755)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X32758,X32759),X32752),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X32758,X32756),X32754))
        | X32755 != X32754
        | X32757 != X32756
        | ~ class_Groups_Ocomm__monoid__add(X32759)
        | ~ class_Orderings_Oord(X32758) ) ),
    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_6102,plain,
    ! [X25228] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X25228) = 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,X25228)),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_6103,plain,
    ! [X33662,X33663,X33664,X33665,X33666,X33667,X33668] :
      ( ( hBOOL(hAPP(hAPP(X33668,esk534_7(X33662,X33663,X33664,X33665,X33666,X33667,X33668)),esk533_7(X33662,X33663,X33664,X33665,X33666,X33667,X33668)))
        | hBOOL(hAPP(X33664,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X33667,X33666,X33662),X33663),X33665)))
        | ~ hBOOL(hAPP(hAPP(X33668,hAPP(c_Product__Type_Osnd(X33667,X33666),X33665)),hAPP(c_Product__Type_Ofst(X33667,X33666),X33665))) )
      & ( ~ hBOOL(hAPP(X33664,hAPP(hAPP(X33663,esk533_7(X33662,X33663,X33664,X33665,X33666,X33667,X33668)),esk534_7(X33662,X33663,X33664,X33665,X33666,X33667,X33668))))
        | hBOOL(hAPP(X33664,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X33667,X33666,X33662),X33663),X33665)))
        | ~ hBOOL(hAPP(hAPP(X33668,hAPP(c_Product__Type_Osnd(X33667,X33666),X33665)),hAPP(c_Product__Type_Ofst(X33667,X33666),X33665))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_exE__realizer])])])]) ).

fof(i_0_6104,plain,
    ! [X23071,X23072] : c_FunDef_Orp__inv__image(X23072,X23071) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(X23072,X23072),tc_HOL_Obool),tc_fun(tc_prod(X23072,X23072),tc_HOL_Obool),tc_fun(tc_fun(X23071,X23072),tc_prod(tc_fun(tc_prod(X23071,X23071),tc_HOL_Obool),tc_fun(tc_prod(X23071,X23071),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(X23072,X23072),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X23072,X23072),tc_HOL_Obool),tc_fun(tc_fun(X23071,X23072),tc_fun(tc_prod(X23071,X23071),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X23072,X23072),tc_HOL_Obool),tc_fun(tc_fun(X23071,X23072),tc_prod(tc_fun(tc_prod(X23071,X23071),tc_HOL_Obool),tc_fun(tc_prod(X23071,X23071),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(X23071,X23072),tc_fun(tc_prod(X23071,X23071),tc_HOL_Obool)),tc_fun(tc_fun(X23071,X23072),tc_prod(tc_fun(tc_prod(X23071,X23071),tc_HOL_Obool),tc_fun(tc_prod(X23071,X23071),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(X23072,X23072),tc_HOL_Obool),tc_fun(tc_fun(X23071,X23072),tc_fun(tc_prod(X23071,X23071),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X23072,X23072),tc_HOL_Obool),tc_fun(tc_fun(X23071,X23072),tc_prod(tc_fun(tc_prod(X23071,X23071),tc_HOL_Obool),tc_fun(tc_prod(X23071,X23071),tc_HOL_Obool))))),tc_fun(tc_prod(X23072,X23072),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(X23071,X23072),tc_fun(tc_prod(X23071,X23071),tc_HOL_Obool)),tc_fun(tc_fun(X23071,X23072),tc_prod(tc_fun(tc_prod(X23071,X23071),tc_HOL_Obool),tc_fun(tc_prod(X23071,X23071),tc_HOL_Obool))),tc_fun(tc_prod(X23072,X23072),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X23071,X23072),tc_fun(tc_fun(tc_prod(X23071,X23071),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X23071,X23071),tc_HOL_Obool),tc_fun(tc_prod(X23071,X23071),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(X23071,X23072),tc_fun(tc_prod(X23071,X23071),tc_HOL_Obool)),tc_fun(tc_fun(X23071,X23072),tc_prod(tc_fun(tc_prod(X23071,X23071),tc_HOL_Obool),tc_fun(tc_prod(X23071,X23071),tc_HOL_Obool)))),tc_fun(tc_prod(X23072,X23072),tc_HOL_Obool)),c_COMBS(tc_fun(X23071,X23072),tc_fun(tc_prod(X23071,X23071),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X23071,X23071),tc_HOL_Obool),tc_fun(tc_prod(X23071,X23071),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X23071,X23072),tc_fun(tc_prod(X23071,X23071),tc_HOL_Obool)),tc_fun(tc_fun(X23071,X23072),tc_fun(tc_fun(tc_prod(X23071,X23071),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X23071,X23071),tc_HOL_Obool),tc_fun(tc_prod(X23071,X23071),tc_HOL_Obool)))),tc_fun(tc_prod(X23072,X23072),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(X23071,X23071),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X23071,X23071),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X23071,X23071),tc_HOL_Obool),tc_fun(tc_prod(X23071,X23071),tc_HOL_Obool))),tc_fun(X23071,X23072)),c_Product__Type_OPair(tc_fun(tc_prod(X23071,X23071),tc_HOL_Obool),tc_fun(tc_prod(X23071,X23071),tc_HOL_Obool)))),c_Relation_Oinv__image(X23072,X23071))))),c_Relation_Oinv__image(X23072,X23071))),
    inference(variable_rename,[status(thm)],[fact_rp__inv__image__def]) ).

fof(i_0_6105,plain,
    ! [X27860,X27861,X27862,X27863] : hAPP(hAPP(c_Relation_Oinv__image(X27863,X27862),X27861),X27860) = hAPP(c_Set_OCollect(tc_prod(X27862,X27862)),hAPP(c_Product__Type_Oprod_Oprod__case(X27862,X27862,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X27862,tc_fun(tc_prod(X27863,X27863),tc_HOL_Obool),tc_fun(X27862,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27862,tc_fun(tc_fun(tc_prod(X27863,X27863),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X27863,X27863),tc_HOL_Obool),tc_fun(X27862,tc_HOL_Obool)),X27862),c_COMBC(X27862,tc_fun(tc_prod(X27863,X27863),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27862,tc_prod(X27863,X27863)),tc_fun(X27862,tc_fun(tc_fun(tc_prod(X27863,X27863),tc_HOL_Obool),tc_HOL_Obool)),X27862),hAPP(c_COMBB(tc_prod(X27863,X27863),tc_fun(tc_fun(tc_prod(X27863,X27863),tc_HOL_Obool),tc_HOL_Obool),X27862),c_member(tc_prod(X27863,X27863)))),hAPP(hAPP(c_COMBC(X27862,tc_fun(X27862,X27863),tc_fun(X27862,tc_prod(X27863,X27863))),hAPP(hAPP(c_COMBB(tc_fun(X27863,tc_prod(X27863,X27863)),tc_fun(tc_fun(X27862,X27863),tc_fun(X27862,tc_prod(X27863,X27863))),X27862),c_COMBB(X27863,tc_prod(X27863,X27863),X27862)),hAPP(hAPP(c_COMBB(X27863,tc_fun(X27863,tc_prod(X27863,X27863)),X27862),c_Product__Type_OPair(X27863,X27863)),X27860))),X27860)))),X27861))),
    inference(variable_rename,[status(thm)],[fact_inv__image__def]) ).

fof(i_0_6106,plain,
    ! [X29020,X29021,X29022,X29023] : hAPP(c_List_Oset(tc_prod(X29023,X29022)),hAPP(hAPP(c_List_Ozip(X29023,X29022),X29021),X29020)) = hAPP(c_Set_OCollect(tc_prod(X29023,X29022)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(X29023,X29022)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(X29023,X29022),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(X29023,X29022)),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(X29023,X29022)),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(X29023,X29022),tc_fun(tc_Nat_Onat,tc_prod(X29023,X29022)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X29023,X29022),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(X29023,X29022)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(X29023,X29022)),c_COMBB(tc_prod(X29023,X29022),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X29022,tc_prod(X29023,X29022)),hAPP(hAPP(c_COMBB(X29023,tc_fun(X29022,tc_prod(X29023,X29022)),tc_Nat_Onat),c_Product__Type_OPair(X29023,X29022)),hAPP(c_List_Onth(X29023),X29021))),hAPP(c_List_Onth(X29022),X29020)))))),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(X29023)),X29021)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29022)),X29020)))))),
    inference(variable_rename,[status(thm)],[fact_set__zip]) ).

fof(i_0_6107,plain,
    ! [X21763,X21764,X21765,X21766,X21767] : c_Hoare__Mirabelle_Ohoare__derivs(X21767,X21766,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X21767)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X21767),hAPP(hAPP(c_COMBC(X21767,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),X21767),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X21767),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj)),X21765))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate),c_fNot),X21764))),c_Com_Ocom_OWhile(X21764,X21763)),X21765)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X21767),tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_LoopF]) ).

fof(i_0_6108,plain,
    ! [X22188,X22189,X22190,X22191] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22191,tc_fun(X22190,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X22191,tc_fun(tc_prod(X22191,X22190),tc_HOL_Obool),tc_fun(X22190,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X22190,tc_fun(tc_fun(tc_prod(X22191,X22190),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X22191,X22190),tc_HOL_Obool),tc_fun(X22190,tc_HOL_Obool)),X22191),c_COMBC(X22190,tc_fun(tc_prod(X22191,X22190),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X22190,tc_prod(X22191,X22190)),tc_fun(X22190,tc_fun(tc_fun(tc_prod(X22191,X22190),tc_HOL_Obool),tc_HOL_Obool)),X22191),hAPP(c_COMBB(tc_prod(X22191,X22190),tc_fun(tc_fun(tc_prod(X22191,X22190),tc_HOL_Obool),tc_HOL_Obool),X22190),c_member(tc_prod(X22191,X22190)))),c_Product__Type_OPair(X22191,X22190)))),X22189)),hAPP(hAPP(c_COMBC(X22191,tc_fun(tc_prod(X22191,X22190),tc_HOL_Obool),tc_fun(X22190,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X22190,tc_fun(tc_fun(tc_prod(X22191,X22190),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X22191,X22190),tc_HOL_Obool),tc_fun(X22190,tc_HOL_Obool)),X22191),c_COMBC(X22190,tc_fun(tc_prod(X22191,X22190),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X22190,tc_prod(X22191,X22190)),tc_fun(X22190,tc_fun(tc_fun(tc_prod(X22191,X22190),tc_HOL_Obool),tc_HOL_Obool)),X22191),hAPP(c_COMBB(tc_prod(X22191,X22190),tc_fun(tc_fun(tc_prod(X22191,X22190),tc_HOL_Obool),tc_HOL_Obool),X22190),c_member(tc_prod(X22191,X22190)))),c_Product__Type_OPair(X22191,X22190)))),X22188)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X22191,X22190),tc_HOL_Obool)),X22189),X22188)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X22191,X22190),tc_HOL_Obool)),X22189),X22188))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22191,tc_fun(X22190,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X22191,tc_fun(tc_prod(X22191,X22190),tc_HOL_Obool),tc_fun(X22190,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X22190,tc_fun(tc_fun(tc_prod(X22191,X22190),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X22191,X22190),tc_HOL_Obool),tc_fun(X22190,tc_HOL_Obool)),X22191),c_COMBC(X22190,tc_fun(tc_prod(X22191,X22190),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X22190,tc_prod(X22191,X22190)),tc_fun(X22190,tc_fun(tc_fun(tc_prod(X22191,X22190),tc_HOL_Obool),tc_HOL_Obool)),X22191),hAPP(c_COMBB(tc_prod(X22191,X22190),tc_fun(tc_fun(tc_prod(X22191,X22190),tc_HOL_Obool),tc_HOL_Obool),X22190),c_member(tc_prod(X22191,X22190)))),c_Product__Type_OPair(X22191,X22190)))),X22189)),hAPP(hAPP(c_COMBC(X22191,tc_fun(tc_prod(X22191,X22190),tc_HOL_Obool),tc_fun(X22190,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X22190,tc_fun(tc_fun(tc_prod(X22191,X22190),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X22191,X22190),tc_HOL_Obool),tc_fun(X22190,tc_HOL_Obool)),X22191),c_COMBC(X22190,tc_fun(tc_prod(X22191,X22190),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X22190,tc_prod(X22191,X22190)),tc_fun(X22190,tc_fun(tc_fun(tc_prod(X22191,X22190),tc_HOL_Obool),tc_HOL_Obool)),X22191),hAPP(c_COMBB(tc_prod(X22191,X22190),tc_fun(tc_fun(tc_prod(X22191,X22190),tc_HOL_Obool),tc_HOL_Obool),X22190),c_member(tc_prod(X22191,X22190)))),c_Product__Type_OPair(X22191,X22190)))),X22188))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__subset__eq2])]) ).

fof(i_0_6109,plain,
    ! [X27841,X27842] : hAPP(c_Set_OPow(X27842),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X27842,tc_HOL_Obool)),X27841)) = hAPP(c_Set_OCollect(tc_fun(X27842,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X27842,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(X27842,tc_HOL_Obool)),c_HOL_OEx(tc_fun(X27842,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(X27842,tc_HOL_Obool),tc_fun(tc_fun(X27842,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X27842,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X27842,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(X27842,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X27842,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X27842,tc_HOL_Obool)),c_COMBS(tc_fun(X27842,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X27842,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X27842,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(X27842,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X27842,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(X27842,tc_HOL_Obool),tc_fun(tc_fun(X27842,tc_HOL_Obool),tc_fun(X27842,tc_HOL_Obool)),tc_fun(tc_fun(X27842,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X27842,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X27842,tc_HOL_Obool),tc_fun(X27842,tc_HOL_Obool)),tc_fun(tc_fun(X27842,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X27842,tc_HOL_Obool)),c_COMBB(tc_fun(X27842,tc_HOL_Obool),tc_HOL_Obool,tc_fun(X27842,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(X27842,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X27842,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(X27842,tc_HOL_Obool)),hAPP(c_member(tc_fun(X27842,tc_HOL_Obool)),X27841)),c_Set_OPow(X27842))))),
    inference(variable_rename,[status(thm)],[fact_Pow__Compl]) ).

fof(i_0_6110,plain,
    ! [X25251,X25252,X25253,X25254,X25255,X25256,X25257] :
      ( ( hBOOL(hAPP(hAPP(c_member(X25257),esk163_7(X25251,X25252,X25253,X25254,X25255,X25256,X25257)),X25256))
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X25254,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25257,tc_fun(X25254,tc_HOL_Obool)),X25252),X25253)),X25251))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X25257,tc_HOL_Obool)),X25252),hAPP(hAPP(c_Equiv__Relations_Oquotient(X25257),X25256),X25255)))
        | ~ c_Equiv__Relations_Ocongruent(X25257,tc_fun(X25254,tc_HOL_Obool),X25255,X25253)
        | ~ c_Equiv__Relations_Oequiv(X25257,X25256,X25255) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X25254,tc_HOL_Obool)),hAPP(X25253,esk163_7(X25251,X25252,X25253,X25254,X25255,X25256,X25257))),X25251))
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X25254,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25257,tc_fun(X25254,tc_HOL_Obool)),X25252),X25253)),X25251))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X25257,tc_HOL_Obool)),X25252),hAPP(hAPP(c_Equiv__Relations_Oquotient(X25257),X25256),X25255)))
        | ~ c_Equiv__Relations_Ocongruent(X25257,tc_fun(X25254,tc_HOL_Obool),X25255,X25253)
        | ~ c_Equiv__Relations_Oequiv(X25257,X25256,X25255) ) ),
    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_6111,plain,
    ! [X33609,X33610,X33611,X33612,X33613,X33614,X33615] :
      ( ( hBOOL(hAPP(hAPP(c_member(X33615),esk529_7(X33609,X33610,X33611,X33612,X33613,X33614,X33615)),X33614))
        | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X33615,tc_fun(X33610,tc_fun(X33609,tc_HOL_Obool))),X33614),X33613),X33612),X33611)) )
      & ( ~ hBOOL(hAPP(hAPP(hAPP(X33613,esk529_7(X33609,X33610,X33611,X33612,X33613,X33614,X33615)),X33612),X33611))
        | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X33615,tc_fun(X33610,tc_fun(X33609,tc_HOL_Obool))),X33614),X33613),X33612),X33611)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF2__I])])])]) ).

fof(i_0_6112,plain,
    ! [X30229,X30230,X30231,X30232,X30233,X30234,X30235,X30236,X30237,X30238,X30239,X30240,X30241,X30242,X30243] :
      ( ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30235,tc_fun(X30234,tc_fun(X30233,tc_HOL_Obool))),X30232),X30231),X30230),X30229))
        | ~ hBOOL(hAPP(hAPP(c_member(X30235),X30236),X30232))
        | hBOOL(hAPP(hAPP(hAPP(X30231,X30236),X30230),X30229)) )
      & ( hBOOL(hAPP(hAPP(c_member(X30243),esk358_7(X30237,X30238,X30239,X30240,X30241,X30242,X30243)),X30240))
        | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30243,tc_fun(X30242,tc_fun(X30241,tc_HOL_Obool))),X30240),X30239),X30238),X30237)) )
      & ( ~ hBOOL(hAPP(hAPP(hAPP(X30239,esk358_7(X30237,X30238,X30239,X30240,X30241,X30242,X30243)),X30238),X30237))
        | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30243,tc_fun(X30242,tc_fun(X30241,tc_HOL_Obool))),X30240),X30239),X30238),X30237)) ) ),
    inference(distribute,[status(thm)],[inference(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_6113,plain,
    ! [X27887,X27888,X27889] :
      ( ~ class_Orderings_Olinorder(X27889)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27889),X27888))
      | X27888 = c_Orderings_Obot__class_Obot(tc_fun(X27889,tc_HOL_Obool))
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X27889),X27887),c_Big__Operators_Olattice_OInf__fin(X27889,c_Orderings_Oord__class_Omin(X27889),X27888)) = c_Big__Operators_Olattice_OInf__fin(X27889,c_Orderings_Oord__class_Omin(X27889),hAPP(c_Set_OCollect(X27889),hAPP(hAPP(c_COMBB(tc_fun(X27889,tc_HOL_Obool),tc_HOL_Obool,X27889),c_HOL_OEx(X27889)),hAPP(hAPP(c_COMBC(X27889,tc_fun(X27889,tc_HOL_Obool),tc_fun(X27889,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27889,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X27889,tc_HOL_Obool),tc_fun(X27889,tc_HOL_Obool)),X27889),c_COMBS(X27889,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27889,tc_HOL_Obool),tc_fun(X27889,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X27889),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27889),c_fconj)),hAPP(hAPP(c_COMBC(X27889,tc_fun(X27889,X27889),tc_fun(X27889,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27889,tc_HOL_Obool),tc_fun(tc_fun(X27889,X27889),tc_fun(X27889,tc_HOL_Obool)),X27889),c_COMBB(X27889,tc_HOL_Obool,X27889)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(X27889),X27887))))),hAPP(hAPP(c_COMBC(X27889,tc_fun(X27889,tc_HOL_Obool),tc_HOL_Obool),c_member(X27889)),X27888))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__Inf1__distrib])]) ).

fof(i_0_6114,plain,
    ! [X27833,X27834,X27835] :
      ( ~ class_Orderings_Olinorder(X27835)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27835),X27834))
      | X27834 = c_Orderings_Obot__class_Obot(tc_fun(X27835,tc_HOL_Obool))
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X27835),X27833),c_Big__Operators_Olattice_OSup__fin(X27835,c_Orderings_Oord__class_Omax(X27835),X27834)) = c_Big__Operators_Olattice_OSup__fin(X27835,c_Orderings_Oord__class_Omax(X27835),hAPP(c_Set_OCollect(X27835),hAPP(hAPP(c_COMBB(tc_fun(X27835,tc_HOL_Obool),tc_HOL_Obool,X27835),c_HOL_OEx(X27835)),hAPP(hAPP(c_COMBC(X27835,tc_fun(X27835,tc_HOL_Obool),tc_fun(X27835,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27835,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X27835,tc_HOL_Obool),tc_fun(X27835,tc_HOL_Obool)),X27835),c_COMBS(X27835,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27835,tc_HOL_Obool),tc_fun(X27835,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X27835),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27835),c_fconj)),hAPP(hAPP(c_COMBC(X27835,tc_fun(X27835,X27835),tc_fun(X27835,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27835,tc_HOL_Obool),tc_fun(tc_fun(X27835,X27835),tc_fun(X27835,tc_HOL_Obool)),X27835),c_COMBB(X27835,tc_HOL_Obool,X27835)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(X27835),X27833))))),hAPP(hAPP(c_COMBC(X27835,tc_fun(X27835,tc_HOL_Obool),tc_HOL_Obool),c_member(X27835)),X27834))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__Sup1__distrib])]) ).

fof(i_0_6115,plain,
    ! [X27881,X27882,X27883] :
      ( ~ class_Lattices_Odistrib__lattice(X27883)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27883),X27882))
      | X27882 = c_Orderings_Obot__class_Obot(tc_fun(X27883,tc_HOL_Obool))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27883),X27881),c_Big__Operators_Olattice__class_OSup__fin(X27883,X27882)) = c_Big__Operators_Olattice__class_OSup__fin(X27883,hAPP(c_Set_OCollect(X27883),hAPP(hAPP(c_COMBB(tc_fun(X27883,tc_HOL_Obool),tc_HOL_Obool,X27883),c_HOL_OEx(X27883)),hAPP(hAPP(c_COMBC(X27883,tc_fun(X27883,tc_HOL_Obool),tc_fun(X27883,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27883,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X27883,tc_HOL_Obool),tc_fun(X27883,tc_HOL_Obool)),X27883),c_COMBS(X27883,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27883,tc_HOL_Obool),tc_fun(X27883,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X27883),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27883),c_fconj)),hAPP(hAPP(c_COMBC(X27883,tc_fun(X27883,X27883),tc_fun(X27883,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27883,tc_HOL_Obool),tc_fun(tc_fun(X27883,X27883),tc_fun(X27883,tc_HOL_Obool)),X27883),c_COMBB(X27883,tc_HOL_Obool,X27883)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27883),X27881))))),hAPP(hAPP(c_COMBC(X27883,tc_fun(X27883,tc_HOL_Obool),tc_HOL_Obool),c_member(X27883)),X27882))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__Sup1__distrib])]) ).

fof(i_0_6116,plain,
    ! [X27872,X27873,X27874] :
      ( ~ class_Lattices_Odistrib__lattice(X27874)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27874),X27873))
      | X27873 = c_Orderings_Obot__class_Obot(tc_fun(X27874,tc_HOL_Obool))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27874),X27872),c_Big__Operators_Olattice__class_OInf__fin(X27874,X27873)) = c_Big__Operators_Olattice__class_OInf__fin(X27874,hAPP(c_Set_OCollect(X27874),hAPP(hAPP(c_COMBB(tc_fun(X27874,tc_HOL_Obool),tc_HOL_Obool,X27874),c_HOL_OEx(X27874)),hAPP(hAPP(c_COMBC(X27874,tc_fun(X27874,tc_HOL_Obool),tc_fun(X27874,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27874,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X27874,tc_HOL_Obool),tc_fun(X27874,tc_HOL_Obool)),X27874),c_COMBS(X27874,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27874,tc_HOL_Obool),tc_fun(X27874,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X27874),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27874),c_fconj)),hAPP(hAPP(c_COMBC(X27874,tc_fun(X27874,X27874),tc_fun(X27874,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27874,tc_HOL_Obool),tc_fun(tc_fun(X27874,X27874),tc_fun(X27874,tc_HOL_Obool)),X27874),c_COMBB(X27874,tc_HOL_Obool,X27874)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27874),X27872))))),hAPP(hAPP(c_COMBC(X27874,tc_fun(X27874,tc_HOL_Obool),tc_HOL_Obool),c_member(X27874)),X27873))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__Inf1__distrib])]) ).

fof(i_0_6117,plain,
    ! [X27866,X27867,X27868] :
      ( ~ class_Groups_Olinordered__ab__semigroup__add(X27868)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27868),X27867))
      | X27867 = c_Orderings_Obot__class_Obot(tc_fun(X27868,tc_HOL_Obool))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27868),X27866),c_Big__Operators_Olinorder__class_OMin(X27868,X27867)) = c_Big__Operators_Olinorder__class_OMin(X27868,hAPP(c_Set_OCollect(X27868),hAPP(hAPP(c_COMBB(tc_fun(X27868,tc_HOL_Obool),tc_HOL_Obool,X27868),c_HOL_OEx(X27868)),hAPP(hAPP(c_COMBC(X27868,tc_fun(X27868,tc_HOL_Obool),tc_fun(X27868,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27868,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X27868,tc_HOL_Obool),tc_fun(X27868,tc_HOL_Obool)),X27868),c_COMBS(X27868,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27868,tc_HOL_Obool),tc_fun(X27868,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X27868),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27868),c_fconj)),hAPP(hAPP(c_COMBC(X27868,tc_fun(X27868,X27868),tc_fun(X27868,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27868,tc_HOL_Obool),tc_fun(tc_fun(X27868,X27868),tc_fun(X27868,tc_HOL_Obool)),X27868),c_COMBB(X27868,tc_HOL_Obool,X27868)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(X27868),X27866))))),hAPP(hAPP(c_COMBC(X27868,tc_fun(X27868,tc_HOL_Obool),tc_HOL_Obool),c_member(X27868)),X27867))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__Min__commute])]) ).

fof(i_0_6118,plain,
    ! [X27869,X27870,X27871] :
      ( ~ class_Groups_Olinordered__ab__semigroup__add(X27871)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27871),X27870))
      | X27870 = c_Orderings_Obot__class_Obot(tc_fun(X27871,tc_HOL_Obool))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27871),X27869),c_Big__Operators_Olinorder__class_OMax(X27871,X27870)) = c_Big__Operators_Olinorder__class_OMax(X27871,hAPP(c_Set_OCollect(X27871),hAPP(hAPP(c_COMBB(tc_fun(X27871,tc_HOL_Obool),tc_HOL_Obool,X27871),c_HOL_OEx(X27871)),hAPP(hAPP(c_COMBC(X27871,tc_fun(X27871,tc_HOL_Obool),tc_fun(X27871,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27871,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X27871,tc_HOL_Obool),tc_fun(X27871,tc_HOL_Obool)),X27871),c_COMBS(X27871,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27871,tc_HOL_Obool),tc_fun(X27871,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X27871),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27871),c_fconj)),hAPP(hAPP(c_COMBC(X27871,tc_fun(X27871,X27871),tc_fun(X27871,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27871,tc_HOL_Obool),tc_fun(tc_fun(X27871,X27871),tc_fun(X27871,tc_HOL_Obool)),X27871),c_COMBB(X27871,tc_HOL_Obool,X27871)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(X27871),X27869))))),hAPP(hAPP(c_COMBC(X27871,tc_fun(X27871,tc_HOL_Obool),tc_HOL_Obool),c_member(X27871)),X27870))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__Max__commute])]) ).

fof(i_0_6119,plain,
    ! [X23083,X23084,X23085,X23086,X23087] :
      ( ( hBOOL(hAPP(hAPP(X23087,esk104_5(X23083,X23084,X23085,X23086,X23087)),esk105_5(X23083,X23084,X23085,X23086,X23087)))
        | c_Hoare__Mirabelle_Ohoare__derivs(X23086,X23085,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X23086)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X23086),X23087),X23084),X23083)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X23086),tc_HOL_Obool)))) )
      & ( ~ c_Hoare__Mirabelle_Ohoare__derivs(X23086,X23085,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X23086)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X23086),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),X23086),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),esk105_5(X23083,X23084,X23085,X23086,X23087)))),X23084),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),X23086),hAPP(X23083,esk104_5(X23083,X23084,X23085,X23086,X23087))))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X23086),tc_HOL_Obool))))
        | c_Hoare__Mirabelle_Ohoare__derivs(X23086,X23085,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X23086)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X23086),X23087),X23084),X23083)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X23086),tc_HOL_Obool)))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_escape])])])]) ).

fof(i_0_6120,plain,
    ! [X29210,X29211,X29212,X29213,X29214,X29215,X29216,X29217,X29218] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29213)),X29212) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29213)),X29211)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29213),tc_List_Olist(X29213))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29213),tc_List_Olist(X29213)),X29212),X29211)),c_List_Olistrel(X29213,X29210))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29213,X29213)),X29214),hAPP(c_List_Oset(tc_prod(X29213,X29213)),hAPP(hAPP(c_List_Ozip(X29213,X29213),X29212),X29211))))
        | hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X29213,X29213,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X29213,tc_fun(tc_prod(X29213,X29213),tc_HOL_Obool),tc_fun(X29213,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29213,tc_fun(tc_fun(tc_prod(X29213,X29213),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X29213,X29213),tc_HOL_Obool),tc_fun(X29213,tc_HOL_Obool)),X29213),c_COMBC(X29213,tc_fun(tc_prod(X29213,X29213),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29213,tc_prod(X29213,X29213)),tc_fun(X29213,tc_fun(tc_fun(tc_prod(X29213,X29213),tc_HOL_Obool),tc_HOL_Obool)),X29213),hAPP(c_COMBB(tc_prod(X29213,X29213),tc_fun(tc_fun(tc_prod(X29213,X29213),tc_HOL_Obool),tc_HOL_Obool),X29213),c_member(tc_prod(X29213,X29213)))),c_Product__Type_OPair(X29213,X29213)))),X29210)),X29214))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29213),tc_List_Olist(X29213))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29213),tc_List_Olist(X29213)),X29212),X29211)),c_List_Olistrel(X29213,X29210))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29218,X29218)),esk329_4(X29215,X29216,X29217,X29218)),hAPP(c_List_Oset(tc_prod(X29218,X29218)),hAPP(hAPP(c_List_Ozip(X29218,X29218),X29217),X29216))))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29218)),X29217) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29218)),X29216)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29218),tc_List_Olist(X29218))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29218),tc_List_Olist(X29218)),X29217),X29216)),c_List_Olistrel(X29218,X29215))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X29218,X29218,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X29218,tc_fun(tc_prod(X29218,X29218),tc_HOL_Obool),tc_fun(X29218,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29218,tc_fun(tc_fun(tc_prod(X29218,X29218),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X29218,X29218),tc_HOL_Obool),tc_fun(X29218,tc_HOL_Obool)),X29218),c_COMBC(X29218,tc_fun(tc_prod(X29218,X29218),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29218,tc_prod(X29218,X29218)),tc_fun(X29218,tc_fun(tc_fun(tc_prod(X29218,X29218),tc_HOL_Obool),tc_HOL_Obool)),X29218),hAPP(c_COMBB(tc_prod(X29218,X29218),tc_fun(tc_fun(tc_prod(X29218,X29218),tc_HOL_Obool),tc_HOL_Obool),X29218),c_member(tc_prod(X29218,X29218)))),c_Product__Type_OPair(X29218,X29218)))),X29215)),esk329_4(X29215,X29216,X29217,X29218)))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29218)),X29217) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29218)),X29216)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29218),tc_List_Olist(X29218))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29218),tc_List_Olist(X29218)),X29217),X29216)),c_List_Olistrel(X29218,X29215))) ) ),
    inference(distribute,[status(thm)],[inference(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_6121,plain,
    ! [X30958,X30959,X30960,X30961] :
      ( ( ~ hBOOL(hAPP(c_Predicate_ODomainP(X30961,X30960,hAPP(hAPP(c_COMBC(X30961,tc_fun(tc_prod(X30961,X30960),tc_HOL_Obool),tc_fun(X30960,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X30960,tc_fun(tc_fun(tc_prod(X30961,X30960),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X30961,X30960),tc_HOL_Obool),tc_fun(X30960,tc_HOL_Obool)),X30961),c_COMBC(X30960,tc_fun(tc_prod(X30961,X30960),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X30960,tc_prod(X30961,X30960)),tc_fun(X30960,tc_fun(tc_fun(tc_prod(X30961,X30960),tc_HOL_Obool),tc_HOL_Obool)),X30961),hAPP(c_COMBB(tc_prod(X30961,X30960),tc_fun(tc_fun(tc_prod(X30961,X30960),tc_HOL_Obool),tc_HOL_Obool),X30960),c_member(tc_prod(X30961,X30960)))),c_Product__Type_OPair(X30961,X30960)))),X30959)),X30958))
        | hBOOL(hAPP(hAPP(c_member(X30961),X30958),hAPP(c_Relation_ODomain(X30961,X30960),X30959))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X30961),X30958),hAPP(c_Relation_ODomain(X30961,X30960),X30959)))
        | hBOOL(hAPP(c_Predicate_ODomainP(X30961,X30960,hAPP(hAPP(c_COMBC(X30961,tc_fun(tc_prod(X30961,X30960),tc_HOL_Obool),tc_fun(X30960,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X30960,tc_fun(tc_fun(tc_prod(X30961,X30960),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X30961,X30960),tc_HOL_Obool),tc_fun(X30960,tc_HOL_Obool)),X30961),c_COMBC(X30960,tc_fun(tc_prod(X30961,X30960),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X30960,tc_prod(X30961,X30960)),tc_fun(X30960,tc_fun(tc_fun(tc_prod(X30961,X30960),tc_HOL_Obool),tc_HOL_Obool)),X30961),hAPP(c_COMBB(tc_prod(X30961,X30960),tc_fun(tc_fun(tc_prod(X30961,X30960),tc_HOL_Obool),tc_HOL_Obool),X30960),c_member(tc_prod(X30961,X30960)))),c_Product__Type_OPair(X30961,X30960)))),X30959)),X30958)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DomainP__Domain__eq])]) ).

fof(i_0_6122,plain,
    ! [X28301,X28302,X28303,X28304] :
      ( ( ~ hBOOL(hAPP(c_Predicate_ORangeP(X28304,X28303,hAPP(hAPP(c_COMBC(X28304,tc_fun(tc_prod(X28304,X28303),tc_HOL_Obool),tc_fun(X28303,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28303,tc_fun(tc_fun(tc_prod(X28304,X28303),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X28304,X28303),tc_HOL_Obool),tc_fun(X28303,tc_HOL_Obool)),X28304),c_COMBC(X28303,tc_fun(tc_prod(X28304,X28303),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28303,tc_prod(X28304,X28303)),tc_fun(X28303,tc_fun(tc_fun(tc_prod(X28304,X28303),tc_HOL_Obool),tc_HOL_Obool)),X28304),hAPP(c_COMBB(tc_prod(X28304,X28303),tc_fun(tc_fun(tc_prod(X28304,X28303),tc_HOL_Obool),tc_HOL_Obool),X28303),c_member(tc_prod(X28304,X28303)))),c_Product__Type_OPair(X28304,X28303)))),X28302)),X28301))
        | hBOOL(hAPP(hAPP(c_member(X28303),X28301),hAPP(c_Relation_ORange(X28304,X28303),X28302))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X28303),X28301),hAPP(c_Relation_ORange(X28304,X28303),X28302)))
        | hBOOL(hAPP(c_Predicate_ORangeP(X28304,X28303,hAPP(hAPP(c_COMBC(X28304,tc_fun(tc_prod(X28304,X28303),tc_HOL_Obool),tc_fun(X28303,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28303,tc_fun(tc_fun(tc_prod(X28304,X28303),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X28304,X28303),tc_HOL_Obool),tc_fun(X28303,tc_HOL_Obool)),X28304),c_COMBC(X28303,tc_fun(tc_prod(X28304,X28303),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28303,tc_prod(X28304,X28303)),tc_fun(X28303,tc_fun(tc_fun(tc_prod(X28304,X28303),tc_HOL_Obool),tc_HOL_Obool)),X28304),hAPP(c_COMBB(tc_prod(X28304,X28303),tc_fun(tc_fun(tc_prod(X28304,X28303),tc_HOL_Obool),tc_HOL_Obool),X28303),c_member(tc_prod(X28304,X28303)))),c_Product__Type_OPair(X28304,X28303)))),X28302)),X28301)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_RangeP__Range__eq])]) ).

fof(i_0_6123,plain,
    ! [X23462,X23463,X23464] :
      ( ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X23464,hAPP(hAPP(c_COMBC(X23464,tc_fun(tc_prod(X23464,X23464),tc_HOL_Obool),tc_fun(X23464,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X23464,tc_fun(tc_fun(tc_prod(X23464,X23464),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X23464,X23464),tc_HOL_Obool),tc_fun(X23464,tc_HOL_Obool)),X23464),c_COMBC(X23464,tc_fun(tc_prod(X23464,X23464),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X23464,tc_prod(X23464,X23464)),tc_fun(X23464,tc_fun(tc_fun(tc_prod(X23464,X23464),tc_HOL_Obool),tc_HOL_Obool)),X23464),hAPP(c_COMBB(tc_prod(X23464,X23464),tc_fun(tc_fun(tc_prod(X23464,X23464),tc_HOL_Obool),tc_HOL_Obool),X23464),c_member(tc_prod(X23464,X23464)))),c_Product__Type_OPair(X23464,X23464)))),X23463)),X23462))
        | hBOOL(hAPP(hAPP(c_member(X23464),X23462),c_Wellfounded_Oacc(X23464,X23463))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X23464),X23462),c_Wellfounded_Oacc(X23464,X23463)))
        | hBOOL(hAPP(c_Wellfounded_Oaccp(X23464,hAPP(hAPP(c_COMBC(X23464,tc_fun(tc_prod(X23464,X23464),tc_HOL_Obool),tc_fun(X23464,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X23464,tc_fun(tc_fun(tc_prod(X23464,X23464),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X23464,X23464),tc_HOL_Obool),tc_fun(X23464,tc_HOL_Obool)),X23464),c_COMBC(X23464,tc_fun(tc_prod(X23464,X23464),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X23464,tc_prod(X23464,X23464)),tc_fun(X23464,tc_fun(tc_fun(tc_prod(X23464,X23464),tc_HOL_Obool),tc_HOL_Obool)),X23464),hAPP(c_COMBB(tc_prod(X23464,X23464),tc_fun(tc_fun(tc_prod(X23464,X23464),tc_HOL_Obool),tc_HOL_Obool),X23464),c_member(tc_prod(X23464,X23464)))),c_Product__Type_OPair(X23464,X23464)))),X23463)),X23462)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_accp__acc__eq])]) ).

fof(i_0_6124,plain,
    ! [X33547,X33548,X33549] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X33549,X33548),X33547) = c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(X33549,tc_Lazy__Sequence_Olazy__sequence(X33549)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(X33549,tc_Lazy__Sequence_Olazy__sequence(X33549),tc_Nat_Onat),hAPP(hAPP(c_COMBC(X33549,tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(X33549),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X33549),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(X33549),tc_Nat_Onat)),X33549),c_COMBC(tc_Lazy__Sequence_Olazy__sequence(X33549),tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X33549),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(X33549),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),X33549),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(X33549)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat))),hAPP(hAPP(c_COMBC(X33549,tc_fun(tc_Lazy__Sequence_Olazy__sequence(X33549),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(X33549),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X33549),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(X33549),tc_Nat_Onat)),X33549),c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Lazy__Sequence_Olazy__sequence(X33549))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),X33549),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X33548))),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X33549,X33548))))),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Lazy__Sequence_Oyield(X33549),X33547)),
    inference(variable_rename,[status(thm)],[fact_lazy__sequence__size__code]) ).

fof(i_0_6125,plain,
    ! [X17135,X17136,X17137,X17138,X17139,X17140,X17141,X17145] :
      ( ( hBOOL(hAPP(hAPP(X17136,esk9_7(X17135,X17136,X17137,X17138,X17139,X17140,X17141)),esk10_7(X17135,X17136,X17137,X17138,X17139,X17140,X17141)))
        | c_Hoare__Mirabelle_Ohoare__derivs(X17141,X17140,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X17141)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17141),X17136),X17138),X17135)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X17141),tc_HOL_Obool))))
        | ~ c_Hoare__Mirabelle_Ohoare__derivs(X17141,X17140,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X17141)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17141),X17139),X17138),X17137)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X17141),tc_HOL_Obool)))) )
      & ( ~ hBOOL(hAPP(hAPP(X17139,X17145),esk10_7(X17135,X17136,X17137,X17138,X17139,X17140,X17141)))
        | hBOOL(hAPP(hAPP(X17137,X17145),esk11_7(X17135,X17136,X17137,X17138,X17139,X17140,X17141)))
        | c_Hoare__Mirabelle_Ohoare__derivs(X17141,X17140,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X17141)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17141),X17136),X17138),X17135)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X17141),tc_HOL_Obool))))
        | ~ c_Hoare__Mirabelle_Ohoare__derivs(X17141,X17140,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X17141)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17141),X17139),X17138),X17137)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X17141),tc_HOL_Obool)))) )
      & ( ~ hBOOL(hAPP(hAPP(X17135,esk9_7(X17135,X17136,X17137,X17138,X17139,X17140,X17141)),esk11_7(X17135,X17136,X17137,X17138,X17139,X17140,X17141)))
        | c_Hoare__Mirabelle_Ohoare__derivs(X17141,X17140,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X17141)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17141),X17136),X17138),X17135)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X17141),tc_HOL_Obool))))
        | ~ c_Hoare__Mirabelle_Ohoare__derivs(X17141,X17140,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X17141)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17141),X17139),X17138),X17137)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X17141),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_conseq12])])])])]) ).

fof(i_0_6126,plain,
    ! [X21659,X21660,X21661,X21662,X21663,X21664,X21665,X21668,X21669,X21670,X21671,X21672,X21673,X21674,X21675,X21676] :
      ( ( hAPP(hAPP(X21663,X21660),X21659) = hAPP(hAPP(X21663,esk78_7(X21659,X21660,X21661,X21662,X21663,X21664,X21665)),esk79_7(X21659,X21660,X21661,X21662,X21663,X21664,X21665))
        | X21661 = c_Orderings_Obot__class_Obot(tc_fun(X21665,tc_HOL_Obool))
        | ~ c_Nitpick_Ofold__graph_H(X21665,X21664,X21663,X21662,X21661,hAPP(hAPP(X21663,X21660),X21659)) )
      & ( hBOOL(hAPP(hAPP(c_member(X21665),esk78_7(X21659,X21660,X21661,X21662,X21663,X21664,X21665)),X21661))
        | X21661 = c_Orderings_Obot__class_Obot(tc_fun(X21665,tc_HOL_Obool))
        | ~ c_Nitpick_Ofold__graph_H(X21665,X21664,X21663,X21662,X21661,hAPP(hAPP(X21663,X21660),X21659)) )
      & ( c_Nitpick_Ofold__graph_H(X21665,X21664,X21663,X21662,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X21665,tc_HOL_Obool)),X21661),hAPP(hAPP(c_Set_Oinsert(X21665),esk78_7(X21659,X21660,X21661,X21662,X21663,X21664,X21665)),c_Orderings_Obot__class_Obot(tc_fun(X21665,tc_HOL_Obool)))),esk79_7(X21659,X21660,X21661,X21662,X21663,X21664,X21665))
        | X21661 = c_Orderings_Obot__class_Obot(tc_fun(X21665,tc_HOL_Obool))
        | ~ c_Nitpick_Ofold__graph_H(X21665,X21664,X21663,X21662,X21661,hAPP(hAPP(X21663,X21660),X21659)) )
      & ( hAPP(hAPP(X21663,X21660),X21659) = hAPP(hAPP(X21663,esk78_7(X21659,X21660,X21661,X21662,X21663,X21664,X21665)),esk79_7(X21659,X21660,X21661,X21662,X21663,X21664,X21665))
        | hAPP(hAPP(X21663,X21660),X21659) = X21662
        | ~ c_Nitpick_Ofold__graph_H(X21665,X21664,X21663,X21662,X21661,hAPP(hAPP(X21663,X21660),X21659)) )
      & ( hBOOL(hAPP(hAPP(c_member(X21665),esk78_7(X21659,X21660,X21661,X21662,X21663,X21664,X21665)),X21661))
        | hAPP(hAPP(X21663,X21660),X21659) = X21662
        | ~ c_Nitpick_Ofold__graph_H(X21665,X21664,X21663,X21662,X21661,hAPP(hAPP(X21663,X21660),X21659)) )
      & ( c_Nitpick_Ofold__graph_H(X21665,X21664,X21663,X21662,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X21665,tc_HOL_Obool)),X21661),hAPP(hAPP(c_Set_Oinsert(X21665),esk78_7(X21659,X21660,X21661,X21662,X21663,X21664,X21665)),c_Orderings_Obot__class_Obot(tc_fun(X21665,tc_HOL_Obool)))),esk79_7(X21659,X21660,X21661,X21662,X21663,X21664,X21665))
        | hAPP(hAPP(X21663,X21660),X21659) = X21662
        | ~ c_Nitpick_Ofold__graph_H(X21665,X21664,X21663,X21662,X21661,hAPP(hAPP(X21663,X21660),X21659)) )
      & ( X21670 != c_Orderings_Obot__class_Obot(tc_fun(X21674,tc_HOL_Obool))
        | hAPP(hAPP(X21672,X21669),X21668) != X21671
        | c_Nitpick_Ofold__graph_H(X21674,X21673,X21672,X21671,X21670,hAPP(hAPP(X21672,X21669),X21668)) )
      & ( hAPP(hAPP(X21672,X21669),X21668) != hAPP(hAPP(X21672,X21675),X21676)
        | ~ hBOOL(hAPP(hAPP(c_member(X21674),X21675),X21670))
        | ~ c_Nitpick_Ofold__graph_H(X21674,X21673,X21672,X21671,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X21674,tc_HOL_Obool)),X21670),hAPP(hAPP(c_Set_Oinsert(X21674),X21675),c_Orderings_Obot__class_Obot(tc_fun(X21674,tc_HOL_Obool)))),X21676)
        | c_Nitpick_Ofold__graph_H(X21674,X21673,X21672,X21671,X21670,hAPP(hAPP(X21672,X21669),X21668)) ) ),
    inference(distribute,[status(thm)],[inference(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_6127,plain,
    ! [X33617,X33618,X33619,X33620,X33621,X33622,X33623] :
      ( ( hBOOL(hAPP(hAPP(c_member(X33623),esk530_7(X33617,X33618,X33619,X33620,X33621,X33622,X33623)),X33620))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X33623,tc_fun(X33622,tc_fun(X33621,tc_HOL_Obool))),X33620),X33619),X33618),X33617)) )
      & ( hBOOL(hAPP(hAPP(hAPP(X33619,esk530_7(X33617,X33618,X33619,X33620,X33621,X33622,X33623)),X33618),X33617))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X33623,tc_fun(X33622,tc_fun(X33621,tc_HOL_Obool))),X33620),X33619),X33618),X33617)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5242])])])]) ).

fof(i_0_6128,plain,
    ! [X25293,X25294,X25295,X25296,X25297,X25298,X25299,X25301,X25302,X25303,X25304,X25305,X25306,X25307,X25308] :
      ( ( hBOOL(hAPP(hAPP(c_member(X25299),esk165_7(X25293,X25294,X25295,X25296,X25297,X25298,X25299)),X25296))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25299,tc_fun(X25298,tc_fun(X25297,tc_HOL_Obool))),X25296),X25295),X25294),X25293)) )
      & ( hBOOL(hAPP(hAPP(hAPP(X25295,esk165_7(X25293,X25294,X25295,X25296,X25297,X25298,X25299)),X25294),X25293))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25299,tc_fun(X25298,tc_fun(X25297,tc_HOL_Obool))),X25296),X25295),X25294),X25293)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X25307),X25308),X25304))
        | ~ hBOOL(hAPP(hAPP(hAPP(X25303,X25308),X25302),X25301))
        | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25307,tc_fun(X25306,tc_fun(X25305,tc_HOL_Obool))),X25304),X25303),X25302),X25301)) ) ),
    inference(distribute,[status(thm)],[inference(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_6129,plain,
    ! [X30487,X30488,X30489,X30490] : c_List_Opartition(X30490,X30489,hAPP(hAPP(c_List_Olist_OCons(X30490),X30488),X30487)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X30490),tc_List_Olist(X30490),tc_prod(tc_List_Olist(X30490),tc_List_Olist(X30490))),hAPP(hAPP(c_COMBS(tc_List_Olist(X30490),tc_fun(tc_List_Olist(X30490),tc_prod(tc_List_Olist(X30490),tc_List_Olist(X30490))),tc_fun(tc_List_Olist(X30490),tc_prod(tc_List_Olist(X30490),tc_List_Olist(X30490)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X30490),tc_fun(tc_prod(tc_List_Olist(X30490),tc_List_Olist(X30490)),tc_prod(tc_List_Olist(X30490),tc_List_Olist(X30490)))),tc_fun(tc_fun(tc_List_Olist(X30490),tc_prod(tc_List_Olist(X30490),tc_List_Olist(X30490))),tc_fun(tc_List_Olist(X30490),tc_prod(tc_List_Olist(X30490),tc_List_Olist(X30490)))),tc_List_Olist(X30490)),c_COMBS(tc_List_Olist(X30490),tc_prod(tc_List_Olist(X30490),tc_List_Olist(X30490)),tc_prod(tc_List_Olist(X30490),tc_List_Olist(X30490)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X30490),tc_prod(tc_List_Olist(X30490),tc_List_Olist(X30490))),tc_fun(tc_List_Olist(X30490),tc_fun(tc_prod(tc_List_Olist(X30490),tc_List_Olist(X30490)),tc_prod(tc_List_Olist(X30490),tc_List_Olist(X30490)))),tc_List_Olist(X30490)),hAPP(c_COMBB(tc_prod(tc_List_Olist(X30490),tc_List_Olist(X30490)),tc_fun(tc_prod(tc_List_Olist(X30490),tc_List_Olist(X30490)),tc_prod(tc_List_Olist(X30490),tc_List_Olist(X30490))),tc_List_Olist(X30490)),hAPP(c_If(tc_prod(tc_List_Olist(X30490),tc_List_Olist(X30490))),hAPP(X30489,X30488)))),hAPP(hAPP(c_COMBB(tc_List_Olist(X30490),tc_fun(tc_List_Olist(X30490),tc_prod(tc_List_Olist(X30490),tc_List_Olist(X30490))),tc_List_Olist(X30490)),c_Product__Type_OPair(tc_List_Olist(X30490),tc_List_Olist(X30490))),hAPP(c_List_Olist_OCons(X30490),X30488))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X30490),tc_fun(tc_List_Olist(X30490),tc_List_Olist(X30490)),tc_fun(tc_List_Olist(X30490),tc_prod(tc_List_Olist(X30490),tc_List_Olist(X30490)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X30490),tc_prod(tc_List_Olist(X30490),tc_List_Olist(X30490))),tc_fun(tc_fun(tc_List_Olist(X30490),tc_List_Olist(X30490)),tc_fun(tc_List_Olist(X30490),tc_prod(tc_List_Olist(X30490),tc_List_Olist(X30490)))),tc_List_Olist(X30490)),c_COMBB(tc_List_Olist(X30490),tc_prod(tc_List_Olist(X30490),tc_List_Olist(X30490)),tc_List_Olist(X30490))),c_Product__Type_OPair(tc_List_Olist(X30490),tc_List_Olist(X30490)))),hAPP(c_List_Olist_OCons(X30490),X30488)))),c_List_Opartition(X30490,X30489,X30487)),
    inference(variable_rename,[status(thm)],[fact_partition_Osimps_I2_J]) ).

fof(i_0_6130,plain,
    ! [X22511,X22512,X22513,X22514,X22515] : c_Hoare__Mirabelle_Ohoare__derivs(X22515,X22514,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X22515)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X22515),hAPP(hAPP(c_COMBC(X22515,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),X22515),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),X22513)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),X22512)),X22511))),c_Com_Ocom_OAss(X22512,X22511)),X22513)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X22515),tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_hoare__derivs_Oequations_I8_J]) ).

fof(i_0_6131,plain,
    ! [X22367,X22368,X22369,X22370,X22371] : c_Hoare__Mirabelle_Ohoare__derivs(X22371,X22370,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X22371)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X22371),hAPP(hAPP(c_COMBC(X22371,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),X22371),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),X22369)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),X22368)),X22367))),c_Com_Ocom_OAss(X22368,X22367)),X22369)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X22371),tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_Ass]) ).

fof(i_0_6132,plain,
    ! [X28343,X28344,X28345] : hAPP(c_List_Olexn(X28345,X28344),hAPP(c_Nat_OSuc,X28343)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(X28345),tc_List_Olist(X28345)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(X28345,tc_List_Olist(X28345)),tc_prod(X28345,tc_List_Olist(X28345))),tc_prod(tc_List_Olist(X28345),tc_List_Olist(X28345)),c_Product__Type_Omap__pair(tc_prod(X28345,tc_List_Olist(X28345)),tc_List_Olist(X28345),tc_prod(X28345,tc_List_Olist(X28345)),tc_List_Olist(X28345),hAPP(c_Product__Type_Oprod_Oprod__case(X28345,tc_List_Olist(X28345),tc_List_Olist(X28345)),c_List_Olist_OCons(X28345)),hAPP(c_Product__Type_Oprod_Oprod__case(X28345,tc_List_Olist(X28345),tc_List_Olist(X28345)),c_List_Olist_OCons(X28345)))),c_Wellfounded_Olex__prod(X28345,tc_List_Olist(X28345),X28344,hAPP(c_List_Olexn(X28345,X28344),X28343)))),hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(X28345),tc_List_Olist(X28345))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X28345),tc_List_Olist(X28345),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X28345),tc_fun(tc_List_Olist(X28345),tc_HOL_Obool),tc_fun(tc_List_Olist(X28345),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X28345),tc_HOL_Obool),tc_fun(tc_List_Olist(X28345),tc_HOL_Obool)),tc_List_Olist(X28345)),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X28345))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X28345)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X28345),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X28345)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X28345)))),hAPP(c_Nat_OSuc,X28343))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X28345),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X28345)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X28345)))),hAPP(c_Nat_OSuc,X28343)))))),
    inference(variable_rename,[status(thm)],[fact_lexn_Osimps_I2_J]) ).

cnf(i_0_6133,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_5243]) ).

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),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_5243]) ).

cnf(i_0_6135,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_5244]) ).

fof(i_0_6136,plain,
    ! [X28991,X28992,X28993] : hAPP(c_List_Oset(X28993),c_List_Osublist(X28993,X28992,X28991)) = hAPP(c_Set_OCollect(X28993),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,X28993),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(X28993,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)),X28993),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)),X28993),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(X28993,tc_fun(tc_Nat_Onat,X28993),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28993,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,X28993),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X28993),c_COMBB(X28993,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(X28993),X28992))))),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(X28993)),X28992)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X28991))))),
    inference(variable_rename,[status(thm)],[fact_set__sublist]) ).

cnf(i_0_6137,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_5245]) ).

cnf(i_0_6138,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_5246]) ).

cnf(i_0_6139,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_5247]) ).

fof(i_0_6140,plain,
    ! [X27970,X27971,X27972,X27973,X27974,X27975] :
      ( ( hBOOL(hAPP(hAPP(c_member(X27973),esk293_6(X27970,X27971,X27972,X27973,X27974,X27975)),X27972))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27975,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X27973,tc_HOL_Obool),tc_Nat_Onat,X27975),c_Finite__Set_Ocard(X27973)),hAPP(hAPP(c_COMBB(tc_fun(X27973,tc_HOL_Obool),tc_fun(X27973,tc_HOL_Obool),X27975),c_Set_OCollect(X27973)),hAPP(hAPP(c_COMBB(tc_fun(X27973,tc_HOL_Obool),tc_fun(X27973,tc_HOL_Obool),X27975),hAPP(c_COMBS(X27973,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27973),c_fconj),hAPP(hAPP(c_COMBC(X27973,tc_fun(X27973,tc_HOL_Obool),tc_HOL_Obool),c_member(X27973)),X27972)))),X27971)))),X27974) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27973,tc_Nat_Onat),X27970),X27972)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27973),X27972))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27975),X27974)) )
      & ( hAPP(c_Finite__Set_Ocard(X27975),hAPP(c_Set_OCollect(X27975),hAPP(hAPP(c_COMBS(X27975,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27975),c_fconj),hAPP(hAPP(c_COMBC(X27975,tc_fun(X27975,tc_HOL_Obool),tc_HOL_Obool),c_member(X27975)),X27974))),hAPP(hAPP(c_COMBC(X27975,X27973,tc_HOL_Obool),X27971),esk293_6(X27970,X27971,X27972,X27973,X27974,X27975))))) != hAPP(X27970,esk293_6(X27970,X27971,X27972,X27973,X27974,X27975))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27975,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X27973,tc_HOL_Obool),tc_Nat_Onat,X27975),c_Finite__Set_Ocard(X27973)),hAPP(hAPP(c_COMBB(tc_fun(X27973,tc_HOL_Obool),tc_fun(X27973,tc_HOL_Obool),X27975),c_Set_OCollect(X27973)),hAPP(hAPP(c_COMBB(tc_fun(X27973,tc_HOL_Obool),tc_fun(X27973,tc_HOL_Obool),X27975),hAPP(c_COMBS(X27973,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27973),c_fconj),hAPP(hAPP(c_COMBC(X27973,tc_fun(X27973,tc_HOL_Obool),tc_HOL_Obool),c_member(X27973)),X27972)))),X27971)))),X27974) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27973,tc_Nat_Onat),X27970),X27972)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27973),X27972))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27975),X27974)) ) ),
    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_6141,plain,
    ! [X28975,X28976] : hAPP(c_List_Oset(X28976),X28975) = hAPP(c_Set_OCollect(X28976),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,X28976),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(X28976,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)),X28976),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)),X28976),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(X28976,tc_fun(tc_Nat_Onat,X28976),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28976,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,X28976),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X28976),c_COMBB(X28976,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(X28976),X28975))))),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(X28976)),X28975))))),
    inference(variable_rename,[status(thm)],[fact_set__conv__nth]) ).

fof(i_0_6142,plain,
    ! [X27435,X27436,X27437,X27438] : hAPP(hAPP(c_Product__Type_OSigma(X27438,X27437),X27436),X27435) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27438,tc_fun(tc_prod(X27438,X27437),tc_HOL_Obool)),X27436),hAPP(hAPP(c_COMBS(X27438,tc_fun(X27437,tc_fun(tc_prod(X27438,X27437),tc_HOL_Obool)),tc_fun(tc_prod(X27438,X27437),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27437,tc_HOL_Obool),tc_fun(tc_fun(X27437,tc_fun(tc_prod(X27438,X27437),tc_HOL_Obool)),tc_fun(tc_prod(X27438,X27437),tc_HOL_Obool)),X27438),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27437,tc_fun(tc_prod(X27438,X27437),tc_HOL_Obool))),X27435)),hAPP(hAPP(c_COMBC(X27438,tc_fun(tc_prod(X27438,X27437),tc_HOL_Obool),tc_fun(X27437,tc_fun(tc_prod(X27438,X27437),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X27437,tc_fun(tc_fun(tc_prod(X27438,X27437),tc_HOL_Obool),tc_fun(tc_prod(X27438,X27437),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X27438,X27437),tc_HOL_Obool),tc_fun(X27437,tc_fun(tc_prod(X27438,X27437),tc_HOL_Obool))),X27438),c_COMBC(X27437,tc_fun(tc_prod(X27438,X27437),tc_HOL_Obool),tc_fun(tc_prod(X27438,X27437),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X27437,tc_prod(X27438,X27437)),tc_fun(X27437,tc_fun(tc_fun(tc_prod(X27438,X27437),tc_HOL_Obool),tc_fun(tc_prod(X27438,X27437),tc_HOL_Obool))),X27438),hAPP(c_COMBB(tc_prod(X27438,X27437),tc_fun(tc_fun(tc_prod(X27438,X27437),tc_HOL_Obool),tc_fun(tc_prod(X27438,X27437),tc_HOL_Obool)),X27437),c_Set_Oinsert(tc_prod(X27438,X27437)))),c_Product__Type_OPair(X27438,X27437)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27438,X27437),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[fact_Sigma__def]) ).

cnf(i_0_6143,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_5248]) ).

fof(i_0_6144,plain,
    ! [X27826,X27827,X27828,X27829,X27830,X27831] :
      ( ( hBOOL(hAPP(hAPP(c_member(X27829),esk291_6(X27826,X27827,X27828,X27829,X27830,X27831)),X27828))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27831,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X27829,tc_HOL_Obool),tc_Nat_Onat,X27831),c_Finite__Set_Ocard(X27829)),hAPP(hAPP(c_COMBB(tc_fun(X27829,tc_HOL_Obool),tc_fun(X27829,tc_HOL_Obool),X27831),c_Set_OCollect(X27829)),hAPP(hAPP(c_COMBB(tc_fun(X27829,tc_HOL_Obool),tc_fun(X27829,tc_HOL_Obool),X27831),hAPP(c_COMBS(X27829,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27829),c_fconj),hAPP(hAPP(c_COMBC(X27829,tc_fun(X27829,tc_HOL_Obool),tc_HOL_Obool),c_member(X27829)),X27828)))),X27827)))),X27830) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X27826),hAPP(c_Finite__Set_Ocard(X27829),X27828))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27829),X27828))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27831),X27830)) )
      & ( hAPP(c_Finite__Set_Ocard(X27831),hAPP(c_Set_OCollect(X27831),hAPP(hAPP(c_COMBS(X27831,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27831),c_fconj),hAPP(hAPP(c_COMBC(X27831,tc_fun(X27831,tc_HOL_Obool),tc_HOL_Obool),c_member(X27831)),X27830))),hAPP(hAPP(c_COMBC(X27831,X27829,tc_HOL_Obool),X27827),esk291_6(X27826,X27827,X27828,X27829,X27830,X27831))))) != X27826
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27831,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X27829,tc_HOL_Obool),tc_Nat_Onat,X27831),c_Finite__Set_Ocard(X27829)),hAPP(hAPP(c_COMBB(tc_fun(X27829,tc_HOL_Obool),tc_fun(X27829,tc_HOL_Obool),X27831),c_Set_OCollect(X27829)),hAPP(hAPP(c_COMBB(tc_fun(X27829,tc_HOL_Obool),tc_fun(X27829,tc_HOL_Obool),X27831),hAPP(c_COMBS(X27829,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27829),c_fconj),hAPP(hAPP(c_COMBC(X27829,tc_fun(X27829,tc_HOL_Obool),tc_HOL_Obool),c_member(X27829)),X27828)))),X27827)))),X27830) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X27826),hAPP(c_Finite__Set_Ocard(X27829),X27828))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27829),X27828))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27831),X27830)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__multicount])])])]) ).

fof(i_0_6145,plain,
    ! [X27788,X27789,X27790,X27791,X27792,X27793,X27794] :
      ( ~ class_Groups_Ocomm__monoid__add(X27794)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27793),X27792))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27791),X27790))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27793,X27794),hAPP(hAPP(c_COMBS(X27793,tc_fun(X27791,tc_HOL_Obool),X27794),hAPP(hAPP(c_COMBB(tc_fun(X27791,X27794),tc_fun(tc_fun(X27791,tc_HOL_Obool),X27794),X27793),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27791,X27794)),X27789)),hAPP(hAPP(c_COMBB(tc_fun(X27791,tc_HOL_Obool),tc_fun(X27791,tc_HOL_Obool),X27793),c_Set_OCollect(X27791)),hAPP(hAPP(c_COMBB(tc_fun(X27791,tc_HOL_Obool),tc_fun(X27791,tc_HOL_Obool),X27793),hAPP(c_COMBS(X27791,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27791),c_fconj),hAPP(hAPP(c_COMBC(X27791,tc_fun(X27791,tc_HOL_Obool),tc_HOL_Obool),c_member(X27791)),X27790)))),X27788)))),X27792) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27791,X27794),hAPP(hAPP(c_COMBS(X27791,tc_fun(X27793,tc_HOL_Obool),X27794),hAPP(hAPP(c_COMBB(tc_fun(X27793,X27794),tc_fun(tc_fun(X27793,tc_HOL_Obool),X27794),X27791),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27793,X27794)),hAPP(c_COMBC(X27793,X27791,X27794),X27789))),hAPP(hAPP(c_COMBB(tc_fun(X27793,tc_HOL_Obool),tc_fun(X27793,tc_HOL_Obool),X27791),c_Set_OCollect(X27793)),hAPP(hAPP(c_COMBB(tc_fun(X27793,tc_HOL_Obool),tc_fun(X27793,tc_HOL_Obool),X27791),hAPP(c_COMBS(X27793,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27793),c_fconj),hAPP(hAPP(c_COMBC(X27793,tc_fun(X27793,tc_HOL_Obool),tc_HOL_Obool),c_member(X27793)),X27792)))),hAPP(c_COMBC(X27793,X27791,tc_HOL_Obool),X27788))))),X27790) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__setsum__restrict])]) ).

fof(i_0_6146,plain,
    ! [X28634,X28635,X28636,X28637,X28638] :
      ( ( X28638 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
        | hAPP(hAPP(c_Lazy__Sequence_Oanamorph(X28637,X28636,X28635),X28638),X28634) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28636),X28637),c_List_Olist_ONil(X28636)),X28634) )
      & ( X28638 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
        | hAPP(hAPP(c_Lazy__Sequence_Oanamorph(X28637,X28636,X28635),X28638),X28634) = c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(X28636),X28637),tc_prod(X28636,X28637),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28636),X28637),c_List_Olist_ONil(X28636)),X28634),hAPP(c_Product__Type_Oprod_Oprod__case(X28636,X28637,tc_prod(tc_List_Olist(X28636),X28637)),hAPP(hAPP(c_COMBC(X28636,tc_fun(X28637,tc_prod(tc_List_Olist(X28636),X28637)),tc_fun(X28637,tc_prod(tc_List_Olist(X28636),X28637))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(X28636),X28637),tc_prod(tc_List_Olist(X28636),X28637)),tc_fun(tc_fun(X28637,tc_prod(tc_List_Olist(X28636),X28637)),tc_fun(X28637,tc_prod(tc_List_Olist(X28636),X28637))),X28636),c_COMBB(tc_prod(tc_List_Olist(X28636),X28637),tc_prod(tc_List_Olist(X28636),X28637),X28637)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X28636),tc_fun(X28637,tc_prod(tc_List_Olist(X28636),X28637))),tc_fun(tc_prod(tc_List_Olist(X28636),X28637),tc_prod(tc_List_Olist(X28636),X28637)),X28636),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X28636),X28637,tc_prod(tc_List_Olist(X28636),X28637))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X28636),tc_List_Olist(X28636)),tc_fun(tc_List_Olist(X28636),tc_fun(X28637,tc_prod(tc_List_Olist(X28636),X28637))),X28636),hAPP(c_COMBB(tc_List_Olist(X28636),tc_fun(X28637,tc_prod(tc_List_Olist(X28636),X28637)),tc_List_Olist(X28636)),c_Product__Type_OPair(tc_List_Olist(X28636),X28637))),c_List_Olist_OCons(X28636))))),hAPP(c_Lazy__Sequence_Oanamorph(X28637,X28636,X28635),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X28638),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))))),hAPP(X28635,X28634)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_anamorph_Osimps])]) ).

fof(i_0_6147,plain,
    ! [X32283,X32284,X32285,X32286,X32287] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32287,X32287)),hAPP(hAPP(c_Product__Type_OPair(X32287,X32287),hAPP(X32286,hAPP(c_Nat_OSuc,esk441_5(X32283,X32284,X32285,X32286,X32287)))),hAPP(X32286,esk441_5(X32283,X32284,X32285,X32286,X32287)))),c_Transitive__Closure_Ortrancl(X32287,X32285)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X32287,X32287)),hAPP(hAPP(c_Product__Type_OPair(X32287,X32287),hAPP(X32286,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X32284),X32283))),hAPP(X32286,X32284))),c_Transitive__Closure_Ortrancl(X32287,X32285))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sequence__trans])])]) ).

fof(i_0_6148,plain,
    ! [X33764,X33765,X33766,X33767,X33768,X33769] : c_Partial__Function_Ofun__lub(X33769,X33768,X33767,X33766,X33765,X33764) = hAPP(X33766,hAPP(c_Set_OCollect(X33769),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X33767,X33769),tc_HOL_Obool),tc_HOL_Obool,X33769),c_HOL_OEx(tc_fun(X33767,X33769))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X33767,X33769),tc_HOL_Obool),tc_fun(tc_fun(X33767,X33769),tc_HOL_Obool),X33769),hAPP(c_COMBS(tc_fun(X33767,X33769),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X33767,X33769)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(X33767,X33769),tc_fun(tc_fun(X33767,X33769),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X33767,X33769))),X33765)))),hAPP(hAPP(c_COMBC(X33769,tc_fun(tc_fun(X33767,X33769),X33769),tc_fun(tc_fun(X33767,X33769),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X33769,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X33767,X33769),X33769),tc_fun(tc_fun(X33767,X33769),tc_HOL_Obool)),X33769),c_COMBB(X33769,tc_HOL_Obool,tc_fun(X33767,X33769))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(X33767,X33769),X33767,X33769),c_COMBI(tc_fun(X33767,X33769))),X33764)))))),
    inference(variable_rename,[status(thm)],[fact_fun__lub__def]) ).

fof(i_0_6149,plain,
    ! [X33742,X33743,X33744,X33745] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X33745)
      | hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X33744,X33745),X33743),X33742) = c_Complete__Lattice_OInf__class_OInf(X33745,hAPP(c_Set_OCollect(X33745),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X33744,X33745),tc_HOL_Obool),tc_HOL_Obool,X33745),c_HOL_OEx(tc_fun(X33744,X33745))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X33744,X33745),tc_HOL_Obool),tc_fun(tc_fun(X33744,X33745),tc_HOL_Obool),X33745),hAPP(c_COMBS(tc_fun(X33744,X33745),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X33744,X33745)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(X33744,X33745),tc_fun(tc_fun(X33744,X33745),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X33744,X33745))),X33743)))),hAPP(hAPP(c_COMBC(X33745,tc_fun(tc_fun(X33744,X33745),X33745),tc_fun(tc_fun(X33744,X33745),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X33745,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X33744,X33745),X33745),tc_fun(tc_fun(X33744,X33745),tc_HOL_Obool)),X33745),c_COMBB(X33745,tc_HOL_Obool,tc_fun(X33744,X33745))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(X33744,X33745),X33744,X33745),c_COMBI(tc_fun(X33744,X33745))),X33742)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fun__def])]) ).

fof(i_0_6150,plain,
    ! [X33738,X33739,X33740,X33741] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X33741)
      | hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X33740,X33741),X33739),X33738) = c_Complete__Lattice_OInf__class_OInf(X33741,hAPP(c_Set_OCollect(X33741),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X33740,X33741),tc_HOL_Obool),tc_HOL_Obool,X33741),c_HOL_OEx(tc_fun(X33740,X33741))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X33740,X33741),tc_HOL_Obool),tc_fun(tc_fun(X33740,X33741),tc_HOL_Obool),X33741),hAPP(c_COMBS(tc_fun(X33740,X33741),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X33740,X33741)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(X33740,X33741),tc_fun(tc_fun(X33740,X33741),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X33740,X33741))),X33739)))),hAPP(hAPP(c_COMBC(X33741,tc_fun(tc_fun(X33740,X33741),X33741),tc_fun(tc_fun(X33740,X33741),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X33741,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X33740,X33741),X33741),tc_fun(tc_fun(X33740,X33741),tc_HOL_Obool)),X33741),c_COMBB(X33741,tc_HOL_Obool,tc_fun(X33740,X33741))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(X33740,X33741),X33740,X33741),c_COMBI(tc_fun(X33740,X33741))),X33738)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__apply])]) ).

fof(i_0_6151,plain,
    ! [X33734,X33735,X33736,X33737] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X33737)
      | hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X33736,X33737),X33735),X33734) = c_Complete__Lattice_OSup__class_OSup(X33737,hAPP(c_Set_OCollect(X33737),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X33736,X33737),tc_HOL_Obool),tc_HOL_Obool,X33737),c_HOL_OEx(tc_fun(X33736,X33737))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X33736,X33737),tc_HOL_Obool),tc_fun(tc_fun(X33736,X33737),tc_HOL_Obool),X33737),hAPP(c_COMBS(tc_fun(X33736,X33737),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X33736,X33737)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(X33736,X33737),tc_fun(tc_fun(X33736,X33737),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X33736,X33737))),X33735)))),hAPP(hAPP(c_COMBC(X33737,tc_fun(tc_fun(X33736,X33737),X33737),tc_fun(tc_fun(X33736,X33737),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X33737,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X33736,X33737),X33737),tc_fun(tc_fun(X33736,X33737),tc_HOL_Obool)),X33737),c_COMBB(X33737,tc_HOL_Obool,tc_fun(X33736,X33737))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(X33736,X33737),X33736,X33737),c_COMBI(tc_fun(X33736,X33737))),X33734)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__apply])]) ).

fof(i_0_6152,plain,
    ! [X33730,X33731,X33732,X33733] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X33733)
      | hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X33732,X33733),X33731),X33730) = c_Complete__Lattice_OSup__class_OSup(X33733,hAPP(c_Set_OCollect(X33733),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X33732,X33733),tc_HOL_Obool),tc_HOL_Obool,X33733),c_HOL_OEx(tc_fun(X33732,X33733))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X33732,X33733),tc_HOL_Obool),tc_fun(tc_fun(X33732,X33733),tc_HOL_Obool),X33733),hAPP(c_COMBS(tc_fun(X33732,X33733),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X33732,X33733)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(X33732,X33733),tc_fun(tc_fun(X33732,X33733),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X33732,X33733))),X33731)))),hAPP(hAPP(c_COMBC(X33733,tc_fun(tc_fun(X33732,X33733),X33733),tc_fun(tc_fun(X33732,X33733),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X33733,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X33732,X33733),X33733),tc_fun(tc_fun(X33732,X33733),tc_HOL_Obool)),X33733),c_COMBB(X33733,tc_HOL_Obool,tc_fun(X33732,X33733))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(X33732,X33733),X33732,X33733),c_COMBI(tc_fun(X33732,X33733))),X33730)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fun__def])]) ).

fof(i_0_6153,plain,
    ! [X33122,X33123,X33124,X33125,X33126,X33127] :
      ( ( X33125 = hAPP(hAPP(c_Product__Type_OPair(X33127,X33126),esk502_6(X33122,X33123,X33124,X33125,X33126,X33127)),esk504_6(X33122,X33123,X33124,X33125,X33126,X33127))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X33127,X33126)),X33125),hAPP(hAPP(c_Relation_Orel__comp(X33127,X33124,X33126),X33123),X33122))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X33127,X33124)),hAPP(hAPP(c_Product__Type_OPair(X33127,X33124),esk502_6(X33122,X33123,X33124,X33125,X33126,X33127)),esk503_6(X33122,X33123,X33124,X33125,X33126,X33127))),X33123))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X33127,X33126)),X33125),hAPP(hAPP(c_Relation_Orel__comp(X33127,X33124,X33126),X33123),X33122))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X33124,X33126)),hAPP(hAPP(c_Product__Type_OPair(X33124,X33126),esk503_6(X33122,X33123,X33124,X33125,X33126,X33127)),esk504_6(X33122,X33123,X33124,X33125,X33126,X33127))),X33122))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X33127,X33126)),X33125),hAPP(hAPP(c_Relation_Orel__comp(X33127,X33124,X33126),X33123),X33122))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5249])])])]) ).

fof(i_0_6154,plain,
    ! [X22130,X22131] : c_Divides_Odivmod__int__rel(X22131,X22130) = 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,X22131))),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),X22130)))))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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)),X22130))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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)),X22130))))),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)),X22130)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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),X22130))),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_6155,plain,
    ! [X26209,X26210,X26211,X26212,X26213,X26214,X26215] :
      ( ~ class_Rings_Osemiring__0(X26215)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26215),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26214,X26215),X26213),X26212)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26211,X26215),X26210),X26209)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26214,X26215),hAPP(hAPP(c_COMBC(X26214,tc_fun(X26211,tc_HOL_Obool),X26215),hAPP(hAPP(c_COMBB(tc_fun(X26211,X26215),tc_fun(tc_fun(X26211,tc_HOL_Obool),X26215),X26214),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26211,X26215)),hAPP(hAPP(c_COMBC(X26214,tc_fun(X26211,X26215),tc_fun(X26211,X26215)),hAPP(hAPP(c_COMBB(tc_fun(X26215,X26215),tc_fun(tc_fun(X26211,X26215),tc_fun(X26211,X26215)),X26214),c_COMBB(X26215,X26215,X26211)),hAPP(hAPP(c_COMBB(X26215,tc_fun(X26215,X26215),X26214),c_Groups_Otimes__class_Otimes(X26215)),X26213))),X26210))),X26209)),X26212) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__product])]) ).

fof(i_0_6156,plain,
    ! [X27447,X27448,X27449,X27450,X27451,X27452] :
      ( ( hBOOL(hAPP(hAPP(c_member(X27451),esk276_6(X27447,X27448,X27449,X27450,X27451,X27452)),X27450))
        | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X27452,X27451,c_Groups_Otimes__class_Otimes(X27452)),hAPP(hAPP(c_COMBS(X27451,tc_fun(X27449,tc_HOL_Obool),X27452),hAPP(hAPP(c_COMBC(X27451,X27452,tc_fun(tc_fun(X27449,tc_HOL_Obool),X27452)),hAPP(hAPP(c_COMBB(tc_fun(X27449,X27452),tc_fun(X27452,tc_fun(tc_fun(X27449,tc_HOL_Obool),X27452)),X27451),c_Finite__Set_Ofold__image(X27452,X27449,c_Groups_Otimes__class_Otimes(X27452))),X27447)),c_Groups_Oone__class_Oone(X27452))),X27448)),c_Groups_Oone__class_Oone(X27452)),X27450) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X27452,tc_prod(X27451,X27449),c_Groups_Otimes__class_Otimes(X27452)),hAPP(c_Product__Type_Oprod_Oprod__case(X27451,X27449,X27452),X27447)),c_Groups_Oone__class_Oone(X27452)),hAPP(hAPP(c_Product__Type_OSigma(X27451,X27449),X27450),X27448))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27451),X27450))
        | ~ class_Groups_Ocomm__monoid__mult(X27452) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27449),hAPP(X27448,esk276_6(X27447,X27448,X27449,X27450,X27451,X27452))))
        | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X27452,X27451,c_Groups_Otimes__class_Otimes(X27452)),hAPP(hAPP(c_COMBS(X27451,tc_fun(X27449,tc_HOL_Obool),X27452),hAPP(hAPP(c_COMBC(X27451,X27452,tc_fun(tc_fun(X27449,tc_HOL_Obool),X27452)),hAPP(hAPP(c_COMBB(tc_fun(X27449,X27452),tc_fun(X27452,tc_fun(tc_fun(X27449,tc_HOL_Obool),X27452)),X27451),c_Finite__Set_Ofold__image(X27452,X27449,c_Groups_Otimes__class_Otimes(X27452))),X27447)),c_Groups_Oone__class_Oone(X27452))),X27448)),c_Groups_Oone__class_Oone(X27452)),X27450) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X27452,tc_prod(X27451,X27449),c_Groups_Otimes__class_Otimes(X27452)),hAPP(c_Product__Type_Oprod_Oprod__case(X27451,X27449,X27452),X27447)),c_Groups_Oone__class_Oone(X27452)),hAPP(hAPP(c_Product__Type_OSigma(X27451,X27449),X27450),X27448))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27451),X27450))
        | ~ class_Groups_Ocomm__monoid__mult(X27452) ) ),
    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_6157,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_5250]) ).

fof(i_0_6158,plain,
    ! [X28805,X28806,X28807] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28807),X28806))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X28807)),hAPP(c_Set_OCollect(tc_List_Olist(X28807)),hAPP(hAPP(c_COMBS(tc_List_Olist(X28807),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X28807)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X28807),tc_fun(X28807,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X28807,tc_HOL_Obool),tc_fun(tc_fun(X28807,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X28807)),c_Orderings_Oord__class_Oless__eq(tc_fun(X28807,tc_HOL_Obool))),c_List_Oset(X28807))),X28806))),hAPP(hAPP(c_COMBC(tc_List_Olist(X28807),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X28807)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X28807)))),X28805))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__lists__length__le])]) ).

fof(i_0_6159,plain,
    ! [X28988,X28989,X28990] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28990),X28989))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X28990)),hAPP(c_Set_OCollect(tc_List_Olist(X28990)),hAPP(hAPP(c_COMBS(tc_List_Olist(X28990),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X28990)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X28990),tc_fun(X28990,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X28990,tc_HOL_Obool),tc_fun(tc_fun(X28990,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X28990)),c_Orderings_Oord__class_Oless__eq(tc_fun(X28990,tc_HOL_Obool))),c_List_Oset(X28990))),X28989))),hAPP(hAPP(c_COMBC(tc_List_Olist(X28990),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X28990)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X28990)))),X28988))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__lists__length__eq])]) ).

cnf(i_0_6160,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_5243]) ).

fof(i_0_6161,plain,
    ! [X27647,X27648,X27649,X27650,X27651,X27652,X27653,X27654] :
      ( ( hBOOL(hAPP(hAPP(c_member(X27653),esk288_7(X27647,X27648,X27649,X27650,X27651,X27652,X27653)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27653,tc_HOL_Obool)),X27648),X27647)))
        | hAPP(X27649,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27653,tc_HOL_Obool)),X27648),X27647)) = hAPP(hAPP(X27652,hAPP(X27649,X27648)),hAPP(X27649,X27647))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27653),X27647))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27653),X27648))
        | ~ c_Finite__Set_Ofolding__image__simple(X27654,X27653,X27652,X27651,X27650,X27649) )
      & ( hAPP(X27650,esk288_7(X27647,X27648,X27649,X27650,X27651,X27652,X27653)) != X27651
        | hAPP(X27649,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27653,tc_HOL_Obool)),X27648),X27647)) = hAPP(hAPP(X27652,hAPP(X27649,X27648)),hAPP(X27649,X27647))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27653),X27647))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27653),X27648))
        | ~ c_Finite__Set_Ofolding__image__simple(X27654,X27653,X27652,X27651,X27650,X27649) ) ),
    inference(distribute,[status(thm)],[inference(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_6162,plain,
    ! [X25270] : hAPP(c_Int_Onat,X25270) = 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,X25270)),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_6163,plain,
    ! [X32585,X32586,X32587,X32588,X32589,X32592,X32593,X32594,X32595,X32596,X32597,X32598,X32599] :
      ( ( X32585 = hAPP(hAPP(c_List_Oappend(X32589),esk452_5(X32585,X32586,X32587,X32588,X32589)),hAPP(hAPP(c_List_Olist_OCons(X32589),X32588),esk453_5(X32585,X32586,X32587,X32588,X32589)))
        | hAPP(hAPP(c_List_Olist_OCons(X32589),X32588),X32587) != hAPP(c_List_Ofilter(X32589,X32586),X32585) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X32589),X32592),hAPP(c_List_Oset(X32589),esk452_5(X32585,X32586,X32587,X32588,X32589))))
        | ~ hBOOL(hAPP(X32586,X32592))
        | hAPP(hAPP(c_List_Olist_OCons(X32589),X32588),X32587) != hAPP(c_List_Ofilter(X32589,X32586),X32585) )
      & ( hBOOL(hAPP(X32586,X32588))
        | hAPP(hAPP(c_List_Olist_OCons(X32589),X32588),X32587) != hAPP(c_List_Ofilter(X32589,X32586),X32585) )
      & ( X32587 = hAPP(c_List_Ofilter(X32589,X32586),esk453_5(X32585,X32586,X32587,X32588,X32589))
        | hAPP(hAPP(c_List_Olist_OCons(X32589),X32588),X32587) != hAPP(c_List_Ofilter(X32589,X32586),X32585) )
      & ( hBOOL(hAPP(hAPP(c_member(X32597),esk454_7(X32593,X32594,X32595,X32596,X32597,X32598,X32599)),hAPP(c_List_Oset(X32597),X32598)))
        | X32593 != hAPP(hAPP(c_List_Oappend(X32597),X32598),hAPP(hAPP(c_List_Olist_OCons(X32597),X32596),X32599))
        | ~ hBOOL(hAPP(X32594,X32596))
        | X32595 != hAPP(c_List_Ofilter(X32597,X32594),X32599)
        | hAPP(hAPP(c_List_Olist_OCons(X32597),X32596),X32595) = hAPP(c_List_Ofilter(X32597,X32594),X32593) )
      & ( hBOOL(hAPP(X32594,esk454_7(X32593,X32594,X32595,X32596,X32597,X32598,X32599)))
        | X32593 != hAPP(hAPP(c_List_Oappend(X32597),X32598),hAPP(hAPP(c_List_Olist_OCons(X32597),X32596),X32599))
        | ~ hBOOL(hAPP(X32594,X32596))
        | X32595 != hAPP(c_List_Ofilter(X32597,X32594),X32599)
        | hAPP(hAPP(c_List_Olist_OCons(X32597),X32596),X32595) = hAPP(c_List_Ofilter(X32597,X32594),X32593) ) ),
    inference(distribute,[status(thm)],[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_5251])])])])])]) ).

fof(i_0_6164,plain,
    ! [X32118,X32119,X32120,X32121,X32122,X32125,X32126,X32127,X32128,X32129,X32130,X32131,X32132] :
      ( ( X32120 = hAPP(hAPP(c_List_Oappend(X32122),esk437_5(X32118,X32119,X32120,X32121,X32122)),hAPP(hAPP(c_List_Olist_OCons(X32122),X32119),esk438_5(X32118,X32119,X32120,X32121,X32122)))
        | hAPP(c_List_Ofilter(X32122,X32121),X32120) != hAPP(hAPP(c_List_Olist_OCons(X32122),X32119),X32118) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X32122),X32125),hAPP(c_List_Oset(X32122),esk437_5(X32118,X32119,X32120,X32121,X32122))))
        | ~ hBOOL(hAPP(X32121,X32125))
        | hAPP(c_List_Ofilter(X32122,X32121),X32120) != hAPP(hAPP(c_List_Olist_OCons(X32122),X32119),X32118) )
      & ( hBOOL(hAPP(X32121,X32119))
        | hAPP(c_List_Ofilter(X32122,X32121),X32120) != hAPP(hAPP(c_List_Olist_OCons(X32122),X32119),X32118) )
      & ( X32118 = hAPP(c_List_Ofilter(X32122,X32121),esk438_5(X32118,X32119,X32120,X32121,X32122))
        | hAPP(c_List_Ofilter(X32122,X32121),X32120) != hAPP(hAPP(c_List_Olist_OCons(X32122),X32119),X32118) )
      & ( hBOOL(hAPP(hAPP(c_member(X32130),esk439_7(X32126,X32127,X32128,X32129,X32130,X32131,X32132)),hAPP(c_List_Oset(X32130),X32131)))
        | X32128 != hAPP(hAPP(c_List_Oappend(X32130),X32131),hAPP(hAPP(c_List_Olist_OCons(X32130),X32127),X32132))
        | ~ hBOOL(hAPP(X32129,X32127))
        | X32126 != hAPP(c_List_Ofilter(X32130,X32129),X32132)
        | hAPP(c_List_Ofilter(X32130,X32129),X32128) = hAPP(hAPP(c_List_Olist_OCons(X32130),X32127),X32126) )
      & ( hBOOL(hAPP(X32129,esk439_7(X32126,X32127,X32128,X32129,X32130,X32131,X32132)))
        | X32128 != hAPP(hAPP(c_List_Oappend(X32130),X32131),hAPP(hAPP(c_List_Olist_OCons(X32130),X32127),X32132))
        | ~ hBOOL(hAPP(X32129,X32127))
        | X32126 != hAPP(c_List_Ofilter(X32130,X32129),X32132)
        | hAPP(c_List_Ofilter(X32130,X32129),X32128) = hAPP(hAPP(c_List_Olist_OCons(X32130),X32127),X32126) ) ),
    inference(distribute,[status(thm)],[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_5252])])])])])]) ).

fof(i_0_6165,plain,
    ! [X21243,X21244,X21245,X21246] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21246),esk77_4(X21243,X21244,X21245,X21246)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21243),hAPP(X21244,X21245)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X21244,X21246)),X21243))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21246),X21245))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21246),esk76_4(X21243,X21244,X21245,X21246))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk77_4(X21243,X21244,X21245,X21246)),X21245))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21243),hAPP(X21244,X21245)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X21244,X21246)),X21243))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21246),X21245))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21246),esk76_4(X21243,X21244,X21245,X21246))) )
      & ( hAPP(X21244,esk77_4(X21243,X21244,X21245,X21246)) = X21243
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21243),hAPP(X21244,X21245)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X21244,X21246)),X21243))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21246),X21245))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21246),esk76_4(X21243,X21244,X21245,X21246))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21246),esk77_4(X21243,X21244,X21245,X21246)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21243),hAPP(X21244,X21245)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X21244,X21246)),X21243))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21246),X21245))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk76_4(X21243,X21244,X21245,X21246)),X21245)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk77_4(X21243,X21244,X21245,X21246)),X21245))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21243),hAPP(X21244,X21245)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X21244,X21246)),X21243))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21246),X21245))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk76_4(X21243,X21244,X21245,X21246)),X21245)) )
      & ( hAPP(X21244,esk77_4(X21243,X21244,X21245,X21246)) = X21243
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21243),hAPP(X21244,X21245)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X21244,X21246)),X21243))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21246),X21245))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk76_4(X21243,X21244,X21245,X21246)),X21245)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21246),esk77_4(X21243,X21244,X21245,X21246)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21243),hAPP(X21244,X21245)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X21244,X21246)),X21243))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21246),X21245))
        | ~ 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(X21244,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk76_4(X21243,X21244,X21245,X21246)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X21244,esk76_4(X21243,X21244,X21245,X21246))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk77_4(X21243,X21244,X21245,X21246)),X21245))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21243),hAPP(X21244,X21245)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X21244,X21246)),X21243))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21246),X21245))
        | ~ 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(X21244,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk76_4(X21243,X21244,X21245,X21246)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X21244,esk76_4(X21243,X21244,X21245,X21246))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) )
      & ( hAPP(X21244,esk77_4(X21243,X21244,X21245,X21246)) = X21243
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21243),hAPP(X21244,X21245)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X21244,X21246)),X21243))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21246),X21245))
        | ~ 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(X21244,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk76_4(X21243,X21244,X21245,X21246)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X21244,esk76_4(X21243,X21244,X21245,X21246))))),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_6166,plain,
    ! [X33718,X33719,X33720,X33721,X33722] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33719),hAPP(c_Set_OCollect(X33719),hAPP(hAPP(c_COMBB(tc_fun(X33721,tc_HOL_Obool),tc_HOL_Obool,X33719),c_HOL_OEx(X33721)),hAPP(hAPP(c_COMBB(tc_fun(X33721,tc_HOL_Obool),tc_fun(X33721,tc_HOL_Obool),X33719),hAPP(c_COMBS(X33721,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X33721),c_fconj),hAPP(hAPP(c_COMBC(X33721,tc_fun(X33721,tc_HOL_Obool),tc_HOL_Obool),c_member(X33721)),X33720)))),X33718)))))
        | ~ hBOOL(hAPP(hAPP(c_member(X33721),X33722),X33720))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X33719),hAPP(c_Set_OCollect(X33719),hAPP(hAPP(c_COMBC(X33719,X33721,tc_HOL_Obool),X33718),X33722))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33721),X33720)) )
      & ( hBOOL(hAPP(hAPP(c_member(X33721),esk539_4(X33718,X33719,X33720,X33721)),X33720))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X33719),hAPP(c_Set_OCollect(X33719),hAPP(hAPP(c_COMBB(tc_fun(X33721,tc_HOL_Obool),tc_HOL_Obool,X33719),c_HOL_OEx(X33721)),hAPP(hAPP(c_COMBB(tc_fun(X33721,tc_HOL_Obool),tc_fun(X33721,tc_HOL_Obool),X33719),hAPP(c_COMBS(X33721,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X33721),c_fconj),hAPP(hAPP(c_COMBC(X33721,tc_fun(X33721,tc_HOL_Obool),tc_HOL_Obool),c_member(X33721)),X33720)))),X33718)))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33721),X33720)) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33719),hAPP(c_Set_OCollect(X33719),hAPP(hAPP(c_COMBC(X33719,X33721,tc_HOL_Obool),X33718),esk539_4(X33718,X33719,X33720,X33721)))))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X33719),hAPP(c_Set_OCollect(X33719),hAPP(hAPP(c_COMBB(tc_fun(X33721,tc_HOL_Obool),tc_HOL_Obool,X33719),c_HOL_OEx(X33721)),hAPP(hAPP(c_COMBB(tc_fun(X33721,tc_HOL_Obool),tc_fun(X33721,tc_HOL_Obool),X33719),hAPP(c_COMBS(X33721,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X33721),c_fconj),hAPP(hAPP(c_COMBC(X33721,tc_fun(X33721,tc_HOL_Obool),tc_HOL_Obool),c_member(X33721)),X33720)))),X33718)))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33721),X33720)) ) ),
    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_6167,plain,
    ! [X32619,X32620,X32621,X32622,X32623,X32624] :
      ( ( hBOOL(hAPP(hAPP(c_member(X32624),esk458_6(X32619,X32620,X32621,X32622,X32623,X32624)),X32623))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X32624,X32621),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X32624,X32621),X32623),X32620)),hAPP(hAPP(c_Product__Type_OSigma(X32624,X32621),X32622),X32619)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X32624,tc_HOL_Obool)),X32623),X32622)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X32621,tc_HOL_Obool)),hAPP(X32620,esk458_6(X32619,X32620,X32621,X32622,X32623,X32624))),hAPP(X32619,esk458_6(X32619,X32620,X32621,X32622,X32623,X32624))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X32624,X32621),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X32624,X32621),X32623),X32620)),hAPP(hAPP(c_Product__Type_OSigma(X32624,X32621),X32622),X32619)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X32624,tc_HOL_Obool)),X32623),X32622)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sigma__mono])])])]) ).

fof(i_0_6168,plain,
    ! [X32076,X32077,X32078,X32079,X32080,X32081] :
      ( ( X32081 = hAPP(hAPP(c_Product__Type_OPair(X32080,X32079),esk428_6(X32076,X32077,X32078,X32079,X32080,X32081)),esk429_6(X32076,X32077,X32078,X32079,X32080,X32081))
        | hBOOL(hAPP(hAPP(c_member(X32078),X32077),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X32080,X32079,tc_fun(X32078,tc_HOL_Obool)),X32076),X32081))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X32078),X32077),hAPP(hAPP(X32076,esk428_6(X32076,X32077,X32078,X32079,X32080,X32081)),esk429_6(X32076,X32077,X32078,X32079,X32080,X32081))))
        | hBOOL(hAPP(hAPP(c_member(X32078),X32077),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X32080,X32079,tc_fun(X32078,tc_HOL_Obool)),X32076),X32081))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__splitI2])])])]) ).

cnf(i_0_6169,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_5253]) ).

cnf(i_0_6170,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_5254]) ).

fof(i_0_6171,plain,
    ! [X32519,X32520,X32521] : hAPP(c_Relation_Oconverse(X32521,X32520),X32519) = hAPP(c_Set_OCollect(tc_prod(X32520,X32521)),hAPP(c_Product__Type_Oprod_Oprod__case(X32520,X32521,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X32520,tc_fun(tc_prod(X32521,X32520),tc_HOL_Obool),tc_fun(X32521,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X32521,tc_fun(tc_fun(tc_prod(X32521,X32520),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X32521,X32520),tc_HOL_Obool),tc_fun(X32521,tc_HOL_Obool)),X32520),c_COMBC(X32521,tc_fun(tc_prod(X32521,X32520),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X32521,tc_prod(X32521,X32520)),tc_fun(X32521,tc_fun(tc_fun(tc_prod(X32521,X32520),tc_HOL_Obool),tc_HOL_Obool)),X32520),hAPP(c_COMBB(tc_prod(X32521,X32520),tc_fun(tc_fun(tc_prod(X32521,X32520),tc_HOL_Obool),tc_HOL_Obool),X32521),c_member(tc_prod(X32521,X32520)))),hAPP(c_COMBC(X32521,X32520,tc_prod(X32521,X32520)),c_Product__Type_OPair(X32521,X32520))))),X32519))),
    inference(variable_rename,[status(thm)],[fact_converse__def]) ).

fof(i_0_6172,plain,
    ! [X30213,X30214,X30215,X30216] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30215),X30214))
        | c_Nitpick_Osetsum_H(X30215,X30216,X30213,X30214) = hAPP(c_List_Omonoid__add__class_Olistsum(X30216),hAPP(hAPP(c_List_Omap(X30215,X30216),X30213),c_Hilbert__Choice_OEps(tc_List_Olist(X30215),hAPP(hAPP(c_COMBS(tc_List_Olist(X30215),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X30215)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X30215),tc_fun(X30215,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X30215,tc_HOL_Obool),tc_fun(tc_fun(X30215,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X30215)),c_fequal),c_List_Oset(X30215))),X30214))),c_List_Odistinct(X30215)))))
        | ~ class_Groups_Ocomm__monoid__add(X30216) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X30215),X30214))
        | c_Nitpick_Osetsum_H(X30215,X30216,X30213,X30214) = c_Groups_Ozero__class_Ozero(X30216)
        | ~ class_Groups_Ocomm__monoid__add(X30216) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5255])])]) ).

fof(i_0_6173,plain,
    ! [X34074,X34075,X34076,X34077,X34078,X34079] :
      ( ( hBOOL(hAPP(hAPP(c_member(X34078),esk559_6(X34074,X34075,X34076,X34077,X34078,X34079)),X34077))
        | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X34079,X34076,c_Groups_Otimes__class_Otimes(X34079)),X34074),c_Groups_Oone__class_Oone(X34079)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X34078,tc_fun(X34076,tc_HOL_Obool)),X34077),X34075)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X34079,X34078,c_Groups_Otimes__class_Otimes(X34079)),hAPP(hAPP(c_COMBB(tc_fun(X34076,tc_HOL_Obool),X34079,X34078),hAPP(hAPP(c_Finite__Set_Ofold__image(X34079,X34076,c_Groups_Otimes__class_Otimes(X34079)),X34074),c_Groups_Oone__class_Oone(X34079))),X34075)),c_Groups_Oone__class_Oone(X34079)),X34077)
        | hBOOL(hAPP(hAPP(c_member(X34078),esk558_6(X34074,X34075,X34076,X34077,X34078,X34079)),X34077))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X34078),X34077))
        | ~ class_Groups_Ocomm__monoid__mult(X34079) )
      & ( hBOOL(hAPP(hAPP(c_member(X34078),esk560_6(X34074,X34075,X34076,X34077,X34078,X34079)),X34077))
        | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X34079,X34076,c_Groups_Otimes__class_Otimes(X34079)),X34074),c_Groups_Oone__class_Oone(X34079)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X34078,tc_fun(X34076,tc_HOL_Obool)),X34077),X34075)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X34079,X34078,c_Groups_Otimes__class_Otimes(X34079)),hAPP(hAPP(c_COMBB(tc_fun(X34076,tc_HOL_Obool),X34079,X34078),hAPP(hAPP(c_Finite__Set_Ofold__image(X34079,X34076,c_Groups_Otimes__class_Otimes(X34079)),X34074),c_Groups_Oone__class_Oone(X34079))),X34075)),c_Groups_Oone__class_Oone(X34079)),X34077)
        | hBOOL(hAPP(hAPP(c_member(X34078),esk558_6(X34074,X34075,X34076,X34077,X34078,X34079)),X34077))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X34078),X34077))
        | ~ class_Groups_Ocomm__monoid__mult(X34079) )
      & ( esk559_6(X34074,X34075,X34076,X34077,X34078,X34079) != esk560_6(X34074,X34075,X34076,X34077,X34078,X34079)
        | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X34079,X34076,c_Groups_Otimes__class_Otimes(X34079)),X34074),c_Groups_Oone__class_Oone(X34079)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X34078,tc_fun(X34076,tc_HOL_Obool)),X34077),X34075)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X34079,X34078,c_Groups_Otimes__class_Otimes(X34079)),hAPP(hAPP(c_COMBB(tc_fun(X34076,tc_HOL_Obool),X34079,X34078),hAPP(hAPP(c_Finite__Set_Ofold__image(X34079,X34076,c_Groups_Otimes__class_Otimes(X34079)),X34074),c_Groups_Oone__class_Oone(X34079))),X34075)),c_Groups_Oone__class_Oone(X34079)),X34077)
        | hBOOL(hAPP(hAPP(c_member(X34078),esk558_6(X34074,X34075,X34076,X34077,X34078,X34079)),X34077))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X34078),X34077))
        | ~ class_Groups_Ocomm__monoid__mult(X34079) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X34076,tc_HOL_Obool)),hAPP(X34075,esk559_6(X34074,X34075,X34076,X34077,X34078,X34079))),hAPP(X34075,esk560_6(X34074,X34075,X34076,X34077,X34078,X34079))) != c_Orderings_Obot__class_Obot(tc_fun(X34076,tc_HOL_Obool))
        | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X34079,X34076,c_Groups_Otimes__class_Otimes(X34079)),X34074),c_Groups_Oone__class_Oone(X34079)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X34078,tc_fun(X34076,tc_HOL_Obool)),X34077),X34075)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X34079,X34078,c_Groups_Otimes__class_Otimes(X34079)),hAPP(hAPP(c_COMBB(tc_fun(X34076,tc_HOL_Obool),X34079,X34078),hAPP(hAPP(c_Finite__Set_Ofold__image(X34079,X34076,c_Groups_Otimes__class_Otimes(X34079)),X34074),c_Groups_Oone__class_Oone(X34079))),X34075)),c_Groups_Oone__class_Oone(X34079)),X34077)
        | hBOOL(hAPP(hAPP(c_member(X34078),esk558_6(X34074,X34075,X34076,X34077,X34078,X34079)),X34077))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X34078),X34077))
        | ~ class_Groups_Ocomm__monoid__mult(X34079) )
      & ( hBOOL(hAPP(hAPP(c_member(X34078),esk559_6(X34074,X34075,X34076,X34077,X34078,X34079)),X34077))
        | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X34079,X34076,c_Groups_Otimes__class_Otimes(X34079)),X34074),c_Groups_Oone__class_Oone(X34079)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X34078,tc_fun(X34076,tc_HOL_Obool)),X34077),X34075)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X34079,X34078,c_Groups_Otimes__class_Otimes(X34079)),hAPP(hAPP(c_COMBB(tc_fun(X34076,tc_HOL_Obool),X34079,X34078),hAPP(hAPP(c_Finite__Set_Ofold__image(X34079,X34076,c_Groups_Otimes__class_Otimes(X34079)),X34074),c_Groups_Oone__class_Oone(X34079))),X34075)),c_Groups_Oone__class_Oone(X34079)),X34077)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X34076),hAPP(X34075,esk558_6(X34074,X34075,X34076,X34077,X34078,X34079))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X34078),X34077))
        | ~ class_Groups_Ocomm__monoid__mult(X34079) )
      & ( hBOOL(hAPP(hAPP(c_member(X34078),esk560_6(X34074,X34075,X34076,X34077,X34078,X34079)),X34077))
        | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X34079,X34076,c_Groups_Otimes__class_Otimes(X34079)),X34074),c_Groups_Oone__class_Oone(X34079)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X34078,tc_fun(X34076,tc_HOL_Obool)),X34077),X34075)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X34079,X34078,c_Groups_Otimes__class_Otimes(X34079)),hAPP(hAPP(c_COMBB(tc_fun(X34076,tc_HOL_Obool),X34079,X34078),hAPP(hAPP(c_Finite__Set_Ofold__image(X34079,X34076,c_Groups_Otimes__class_Otimes(X34079)),X34074),c_Groups_Oone__class_Oone(X34079))),X34075)),c_Groups_Oone__class_Oone(X34079)),X34077)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X34076),hAPP(X34075,esk558_6(X34074,X34075,X34076,X34077,X34078,X34079))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X34078),X34077))
        | ~ class_Groups_Ocomm__monoid__mult(X34079) )
      & ( esk559_6(X34074,X34075,X34076,X34077,X34078,X34079) != esk560_6(X34074,X34075,X34076,X34077,X34078,X34079)
        | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X34079,X34076,c_Groups_Otimes__class_Otimes(X34079)),X34074),c_Groups_Oone__class_Oone(X34079)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X34078,tc_fun(X34076,tc_HOL_Obool)),X34077),X34075)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X34079,X34078,c_Groups_Otimes__class_Otimes(X34079)),hAPP(hAPP(c_COMBB(tc_fun(X34076,tc_HOL_Obool),X34079,X34078),hAPP(hAPP(c_Finite__Set_Ofold__image(X34079,X34076,c_Groups_Otimes__class_Otimes(X34079)),X34074),c_Groups_Oone__class_Oone(X34079))),X34075)),c_Groups_Oone__class_Oone(X34079)),X34077)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X34076),hAPP(X34075,esk558_6(X34074,X34075,X34076,X34077,X34078,X34079))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X34078),X34077))
        | ~ class_Groups_Ocomm__monoid__mult(X34079) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X34076,tc_HOL_Obool)),hAPP(X34075,esk559_6(X34074,X34075,X34076,X34077,X34078,X34079))),hAPP(X34075,esk560_6(X34074,X34075,X34076,X34077,X34078,X34079))) != c_Orderings_Obot__class_Obot(tc_fun(X34076,tc_HOL_Obool))
        | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X34079,X34076,c_Groups_Otimes__class_Otimes(X34079)),X34074),c_Groups_Oone__class_Oone(X34079)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X34078,tc_fun(X34076,tc_HOL_Obool)),X34077),X34075)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X34079,X34078,c_Groups_Otimes__class_Otimes(X34079)),hAPP(hAPP(c_COMBB(tc_fun(X34076,tc_HOL_Obool),X34079,X34078),hAPP(hAPP(c_Finite__Set_Ofold__image(X34079,X34076,c_Groups_Otimes__class_Otimes(X34079)),X34074),c_Groups_Oone__class_Oone(X34079))),X34075)),c_Groups_Oone__class_Oone(X34079)),X34077)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X34076),hAPP(X34075,esk558_6(X34074,X34075,X34076,X34077,X34078,X34079))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X34078),X34077))
        | ~ class_Groups_Ocomm__monoid__mult(X34079) ) ),
    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_6174,plain,
    ! [X33726,X33727,X33728,X33729] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X33729,tc_fun(X33728,tc_HOL_Obool)),X33727),X33726) = c_Complete__Lattice_OInf__class_OInf(tc_fun(X33728,tc_HOL_Obool),hAPP(c_Set_OCollect(tc_fun(X33728,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X33729,tc_HOL_Obool),tc_HOL_Obool,tc_fun(X33728,tc_HOL_Obool)),c_HOL_OEx(X33729)),hAPP(hAPP(c_COMBB(tc_fun(X33729,tc_HOL_Obool),tc_fun(X33729,tc_HOL_Obool),tc_fun(X33728,tc_HOL_Obool)),hAPP(c_COMBS(X33729,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X33729),c_fconj),hAPP(hAPP(c_COMBC(X33729,tc_fun(X33729,tc_HOL_Obool),tc_HOL_Obool),c_member(X33729)),X33727)))),hAPP(hAPP(c_COMBC(tc_fun(X33728,tc_HOL_Obool),tc_fun(X33729,tc_fun(X33728,tc_HOL_Obool)),tc_fun(X33729,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X33728,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X33729,tc_fun(X33728,tc_HOL_Obool)),tc_fun(X33729,tc_HOL_Obool)),tc_fun(X33728,tc_HOL_Obool)),c_COMBB(tc_fun(X33728,tc_HOL_Obool),tc_HOL_Obool,X33729)),c_fequal)),X33726))))),
    inference(variable_rename,[status(thm)],[fact_INT__eq]) ).

fof(i_0_6175,plain,
    ! [X33702,X33703,X33704,X33705] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X33705,tc_fun(X33704,tc_HOL_Obool)),X33703),X33702) = c_Complete__Lattice_OSup__class_OSup(tc_fun(X33704,tc_HOL_Obool),hAPP(c_Set_OCollect(tc_fun(X33704,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X33705,tc_HOL_Obool),tc_HOL_Obool,tc_fun(X33704,tc_HOL_Obool)),c_HOL_OEx(X33705)),hAPP(hAPP(c_COMBB(tc_fun(X33705,tc_HOL_Obool),tc_fun(X33705,tc_HOL_Obool),tc_fun(X33704,tc_HOL_Obool)),hAPP(c_COMBS(X33705,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X33705),c_fconj),hAPP(hAPP(c_COMBC(X33705,tc_fun(X33705,tc_HOL_Obool),tc_HOL_Obool),c_member(X33705)),X33703)))),hAPP(hAPP(c_COMBC(tc_fun(X33704,tc_HOL_Obool),tc_fun(X33705,tc_fun(X33704,tc_HOL_Obool)),tc_fun(X33705,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X33704,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X33705,tc_fun(X33704,tc_HOL_Obool)),tc_fun(X33705,tc_HOL_Obool)),tc_fun(X33704,tc_HOL_Obool)),c_COMBB(tc_fun(X33704,tc_HOL_Obool),tc_HOL_Obool,X33705)),c_fequal)),X33702))))),
    inference(variable_rename,[status(thm)],[fact_UN__eq]) ).

cnf(i_0_6176,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_5256]) ).

cnf(i_0_6177,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_5257]) ).

cnf(i_0_6178,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_5258]) ).

fof(i_0_6179,plain,
    ! [X33952,X33953] :
      ( ~ c_Equiv__Relations_Opart__equivp(X33953,X33952)
      | hBOOL(hAPP(hAPP(c_member(tc_fun(X33953,tc_HOL_Obool)),esk555_2(X33952,X33953)),hAPP(hAPP(c_COMBB(tc_fun(X33953,tc_HOL_Obool),tc_HOL_Obool,tc_fun(X33953,tc_HOL_Obool)),c_HOL_OEx(X33953)),hAPP(hAPP(c_COMBB(tc_fun(X33953,tc_HOL_Obool),tc_fun(X33953,tc_HOL_Obool),tc_fun(X33953,tc_HOL_Obool)),hAPP(c_COMBS(X33953,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X33953),c_fconj),hAPP(hAPP(c_COMBS(X33953,X33953,tc_HOL_Obool),X33952),c_COMBI(X33953))))),hAPP(hAPP(c_COMBC(tc_fun(X33953,tc_HOL_Obool),tc_fun(X33953,tc_fun(X33953,tc_HOL_Obool)),tc_fun(X33953,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X33953,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X33953,tc_fun(X33953,tc_HOL_Obool)),tc_fun(X33953,tc_HOL_Obool)),tc_fun(X33953,tc_HOL_Obool)),c_COMBB(tc_fun(X33953,tc_HOL_Obool),tc_HOL_Obool,X33953)),c_fequal)),X33952))))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_part__equivp__typedef])])]) ).

cnf(i_0_6180,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_5259]) ).

cnf(i_0_6181,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_5260]) ).

fof(i_0_6182,plain,
    ! [X27676,X27677] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X27677))
      | 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)),X27677))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X27676))))) = 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)),X27677))),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,X27676))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__less__Suc])]) ).

fof(i_0_6183,plain,
    ! [X27810,X27811,X27812,X27813,X27814,X27815] :
      ( ~ class_Groups_Ocomm__monoid__add(X27815)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27814),X27813))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27814,X27815),X27812),X27813) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27811,X27815),hAPP(hAPP(c_COMBB(tc_fun(X27814,tc_HOL_Obool),X27815,X27811),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27814,X27815),X27812)),hAPP(hAPP(c_COMBB(tc_fun(X27814,tc_HOL_Obool),tc_fun(X27814,tc_HOL_Obool),X27811),c_Set_OCollect(X27814)),hAPP(hAPP(c_COMBB(tc_fun(X27814,tc_HOL_Obool),tc_fun(X27814,tc_HOL_Obool),X27811),hAPP(c_COMBS(X27814,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27814),c_fconj),hAPP(hAPP(c_COMBC(X27814,tc_fun(X27814,tc_HOL_Obool),tc_HOL_Obool),c_member(X27814)),X27813)))),hAPP(c_COMBC(X27814,X27811,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X27811,tc_fun(X27811,tc_HOL_Obool),X27814),c_fequal),X27810)))))),hAPP(c_Set_Oimage(X27814,X27811,X27810),X27813)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__image__gen])]) ).

fof(i_0_6184,plain,
    ! [X29249,X29250,X29251,X29252,X29253,X29254,X29255,X29256] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29251,X29251)),X29252),X29249))
        | hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X29251,X29251,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X29251,tc_fun(X29251,tc_HOL_Obool),tc_fun(X29251,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X29251,tc_HOL_Obool),tc_fun(X29251,tc_HOL_Obool)),X29251),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X29251)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29251),c_fconj),hAPP(hAPP(c_COMBC(X29251,tc_fun(X29251,tc_HOL_Obool),tc_HOL_Obool),c_member(X29251)),X29250)))),hAPP(hAPP(c_COMBC(X29251,tc_fun(X29251,tc_HOL_Obool),tc_HOL_Obool),c_member(X29251)),X29250))),X29252))
        | ~ c_Relation_Orefl__on(X29251,X29250,X29249) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X29251),X29253),X29250))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X29251,X29251)),hAPP(hAPP(c_Product__Type_OPair(X29251,X29251),X29253),X29253)),X29249))
        | ~ c_Relation_Orefl__on(X29251,X29250,X29249) )
      & ( hBOOL(hAPP(hAPP(c_member(X29256),esk334_3(X29254,X29255,X29256)),X29255))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X29256,X29256)),esk333_3(X29254,X29255,X29256)),X29254))
        | c_Relation_Orefl__on(X29256,X29255,X29254) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29256,X29256)),hAPP(hAPP(c_Product__Type_OPair(X29256,X29256),esk334_3(X29254,X29255,X29256)),esk334_3(X29254,X29255,X29256))),X29254))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X29256,X29256)),esk333_3(X29254,X29255,X29256)),X29254))
        | c_Relation_Orefl__on(X29256,X29255,X29254) )
      & ( hBOOL(hAPP(hAPP(c_member(X29256),esk334_3(X29254,X29255,X29256)),X29255))
        | ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X29256,X29256,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X29256,tc_fun(X29256,tc_HOL_Obool),tc_fun(X29256,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X29256,tc_HOL_Obool),tc_fun(X29256,tc_HOL_Obool)),X29256),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X29256)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29256),c_fconj),hAPP(hAPP(c_COMBC(X29256,tc_fun(X29256,tc_HOL_Obool),tc_HOL_Obool),c_member(X29256)),X29255)))),hAPP(hAPP(c_COMBC(X29256,tc_fun(X29256,tc_HOL_Obool),tc_HOL_Obool),c_member(X29256)),X29255))),esk333_3(X29254,X29255,X29256)))
        | c_Relation_Orefl__on(X29256,X29255,X29254) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29256,X29256)),hAPP(hAPP(c_Product__Type_OPair(X29256,X29256),esk334_3(X29254,X29255,X29256)),esk334_3(X29254,X29255,X29256))),X29254))
        | ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X29256,X29256,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X29256,tc_fun(X29256,tc_HOL_Obool),tc_fun(X29256,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X29256,tc_HOL_Obool),tc_fun(X29256,tc_HOL_Obool)),X29256),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X29256)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29256),c_fconj),hAPP(hAPP(c_COMBC(X29256,tc_fun(X29256,tc_HOL_Obool),tc_HOL_Obool),c_member(X29256)),X29255)))),hAPP(hAPP(c_COMBC(X29256,tc_fun(X29256,tc_HOL_Obool),tc_HOL_Obool),c_member(X29256)),X29255))),esk333_3(X29254,X29255,X29256)))
        | c_Relation_Orefl__on(X29256,X29255,X29254) ) ),
    inference(distribute,[status(thm)],[inference(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_6185,plain,
    ! [X33658,X33659,X33660,X33661] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X33661),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))
        | c_Random__Sequence_ORandom(X33660,X33659,X33661,X33658) = 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(X33660)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(X33660)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X33661),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))
        | c_Random__Sequence_ORandom(X33660,X33659,X33661,X33658) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X33660,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(X33660)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(X33659,X33658)),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(X33660)))),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(X33660)))),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(X33660)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_prod(X33660,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(X33660)))),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(X33660)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random__Sequence_ORandom(X33660,X33659,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X33661),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X33658))),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(X33660)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X33660))))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X33660)))),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(X33660)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_prod(X33660,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(X33660)))),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(X33660)))),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(X33660))))),c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X33660)))),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(X33660)))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X33660)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X33660))))),tc_prod(X33660,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Ounion(X33660)),hAPP(hAPP(c_COMBB(X33660,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X33660)))),tc_prod(X33660,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Osingle(X33660)),c_Product__Type_Ofst(X33660,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))))))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5261])]) ).

cnf(i_0_6186,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_5262]) ).

cnf(i_0_6187,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_5263]) ).

cnf(i_0_6188,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_5264]) ).

fof(i_0_6189,plain,
    ! [X29264,X29265,X29266,X29267,X29268] : hAPP(hAPP(c_List_Ozip(X29268,X29267),X29266),hAPP(hAPP(c_List_Olist_OCons(X29267),X29265),X29264)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(X29268,X29267)),X29268,c_List_Olist_ONil(tc_prod(X29268,X29267)),hAPP(hAPP(c_COMBC(X29268,tc_fun(tc_List_Olist(X29268),tc_List_Olist(tc_prod(X29268,X29267))),tc_fun(tc_List_Olist(X29268),tc_List_Olist(tc_prod(X29268,X29267)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(X29268,X29267)),tc_List_Olist(tc_prod(X29268,X29267))),tc_fun(tc_fun(tc_List_Olist(X29268),tc_List_Olist(tc_prod(X29268,X29267))),tc_fun(tc_List_Olist(X29268),tc_List_Olist(tc_prod(X29268,X29267)))),X29268),c_COMBB(tc_List_Olist(tc_prod(X29268,X29267)),tc_List_Olist(tc_prod(X29268,X29267)),tc_List_Olist(X29268))),hAPP(hAPP(c_COMBB(tc_prod(X29268,X29267),tc_fun(tc_List_Olist(tc_prod(X29268,X29267)),tc_List_Olist(tc_prod(X29268,X29267))),X29268),c_List_Olist_OCons(tc_prod(X29268,X29267))),hAPP(hAPP(c_COMBC(X29268,X29267,tc_prod(X29268,X29267)),c_Product__Type_OPair(X29268,X29267)),X29265)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X29268),tc_List_Olist(X29267),tc_List_Olist(tc_prod(X29268,X29267))),c_List_Ozip(X29268,X29267)),X29264))),X29266),
    inference(variable_rename,[status(thm)],[fact_zip__Cons]) ).

fof(i_0_6190,plain,
    ! [X23103,X23104,X23105,X23106] :
      ( ( ~ c_Wellfounded_Omax__extp(X23106,hAPP(hAPP(c_COMBC(X23106,tc_fun(tc_prod(X23106,X23106),tc_HOL_Obool),tc_fun(X23106,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X23106,tc_fun(tc_fun(tc_prod(X23106,X23106),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X23106,X23106),tc_HOL_Obool),tc_fun(X23106,tc_HOL_Obool)),X23106),c_COMBC(X23106,tc_fun(tc_prod(X23106,X23106),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X23106,tc_prod(X23106,X23106)),tc_fun(X23106,tc_fun(tc_fun(tc_prod(X23106,X23106),tc_HOL_Obool),tc_HOL_Obool)),X23106),hAPP(c_COMBB(tc_prod(X23106,X23106),tc_fun(tc_fun(tc_prod(X23106,X23106),tc_HOL_Obool),tc_HOL_Obool),X23106),c_member(tc_prod(X23106,X23106)))),c_Product__Type_OPair(X23106,X23106)))),X23105),X23104,X23103)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X23106,tc_HOL_Obool),tc_fun(X23106,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X23106,tc_HOL_Obool),tc_fun(X23106,tc_HOL_Obool)),X23104),X23103)),c_Wellfounded_Omax__ext(X23106,X23105))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X23106,tc_HOL_Obool),tc_fun(X23106,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X23106,tc_HOL_Obool),tc_fun(X23106,tc_HOL_Obool)),X23104),X23103)),c_Wellfounded_Omax__ext(X23106,X23105)))
        | c_Wellfounded_Omax__extp(X23106,hAPP(hAPP(c_COMBC(X23106,tc_fun(tc_prod(X23106,X23106),tc_HOL_Obool),tc_fun(X23106,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X23106,tc_fun(tc_fun(tc_prod(X23106,X23106),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X23106,X23106),tc_HOL_Obool),tc_fun(X23106,tc_HOL_Obool)),X23106),c_COMBC(X23106,tc_fun(tc_prod(X23106,X23106),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X23106,tc_prod(X23106,X23106)),tc_fun(X23106,tc_fun(tc_fun(tc_prod(X23106,X23106),tc_HOL_Obool),tc_HOL_Obool)),X23106),hAPP(c_COMBB(tc_prod(X23106,X23106),tc_fun(tc_fun(tc_prod(X23106,X23106),tc_HOL_Obool),tc_HOL_Obool),X23106),c_member(tc_prod(X23106,X23106)))),c_Product__Type_OPair(X23106,X23106)))),X23105),X23104,X23103) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__extp__max__ext__eq])]) ).

fof(i_0_6191,plain,
    ! [X28600,X28601,X28602,X28603] :
      ( ( ~ c_List_Olistrelp(X28603,hAPP(hAPP(c_COMBC(X28603,tc_fun(tc_prod(X28603,X28603),tc_HOL_Obool),tc_fun(X28603,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28603,tc_fun(tc_fun(tc_prod(X28603,X28603),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X28603,X28603),tc_HOL_Obool),tc_fun(X28603,tc_HOL_Obool)),X28603),c_COMBC(X28603,tc_fun(tc_prod(X28603,X28603),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28603,tc_prod(X28603,X28603)),tc_fun(X28603,tc_fun(tc_fun(tc_prod(X28603,X28603),tc_HOL_Obool),tc_HOL_Obool)),X28603),hAPP(c_COMBB(tc_prod(X28603,X28603),tc_fun(tc_fun(tc_prod(X28603,X28603),tc_HOL_Obool),tc_HOL_Obool),X28603),c_member(tc_prod(X28603,X28603)))),c_Product__Type_OPair(X28603,X28603)))),X28602),X28601,X28600)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28603),tc_List_Olist(X28603))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28603),tc_List_Olist(X28603)),X28601),X28600)),c_List_Olistrel(X28603,X28602))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28603),tc_List_Olist(X28603))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28603),tc_List_Olist(X28603)),X28601),X28600)),c_List_Olistrel(X28603,X28602)))
        | c_List_Olistrelp(X28603,hAPP(hAPP(c_COMBC(X28603,tc_fun(tc_prod(X28603,X28603),tc_HOL_Obool),tc_fun(X28603,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28603,tc_fun(tc_fun(tc_prod(X28603,X28603),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X28603,X28603),tc_HOL_Obool),tc_fun(X28603,tc_HOL_Obool)),X28603),c_COMBC(X28603,tc_fun(tc_prod(X28603,X28603),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28603,tc_prod(X28603,X28603)),tc_fun(X28603,tc_fun(tc_fun(tc_prod(X28603,X28603),tc_HOL_Obool),tc_HOL_Obool)),X28603),hAPP(c_COMBB(tc_prod(X28603,X28603),tc_fun(tc_fun(tc_prod(X28603,X28603),tc_HOL_Obool),tc_HOL_Obool),X28603),c_member(tc_prod(X28603,X28603)))),c_Product__Type_OPair(X28603,X28603)))),X28602),X28601,X28600) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrelp__listrel__eq])]) ).

fof(i_0_6192,plain,
    ! [X27427,X27428,X27429,X27430,X27431,X27432,X27433,X27434] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(X27434,X27433),tc_fun(tc_prod(X27432,X27431),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X27434,X27433),X27430),hAPP(c_COMBK(tc_fun(X27433,tc_HOL_Obool),X27434),X27429))),hAPP(c_Product__Type_Oprod_Oprod__case(X27434,X27433,tc_fun(tc_prod(X27432,X27431),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X27434,tc_fun(X27433,tc_fun(X27432,tc_fun(X27431,tc_HOL_Obool))),tc_fun(X27433,tc_fun(tc_prod(X27432,X27431),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X27432,tc_fun(X27431,tc_HOL_Obool)),tc_fun(tc_prod(X27432,X27431),tc_HOL_Obool)),tc_fun(tc_fun(X27433,tc_fun(X27432,tc_fun(X27431,tc_HOL_Obool))),tc_fun(X27433,tc_fun(tc_prod(X27432,X27431),tc_HOL_Obool))),X27434),c_COMBB(tc_fun(X27432,tc_fun(X27431,tc_HOL_Obool)),tc_fun(tc_prod(X27432,X27431),tc_HOL_Obool),X27433)),hAPP(hAPP(c_COMBB(tc_fun(X27432,tc_HOL_Obool),tc_fun(tc_fun(X27432,tc_fun(X27431,tc_HOL_Obool)),tc_fun(tc_prod(X27432,X27431),tc_HOL_Obool)),X27434),c_Product__Type_OSigma(X27432,X27431)),X27428))),hAPP(hAPP(c_COMBB(tc_fun(X27431,tc_HOL_Obool),tc_fun(X27432,tc_fun(X27431,tc_HOL_Obool)),X27433),c_COMBK(tc_fun(X27431,tc_HOL_Obool),X27432)),X27427)))) = hAPP(hAPP(c_Product__Type_OSigma(X27432,X27431),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27434,tc_fun(X27432,tc_HOL_Obool)),X27430),X27428)),hAPP(c_COMBK(tc_fun(X27431,tc_HOL_Obool),X27432),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27433,tc_fun(X27431,tc_HOL_Obool)),X27429),X27427))),
    inference(variable_rename,[status(thm)],[fact_UN__Times__distrib]) ).

fof(i_0_6193,plain,
    ! [X26878,X26879] :
      ( ( ~ c_Equiv__Relations_Oequiv(X26879,c_Orderings_Otop__class_Otop(tc_fun(X26879,tc_HOL_Obool)),X26878)
        | c_Equiv__Relations_Oequivp(X26879,hAPP(hAPP(c_COMBC(X26879,tc_fun(tc_prod(X26879,X26879),tc_HOL_Obool),tc_fun(X26879,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26879,tc_fun(tc_fun(tc_prod(X26879,X26879),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X26879,X26879),tc_HOL_Obool),tc_fun(X26879,tc_HOL_Obool)),X26879),c_COMBC(X26879,tc_fun(tc_prod(X26879,X26879),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26879,tc_prod(X26879,X26879)),tc_fun(X26879,tc_fun(tc_fun(tc_prod(X26879,X26879),tc_HOL_Obool),tc_HOL_Obool)),X26879),hAPP(c_COMBB(tc_prod(X26879,X26879),tc_fun(tc_fun(tc_prod(X26879,X26879),tc_HOL_Obool),tc_HOL_Obool),X26879),c_member(tc_prod(X26879,X26879)))),c_Product__Type_OPair(X26879,X26879)))),X26878)) )
      & ( ~ c_Equiv__Relations_Oequivp(X26879,hAPP(hAPP(c_COMBC(X26879,tc_fun(tc_prod(X26879,X26879),tc_HOL_Obool),tc_fun(X26879,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26879,tc_fun(tc_fun(tc_prod(X26879,X26879),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X26879,X26879),tc_HOL_Obool),tc_fun(X26879,tc_HOL_Obool)),X26879),c_COMBC(X26879,tc_fun(tc_prod(X26879,X26879),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26879,tc_prod(X26879,X26879)),tc_fun(X26879,tc_fun(tc_fun(tc_prod(X26879,X26879),tc_HOL_Obool),tc_HOL_Obool)),X26879),hAPP(c_COMBB(tc_prod(X26879,X26879),tc_fun(tc_fun(tc_prod(X26879,X26879),tc_HOL_Obool),tc_HOL_Obool),X26879),c_member(tc_prod(X26879,X26879)))),c_Product__Type_OPair(X26879,X26879)))),X26878))
        | c_Equiv__Relations_Oequiv(X26879,c_Orderings_Otop__class_Otop(tc_fun(X26879,tc_HOL_Obool)),X26878) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equivp__equiv])]) ).

fof(i_0_6194,plain,
    ! [X31991,X31992] :
      ( ( ~ c_Wellfounded_OwfP(X31992,hAPP(hAPP(c_COMBC(X31992,tc_fun(tc_prod(X31992,X31992),tc_HOL_Obool),tc_fun(X31992,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X31992,tc_fun(tc_fun(tc_prod(X31992,X31992),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X31992,X31992),tc_HOL_Obool),tc_fun(X31992,tc_HOL_Obool)),X31992),c_COMBC(X31992,tc_fun(tc_prod(X31992,X31992),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X31992,tc_prod(X31992,X31992)),tc_fun(X31992,tc_fun(tc_fun(tc_prod(X31992,X31992),tc_HOL_Obool),tc_HOL_Obool)),X31992),hAPP(c_COMBB(tc_prod(X31992,X31992),tc_fun(tc_fun(tc_prod(X31992,X31992),tc_HOL_Obool),tc_HOL_Obool),X31992),c_member(tc_prod(X31992,X31992)))),c_Product__Type_OPair(X31992,X31992)))),X31991))
        | c_Wellfounded_Owf(X31992,X31991) )
      & ( ~ c_Wellfounded_Owf(X31992,X31991)
        | c_Wellfounded_OwfP(X31992,hAPP(hAPP(c_COMBC(X31992,tc_fun(tc_prod(X31992,X31992),tc_HOL_Obool),tc_fun(X31992,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X31992,tc_fun(tc_fun(tc_prod(X31992,X31992),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X31992,X31992),tc_HOL_Obool),tc_fun(X31992,tc_HOL_Obool)),X31992),c_COMBC(X31992,tc_fun(tc_prod(X31992,X31992),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X31992,tc_prod(X31992,X31992)),tc_fun(X31992,tc_fun(tc_fun(tc_prod(X31992,X31992),tc_HOL_Obool),tc_HOL_Obool)),X31992),hAPP(c_COMBB(tc_prod(X31992,X31992),tc_fun(tc_fun(tc_prod(X31992,X31992),tc_HOL_Obool),tc_HOL_Obool),X31992),c_member(tc_prod(X31992,X31992)))),c_Product__Type_OPair(X31992,X31992)))),X31991)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wfP__wf__eq])]) ).

fof(i_0_6195,plain,
    ! [X22315,X22316,X22317,X22318] :
      ( ( hAPP(hAPP(c_COMBC(X22318,tc_fun(tc_prod(X22318,X22317),tc_HOL_Obool),tc_fun(X22317,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X22317,tc_fun(tc_fun(tc_prod(X22318,X22317),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X22318,X22317),tc_HOL_Obool),tc_fun(X22317,tc_HOL_Obool)),X22318),c_COMBC(X22317,tc_fun(tc_prod(X22318,X22317),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X22317,tc_prod(X22318,X22317)),tc_fun(X22317,tc_fun(tc_fun(tc_prod(X22318,X22317),tc_HOL_Obool),tc_HOL_Obool)),X22318),hAPP(c_COMBB(tc_prod(X22318,X22317),tc_fun(tc_fun(tc_prod(X22318,X22317),tc_HOL_Obool),tc_HOL_Obool),X22317),c_member(tc_prod(X22318,X22317)))),c_Product__Type_OPair(X22318,X22317)))),X22316) != hAPP(hAPP(c_COMBC(X22318,tc_fun(tc_prod(X22318,X22317),tc_HOL_Obool),tc_fun(X22317,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X22317,tc_fun(tc_fun(tc_prod(X22318,X22317),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X22318,X22317),tc_HOL_Obool),tc_fun(X22317,tc_HOL_Obool)),X22318),c_COMBC(X22317,tc_fun(tc_prod(X22318,X22317),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X22317,tc_prod(X22318,X22317)),tc_fun(X22317,tc_fun(tc_fun(tc_prod(X22318,X22317),tc_HOL_Obool),tc_HOL_Obool)),X22318),hAPP(c_COMBB(tc_prod(X22318,X22317),tc_fun(tc_fun(tc_prod(X22318,X22317),tc_HOL_Obool),tc_HOL_Obool),X22317),c_member(tc_prod(X22318,X22317)))),c_Product__Type_OPair(X22318,X22317)))),X22315)
        | X22316 = X22315 )
      & ( X22316 != X22315
        | hAPP(hAPP(c_COMBC(X22318,tc_fun(tc_prod(X22318,X22317),tc_HOL_Obool),tc_fun(X22317,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X22317,tc_fun(tc_fun(tc_prod(X22318,X22317),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X22318,X22317),tc_HOL_Obool),tc_fun(X22317,tc_HOL_Obool)),X22318),c_COMBC(X22317,tc_fun(tc_prod(X22318,X22317),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X22317,tc_prod(X22318,X22317)),tc_fun(X22317,tc_fun(tc_fun(tc_prod(X22318,X22317),tc_HOL_Obool),tc_HOL_Obool)),X22318),hAPP(c_COMBB(tc_prod(X22318,X22317),tc_fun(tc_fun(tc_prod(X22318,X22317),tc_HOL_Obool),tc_HOL_Obool),X22317),c_member(tc_prod(X22318,X22317)))),c_Product__Type_OPair(X22318,X22317)))),X22316) = hAPP(hAPP(c_COMBC(X22318,tc_fun(tc_prod(X22318,X22317),tc_HOL_Obool),tc_fun(X22317,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X22317,tc_fun(tc_fun(tc_prod(X22318,X22317),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X22318,X22317),tc_HOL_Obool),tc_fun(X22317,tc_HOL_Obool)),X22318),c_COMBC(X22317,tc_fun(tc_prod(X22318,X22317),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X22317,tc_prod(X22318,X22317)),tc_fun(X22317,tc_fun(tc_fun(tc_prod(X22318,X22317),tc_HOL_Obool),tc_HOL_Obool)),X22318),hAPP(c_COMBB(tc_prod(X22318,X22317),tc_fun(tc_fun(tc_prod(X22318,X22317),tc_HOL_Obool),tc_HOL_Obool),X22317),c_member(tc_prod(X22318,X22317)))),c_Product__Type_OPair(X22318,X22317)))),X22315) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__equals__eq2])]) ).

fof(i_0_6196,plain,
    ! [X32084,X32085,X32086,X32087,X32088,X32089] :
      ( ( X32084 = hAPP(hAPP(c_Product__Type_OPair(X32087,X32086),esk430_6(X32084,X32085,X32086,X32087,X32088,X32089)),esk431_6(X32084,X32085,X32086,X32087,X32088,X32089))
        | ~ hBOOL(hAPP(hAPP(c_member(X32089),X32088),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X32087,X32086,tc_fun(X32089,tc_HOL_Obool)),X32085),X32084))) )
      & ( hBOOL(hAPP(hAPP(c_member(X32089),X32088),hAPP(hAPP(X32085,esk430_6(X32084,X32085,X32086,X32087,X32088,X32089)),esk431_6(X32084,X32085,X32086,X32087,X32088,X32089))))
        | ~ hBOOL(hAPP(hAPP(c_member(X32089),X32088),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X32087,X32086,tc_fun(X32089,tc_HOL_Obool)),X32085),X32084))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5265])])])]) ).

fof(i_0_6197,plain,
    ! [X29798,X29799,X29800,X29801,X29802,X29803,X29804,X29805] : hAPP(hAPP(c_List_Omap(tc_prod(X29805,X29804),X29803),X29802),hAPP(hAPP(c_List_Ozip(X29805,X29804),X29801),hAPP(hAPP(c_List_Omap(X29800,X29804),X29799),X29798))) = hAPP(hAPP(c_List_Omap(tc_prod(X29805,X29800),X29803),hAPP(c_Product__Type_Oprod_Oprod__case(X29805,X29800,X29803),hAPP(hAPP(c_COMBB(tc_fun(X29800,tc_prod(X29805,X29804)),tc_fun(X29800,X29803),X29805),hAPP(c_COMBB(tc_prod(X29805,X29804),X29803,X29800),X29802)),hAPP(hAPP(c_COMBC(X29805,tc_fun(X29800,X29804),tc_fun(X29800,tc_prod(X29805,X29804))),hAPP(hAPP(c_COMBB(tc_fun(X29804,tc_prod(X29805,X29804)),tc_fun(tc_fun(X29800,X29804),tc_fun(X29800,tc_prod(X29805,X29804))),X29805),c_COMBB(X29804,tc_prod(X29805,X29804),X29800)),c_Product__Type_OPair(X29805,X29804))),X29799)))),hAPP(hAPP(c_List_Ozip(X29805,X29800),X29801),X29798)),
    inference(variable_rename,[status(thm)],[fact_map__zip__map2]) ).

fof(i_0_6198,plain,
    ! [X33016,X33017,X33018,X33019,X33020,X33021,X33022] :
      ( ( X33017 = hAPP(hAPP(X33020,X33016),esk487_7(X33016,X33017,X33018,X33019,X33020,X33021,X33022))
        | ~ hBOOL(hAPP(hAPP(c_member(X33022),X33016),X33018))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X33022,X33021,X33020,X33019,X33018),X33017))
        | ~ c_Finite__Set_Ofun__left__comm(X33022,X33021,X33020) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X33022,X33021,X33020,X33019,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X33022,tc_HOL_Obool)),X33018),hAPP(hAPP(c_Set_Oinsert(X33022),X33016),c_Orderings_Obot__class_Obot(tc_fun(X33022,tc_HOL_Obool))))),esk487_7(X33016,X33017,X33018,X33019,X33020,X33021,X33022)))
        | ~ hBOOL(hAPP(hAPP(c_member(X33022),X33016),X33018))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X33022,X33021,X33020,X33019,X33018),X33017))
        | ~ c_Finite__Set_Ofun__left__comm(X33022,X33021,X33020) ) ),
    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_6199,plain,
    ! [X33024,X33025,X33026,X33027,X33028,X33029,X33030] :
      ( ( X33024 = hAPP(hAPP(X33028,X33026),esk488_7(X33024,X33025,X33026,X33027,X33028,X33029,X33030))
        | hBOOL(hAPP(hAPP(c_member(X33030),X33026),X33025))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X33030,X33029,X33028,X33027,hAPP(hAPP(c_Set_Oinsert(X33030),X33026),X33025)),X33024))
        | ~ c_Finite__Set_Ofun__left__comm(X33030,X33029,X33028) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X33030,X33029,X33028,X33027,X33025),esk488_7(X33024,X33025,X33026,X33027,X33028,X33029,X33030)))
        | hBOOL(hAPP(hAPP(c_member(X33030),X33026),X33025))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X33030,X33029,X33028,X33027,hAPP(hAPP(c_Set_Oinsert(X33030),X33026),X33025)),X33024))
        | ~ c_Finite__Set_Ofun__left__comm(X33030,X33029,X33028) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5266])])])]) ).

fof(i_0_6200,plain,
    ! [X29259,X29260,X29261,X29262,X29263] : hAPP(hAPP(c_List_Ozip(X29263,X29262),hAPP(hAPP(c_List_Olist_OCons(X29263),X29261),X29260)),X29259) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(X29263,X29262)),X29262,c_List_Olist_ONil(tc_prod(X29263,X29262)),hAPP(hAPP(c_COMBC(X29262,tc_fun(tc_List_Olist(X29262),tc_List_Olist(tc_prod(X29263,X29262))),tc_fun(tc_List_Olist(X29262),tc_List_Olist(tc_prod(X29263,X29262)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(X29263,X29262)),tc_List_Olist(tc_prod(X29263,X29262))),tc_fun(tc_fun(tc_List_Olist(X29262),tc_List_Olist(tc_prod(X29263,X29262))),tc_fun(tc_List_Olist(X29262),tc_List_Olist(tc_prod(X29263,X29262)))),X29262),c_COMBB(tc_List_Olist(tc_prod(X29263,X29262)),tc_List_Olist(tc_prod(X29263,X29262)),tc_List_Olist(X29262))),hAPP(hAPP(c_COMBB(tc_prod(X29263,X29262),tc_fun(tc_List_Olist(tc_prod(X29263,X29262)),tc_List_Olist(tc_prod(X29263,X29262))),X29262),c_List_Olist_OCons(tc_prod(X29263,X29262))),hAPP(c_Product__Type_OPair(X29263,X29262),X29261)))),hAPP(c_List_Ozip(X29263,X29262),X29260))),X29259),
    inference(variable_rename,[status(thm)],[fact_zip__Cons1]) ).

cnf(i_0_6201,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_5267]) ).

cnf(i_0_6202,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_5256]) ).

cnf(i_0_6203,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_5256]) ).

cnf(i_0_6204,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_5268]) ).

fof(i_0_6205,plain,
    ! [X32037,X32038,X32039,X32040] :
      ( ( hBOOL(hAPP(hAPP(c_member(X32040),esk418_4(X32037,X32038,X32039,X32040)),X32039))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32038),hAPP(c_Set_Oimage(X32040,X32038,X32037),X32039)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X32040),X32039)) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32040),hAPP(c_Set_OCollect(X32040),hAPP(hAPP(c_COMBS(X32040,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X32040),c_fconj),hAPP(hAPP(c_COMBC(X32040,tc_fun(X32040,tc_HOL_Obool),tc_HOL_Obool),c_member(X32040)),X32039))),hAPP(hAPP(c_COMBC(X32040,X32038,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X32038,tc_fun(X32038,tc_HOL_Obool),X32040),c_fequal),X32037)),hAPP(X32037,esk418_4(X32037,X32038,X32039,X32040)))))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32038),hAPP(c_Set_Oimage(X32040,X32038,X32037),X32039)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X32040),X32039)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5269])])])]) ).

fof(i_0_6206,plain,
    ! [X28247,X28248,X28249,X28250] :
      ( ( hBOOL(hAPP(X28250,esk302_4(X28247,X28248,X28249,X28250)))
        | c_Wellfounded_Owf(X28247,hAPP(c_Set_OCollect(tc_prod(X28247,X28247)),hAPP(c_Product__Type_Oprod_Oprod__case(X28247,X28247,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X28247,tc_HOL_Obool),tc_fun(X28247,tc_HOL_Obool),X28247),hAPP(c_COMBS(X28247,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X28247),c_fconj),X28250))),hAPP(hAPP(c_COMBC(X28247,tc_fun(X28247,X28247),tc_fun(X28247,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28247,tc_HOL_Obool),tc_fun(tc_fun(X28247,X28247),tc_fun(X28247,tc_HOL_Obool)),X28247),c_COMBB(X28247,tc_HOL_Obool,X28247)),c_fequal)),X28248))))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X28249,hAPP(X28248,esk302_4(X28247,X28248,X28249,X28250)))),hAPP(X28249,esk302_4(X28247,X28248,X28249,X28250))))
        | c_Wellfounded_Owf(X28247,hAPP(c_Set_OCollect(tc_prod(X28247,X28247)),hAPP(c_Product__Type_Oprod_Oprod__case(X28247,X28247,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X28247,tc_HOL_Obool),tc_fun(X28247,tc_HOL_Obool),X28247),hAPP(c_COMBS(X28247,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X28247),c_fconj),X28250))),hAPP(hAPP(c_COMBC(X28247,tc_fun(X28247,X28247),tc_fun(X28247,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28247,tc_HOL_Obool),tc_fun(tc_fun(X28247,X28247),tc_fun(X28247,tc_HOL_Obool)),X28247),c_COMBB(X28247,tc_HOL_Obool,X28247)),c_fequal)),X28248))))) ) ),
    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_6207,plain,
    ! [X28078,X28079,X28080] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28080,X28080),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X28080,X28080,X28080),X28079),X28078)),X28079))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(X28080,tc_HOL_Obool),tc_fun(X28080,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(X28080,tc_HOL_Obool),tc_fun(X28080,tc_HOL_Obool),tc_fun(X28080,tc_HOL_Obool)),c_Wellfounded_Omax__ext(X28080,X28079)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(X28080,tc_HOL_Obool),tc_fun(X28080,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(X28080,X28078)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(X28080,tc_HOL_Obool),tc_fun(X28080,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X28080,tc_HOL_Obool),tc_fun(X28080,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X28080,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(X28080,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(X28080,tc_HOL_Obool),tc_fun(X28080,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(X28080,X28079))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__ext__compat])]) ).

fof(i_0_6208,plain,
    ! [X28081,X28082,X28083] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28083,X28083),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X28083,X28083,X28083),X28082),X28081)),X28082))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(X28083,tc_HOL_Obool),tc_fun(X28083,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(X28083,tc_HOL_Obool),tc_fun(X28083,tc_HOL_Obool),tc_fun(X28083,tc_HOL_Obool)),c_Wellfounded_Omin__ext(X28083,X28082)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(X28083,tc_HOL_Obool),tc_fun(X28083,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(X28083,X28081)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(X28083,tc_HOL_Obool),tc_fun(X28083,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X28083,tc_HOL_Obool),tc_fun(X28083,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X28083,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(X28083,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(X28083,tc_HOL_Obool),tc_fun(X28083,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(X28083,X28082))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__ext__compat])]) ).

fof(i_0_6209,plain,
    ! [X17841,X17842,X17843,X17844,X17845,X17846,X17847] :
      ( ~ c_Hoare__Mirabelle_Ohoare__derivs(X17847,X17846,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X17847)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17847),c_Hoare__Mirabelle_Opeek__and(X17847,X17845,X17844)),X17843),X17842)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X17847),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(X17847,X17846,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X17847)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17847),c_Hoare__Mirabelle_Opeek__and(X17847,X17845,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),X17844))),X17841),X17842)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X17847),tc_HOL_Obool))))
      | c_Hoare__Mirabelle_Ohoare__derivs(X17847,X17846,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X17847)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17847),X17845),c_Com_Ocom_OCond(X17844,X17843,X17841)),X17842)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X17847),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hoare__derivs_OIf])]) ).

fof(i_0_6210,plain,
    ! [X17021,X17022,X17023,X17024,X17025,X17026] :
      ( ( hBOOL(hAPP(hAPP(X17021,esk4_6(X17021,X17022,X17023,X17024,X17025,X17026)),esk5_6(X17021,X17022,X17023,X17024,X17025,X17026)))
        | c_Hoare__Mirabelle_Ohoare__derivs(X17026,X17025,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X17026)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17026),X17021),X17023),X17022)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X17026),tc_HOL_Obool))))
        | ~ c_Hoare__Mirabelle_Ohoare__derivs(X17026,X17025,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X17026)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17026),X17024),X17023),X17022)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X17026),tc_HOL_Obool)))) )
      & ( ~ hBOOL(hAPP(hAPP(X17024,esk4_6(X17021,X17022,X17023,X17024,X17025,X17026)),esk5_6(X17021,X17022,X17023,X17024,X17025,X17026)))
        | c_Hoare__Mirabelle_Ohoare__derivs(X17026,X17025,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X17026)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17026),X17021),X17023),X17022)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X17026),tc_HOL_Obool))))
        | ~ c_Hoare__Mirabelle_Ohoare__derivs(X17026,X17025,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X17026)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17026),X17024),X17023),X17022)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X17026),tc_HOL_Obool)))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_conseq1])])])]) ).

fof(i_0_6211,plain,
    ! [X17013,X17014,X17015,X17016,X17017,X17018] :
      ( ( hBOOL(hAPP(hAPP(X17014,esk2_6(X17013,X17014,X17015,X17016,X17017,X17018)),esk3_6(X17013,X17014,X17015,X17016,X17017,X17018)))
        | c_Hoare__Mirabelle_Ohoare__derivs(X17018,X17017,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X17018)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17018),X17016),X17015),X17013)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X17018),tc_HOL_Obool))))
        | ~ c_Hoare__Mirabelle_Ohoare__derivs(X17018,X17017,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X17018)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17018),X17016),X17015),X17014)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X17018),tc_HOL_Obool)))) )
      & ( ~ hBOOL(hAPP(hAPP(X17013,esk2_6(X17013,X17014,X17015,X17016,X17017,X17018)),esk3_6(X17013,X17014,X17015,X17016,X17017,X17018)))
        | c_Hoare__Mirabelle_Ohoare__derivs(X17018,X17017,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X17018)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17018),X17016),X17015),X17013)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X17018),tc_HOL_Obool))))
        | ~ c_Hoare__Mirabelle_Ohoare__derivs(X17018,X17017,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X17018)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17018),X17016),X17015),X17014)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X17018),tc_HOL_Obool)))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_conseq2])])])]) ).

cnf(i_0_6212,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)))),esk388_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_5270]) ).

cnf(i_0_6213,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)))),esk387_3(X3,X2,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_5271]) ).

fof(i_0_6214,plain,
    ! [X27805,X27806,X27807,X27808,X27809] :
      ( ~ class_Groups_Ocomm__monoid__add(X27809)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27808),X27807))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27808,X27809),X27806),hAPP(c_Set_OCollect(X27808),hAPP(hAPP(c_COMBS(X27808,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27808),c_fconj),hAPP(hAPP(c_COMBC(X27808,tc_fun(X27808,tc_HOL_Obool),tc_HOL_Obool),c_member(X27808)),X27807))),hAPP(hAPP(c_COMBC(X27808,tc_fun(X27808,tc_HOL_Obool),tc_HOL_Obool),c_member(X27808)),X27805)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27808,X27809),hAPP(hAPP(c_COMBC(X27808,X27809,X27809),hAPP(hAPP(c_COMBS(X27808,X27809,tc_fun(X27809,X27809)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X27809,tc_fun(X27809,X27809)),X27808),c_If(X27809)),hAPP(hAPP(c_COMBC(X27808,tc_fun(X27808,tc_HOL_Obool),tc_HOL_Obool),c_member(X27808)),X27805))),X27806)),c_Groups_Ozero__class_Ozero(X27809))),X27807) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__restrict__set_H])]) ).

cnf(i_0_6215,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_5272]) ).

cnf(i_0_6216,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_5273]) ).

cnf(i_0_6217,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_5274]) ).

fof(i_0_6218,plain,
    ! [X29776,X29777,X29778,X29779,X29780,X29781,X29782,X29783] : hAPP(hAPP(c_List_Ozip(X29783,X29782),hAPP(hAPP(c_List_Omap(X29781,X29783),X29780),X29779)),hAPP(hAPP(c_List_Omap(X29778,X29782),X29777),X29776)) = hAPP(hAPP(c_List_Omap(tc_prod(X29781,X29778),tc_prod(X29783,X29782)),hAPP(c_Product__Type_Oprod_Oprod__case(X29781,X29778,tc_prod(X29783,X29782)),hAPP(hAPP(c_COMBC(X29781,tc_fun(X29778,X29782),tc_fun(X29778,tc_prod(X29783,X29782))),hAPP(hAPP(c_COMBB(tc_fun(X29782,tc_prod(X29783,X29782)),tc_fun(tc_fun(X29778,X29782),tc_fun(X29778,tc_prod(X29783,X29782))),X29781),c_COMBB(X29782,tc_prod(X29783,X29782),X29778)),hAPP(hAPP(c_COMBB(X29783,tc_fun(X29782,tc_prod(X29783,X29782)),X29781),c_Product__Type_OPair(X29783,X29782)),X29780))),X29777))),hAPP(hAPP(c_List_Ozip(X29781,X29778),X29779),X29776)),
    inference(variable_rename,[status(thm)],[fact_zip__map__map]) ).

cnf(i_0_6219,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_5275]) ).

cnf(i_0_6220,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_5276]) ).

fof(i_0_6221,plain,
    ! [X27859] : c_Wellfounded_Ofinite__psubset(X27859) = hAPP(c_Set_OCollect(tc_prod(tc_fun(X27859,tc_HOL_Obool),tc_fun(X27859,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(X27859,tc_HOL_Obool),tc_fun(X27859,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(X27859,tc_HOL_Obool),tc_fun(tc_fun(X27859,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X27859,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X27859,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(X27859,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X27859,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X27859,tc_HOL_Obool)),c_COMBS(tc_fun(X27859,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X27859,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X27859,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(X27859,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X27859,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(X27859,tc_HOL_Obool))))),c_Finite__Set_Ofinite(X27859)))),
    inference(variable_rename,[status(thm)],[fact_finite__psubset__def]) ).

cnf(i_0_6222,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_5277]) ).

cnf(i_0_6223,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_5278]) ).

fof(i_0_6224,plain,
    ! [X30316,X30317] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30317),X30316))
        | c_Nitpick_Ocard_H(X30317,X30316) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30317)),c_Hilbert__Choice_OEps(tc_List_Olist(X30317),hAPP(hAPP(c_COMBS(tc_List_Olist(X30317),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X30317)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X30317),tc_fun(X30317,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X30317,tc_HOL_Obool),tc_fun(tc_fun(X30317,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X30317)),c_fequal),c_List_Oset(X30317))),X30316))),c_List_Odistinct(X30317)))) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X30317),X30316))
        | c_Nitpick_Ocard_H(X30317,X30316) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5279])]) ).

fof(i_0_6225,plain,
    ! [X27680,X27681] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X27681))
      | 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)),X27681))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X27680)))) = 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)),X27681))),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,X27680))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5280])]) ).

fof(i_0_6226,plain,
    ! [X27499,X27500,X27501,X27502,X27503,X27504,X27505,X27506,X27507] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27507,X27506)),hAPP(hAPP(c_Product__Type_OPair(X27507,X27506),X27505),X27504)),X27503))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X27502,X27501)),hAPP(hAPP(c_Product__Type_OPair(X27502,X27501),hAPP(X27500,X27505)),hAPP(X27499,X27504))),hAPP(c_Set_Oimage(tc_prod(X27507,X27506),tc_prod(X27502,X27501),c_Product__Type_Omap__pair(X27507,X27502,X27506,X27501,X27500,X27499)),X27503))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__pair__imageI])]) ).

cnf(i_0_6227,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_5281]) ).

cnf(i_0_6228,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_5282]) ).

fof(i_0_6229,plain,
    ! [X33250,X33251,X33252,X33253,X33254,X33255,X33256] : c_New__Random__Sequence_Oneg__decr__bind(X33256,X33255,X33254,X33253,X33252,X33251,X33250) = c_New__DSequence_Oneg__decr__bind(X33256,X33255,hAPP(hAPP(hAPP(X33254,X33252),X33251),X33250),hAPP(hAPP(c_COMBC(X33256,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(X33255)))),hAPP(hAPP(c_COMBC(X33256,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(X33255))))),hAPP(hAPP(c_COMBC(X33256,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(X33255)))))),X33253),X33252)),X33251)),X33250)),
    inference(variable_rename,[status(thm)],[fact_New__Random__Sequence_Oneg__decr__bind__def]) ).

fof(i_0_6230,plain,
    ! [X30152,X30153,X30154,X30155] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30155,tc_fun(X30154,tc_HOL_Obool)),X30153),X30152) = hAPP(c_Set_OCollect(X30154),hAPP(hAPP(c_COMBB(tc_fun(X30155,tc_HOL_Obool),tc_HOL_Obool,X30154),c_HOL_OAll(X30155)),hAPP(hAPP(c_COMBB(tc_fun(X30155,tc_HOL_Obool),tc_fun(X30155,tc_HOL_Obool),X30154),hAPP(c_COMBS(X30155,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X30155),c_fimplies),hAPP(hAPP(c_COMBC(X30155,tc_fun(X30155,tc_HOL_Obool),tc_HOL_Obool),c_member(X30155)),X30153)))),hAPP(hAPP(c_COMBC(X30154,tc_fun(X30155,tc_fun(X30154,tc_HOL_Obool)),tc_fun(X30155,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X30154,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X30155,tc_fun(X30154,tc_HOL_Obool)),tc_fun(X30155,tc_HOL_Obool)),X30154),c_COMBB(tc_fun(X30154,tc_HOL_Obool),tc_HOL_Obool,X30155)),c_member(X30154))),X30152)))),
    inference(variable_rename,[status(thm)],[fact_INTER__def]) ).

fof(i_0_6231,plain,
    ! [X29231,X29232,X29233,X29234,X29235,X29236,X29237,X29238,X29239] :
      ( ( ~ c_Equiv__Relations_Ocongruent(X29234,X29233,X29232,X29231)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29234,X29234)),X29235),X29232))
        | hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X29234,X29234,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X29234,tc_fun(X29234,X29233),tc_fun(X29234,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29233,tc_HOL_Obool),tc_fun(tc_fun(X29234,X29233),tc_fun(X29234,tc_HOL_Obool)),X29234),c_COMBB(X29233,tc_HOL_Obool,X29234)),hAPP(hAPP(c_COMBB(X29233,tc_fun(X29233,tc_HOL_Obool),X29234),c_fequal),X29231))),X29231)),X29235)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29239,X29239)),esk331_4(X29236,X29237,X29238,X29239)),X29237))
        | c_Equiv__Relations_Ocongruent(X29239,X29238,X29237,X29236) )
      & ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X29239,X29239,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X29239,tc_fun(X29239,X29238),tc_fun(X29239,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29238,tc_HOL_Obool),tc_fun(tc_fun(X29239,X29238),tc_fun(X29239,tc_HOL_Obool)),X29239),c_COMBB(X29238,tc_HOL_Obool,X29239)),hAPP(hAPP(c_COMBB(X29238,tc_fun(X29238,tc_HOL_Obool),X29239),c_fequal),X29236))),X29236)),esk331_4(X29236,X29237,X29238,X29239)))
        | c_Equiv__Relations_Ocongruent(X29239,X29238,X29237,X29236) ) ),
    inference(distribute,[status(thm)],[inference(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_6232,plain,
    ! [X27850,X27851,X27852,X27853,X27854] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27851),hAPP(c_Set_OCollect(X27851),hAPP(hAPP(c_COMBB(tc_fun(X27853,tc_HOL_Obool),tc_HOL_Obool,X27851),c_HOL_OEx(X27853)),hAPP(hAPP(c_COMBB(tc_fun(X27853,tc_HOL_Obool),tc_fun(X27853,tc_HOL_Obool),X27851),hAPP(c_COMBS(X27853,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27853),c_fconj),X27852))),X27850)))))
        | ~ hBOOL(hAPP(X27852,X27854))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X27851),hAPP(c_Set_OCollect(X27851),hAPP(hAPP(c_COMBC(X27851,X27853,tc_HOL_Obool),X27850),X27854))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27853),hAPP(c_Set_OCollect(X27853),X27852))) )
      & ( hBOOL(hAPP(X27852,esk292_4(X27850,X27851,X27852,X27853)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X27851),hAPP(c_Set_OCollect(X27851),hAPP(hAPP(c_COMBB(tc_fun(X27853,tc_HOL_Obool),tc_HOL_Obool,X27851),c_HOL_OEx(X27853)),hAPP(hAPP(c_COMBB(tc_fun(X27853,tc_HOL_Obool),tc_fun(X27853,tc_HOL_Obool),X27851),hAPP(c_COMBS(X27853,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27853),c_fconj),X27852))),X27850)))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27853),hAPP(c_Set_OCollect(X27853),X27852))) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27851),hAPP(c_Set_OCollect(X27851),hAPP(hAPP(c_COMBC(X27851,X27853,tc_HOL_Obool),X27850),esk292_4(X27850,X27851,X27852,X27853)))))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X27851),hAPP(c_Set_OCollect(X27851),hAPP(hAPP(c_COMBB(tc_fun(X27853,tc_HOL_Obool),tc_HOL_Obool,X27851),c_HOL_OEx(X27853)),hAPP(hAPP(c_COMBB(tc_fun(X27853,tc_HOL_Obool),tc_fun(X27853,tc_HOL_Obool),X27851),hAPP(c_COMBS(X27853,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27853),c_fconj),X27852))),X27850)))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27853),hAPP(c_Set_OCollect(X27853),X27852))) ) ),
    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_6233,plain,
    ! [X27466,X27467,X27468,X27469,X27470,X27471] :
      ( ( hBOOL(hAPP(hAPP(c_member(X27470),esk279_6(X27466,X27467,X27468,X27469,X27470,X27471)),X27469))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27470,X27471),hAPP(hAPP(c_COMBS(X27470,tc_fun(X27468,tc_HOL_Obool),X27471),hAPP(hAPP(c_COMBB(tc_fun(X27468,X27471),tc_fun(tc_fun(X27468,tc_HOL_Obool),X27471),X27470),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27468,X27471)),X27466)),X27467)),X27469) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(X27470,X27468),X27471),hAPP(c_Product__Type_Oprod_Oprod__case(X27470,X27468,X27471),X27466)),hAPP(hAPP(c_Product__Type_OSigma(X27470,X27468),X27469),X27467))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27470),X27469))
        | ~ class_Groups_Ocomm__monoid__add(X27471) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27468),hAPP(X27467,esk279_6(X27466,X27467,X27468,X27469,X27470,X27471))))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27470,X27471),hAPP(hAPP(c_COMBS(X27470,tc_fun(X27468,tc_HOL_Obool),X27471),hAPP(hAPP(c_COMBB(tc_fun(X27468,X27471),tc_fun(tc_fun(X27468,tc_HOL_Obool),X27471),X27470),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27468,X27471)),X27466)),X27467)),X27469) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(X27470,X27468),X27471),hAPP(c_Product__Type_Oprod_Oprod__case(X27470,X27468,X27471),X27466)),hAPP(hAPP(c_Product__Type_OSigma(X27470,X27468),X27469),X27467))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27470),X27469))
        | ~ class_Groups_Ocomm__monoid__add(X27471) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__Sigma])])])]) ).

fof(i_0_6234,plain,
    ! [X27459,X27460,X27461,X27462,X27463,X27464] :
      ( ( hBOOL(hAPP(hAPP(c_member(X27463),esk278_6(X27459,X27460,X27461,X27462,X27463,X27464)),X27462))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27463,X27464),hAPP(hAPP(c_COMBS(X27463,tc_fun(X27461,tc_HOL_Obool),X27464),hAPP(hAPP(c_COMBB(tc_fun(X27461,X27464),tc_fun(tc_fun(X27461,tc_HOL_Obool),X27464),X27463),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27461,X27464)),X27459)),X27460)),X27462) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(X27463,X27461),X27464),hAPP(c_Product__Type_Oprod_Oprod__case(X27463,X27461,X27464),X27459)),hAPP(hAPP(c_Product__Type_OSigma(X27463,X27461),X27462),X27460))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27463),X27462))
        | ~ class_Groups_Ocomm__monoid__mult(X27464) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27461),hAPP(X27460,esk278_6(X27459,X27460,X27461,X27462,X27463,X27464))))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27463,X27464),hAPP(hAPP(c_COMBS(X27463,tc_fun(X27461,tc_HOL_Obool),X27464),hAPP(hAPP(c_COMBB(tc_fun(X27461,X27464),tc_fun(tc_fun(X27461,tc_HOL_Obool),X27464),X27463),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27461,X27464)),X27459)),X27460)),X27462) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(X27463,X27461),X27464),hAPP(c_Product__Type_Oprod_Oprod__case(X27463,X27461,X27464),X27459)),hAPP(hAPP(c_Product__Type_OSigma(X27463,X27461),X27462),X27460))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27463),X27462))
        | ~ class_Groups_Ocomm__monoid__mult(X27464) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__Sigma])])])]) ).

fof(i_0_6235,plain,
    ! [X26362,X26363,X26364,X26365,X26366] :
      ( ~ class_Groups_Ocomm__monoid__add(X26366)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26365),X26364))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26365,X26366),X26363),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26365,tc_HOL_Obool)),X26364),X26362)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26365,X26366),hAPP(hAPP(c_COMBC(X26365,X26366,X26366),hAPP(hAPP(c_COMBS(X26365,X26366,tc_fun(X26366,X26366)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X26366,tc_fun(X26366,X26366)),X26365),c_If(X26366)),hAPP(hAPP(c_COMBC(X26365,tc_fun(X26365,tc_HOL_Obool),tc_HOL_Obool),c_member(X26365)),X26362))),X26363)),c_Groups_Ozero__class_Ozero(X26366))),X26364) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__restrict__set])]) ).

fof(i_0_6236,plain,
    ! [X27229,X27230,X27231,X27232,X27233,X27234] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X27234),X27231),X27232))
        | hAPP(c_Set_Ovimage(X27230,X27234,hAPP(hAPP(c_COMBC(X27230,X27234,X27234),hAPP(hAPP(c_COMBC(X27230,X27234,tc_fun(X27234,X27234)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X27234,tc_fun(X27234,X27234)),X27230),c_If(X27234)),hAPP(hAPP(c_COMBC(X27230,tc_fun(X27230,tc_HOL_Obool),tc_HOL_Obool),c_member(X27230)),X27229))),X27233)),X27231)),X27232) = c_Orderings_Otop__class_Otop(tc_fun(X27230,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(X27234),X27233),X27232)) )
      & ( hBOOL(hAPP(hAPP(c_member(X27234),X27231),X27232))
        | hAPP(c_Set_Ovimage(X27230,X27234,hAPP(hAPP(c_COMBC(X27230,X27234,X27234),hAPP(hAPP(c_COMBC(X27230,X27234,tc_fun(X27234,X27234)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X27234,tc_fun(X27234,X27234)),X27230),c_If(X27234)),hAPP(hAPP(c_COMBC(X27230,tc_fun(X27230,tc_HOL_Obool),tc_HOL_Obool),c_member(X27230)),X27229))),X27233)),X27231)),X27232) = X27229
        | ~ hBOOL(hAPP(hAPP(c_member(X27234),X27233),X27232)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X27234),X27231),X27232))
        | hAPP(c_Set_Ovimage(X27230,X27234,hAPP(hAPP(c_COMBC(X27230,X27234,X27234),hAPP(hAPP(c_COMBC(X27230,X27234,tc_fun(X27234,X27234)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X27234,tc_fun(X27234,X27234)),X27230),c_If(X27234)),hAPP(hAPP(c_COMBC(X27230,tc_fun(X27230,tc_HOL_Obool),tc_HOL_Obool),c_member(X27230)),X27229))),X27233)),X27231)),X27232) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X27230,tc_HOL_Obool)),X27229)
        | hBOOL(hAPP(hAPP(c_member(X27234),X27233),X27232)) )
      & ( hBOOL(hAPP(hAPP(c_member(X27234),X27231),X27232))
        | hAPP(c_Set_Ovimage(X27230,X27234,hAPP(hAPP(c_COMBC(X27230,X27234,X27234),hAPP(hAPP(c_COMBC(X27230,X27234,tc_fun(X27234,X27234)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X27234,tc_fun(X27234,X27234)),X27230),c_If(X27234)),hAPP(hAPP(c_COMBC(X27230,tc_fun(X27230,tc_HOL_Obool),tc_HOL_Obool),c_member(X27230)),X27229))),X27233)),X27231)),X27232) = c_Orderings_Obot__class_Obot(tc_fun(X27230,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_member(X27234),X27233),X27232)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5283])])]) ).

fof(i_0_6237,plain,
    ! [X26851,X26852,X26853,X26854] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26854,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X26854,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk250_4(X26851,X26852,X26853,X26854))),X26853)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X26854,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),esk250_4(X26851,X26852,X26853,X26854)),X26852))),X26851)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26854,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X26854,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X26853)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X26854,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X26851))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__finite2__subset])])]) ).

cnf(i_0_6238,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_5284]) ).

fof(i_0_6239,plain,
    ! [X33257,X33258,X33259,X33260,X33261,X33262,X33263] : c_New__Random__Sequence_Opos__decr__bind(X33263,X33262,X33261,X33260,X33259,X33258,X33257) = c_New__DSequence_Opos__decr__bind(X33263,X33262,hAPP(hAPP(hAPP(X33261,X33259),X33258),X33257),hAPP(hAPP(c_COMBC(X33263,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X33262))),hAPP(hAPP(c_COMBC(X33263,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(X33262)))),hAPP(hAPP(c_COMBC(X33263,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(X33262))))),X33260),X33259)),X33258)),X33257)),
    inference(variable_rename,[status(thm)],[fact_New__Random__Sequence_Opos__decr__bind__def]) ).

cnf(i_0_6240,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_5285]) ).

cnf(i_0_6241,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_5286]) ).

cnf(i_0_6242,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_5287]) ).

cnf(i_0_6243,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_5288]) ).

cnf(i_0_6244,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_5289]) ).

fof(i_0_6245,plain,
    ! [X27235,X27236,X27237,X27238,X27239,X27240] : hAPP(c_Set_Oimage(X27240,tc_prod(X27239,X27238),hAPP(hAPP(c_COMBS(X27240,X27238,tc_prod(X27239,X27238)),hAPP(hAPP(c_COMBB(X27239,tc_fun(X27238,tc_prod(X27239,X27238)),X27240),c_Product__Type_OPair(X27239,X27238)),X27237)),X27236)),X27235) = hAPP(hAPP(c_Product__Type_OSigma(X27239,X27238),hAPP(c_Set_Oimage(X27240,X27239,X27237),X27235)),hAPP(hAPP(c_COMBB(tc_fun(X27240,tc_HOL_Obool),tc_fun(X27238,tc_HOL_Obool),X27239),c_Set_Oimage(X27240,X27238,X27236)),hAPP(hAPP(c_COMBC(X27239,tc_fun(X27240,tc_HOL_Obool),tc_fun(X27240,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27240,tc_HOL_Obool),tc_fun(tc_fun(X27240,tc_HOL_Obool),tc_fun(X27240,tc_HOL_Obool)),X27239),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27240,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X27239,tc_HOL_Obool),tc_fun(X27240,tc_HOL_Obool),X27239),c_Set_Ovimage(X27240,X27239,X27237)),hAPP(hAPP(c_COMBC(X27239,tc_fun(X27239,tc_HOL_Obool),tc_fun(X27239,tc_HOL_Obool)),c_Set_Oinsert(X27239)),c_Orderings_Obot__class_Obot(tc_fun(X27239,tc_HOL_Obool)))))),X27235))),
    inference(variable_rename,[status(thm)],[fact_image__split__eq__Sigma]) ).

cnf(i_0_6246,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_5290]) ).

fof(i_0_6247,plain,
    ! [X33502,X33503] :
      ( ~ class_Lazy__Sequence_Osmall__lazy(X33503)
      | c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(X33503),X33502) = c_Lazy__Sequence_Oappend(tc_List_Olist(X33503),hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(X33503)),c_List_Olist_ONil(X33503)),hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X33503))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X33502)),hAPP(c_Lazy__Sequence_Obind(tc_prod(X33503,tc_List_Olist(X33503)),tc_List_Olist(X33503),c_Lazy__Sequence_Oproduct(X33503,tc_List_Olist(X33503),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(X33503,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X33502),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(X33503),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X33502),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Product__Type_Oprod_Oprod__case(X33503,tc_List_Olist(X33503),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X33503))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X33503),tc_List_Olist(X33503)),tc_fun(tc_List_Olist(X33503),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X33503))),X33503),hAPP(c_COMBB(tc_List_Olist(X33503),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X33503)),tc_List_Olist(X33503)),c_Lazy__Sequence_Osingle(tc_List_Olist(X33503)))),c_List_Olist_OCons(X33503))))),c_Lazy__Sequence_Oempty(tc_List_Olist(X33503)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_small__lazy__list_Osimps])]) ).

fof(i_0_6248,plain,
    ! [X30990,X30991] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X30991)
      | c_Complete__Lattice_OSup__class_OSup(X30991,X30990) = c_Complete__Lattice_OInf__class_OInf(X30991,hAPP(c_Set_OCollect(X30991),hAPP(hAPP(c_COMBB(tc_fun(X30991,tc_HOL_Obool),tc_HOL_Obool,X30991),c_HOL_OAll(X30991)),hAPP(hAPP(c_COMBB(tc_fun(X30991,tc_HOL_Obool),tc_fun(X30991,tc_HOL_Obool),X30991),hAPP(c_COMBS(X30991,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X30991),c_fimplies),hAPP(hAPP(c_COMBC(X30991,tc_fun(X30991,tc_HOL_Obool),tc_HOL_Obool),c_member(X30991)),X30990)))),hAPP(c_COMBC(X30991,X30991,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X30991)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__Inf])]) ).

fof(i_0_6249,plain,
    ! [X26588,X26589,X26590,X26591,X26592,X26593] :
      ( ( hBOOL(hAPP(hAPP(c_member(X26592),esk241_6(X26588,X26589,X26590,X26591,X26592,X26593)),X26591))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26592,X26593),X26590),X26591) != X26589
        | ~ hBOOL(hAPP(hAPP(c_member(X26592),X26588),X26591))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26593),hAPP(X26590,X26588)),X26589))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26592),X26591))
        | ~ class_Groups_Oordered__ab__group__add(X26593) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26593),c_Groups_Ozero__class_Ozero(X26593)),hAPP(X26590,esk241_6(X26588,X26589,X26590,X26591,X26592,X26593))))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26592,X26593),X26590),X26591) != X26589
        | ~ hBOOL(hAPP(hAPP(c_member(X26592),X26588),X26591))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26593),hAPP(X26590,X26588)),X26589))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26592),X26591))
        | ~ class_Groups_Oordered__ab__group__add(X26593) ) ),
    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_6250,plain,
    ! [X24622,X24623,X24624,X24625,X24626,X24627] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X24626),X24624),X24625))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24626,X24627),hAPP(hAPP(c_COMBC(X24626,X24627,X24627),hAPP(hAPP(c_COMBS(X24626,X24627,tc_fun(X24627,X24627)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X24627,tc_fun(X24627,X24627)),X24626),c_If(X24627)),hAPP(hAPP(c_COMBC(X24626,X24626,tc_HOL_Obool),c_fequal),X24624))),X24623)),X24622)),X24625) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24627),hAPP(X24623,X24624)),hAPP(hAPP(c_Power_Opower__class_Opower(X24627),X24622),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X24626),X24625)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24626),X24625))
        | ~ class_Groups_Ocomm__monoid__mult(X24627) )
      & ( hBOOL(hAPP(hAPP(c_member(X24626),X24624),X24625))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24626,X24627),hAPP(hAPP(c_COMBC(X24626,X24627,X24627),hAPP(hAPP(c_COMBS(X24626,X24627,tc_fun(X24627,X24627)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X24627,tc_fun(X24627,X24627)),X24626),c_If(X24627)),hAPP(hAPP(c_COMBC(X24626,X24626,tc_HOL_Obool),c_fequal),X24624))),X24623)),X24622)),X24625) = hAPP(hAPP(c_Power_Opower__class_Opower(X24627),X24622),hAPP(c_Finite__Set_Ocard(X24626),X24625))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24626),X24625))
        | ~ class_Groups_Ocomm__monoid__mult(X24627) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5291])])]) ).

fof(i_0_6251,plain,
    ! [X26299,X26300,X26301,X26302,X26303] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X26302),X26300),X26301))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26302,X26303),hAPP(hAPP(c_COMBC(X26302,X26303,X26303),hAPP(hAPP(c_COMBS(X26302,X26303,tc_fun(X26303,X26303)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X26303,tc_fun(X26303,X26303)),X26302),c_If(X26303)),hAPP(hAPP(c_COMBC(X26302,X26302,tc_HOL_Obool),c_fequal),X26300))),X26299)),c_Groups_Ozero__class_Ozero(X26303))),X26301) = hAPP(X26299,X26300)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26302),X26301))
        | ~ class_Groups_Ocomm__monoid__add(X26303) )
      & ( hBOOL(hAPP(hAPP(c_member(X26302),X26300),X26301))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26302,X26303),hAPP(hAPP(c_COMBC(X26302,X26303,X26303),hAPP(hAPP(c_COMBS(X26302,X26303,tc_fun(X26303,X26303)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X26303,tc_fun(X26303,X26303)),X26302),c_If(X26303)),hAPP(hAPP(c_COMBC(X26302,X26302,tc_HOL_Obool),c_fequal),X26300))),X26299)),c_Groups_Ozero__class_Ozero(X26303))),X26301) = c_Groups_Ozero__class_Ozero(X26303)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26302),X26301))
        | ~ class_Groups_Ocomm__monoid__add(X26303) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5292])])]) ).

fof(i_0_6252,plain,
    ! [X24726,X24727,X24728,X24729,X24730] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X24729),X24727),X24728))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24729,X24730),hAPP(hAPP(c_COMBC(X24729,X24730,X24730),hAPP(hAPP(c_COMBS(X24729,X24730,tc_fun(X24730,X24730)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X24730,tc_fun(X24730,X24730)),X24729),c_If(X24730)),hAPP(hAPP(c_COMBC(X24729,X24729,tc_HOL_Obool),c_fequal),X24727))),X24726)),c_Groups_Oone__class_Oone(X24730))),X24728) = hAPP(X24726,X24727)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24729),X24728))
        | ~ class_Groups_Ocomm__monoid__mult(X24730) )
      & ( hBOOL(hAPP(hAPP(c_member(X24729),X24727),X24728))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24729,X24730),hAPP(hAPP(c_COMBC(X24729,X24730,X24730),hAPP(hAPP(c_COMBS(X24729,X24730,tc_fun(X24730,X24730)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X24730,tc_fun(X24730,X24730)),X24729),c_If(X24730)),hAPP(hAPP(c_COMBC(X24729,X24729,tc_HOL_Obool),c_fequal),X24727))),X24726)),c_Groups_Oone__class_Oone(X24730))),X24728) = c_Groups_Oone__class_Oone(X24730)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24729),X24728))
        | ~ class_Groups_Ocomm__monoid__mult(X24730) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5293])])]) ).

fof(i_0_6253,plain,
    ! [X30992,X30993] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X30993)
      | c_Complete__Lattice_OInf__class_OInf(X30993,X30992) = c_Complete__Lattice_OSup__class_OSup(X30993,hAPP(c_Set_OCollect(X30993),hAPP(hAPP(c_COMBB(tc_fun(X30993,tc_HOL_Obool),tc_HOL_Obool,X30993),c_HOL_OAll(X30993)),hAPP(hAPP(c_COMBB(tc_fun(X30993,tc_HOL_Obool),tc_fun(X30993,tc_HOL_Obool),X30993),hAPP(c_COMBS(X30993,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X30993),c_fimplies),hAPP(hAPP(c_COMBC(X30993,tc_fun(X30993,tc_HOL_Obool),tc_HOL_Obool),c_member(X30993)),X30992)))),c_Orderings_Oord__class_Oless__eq(X30993))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__Sup])]) ).

fof(i_0_6254,plain,
    ! [X25142,X25143,X25144,X25145,X25146,X25147,X25148] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25148,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25147,tc_fun(X25148,tc_HOL_Obool)),X25146),X25145)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25144,tc_fun(X25148,tc_HOL_Obool)),X25143),X25142)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25147,tc_fun(X25148,tc_HOL_Obool)),X25146),hAPP(hAPP(c_COMBB(tc_fun(X25144,tc_fun(X25148,tc_HOL_Obool)),tc_fun(X25148,tc_HOL_Obool),X25147),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25144,tc_fun(X25148,tc_HOL_Obool)),X25143)),hAPP(hAPP(c_COMBC(X25147,tc_fun(X25144,tc_fun(X25148,tc_HOL_Obool)),tc_fun(X25144,tc_fun(X25148,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X25148,tc_HOL_Obool),tc_fun(X25148,tc_HOL_Obool)),tc_fun(tc_fun(X25144,tc_fun(X25148,tc_HOL_Obool)),tc_fun(X25144,tc_fun(X25148,tc_HOL_Obool))),X25147),c_COMBB(tc_fun(X25148,tc_HOL_Obool),tc_fun(X25148,tc_HOL_Obool),X25144)),hAPP(hAPP(c_COMBB(tc_fun(X25148,tc_HOL_Obool),tc_fun(tc_fun(X25148,tc_HOL_Obool),tc_fun(X25148,tc_HOL_Obool)),X25147),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25148,tc_HOL_Obool))),X25145))),X25142))),
    inference(variable_rename,[status(thm)],[fact_Int__UN__distrib2]) ).

fof(i_0_6255,plain,
    ! [X29940,X29941,X29942,X29943,X29944,X29945,X29946] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X29946,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29945,tc_fun(X29946,tc_HOL_Obool)),X29944),X29943)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29942,tc_fun(X29946,tc_HOL_Obool)),X29941),X29940)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29945,tc_fun(X29946,tc_HOL_Obool)),X29944),hAPP(hAPP(c_COMBB(tc_fun(X29942,tc_fun(X29946,tc_HOL_Obool)),tc_fun(X29946,tc_HOL_Obool),X29945),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29942,tc_fun(X29946,tc_HOL_Obool)),X29941)),hAPP(hAPP(c_COMBC(X29945,tc_fun(X29942,tc_fun(X29946,tc_HOL_Obool)),tc_fun(X29942,tc_fun(X29946,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X29946,tc_HOL_Obool),tc_fun(X29946,tc_HOL_Obool)),tc_fun(tc_fun(X29942,tc_fun(X29946,tc_HOL_Obool)),tc_fun(X29942,tc_fun(X29946,tc_HOL_Obool))),X29945),c_COMBB(tc_fun(X29946,tc_HOL_Obool),tc_fun(X29946,tc_HOL_Obool),X29942)),hAPP(hAPP(c_COMBB(tc_fun(X29946,tc_HOL_Obool),tc_fun(tc_fun(X29946,tc_HOL_Obool),tc_fun(X29946,tc_HOL_Obool)),X29945),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X29946,tc_HOL_Obool))),X29943))),X29940))),
    inference(variable_rename,[status(thm)],[fact_Un__INT__distrib2]) ).

cnf(i_0_6256,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_5294]) ).

cnf(i_0_6257,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_5295]) ).

cnf(i_0_6258,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_5296]) ).

cnf(i_0_6259,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_5297]) ).

fof(i_0_6260,plain,
    ! [X33275,X33276,X33277,X33278,X33279,X33280,X33281] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(X33281,X33280,X33279,X33278),X33277),X33276),X33275) = c_New__DSequence_Oneg__bind(X33281,X33280,hAPP(hAPP(hAPP(X33279,X33277),X33276),X33275),hAPP(hAPP(c_COMBC(X33281,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(X33280)))),hAPP(hAPP(c_COMBC(X33281,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(X33280))))),hAPP(hAPP(c_COMBC(X33281,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(X33280)))))),X33278),X33277)),X33276)),X33275)),
    inference(variable_rename,[status(thm)],[fact_neg__bind__def]) ).

fof(i_0_6261,plain,
    ! [X28505,X28506,X28507,X28508,X28509] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28509),tc_List_Olist(X28509))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28509),tc_List_Olist(X28509)),hAPP(hAPP(c_List_Oappend(X28509),X28508),X28507)),hAPP(hAPP(c_List_Oappend(X28509),X28508),X28506))),c_List_Olexord(X28509,X28505)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28509,X28509)),hAPP(hAPP(c_Product__Type_OPair(X28509,X28509),esk308_5(X28505,X28506,X28507,X28508,X28509)),esk308_5(X28505,X28506,X28507,X28508,X28509))),X28505))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28509),tc_List_Olist(X28509))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28509),tc_List_Olist(X28509)),X28507),X28506)),c_List_Olexord(X28509,X28505))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5298])])]) ).

fof(i_0_6262,plain,
    ! [X31008,X31009] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X31009,tc_HOL_Obool),X31008) = hAPP(c_Set_OCollect(X31009),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X31009,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,X31009),c_HOL_OAll(tc_fun(X31009,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X31009,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X31009,tc_HOL_Obool),tc_HOL_Obool),X31009),hAPP(c_COMBS(tc_fun(X31009,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(X31009,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(X31009,tc_HOL_Obool),tc_fun(tc_fun(X31009,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X31009,tc_HOL_Obool))),X31008)))),c_member(X31009)))),
    inference(variable_rename,[status(thm)],[fact_Inter__eq]) ).

fof(i_0_6263,plain,
    ! [X33724,X33725] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X33725,tc_HOL_Obool),X33724) = hAPP(c_Set_OCollect(X33725),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X33725,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,X33725),c_HOL_OEx(tc_fun(X33725,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X33725,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X33725,tc_HOL_Obool),tc_HOL_Obool),X33725),hAPP(c_COMBS(tc_fun(X33725,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(X33725,tc_HOL_Obool)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(X33725,tc_HOL_Obool),tc_fun(tc_fun(X33725,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X33725,tc_HOL_Obool))),X33724)))),c_member(X33725)))),
    inference(variable_rename,[status(thm)],[fact_Union__eq]) ).

fof(i_0_6264,plain,
    ! [X32578,X32579,X32580,X32581,X32582] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X32582,X32582)),hAPP(hAPP(c_Product__Type_OPair(X32582,X32582),X32581),esk450_5(X32578,X32579,X32580,X32581,X32582))),c_Transitive__Closure_Ortrancl(X32582,X32579)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X32582,X32582)),hAPP(hAPP(c_Product__Type_OPair(X32582,X32582),X32581),X32580)),c_Transitive__Closure_Ortrancl(X32582,X32579)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32582,X32582)),hAPP(hAPP(c_Product__Type_OPair(X32582,X32582),X32581),X32580)),c_Transitive__Closure_Ortrancl(X32582,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X32582,X32582),tc_HOL_Obool)),X32579),X32578)))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X32582,X32582)),hAPP(hAPP(c_Product__Type_OPair(X32582,X32582),esk450_5(X32578,X32579,X32580,X32581,X32582)),esk451_5(X32578,X32579,X32580,X32581,X32582))),X32578))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X32582,X32582)),hAPP(hAPP(c_Product__Type_OPair(X32582,X32582),X32581),X32580)),c_Transitive__Closure_Ortrancl(X32582,X32579)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32582,X32582)),hAPP(hAPP(c_Product__Type_OPair(X32582,X32582),X32581),X32580)),c_Transitive__Closure_Ortrancl(X32582,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X32582,X32582),tc_HOL_Obool)),X32579),X32578)))) )
      & ( esk450_5(X32578,X32579,X32580,X32581,X32582) != esk451_5(X32578,X32579,X32580,X32581,X32582)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X32582,X32582)),hAPP(hAPP(c_Product__Type_OPair(X32582,X32582),X32581),X32580)),c_Transitive__Closure_Ortrancl(X32582,X32579)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32582,X32582)),hAPP(hAPP(c_Product__Type_OPair(X32582,X32582),X32581),X32580)),c_Transitive__Closure_Ortrancl(X32582,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X32582,X32582),tc_HOL_Obool)),X32579),X32578)))) ) ),
    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_6265,plain,
    ! [X32571,X32572,X32573,X32574,X32575] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X32575,X32575)),hAPP(hAPP(c_Product__Type_OPair(X32575,X32575),esk448_5(X32571,X32572,X32573,X32574,X32575)),X32573)),c_Transitive__Closure_Ortrancl(X32575,X32572)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X32575,X32575)),hAPP(hAPP(c_Product__Type_OPair(X32575,X32575),X32574),X32573)),c_Transitive__Closure_Ortrancl(X32575,X32572)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32575,X32575)),hAPP(hAPP(c_Product__Type_OPair(X32575,X32575),X32574),X32573)),c_Transitive__Closure_Ortrancl(X32575,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X32575,X32575),tc_HOL_Obool)),X32572),X32571)))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X32575,X32575)),hAPP(hAPP(c_Product__Type_OPair(X32575,X32575),esk449_5(X32571,X32572,X32573,X32574,X32575)),esk448_5(X32571,X32572,X32573,X32574,X32575))),X32571))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X32575,X32575)),hAPP(hAPP(c_Product__Type_OPair(X32575,X32575),X32574),X32573)),c_Transitive__Closure_Ortrancl(X32575,X32572)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32575,X32575)),hAPP(hAPP(c_Product__Type_OPair(X32575,X32575),X32574),X32573)),c_Transitive__Closure_Ortrancl(X32575,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X32575,X32575),tc_HOL_Obool)),X32572),X32571)))) )
      & ( esk449_5(X32571,X32572,X32573,X32574,X32575) != esk448_5(X32571,X32572,X32573,X32574,X32575)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X32575,X32575)),hAPP(hAPP(c_Product__Type_OPair(X32575,X32575),X32574),X32573)),c_Transitive__Closure_Ortrancl(X32575,X32572)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32575,X32575)),hAPP(hAPP(c_Product__Type_OPair(X32575,X32575),X32574),X32573)),c_Transitive__Closure_Ortrancl(X32575,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X32575,X32575),tc_HOL_Obool)),X32572),X32571)))) ) ),
    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_6266,plain,
    ! [X29806,X29807,X29808,X29809,X29810,X29811] : hAPP(hAPP(c_List_Ozip(X29811,X29810),X29809),hAPP(hAPP(c_List_Omap(X29808,X29810),X29807),X29806)) = hAPP(hAPP(c_List_Omap(tc_prod(X29811,X29808),tc_prod(X29811,X29810)),hAPP(c_Product__Type_Oprod_Oprod__case(X29811,X29808,tc_prod(X29811,X29810)),hAPP(hAPP(c_COMBC(X29811,tc_fun(X29808,X29810),tc_fun(X29808,tc_prod(X29811,X29810))),hAPP(hAPP(c_COMBB(tc_fun(X29810,tc_prod(X29811,X29810)),tc_fun(tc_fun(X29808,X29810),tc_fun(X29808,tc_prod(X29811,X29810))),X29811),c_COMBB(X29810,tc_prod(X29811,X29810),X29808)),c_Product__Type_OPair(X29811,X29810))),X29807))),hAPP(hAPP(c_List_Ozip(X29811,X29808),X29809),X29806)),
    inference(variable_rename,[status(thm)],[fact_zip__map2]) ).

cnf(i_0_6267,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_5299]) ).

cnf(i_0_6268,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_5277]) ).

cnf(i_0_6269,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_5278]) ).

fof(i_0_6270,plain,
    ! [X20699,X20700,X20701] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk73_3(X20699,X20700,X20701)),X20701))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20699),hAPP(X20700,X20701)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X20700,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X20699))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk72_3(X20699,X20700,X20701)),X20701)) )
      & ( hAPP(X20700,esk73_3(X20699,X20700,X20701)) = X20699
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20699),hAPP(X20700,X20701)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X20700,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X20699))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk72_3(X20699,X20700,X20701)),X20701)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk73_3(X20699,X20700,X20701)),X20701))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20699),hAPP(X20700,X20701)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X20700,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X20699))
        | ~ 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(X20700,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk72_3(X20699,X20700,X20701)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X20700,esk72_3(X20699,X20700,X20701))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) )
      & ( hAPP(X20700,esk73_3(X20699,X20700,X20701)) = X20699
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20699),hAPP(X20700,X20701)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X20700,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X20699))
        | ~ 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(X20700,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk72_3(X20699,X20700,X20701)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X20700,esk72_3(X20699,X20700,X20701))))),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_6271,plain,
    ! [X20694,X20695,X20696] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk71_3(X20694,X20695,X20696)),X20696))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20694),hAPP(X20695,X20696)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X20695,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X20694))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk70_3(X20694,X20695,X20696)),X20696)) )
      & ( hAPP(X20695,esk71_3(X20694,X20695,X20696)) = X20694
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20694),hAPP(X20695,X20696)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X20695,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X20694))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk70_3(X20694,X20695,X20696)),X20696)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk71_3(X20694,X20695,X20696)),X20696))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20694),hAPP(X20695,X20696)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X20695,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X20694))
        | ~ 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(X20695,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk70_3(X20694,X20695,X20696)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X20695,esk70_3(X20694,X20695,X20696))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) )
      & ( hAPP(X20695,esk71_3(X20694,X20695,X20696)) = X20694
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20694),hAPP(X20695,X20696)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X20695,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X20694))
        | ~ 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(X20695,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk70_3(X20694,X20695,X20696)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X20695,esk70_3(X20694,X20695,X20696))))),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_6272,plain,
    ! [X22794,X22795,X22796,X22797,X22798] :
      ( ( X22795 = hAPP(c_Nat_OSuc,esk97_5(X22794,X22795,X22796,X22797,X22798))
        | X22795 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X22798,X22798)),hAPP(hAPP(c_Product__Type_OPair(X22798,X22798),X22797),X22796)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X22798,X22798),tc_HOL_Obool),X22795),X22794))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X22798,X22798)),hAPP(hAPP(c_Product__Type_OPair(X22798,X22798),X22797),esk96_5(X22794,X22795,X22796,X22797,X22798))),X22794))
        | X22795 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X22798,X22798)),hAPP(hAPP(c_Product__Type_OPair(X22798,X22798),X22797),X22796)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X22798,X22798),tc_HOL_Obool),X22795),X22794))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X22798,X22798)),hAPP(hAPP(c_Product__Type_OPair(X22798,X22798),esk96_5(X22794,X22795,X22796,X22797,X22798)),X22796)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X22798,X22798),tc_HOL_Obool),esk97_5(X22794,X22795,X22796,X22797,X22798)),X22794)))
        | X22795 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X22798,X22798)),hAPP(hAPP(c_Product__Type_OPair(X22798,X22798),X22797),X22796)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X22798,X22798),tc_HOL_Obool),X22795),X22794))) )
      & ( X22795 = hAPP(c_Nat_OSuc,esk97_5(X22794,X22795,X22796,X22797,X22798))
        | X22797 = X22796
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X22798,X22798)),hAPP(hAPP(c_Product__Type_OPair(X22798,X22798),X22797),X22796)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X22798,X22798),tc_HOL_Obool),X22795),X22794))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X22798,X22798)),hAPP(hAPP(c_Product__Type_OPair(X22798,X22798),X22797),esk96_5(X22794,X22795,X22796,X22797,X22798))),X22794))
        | X22797 = X22796
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X22798,X22798)),hAPP(hAPP(c_Product__Type_OPair(X22798,X22798),X22797),X22796)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X22798,X22798),tc_HOL_Obool),X22795),X22794))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X22798,X22798)),hAPP(hAPP(c_Product__Type_OPair(X22798,X22798),esk96_5(X22794,X22795,X22796,X22797,X22798)),X22796)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X22798,X22798),tc_HOL_Obool),esk97_5(X22794,X22795,X22796,X22797,X22798)),X22794)))
        | X22797 = X22796
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X22798,X22798)),hAPP(hAPP(c_Product__Type_OPair(X22798,X22798),X22797),X22796)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X22798,X22798),tc_HOL_Obool),X22795),X22794))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5300])])])]) ).

fof(i_0_6273,plain,
    ! [X27094,X27095,X27096,X27097] :
      ( ~ c_Fun_Oinj__on(X27097,X27096,X27095,c_Orderings_Otop__class_Otop(tc_fun(X27097,tc_HOL_Obool)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27097,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X27097,X27096,X27095),hAPP(hAPP(c_Set_Oinsert(X27096),X27094),c_Orderings_Obot__class_Obot(tc_fun(X27096,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(X27097),c_HOL_OThe(X27097,hAPP(hAPP(c_COMBC(X27097,X27096,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X27096,tc_fun(X27096,tc_HOL_Obool),X27097),c_fequal),X27095)),X27094))),c_Orderings_Obot__class_Obot(tc_fun(X27097,tc_HOL_Obool))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__vimage__singleton])]) ).

fof(i_0_6274,plain,
    ! [X33296,X33297,X33298,X33299,X33300,X33301,X33302] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(X33302,X33301,X33300,X33299),X33298),X33297),X33296) = c_New__DSequence_Opos__bind(X33302,X33301,hAPP(hAPP(hAPP(X33300,X33298),X33297),X33296),hAPP(hAPP(c_COMBC(X33302,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X33301))),hAPP(hAPP(c_COMBC(X33302,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(X33301)))),hAPP(hAPP(c_COMBC(X33302,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(X33301))))),X33299),X33298)),X33297)),X33296)),
    inference(variable_rename,[status(thm)],[fact_pos__bind__def]) ).

fof(i_0_6275,plain,
    ! [X27890,X27891,X27892,X27893] : c_Nitpick_Oprod(X27893,X27892,X27891,X27890) = hAPP(c_Set_OCollect(tc_prod(X27893,X27892)),hAPP(c_Product__Type_Oprod_Oprod__case(X27893,X27892,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X27893,tc_fun(X27892,tc_HOL_Obool),tc_fun(X27892,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X27892,tc_HOL_Obool),tc_fun(X27892,tc_HOL_Obool)),X27893),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X27892)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27893),c_fconj),hAPP(hAPP(c_COMBC(X27893,tc_fun(X27893,tc_HOL_Obool),tc_HOL_Obool),c_member(X27893)),X27891)))),hAPP(hAPP(c_COMBC(X27892,tc_fun(X27892,tc_HOL_Obool),tc_HOL_Obool),c_member(X27892)),X27890)))),
    inference(variable_rename,[status(thm)],[fact_Nitpick_Oprod__def]) ).

cnf(i_0_6276,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_5301]) ).

fof(i_0_6277,plain,
    ! [X27545,X27546,X27547,X27548,X27549,X27550,X27551,X27552,X27553,X27554,X27555] : hAPP(c_Product__Type_Omap__pair(X27555,X27554,X27553,X27552,X27551,X27550),hAPP(c_Product__Type_Omap__pair(X27549,X27555,X27548,X27553,X27547,X27546),X27545)) = hAPP(c_Product__Type_Omap__pair(X27549,X27554,X27548,X27552,hAPP(c_Fun_Ocomp(X27555,X27554,X27549,X27551),X27547),hAPP(c_Fun_Ocomp(X27553,X27552,X27548,X27550),X27546)),X27545),
    inference(variable_rename,[status(thm)],[fact_map__pair_Ocompositionality]) ).

fof(i_0_6278,plain,
    ! [X23310,X23311,X23312,X23313] :
      ( ( ~ 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),X23313),X23312)),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),X23311),X23310)),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),X23313),X23310)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23311),X23312))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23313),X23310)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23311),X23312)))
        | 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),X23313),X23312)),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),X23311),X23310)),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])]) ).

fof(i_0_6279,plain,
    ! [X23314,X23315,X23316,X23317] :
      ( ( ~ 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),X23317),X23316)),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),X23315),X23314)),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),X23317),X23314)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23315),X23316))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23317),X23314)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23315),X23316)))
        | 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),X23317),X23316)),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),X23315),X23314)),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])]) ).

cnf(i_0_6280,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_5302]) ).

cnf(i_0_6281,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_5303]) ).

fof(i_0_6282,plain,
    ! [X26574,X26575,X26576,X26577,X26578,X26579] :
      ( ( hBOOL(hAPP(hAPP(c_member(X26578),esk238_6(X26574,X26575,X26576,X26577,X26578,X26579)),X26577))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26574,X26579),X26575),hAPP(c_Set_Oimage(X26578,X26574,X26576),X26577)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26578,X26579),hAPP(c_Fun_Ocomp(X26574,X26579,X26578,X26575),X26576)),X26577)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26578),X26577))
        | ~ class_Groups_Ocomm__monoid__add(X26579) )
      & ( hBOOL(hAPP(hAPP(c_member(X26578),esk239_6(X26574,X26575,X26576,X26577,X26578,X26579)),X26577))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26574,X26579),X26575),hAPP(c_Set_Oimage(X26578,X26574,X26576),X26577)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26578,X26579),hAPP(c_Fun_Ocomp(X26574,X26579,X26578,X26575),X26576)),X26577)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26578),X26577))
        | ~ class_Groups_Ocomm__monoid__add(X26579) )
      & ( esk238_6(X26574,X26575,X26576,X26577,X26578,X26579) != esk239_6(X26574,X26575,X26576,X26577,X26578,X26579)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26574,X26579),X26575),hAPP(c_Set_Oimage(X26578,X26574,X26576),X26577)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26578,X26579),hAPP(c_Fun_Ocomp(X26574,X26579,X26578,X26575),X26576)),X26577)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26578),X26577))
        | ~ class_Groups_Ocomm__monoid__add(X26579) )
      & ( hAPP(X26576,esk238_6(X26574,X26575,X26576,X26577,X26578,X26579)) = hAPP(X26576,esk239_6(X26574,X26575,X26576,X26577,X26578,X26579))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26574,X26579),X26575),hAPP(c_Set_Oimage(X26578,X26574,X26576),X26577)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26578,X26579),hAPP(c_Fun_Ocomp(X26574,X26579,X26578,X26575),X26576)),X26577)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26578),X26577))
        | ~ class_Groups_Ocomm__monoid__add(X26579) )
      & ( hAPP(X26575,hAPP(X26576,esk238_6(X26574,X26575,X26576,X26577,X26578,X26579))) != c_Groups_Ozero__class_Ozero(X26579)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26574,X26579),X26575),hAPP(c_Set_Oimage(X26578,X26574,X26576),X26577)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26578,X26579),hAPP(c_Fun_Ocomp(X26574,X26579,X26578,X26575),X26576)),X26577)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26578),X26577))
        | ~ class_Groups_Ocomm__monoid__add(X26579) ) ),
    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_6283,plain,
    ! [X27795,X27796,X27797,X27798,X27799,X27800] : hAPP(c_Set_Oimage(X27800,X27799,hAPP(hAPP(c_COMBS(X27800,X27799,X27799),hAPP(hAPP(c_COMBS(X27800,X27799,tc_fun(X27799,X27799)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X27799,tc_fun(X27799,X27799)),X27800),c_If(X27799)),X27798)),X27797)),X27796)),X27795) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27799,tc_HOL_Obool)),hAPP(c_Set_Oimage(X27800,X27799,X27797),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27800,tc_HOL_Obool)),X27795),hAPP(c_Set_OCollect(X27800),X27798)))),hAPP(c_Set_Oimage(X27800,X27799,X27796),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27800,tc_HOL_Obool)),X27795),hAPP(c_Set_OCollect(X27800),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X27800),c_fNot),X27798))))),
    inference(variable_rename,[status(thm)],[fact_if__image__distrib]) ).

cnf(i_0_6284,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_5304]) ).

cnf(i_0_6285,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_5305]) ).

fof(i_0_6286,plain,
    ! [X23306,X23307,X23308,X23309] : 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),X23309),X23308)),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),X23307),X23306)),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),X23309),X23307)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23308),X23306))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23309),X23306)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X23308),X23307)))),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_6287,plain,
    ! [X32692,X32693,X32694,X32695,X32696,X32697] :
      ( ( hBOOL(hAPP(hAPP(c_member(X32696),esk472_6(X32692,X32693,X32694,X32695,X32696,X32697)),X32695))
        | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X32697,X32696,c_Groups_Otimes__class_Otimes(X32697)),X32694),X32692),X32695) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X32697,X32696,c_Groups_Otimes__class_Otimes(X32697)),X32693),X32692),X32695)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32696),X32695))
        | ~ class_Groups_Oab__semigroup__mult(X32697) )
      & ( hAPP(X32694,esk472_6(X32692,X32693,X32694,X32695,X32696,X32697)) != hAPP(X32693,esk472_6(X32692,X32693,X32694,X32695,X32696,X32697))
        | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X32697,X32696,c_Groups_Otimes__class_Otimes(X32697)),X32694),X32692),X32695) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X32697,X32696,c_Groups_Otimes__class_Otimes(X32697)),X32693),X32692),X32695)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32696),X32695))
        | ~ class_Groups_Oab__semigroup__mult(X32697) ) ),
    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_6288,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_5306]) ).

cnf(i_0_6289,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_5306]) ).

fof(i_0_6290,plain,
    ! [X28241,X28242,X28243,X28244] :
      ( ~ c_Wellfounded_Owf(X28244,X28243)
      | ~ c_Fun_Oinj__on(X28244,X28242,X28241,c_Orderings_Otop__class_Otop(tc_fun(X28244,tc_HOL_Obool)))
      | c_Wellfounded_Owf(X28242,hAPP(c_Set_Oimage(tc_prod(X28244,X28244),tc_prod(X28242,X28242),c_Product__Type_Omap__pair(X28244,X28242,X28244,X28242,X28241,X28241)),X28243)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__map__pair__image])]) ).

fof(i_0_6291,plain,
    ! [X32021,X32022,X32023,X32024,X32025,X32026] :
      ( ( hBOOL(hAPP(hAPP(c_member(X32025),esk417_6(X32021,X32022,X32023,X32024,X32025,X32026)),X32026))
        | c_Fun_Oinj__on(X32024,X32023,X32022,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X32025,tc_fun(X32024,tc_HOL_Obool)),X32026),X32021))
        | X32026 = c_Orderings_Obot__class_Obot(tc_fun(X32025,tc_HOL_Obool)) )
      & ( ~ c_Fun_Oinj__on(X32024,X32023,X32022,hAPP(X32021,esk417_6(X32021,X32022,X32023,X32024,X32025,X32026)))
        | c_Fun_Oinj__on(X32024,X32023,X32022,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X32025,tc_fun(X32024,tc_HOL_Obool)),X32026),X32021))
        | X32026 = c_Orderings_Obot__class_Obot(tc_fun(X32025,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_6292,plain,
    ! [X30405,X30406,X30407,X30408,X30409] :
      ( ( hBOOL(hAPP(hAPP(c_member(X30408),esk360_5(X30405,X30406,X30407,X30408,X30409)),hAPP(c_List_Oset(X30408),X30407)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X30409),hAPP(c_List_Omonoid__add__class_Olistsum(X30409),hAPP(hAPP(c_List_Omap(X30408,X30409),X30406),X30407))),hAPP(c_List_Omonoid__add__class_Olistsum(X30409),hAPP(hAPP(c_List_Omap(X30408,X30409),X30405),X30407))))
        | ~ class_Groups_Omonoid__add(X30409)
        | ~ class_Groups_Oordered__ab__semigroup__add(X30409) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X30409),hAPP(X30406,esk360_5(X30405,X30406,X30407,X30408,X30409))),hAPP(X30405,esk360_5(X30405,X30406,X30407,X30408,X30409))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X30409),hAPP(c_List_Omonoid__add__class_Olistsum(X30409),hAPP(hAPP(c_List_Omap(X30408,X30409),X30406),X30407))),hAPP(c_List_Omonoid__add__class_Olistsum(X30409),hAPP(hAPP(c_List_Omap(X30408,X30409),X30405),X30407))))
        | ~ class_Groups_Omonoid__add(X30409)
        | ~ class_Groups_Oordered__ab__semigroup__add(X30409) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__mono])])])]) ).

fof(i_0_6293,plain,
    ! [X32070,X32071,X32072,X32073,X32074] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk427_5(X32070,X32071,X32072,X32073,X32074)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32074)),X32073)))
        | c_List_Olist__all2(X32074,X32072,X32070,X32073,X32071)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32074)),X32073) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32072)),X32071) )
      & ( ~ hBOOL(hAPP(hAPP(X32070,hAPP(hAPP(c_List_Onth(X32074),X32073),esk427_5(X32070,X32071,X32072,X32073,X32074))),hAPP(hAPP(c_List_Onth(X32072),X32071),esk427_5(X32070,X32071,X32072,X32073,X32074))))
        | c_List_Olist__all2(X32074,X32072,X32070,X32073,X32071)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32074)),X32073) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32072)),X32071) ) ),
    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_6294,plain,
    ! [X30700,X30701,X30702,X30703,X30704,X30705,X30706,X30707,X30708,X30709,X30710] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30704)),X30701) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30703)),X30700)
        | ~ c_List_Olist__all2(X30704,X30703,X30702,X30701,X30700) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30705),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30704)),X30701)))
        | hBOOL(hAPP(hAPP(X30702,hAPP(hAPP(c_List_Onth(X30704),X30701),X30705)),hAPP(hAPP(c_List_Onth(X30703),X30700),X30705)))
        | ~ c_List_Olist__all2(X30704,X30703,X30702,X30701,X30700) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk365_5(X30706,X30707,X30708,X30709,X30710)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30710)),X30707)))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30710)),X30707) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30709)),X30706)
        | c_List_Olist__all2(X30710,X30709,X30708,X30707,X30706) )
      & ( ~ hBOOL(hAPP(hAPP(X30708,hAPP(hAPP(c_List_Onth(X30710),X30707),esk365_5(X30706,X30707,X30708,X30709,X30710))),hAPP(hAPP(c_List_Onth(X30709),X30706),esk365_5(X30706,X30707,X30708,X30709,X30710))))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30710)),X30707) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30709)),X30706)
        | c_List_Olist__all2(X30710,X30709,X30708,X30707,X30706) ) ),
    inference(distribute,[status(thm)],[inference(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_6295,plain,
    ! [X26611,X26612,X26613,X26614,X26615] :
      ( ( hBOOL(hAPP(hAPP(c_member(X26614),esk245_5(X26611,X26612,X26613,X26614,X26615)),X26613))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26615),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26614,X26615),X26612),X26613)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26614,X26615),X26611),X26613)))
        | X26613 = c_Orderings_Obot__class_Obot(tc_fun(X26614,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26614),X26613))
        | ~ class_Groups_Ocomm__monoid__add(X26615)
        | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X26615) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26615),hAPP(X26612,esk245_5(X26611,X26612,X26613,X26614,X26615))),hAPP(X26611,esk245_5(X26611,X26612,X26613,X26614,X26615))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26615),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26614,X26615),X26612),X26613)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26614,X26615),X26611),X26613)))
        | X26613 = c_Orderings_Obot__class_Obot(tc_fun(X26614,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26614),X26613))
        | ~ class_Groups_Ocomm__monoid__add(X26615)
        | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X26615) ) ),
    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_6296,plain,
    ! [X27820,X27821,X27822,X27823,X27824,X27825] :
      ( ~ class_Groups_Ocomm__monoid__add(X27825)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27824),X27823))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27824,X27825),hAPP(hAPP(c_COMBS(X27824,X27825,X27825),hAPP(hAPP(c_COMBS(X27824,X27825,tc_fun(X27825,X27825)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X27825,tc_fun(X27825,X27825)),X27824),c_If(X27825)),X27822)),X27821)),X27820)),X27823) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27825),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27824,X27825),X27821),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27824,tc_HOL_Obool)),X27823),hAPP(c_Set_OCollect(X27824),X27822)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27824,X27825),X27820),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27824,tc_HOL_Obool)),X27823),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X27824,tc_HOL_Obool)),hAPP(c_Set_OCollect(X27824),X27822))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__cases])]) ).

cnf(i_0_6297,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_5294]) ).

cnf(i_0_6298,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_5295]) ).

fof(i_0_6299,plain,
    ! [X27241,X27242,X27243,X27244,X27245] :
      ( ~ c_Finite__Set_Ofolding__one__idem(X27245,X27244,X27243)
      | hAPP(X27242,hAPP(hAPP(X27244,esk272_5(X27241,X27242,X27243,X27244,X27245)),esk273_5(X27241,X27242,X27243,X27244,X27245))) != hAPP(hAPP(X27244,hAPP(X27242,esk272_5(X27241,X27242,X27243,X27244,X27245))),hAPP(X27242,esk273_5(X27241,X27242,X27243,X27244,X27245)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27245),X27241))
      | X27241 = c_Orderings_Obot__class_Obot(tc_fun(X27245,tc_HOL_Obool))
      | hAPP(X27242,hAPP(X27243,X27241)) = hAPP(X27243,hAPP(c_Set_Oimage(X27245,X27245,X27242),X27241)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Ohom__commute])])]) ).

cnf(i_0_6300,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk390_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_5307]) ).

cnf(i_0_6301,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk390_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_5307]) ).

cnf(i_0_6302,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),esk390_3(X3,X1,X2))) != X3 ),
    inference(split_conjunct,[status(thm)],[i_0_5307]) ).

cnf(i_0_6303,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),esk390_3(X3,X1,X2))) != X3
    | X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_5307]) ).

cnf(i_0_6304,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_5308]) ).

cnf(i_0_6305,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),esk86_3(X1,X2,X3)),esk87_3(X1,X2,X3))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk87_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(X1,esk86_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)))),esk87_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_5309]) ).

fof(i_0_6306,plain,
    ! [X26294,X26295,X26296,X26297,X26298] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X26297),X26295),X26296))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26297,X26298),hAPP(hAPP(c_COMBC(X26297,X26298,X26298),hAPP(hAPP(c_COMBS(X26297,X26298,tc_fun(X26298,X26298)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X26298,tc_fun(X26298,X26298)),X26297),c_If(X26298)),hAPP(c_fequal,X26295))),X26294)),c_Groups_Ozero__class_Ozero(X26298))),X26296) = hAPP(X26294,X26295)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26297),X26296))
        | ~ class_Groups_Ocomm__monoid__add(X26298) )
      & ( hBOOL(hAPP(hAPP(c_member(X26297),X26295),X26296))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26297,X26298),hAPP(hAPP(c_COMBC(X26297,X26298,X26298),hAPP(hAPP(c_COMBS(X26297,X26298,tc_fun(X26298,X26298)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X26298,tc_fun(X26298,X26298)),X26297),c_If(X26298)),hAPP(c_fequal,X26295))),X26294)),c_Groups_Ozero__class_Ozero(X26298))),X26296) = c_Groups_Ozero__class_Ozero(X26298)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26297),X26296))
        | ~ class_Groups_Ocomm__monoid__add(X26298) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5310])])]) ).

fof(i_0_6307,plain,
    ! [X24721,X24722,X24723,X24724,X24725] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X24724),X24722),X24723))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24724,X24725),hAPP(hAPP(c_COMBC(X24724,X24725,X24725),hAPP(hAPP(c_COMBS(X24724,X24725,tc_fun(X24725,X24725)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X24725,tc_fun(X24725,X24725)),X24724),c_If(X24725)),hAPP(c_fequal,X24722))),X24721)),c_Groups_Oone__class_Oone(X24725))),X24723) = hAPP(X24721,X24722)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24724),X24723))
        | ~ class_Groups_Ocomm__monoid__mult(X24725) )
      & ( hBOOL(hAPP(hAPP(c_member(X24724),X24722),X24723))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24724,X24725),hAPP(hAPP(c_COMBC(X24724,X24725,X24725),hAPP(hAPP(c_COMBS(X24724,X24725,tc_fun(X24725,X24725)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X24725,tc_fun(X24725,X24725)),X24724),c_If(X24725)),hAPP(c_fequal,X24722))),X24721)),c_Groups_Oone__class_Oone(X24725))),X24723) = c_Groups_Oone__class_Oone(X24725)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24724),X24723))
        | ~ class_Groups_Ocomm__monoid__mult(X24725) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5311])])]) ).

fof(i_0_6308,plain,
    ! [X30748,X30749,X30750] : hAPP(c_List_Oset(tc_List_Olist(X30750)),c_Enum_On__lists(X30750,X30749,X30748)) = hAPP(c_Set_OCollect(tc_List_Olist(X30750)),hAPP(hAPP(c_COMBS(tc_List_Olist(X30750),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X30750)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X30750),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X30750)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X30750)))),X30749))),hAPP(hAPP(c_COMBC(tc_List_Olist(X30750),tc_fun(X30750,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X30750,tc_HOL_Obool),tc_fun(tc_fun(X30750,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X30750)),c_Orderings_Oord__class_Oless__eq(tc_fun(X30750,tc_HOL_Obool))),c_List_Oset(X30750))),hAPP(c_List_Oset(X30750),X30748)))),
    inference(variable_rename,[status(thm)],[fact_set__n__lists]) ).

fof(i_0_6309,plain,
    ! [X27566,X27567,X27568,X27569,X27570,X27571,X27572,X27573,X27574,X27575] : hAPP(c_Fun_Ocomp(tc_prod(X27575,X27574),tc_prod(X27573,X27572),tc_prod(X27571,X27570),c_Product__Type_Omap__pair(X27575,X27573,X27574,X27572,X27569,X27568)),c_Product__Type_Omap__pair(X27571,X27575,X27570,X27574,X27567,X27566)) = c_Product__Type_Omap__pair(X27571,X27573,X27570,X27572,hAPP(c_Fun_Ocomp(X27575,X27573,X27571,X27569),X27567),hAPP(c_Fun_Ocomp(X27574,X27572,X27570,X27568),X27566)),
    inference(variable_rename,[status(thm)],[fact_map__pair_Ocomp]) ).

fof(i_0_6310,plain,
    ! [X27556,X27557,X27558,X27559,X27560,X27561,X27562,X27563,X27564,X27565] : c_Product__Type_Omap__pair(X27565,X27564,X27563,X27562,hAPP(c_Fun_Ocomp(X27561,X27564,X27565,X27560),X27559),hAPP(c_Fun_Ocomp(X27558,X27562,X27563,X27557),X27556)) = hAPP(c_Fun_Ocomp(tc_prod(X27561,X27558),tc_prod(X27564,X27562),tc_prod(X27565,X27563),c_Product__Type_Omap__pair(X27561,X27564,X27558,X27562,X27560,X27557)),c_Product__Type_Omap__pair(X27565,X27561,X27563,X27558,X27559,X27556)),
    inference(variable_rename,[status(thm)],[fact_map__pair__compose]) ).

fof(i_0_6311,plain,
    ! [X28691,X28692,X28693,X28694,X28695,X28696,X28697,X28698,X28699] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28694)),X28693) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28694)),X28692)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28694),tc_List_Olist(X28694))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28694),tc_List_Olist(X28694)),X28693),X28692)),c_List_Olistrel(X28694,X28691))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X28695),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28694)),X28693)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X28694,X28694)),hAPP(hAPP(c_Product__Type_OPair(X28694,X28694),hAPP(hAPP(c_List_Onth(X28694),X28693),X28695)),hAPP(hAPP(c_List_Onth(X28694),X28692),X28695))),X28691))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28694),tc_List_Olist(X28694))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28694),tc_List_Olist(X28694)),X28693),X28692)),c_List_Olistrel(X28694,X28691))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk319_4(X28696,X28697,X28698,X28699)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28699)),X28698)))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28699)),X28698) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28699)),X28697)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28699),tc_List_Olist(X28699))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28699),tc_List_Olist(X28699)),X28698),X28697)),c_List_Olistrel(X28699,X28696))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28699,X28699)),hAPP(hAPP(c_Product__Type_OPair(X28699,X28699),hAPP(hAPP(c_List_Onth(X28699),X28698),esk319_4(X28696,X28697,X28698,X28699))),hAPP(hAPP(c_List_Onth(X28699),X28697),esk319_4(X28696,X28697,X28698,X28699)))),X28696))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28699)),X28698) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28699)),X28697)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28699),tc_List_Olist(X28699))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28699),tc_List_Olist(X28699)),X28698),X28697)),c_List_Olistrel(X28699,X28696))) ) ),
    inference(distribute,[status(thm)],[inference(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_6312,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk88_3(X1,X2,X3)),esk89_3(X1,X2,X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk89_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(X1,esk88_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)))),esk89_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_5312]) ).

fof(i_0_6313,plain,
    ! [X28611,X28612,X28613,X28614,X28615] :
      ( ( X28614 = hAPP(hAPP(c_List_Olist_OCons(X28615),esk315_5(X28611,X28612,X28613,X28614,X28615)),esk316_5(X28611,X28612,X28613,X28614,X28615))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28615),tc_List_Olist(X28615))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28615),tc_List_Olist(X28615)),X28614),hAPP(hAPP(c_List_Olist_OCons(X28615),X28613),X28612))),c_List_Olistrel(X28615,X28611))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X28615,X28615)),hAPP(hAPP(c_Product__Type_OPair(X28615,X28615),esk315_5(X28611,X28612,X28613,X28614,X28615)),X28613)),X28611))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28615),tc_List_Olist(X28615))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28615),tc_List_Olist(X28615)),X28614),hAPP(hAPP(c_List_Olist_OCons(X28615),X28613),X28612))),c_List_Olistrel(X28615,X28611))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28615),tc_List_Olist(X28615))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28615),tc_List_Olist(X28615)),esk316_5(X28611,X28612,X28613,X28614,X28615)),X28612)),c_List_Olistrel(X28615,X28611)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28615),tc_List_Olist(X28615))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28615),tc_List_Olist(X28615)),X28614),hAPP(hAPP(c_List_Olist_OCons(X28615),X28613),X28612))),c_List_Olistrel(X28615,X28611))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5313])])])]) ).

cnf(i_0_6314,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_5308]) ).

fof(i_0_6315,plain,
    ! [X32613,X32614,X32615,X32616,X32617] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X32617,X32617)),hAPP(hAPP(c_Product__Type_OPair(X32617,X32617),X32616),esk457_5(X32613,X32614,X32615,X32616,X32617))),X32613))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32617,X32617)),hAPP(hAPP(c_Product__Type_OPair(X32617,X32617),X32616),X32615)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X32617,X32617),tc_HOL_Obool),hAPP(c_Nat_OSuc,X32614)),X32613))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X32617,X32617)),hAPP(hAPP(c_Product__Type_OPair(X32617,X32617),esk457_5(X32613,X32614,X32615,X32616,X32617)),X32615)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X32617,X32617),tc_HOL_Obool),X32614),X32613)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32617,X32617)),hAPP(hAPP(c_Product__Type_OPair(X32617,X32617),X32616),X32615)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X32617,X32617),tc_HOL_Obool),hAPP(c_Nat_OSuc,X32614)),X32613))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5314])])])]) ).

fof(i_0_6316,plain,
    ! [X32601,X32602,X32603,X32604,X32605] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X32605,X32605)),hAPP(hAPP(c_Product__Type_OPair(X32605,X32605),X32604),esk455_5(X32601,X32602,X32603,X32604,X32605))),X32601))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32605,X32605)),hAPP(hAPP(c_Product__Type_OPair(X32605,X32605),X32604),X32603)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X32605,X32605),tc_HOL_Obool),hAPP(c_Nat_OSuc,X32602)),X32601))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X32605,X32605)),hAPP(hAPP(c_Product__Type_OPair(X32605,X32605),esk455_5(X32601,X32602,X32603,X32604,X32605)),X32603)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X32605,X32605),tc_HOL_Obool),X32602),X32601)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32605,X32605)),hAPP(hAPP(c_Product__Type_OPair(X32605,X32605),X32604),X32603)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X32605,X32605),tc_HOL_Obool),hAPP(c_Nat_OSuc,X32602)),X32601))) ) ),
    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_6317,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_5315]) ).

fof(i_0_6318,plain,
    ! [X22743,X22744,X22745,X22746,X22747] :
      ( ( X22744 = hAPP(c_Nat_OSuc,esk95_5(X22743,X22744,X22745,X22746,X22747))
        | X22744 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X22747,X22747)),hAPP(hAPP(c_Product__Type_OPair(X22747,X22747),X22746),X22745)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X22747,X22747),tc_HOL_Obool),X22744),X22743))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X22747,X22747)),hAPP(hAPP(c_Product__Type_OPair(X22747,X22747),X22746),esk94_5(X22743,X22744,X22745,X22746,X22747))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X22747,X22747),tc_HOL_Obool),esk95_5(X22743,X22744,X22745,X22746,X22747)),X22743)))
        | X22744 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X22747,X22747)),hAPP(hAPP(c_Product__Type_OPair(X22747,X22747),X22746),X22745)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X22747,X22747),tc_HOL_Obool),X22744),X22743))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X22747,X22747)),hAPP(hAPP(c_Product__Type_OPair(X22747,X22747),esk94_5(X22743,X22744,X22745,X22746,X22747)),X22745)),X22743))
        | X22744 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X22747,X22747)),hAPP(hAPP(c_Product__Type_OPair(X22747,X22747),X22746),X22745)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X22747,X22747),tc_HOL_Obool),X22744),X22743))) )
      & ( X22744 = hAPP(c_Nat_OSuc,esk95_5(X22743,X22744,X22745,X22746,X22747))
        | X22746 = X22745
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X22747,X22747)),hAPP(hAPP(c_Product__Type_OPair(X22747,X22747),X22746),X22745)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X22747,X22747),tc_HOL_Obool),X22744),X22743))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X22747,X22747)),hAPP(hAPP(c_Product__Type_OPair(X22747,X22747),X22746),esk94_5(X22743,X22744,X22745,X22746,X22747))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X22747,X22747),tc_HOL_Obool),esk95_5(X22743,X22744,X22745,X22746,X22747)),X22743)))
        | X22746 = X22745
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X22747,X22747)),hAPP(hAPP(c_Product__Type_OPair(X22747,X22747),X22746),X22745)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X22747,X22747),tc_HOL_Obool),X22744),X22743))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X22747,X22747)),hAPP(hAPP(c_Product__Type_OPair(X22747,X22747),esk94_5(X22743,X22744,X22745,X22746,X22747)),X22745)),X22743))
        | X22746 = X22745
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X22747,X22747)),hAPP(hAPP(c_Product__Type_OPair(X22747,X22747),X22746),X22745)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X22747,X22747),tc_HOL_Obool),X22744),X22743))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5316])])])]) ).

fof(i_0_6319,plain,
    ! [X32607,X32608,X32609,X32610,X32611] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X32611,X32611)),hAPP(hAPP(c_Product__Type_OPair(X32611,X32611),X32610),esk456_5(X32607,X32608,X32609,X32610,X32611))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X32611,X32611),tc_HOL_Obool),X32608),X32607)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32611,X32611)),hAPP(hAPP(c_Product__Type_OPair(X32611,X32611),X32610),X32609)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X32611,X32611),tc_HOL_Obool),hAPP(c_Nat_OSuc,X32608)),X32607))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X32611,X32611)),hAPP(hAPP(c_Product__Type_OPair(X32611,X32611),esk456_5(X32607,X32608,X32609,X32610,X32611)),X32609)),X32607))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32611,X32611)),hAPP(hAPP(c_Product__Type_OPair(X32611,X32611),X32610),X32609)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X32611,X32611),tc_HOL_Obool),hAPP(c_Nat_OSuc,X32608)),X32607))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5317])])])]) ).

cnf(i_0_6320,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_5318]) ).

cnf(i_0_6321,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_5319]) ).

cnf(i_0_6322,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_5320]) ).

cnf(i_0_6323,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_5321]) ).

cnf(i_0_6324,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_5322]) ).

cnf(i_0_6325,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_5323]) ).

cnf(i_0_6326,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_5324]) ).

cnf(i_0_6327,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_5325]) ).

cnf(i_0_6328,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_5326]) ).

cnf(i_0_6329,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_5327]) ).

fof(i_0_6330,plain,
    ! [X24812,X24813,X24814] : hAPP(hAPP(c_Equiv__Relations_Oquotient(X24814),X24813),X24812) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24814,tc_fun(tc_fun(X24814,tc_HOL_Obool),tc_HOL_Obool)),X24813),hAPP(hAPP(c_COMBC(X24814,tc_fun(tc_fun(X24814,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X24814,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X24814,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X24814,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X24814,tc_HOL_Obool),tc_HOL_Obool)),X24814),c_Set_Oinsert(tc_fun(X24814,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X24814,tc_HOL_Obool),tc_fun(X24814,tc_HOL_Obool),X24814),c_Relation_OImage(X24814,X24814,X24812)),hAPP(hAPP(c_COMBC(X24814,tc_fun(X24814,tc_HOL_Obool),tc_fun(X24814,tc_HOL_Obool)),c_Set_Oinsert(X24814)),c_Orderings_Obot__class_Obot(tc_fun(X24814,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X24814,tc_HOL_Obool),tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_quotient__def]) ).

cnf(i_0_6331,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_5328]) ).

cnf(i_0_6332,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_5329]) ).

cnf(i_0_6333,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),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_5330]) ).

cnf(i_0_6334,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_5331]) ).

cnf(i_0_6335,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_5332]) ).

cnf(i_0_6336,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_5333]) ).

cnf(i_0_6337,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_5334]) ).

cnf(i_0_6338,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_5335]) ).

cnf(i_0_6339,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_5336]) ).

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(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_6341,plain,
    ! [X23354,X23355,X23356,X23357,X23358] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X23356,X23358)),hAPP(hAPP(c_Product__Type_OPair(X23356,X23358),esk112_5(X23354,X23355,X23356,X23357,X23358)),X23357)),X23355))
        | ~ hBOOL(hAPP(hAPP(c_member(X23358),X23357),hAPP(c_Relation_OImage(X23356,X23358,X23355),X23354))) )
      & ( hBOOL(hAPP(hAPP(c_member(X23356),esk112_5(X23354,X23355,X23356,X23357,X23358)),X23354))
        | ~ hBOOL(hAPP(hAPP(c_member(X23358),X23357),hAPP(c_Relation_OImage(X23356,X23358,X23355),X23354))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5337])])])]) ).

fof(i_0_6342,plain,
    ! [X23263,X23264,X23265,X23266,X23267,X23269,X23270,X23271,X23272,X23273,X23274] :
      ( ( hBOOL(hAPP(hAPP(c_member(X23265),esk109_5(X23263,X23264,X23265,X23266,X23267)),X23263))
        | ~ hBOOL(hAPP(hAPP(c_member(X23267),X23266),hAPP(c_Relation_OImage(X23265,X23267,X23264),X23263))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X23265,X23267)),hAPP(hAPP(c_Product__Type_OPair(X23265,X23267),esk109_5(X23263,X23264,X23265,X23266,X23267)),X23266)),X23264))
        | ~ hBOOL(hAPP(hAPP(c_member(X23267),X23266),hAPP(c_Relation_OImage(X23265,X23267,X23264),X23263))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X23271),X23274),X23269))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X23271,X23273)),hAPP(hAPP(c_Product__Type_OPair(X23271,X23273),X23274),X23272)),X23270))
        | hBOOL(hAPP(hAPP(c_member(X23273),X23272),hAPP(c_Relation_OImage(X23271,X23273,X23270),X23269))) ) ),
    inference(distribute,[status(thm)],[inference(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_6343,plain,
    ! [X24476,X24477,X24478,X24479] :
      ( ~ c_Finite__Set_Ofolding__one(X24479,X24478,X24477)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24479),X24476))
      | X24476 = c_Orderings_Obot__class_Obot(tc_fun(X24479,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_member(X24479),hAPP(hAPP(X24478,esk134_4(X24476,X24477,X24478,X24479)),esk135_4(X24476,X24477,X24478,X24479))),hAPP(hAPP(c_Set_Oinsert(X24479),esk134_4(X24476,X24477,X24478,X24479)),hAPP(hAPP(c_Set_Oinsert(X24479),esk135_4(X24476,X24477,X24478,X24479)),c_Orderings_Obot__class_Obot(tc_fun(X24479,tc_HOL_Obool))))))
      | hBOOL(hAPP(hAPP(c_member(X24479),hAPP(X24477,X24476)),X24476)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one_Oclosed])])]) ).

cnf(i_0_6344,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_5338]) ).

cnf(i_0_6345,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_5339]) ).

fof(i_0_6346,plain,
    ! [X33682,X33683,X33684,X33685] : hAPP(c_Relation_OImage(X33685,X33684,hAPP(c_Set_OCollect(tc_prod(X33685,X33684)),hAPP(c_Product__Type_Oprod_Oprod__case(X33685,X33684,tc_HOL_Obool),X33683))),X33682) = hAPP(c_Set_OCollect(X33684),hAPP(hAPP(c_COMBB(tc_fun(X33685,tc_HOL_Obool),tc_HOL_Obool,X33684),c_HOL_OEx(X33685)),hAPP(hAPP(c_COMBB(tc_fun(X33685,tc_HOL_Obool),tc_fun(X33685,tc_HOL_Obool),X33684),hAPP(c_COMBS(X33685,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X33685),c_fconj),hAPP(hAPP(c_COMBC(X33685,tc_fun(X33685,tc_HOL_Obool),tc_HOL_Obool),c_member(X33685)),X33682)))),hAPP(c_COMBC(X33685,X33684,tc_HOL_Obool),X33683)))),
    inference(variable_rename,[status(thm)],[fact_Image__Collect__split]) ).

cnf(i_0_6347,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_5267]) ).

fof(i_0_6348,plain,
    ! [X25982,X25983,X25984,X25985] :
      ( ~ c_Fun_Oinj__on(X25985,tc_fun(tc_fun(X25985,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(X25985,tc_fun(tc_prod(X25985,X25985),tc_HOL_Obool),tc_fun(tc_fun(X25985,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25985,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X25985,X25985),tc_HOL_Obool),tc_fun(tc_fun(X25985,tc_HOL_Obool),tc_HOL_Obool)),X25985),c_Equiv__Relations_Oquotient(X25985)),hAPP(hAPP(c_COMBC(X25985,tc_fun(X25985,tc_HOL_Obool),tc_fun(X25985,tc_HOL_Obool)),c_Set_Oinsert(X25985)),c_Orderings_Obot__class_Obot(tc_fun(X25985,tc_HOL_Obool))))),X25984),X25983)
      | ~ hBOOL(hAPP(hAPP(c_member(X25985),X25982),X25983))
      | hAPP(hAPP(c_Equiv__Relations_Oquotient(X25985),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25985,tc_HOL_Obool)),X25983),hAPP(hAPP(c_Set_Oinsert(X25985),X25982),c_Orderings_Obot__class_Obot(tc_fun(X25985,tc_HOL_Obool))))),X25984) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(X25985,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X25985),X25983),X25984)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X25985),hAPP(hAPP(c_Set_Oinsert(X25985),X25982),c_Orderings_Obot__class_Obot(tc_fun(X25985,tc_HOL_Obool)))),X25984)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_quotient__diff1])]) ).

fof(i_0_6349,plain,
    ! [X30071,X30072,X30073,X30074] : hAPP(c_Set_OCollect(X30074),hAPP(hAPP(c_COMBB(tc_fun(X30073,tc_HOL_Obool),tc_HOL_Obool,X30074),c_HOL_OAll(X30073)),hAPP(hAPP(c_COMBB(tc_fun(X30073,tc_HOL_Obool),tc_fun(X30073,tc_HOL_Obool),X30074),hAPP(c_COMBS(X30073,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X30073),c_fimplies),hAPP(hAPP(c_COMBC(X30073,tc_fun(X30073,tc_HOL_Obool),tc_HOL_Obool),c_member(X30073)),X30072)))),X30071))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30073,tc_fun(X30074,tc_HOL_Obool)),X30072),hAPP(hAPP(c_COMBB(tc_fun(X30074,tc_HOL_Obool),tc_fun(X30074,tc_HOL_Obool),X30073),c_Set_OCollect(X30074)),hAPP(c_COMBC(X30074,X30073,tc_HOL_Obool),X30071))),
    inference(variable_rename,[status(thm)],[fact_Collect__ball__eq]) ).

fof(i_0_6350,plain,
    ! [X28094,X28095,X28096,X28097] : c_List_Osublist(X28097,hAPP(hAPP(c_List_Oappend(X28097),X28096),X28095),X28094) = hAPP(hAPP(c_List_Oappend(X28097),c_List_Osublist(X28097,X28096,X28094)),c_List_Osublist(X28097,X28095,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(X28097)),X28096)))),X28094)))),
    inference(variable_rename,[status(thm)],[fact_sublist__append]) ).

fof(i_0_6351,plain,
    ! [X32028,X32029,X32030,X32031,X32032] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32032)),hAPP(hAPP(c_List_Otake(X32032),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32032)),X32031)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32030)),X32029))),X32031)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32030)),hAPP(hAPP(c_List_Otake(X32030),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32032)),X32031)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32030)),X32029))),X32029))
        | hBOOL(hAPP(X32028,hAPP(hAPP(c_List_Ozip(X32032,X32030),X32031),X32029))) )
      & ( ~ hBOOL(hAPP(X32028,hAPP(hAPP(c_List_Ozip(X32032,X32030),hAPP(hAPP(c_List_Otake(X32032),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32032)),X32031)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32030)),X32029))),X32031)),hAPP(hAPP(c_List_Otake(X32030),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32032)),X32031)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32030)),X32029))),X32029))))
        | hBOOL(hAPP(X32028,hAPP(hAPP(c_List_Ozip(X32032,X32030),X32031),X32029))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zip__obtain__same__length])])]) ).

cnf(i_0_6352,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_5340]) ).

cnf(i_0_6353,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_5341]) ).

cnf(i_0_6354,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_5342]) ).

cnf(i_0_6355,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_5343]) ).

cnf(i_0_6356,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_5344]) ).

cnf(i_0_6357,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_5345]) ).

fof(i_0_6358,plain,
    ! [X25656,X25657,X25658] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25658),X25657))
      | ~ c_Fun_Oinj__on(X25658,tc_fun(tc_fun(X25658,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(X25658,tc_fun(tc_prod(X25658,X25658),tc_HOL_Obool),tc_fun(tc_fun(X25658,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25658,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X25658,X25658),tc_HOL_Obool),tc_fun(tc_fun(X25658,tc_HOL_Obool),tc_HOL_Obool)),X25658),c_Equiv__Relations_Oquotient(X25658)),hAPP(hAPP(c_COMBC(X25658,tc_fun(X25658,tc_HOL_Obool),tc_fun(X25658,tc_HOL_Obool)),c_Set_Oinsert(X25658)),c_Orderings_Obot__class_Obot(tc_fun(X25658,tc_HOL_Obool))))),X25656),X25657)
      | hAPP(c_Finite__Set_Ocard(tc_fun(X25658,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X25658),X25657),X25656)) = hAPP(c_Finite__Set_Ocard(X25658),X25657) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__quotient__disjoint])]) ).

fof(i_0_6359,plain,
    ! [X26441,X26442,X26443,X26444] :
      ( ~ class_Rings_Ocomm__semiring__1(X26444)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26444),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26444),c_Groups_Oone__class_Oone(X26444)),c_Groups_Oone__class_Oone(X26444))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26444),hAPP(hAPP(c_COMBB(X26444,X26444,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(X26444),X26443)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,X26444,X26444),hAPP(hAPP(c_COMBB(X26444,tc_fun(X26444,X26444),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(X26444)),c_Nat_Osemiring__1__class_Oof__nat(X26444))),X26442))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X26441))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26444),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X26444),X26441)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26444),X26443),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26444),X26443),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26444),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X26444),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X26441),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X26442)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_arith__series__general])]) ).

cnf(i_0_6360,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_5346]) ).

fof(i_0_6361,plain,
    ! [X28235,X28236] :
      ( ( c_Wellfounded_Owf(X28236,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X28236,X28236),tc_HOL_Obool),tc_fun(tc_prod(X28236,X28236),tc_HOL_Obool)),X28235))
        | ~ c_FunDef_Oreduction__pair(X28236,X28235) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28236,X28236),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X28236,X28236,X28236),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X28236,X28236),tc_HOL_Obool),tc_fun(tc_prod(X28236,X28236),tc_HOL_Obool)),X28235)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(X28236,X28236),tc_HOL_Obool),tc_fun(tc_prod(X28236,X28236),tc_HOL_Obool)),X28235))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X28236,X28236),tc_HOL_Obool),tc_fun(tc_prod(X28236,X28236),tc_HOL_Obool)),X28235)))
        | ~ c_FunDef_Oreduction__pair(X28236,X28235) )
      & ( ~ c_Wellfounded_Owf(X28236,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X28236,X28236),tc_HOL_Obool),tc_fun(tc_prod(X28236,X28236),tc_HOL_Obool)),X28235))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28236,X28236),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X28236,X28236,X28236),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X28236,X28236),tc_HOL_Obool),tc_fun(tc_prod(X28236,X28236),tc_HOL_Obool)),X28235)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(X28236,X28236),tc_HOL_Obool),tc_fun(tc_prod(X28236,X28236),tc_HOL_Obool)),X28235))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X28236,X28236),tc_HOL_Obool),tc_fun(tc_prod(X28236,X28236),tc_HOL_Obool)),X28235)))
        | c_FunDef_Oreduction__pair(X28236,X28235) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_reduction__pair__def])])]) ).

cnf(i_0_6362,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_5347]) ).

cnf(i_0_6363,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_5348]) ).

cnf(i_0_6364,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_5349]) ).

fof(i_0_6365,plain,
    ! [X25077,X25078,X25079,X25080,X25081,X25082,X25083,X25084,X25085,X25086,X25087] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25081,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25080,tc_fun(X25081,tc_HOL_Obool)),X25079),X25078)),X25077))
        | ~ hBOOL(hAPP(hAPP(c_member(X25080),X25082),X25079))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25081,tc_HOL_Obool)),hAPP(X25078,X25082)),X25077)) )
      & ( hBOOL(hAPP(hAPP(c_member(X25086),esk158_5(X25083,X25084,X25085,X25086,X25087)),X25085))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25087,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25086,tc_fun(X25087,tc_HOL_Obool)),X25085),X25084)),X25083)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25087,tc_HOL_Obool)),hAPP(X25084,esk158_5(X25083,X25084,X25085,X25086,X25087))),X25083))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25087,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25086,tc_fun(X25087,tc_HOL_Obool)),X25085),X25084)),X25083)) ) ),
    inference(distribute,[status(thm)],[inference(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_6366,plain,
    ! [X26460,X26461,X26462,X26463,X26464] :
      ( ( hBOOL(hAPP(hAPP(c_member(X26463),esk228_5(X26460,X26461,X26462,X26463,X26464)),X26462))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26464),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26463,X26464),X26461),X26462)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26464),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X26464),hAPP(c_Finite__Set_Ocard(X26463),X26462))),X26460)))
        | ~ class_Groups_Oordered__ab__semigroup__add(X26464)
        | ~ class_Rings_Osemiring__1(X26464) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26464),hAPP(X26461,esk228_5(X26460,X26461,X26462,X26463,X26464))),X26460))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26464),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26463,X26464),X26461),X26462)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26464),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X26464),hAPP(c_Finite__Set_Ocard(X26463),X26462))),X26460)))
        | ~ class_Groups_Oordered__ab__semigroup__add(X26464)
        | ~ class_Rings_Osemiring__1(X26464) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__bounded])])])]) ).

cnf(i_0_6367,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_5350]) ).

fof(i_0_6368,plain,
    ! [X27576,X27577,X27578,X27579,X27580,X27581] : c_Product__Type_Omap__pair(X27581,X27580,X27579,X27578,X27577,X27576) = hAPP(c_Product__Type_Oprod_Oprod__case(X27581,X27579,tc_prod(X27580,X27578)),hAPP(hAPP(c_COMBC(X27581,tc_fun(X27579,X27578),tc_fun(X27579,tc_prod(X27580,X27578))),hAPP(hAPP(c_COMBB(tc_fun(X27578,tc_prod(X27580,X27578)),tc_fun(tc_fun(X27579,X27578),tc_fun(X27579,tc_prod(X27580,X27578))),X27581),c_COMBB(X27578,tc_prod(X27580,X27578),X27579)),hAPP(hAPP(c_COMBB(X27580,tc_fun(X27578,tc_prod(X27580,X27578)),X27581),c_Product__Type_OPair(X27580,X27578)),X27577))),X27576)),
    inference(variable_rename,[status(thm)],[fact_map__pair__def]) ).

fof(i_0_6369,plain,
    ! [X20184,X20185,X20186] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20186))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20185),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),X20185),X20184))),c_Groups_Oone__class_Oone(tc_Int_Oint))),X20186))),X20184)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_decr__lemma])]) ).

fof(i_0_6370,plain,
    ! [X25020,X25021,X25022,X25023,X25024,X25025] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25024),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25023,X25024),X25022),X25021)),X25020))
        | ~ hBOOL(hAPP(hAPP(c_member(X25023),X25025),X25022))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25024),hAPP(X25021,X25025)),X25020))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X25024) )
      & ( hBOOL(hAPP(hAPP(c_member(X25023),esk153_5(X25020,X25021,X25022,X25023,X25024)),X25022))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25024),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25023,X25024),X25022),X25021)),X25020))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X25024) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25024),hAPP(X25021,esk153_5(X25020,X25021,X25022,X25023,X25024))),X25020))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25024),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25023,X25024),X25022),X25021)),X25020))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X25024) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUP__le__iff])])])])]) ).

cnf(i_0_6371,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_5306]) ).

cnf(i_0_6372,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_6373,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_6374,plain,
    ! [X28741,X28742,X28743,X28744,X28746,X28747,X28748,X28749,X28750] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk321_4(X28741,X28742,X28743,X28744)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28744)),X28743)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28744)),X28742))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28744)),X28743)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28744)),X28742)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28744),tc_List_Olist(X28744))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28744),tc_List_Olist(X28744)),X28743),X28742)),c_List_Olexord(X28744,X28741))) )
      & ( hAPP(hAPP(c_List_Otake(X28744),esk321_4(X28741,X28742,X28743,X28744)),X28743) = hAPP(hAPP(c_List_Otake(X28744),esk321_4(X28741,X28742,X28743,X28744)),X28742)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28744)),X28743)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28744)),X28742)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28744),tc_List_Olist(X28744))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28744),tc_List_Olist(X28744)),X28743),X28742)),c_List_Olexord(X28744,X28741))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X28744,X28744)),hAPP(hAPP(c_Product__Type_OPair(X28744,X28744),hAPP(hAPP(c_List_Onth(X28744),X28743),esk321_4(X28741,X28742,X28743,X28744))),hAPP(hAPP(c_List_Onth(X28744),X28742),esk321_4(X28741,X28742,X28743,X28744)))),X28741))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28744)),X28743)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28744)),X28742)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28744),tc_List_Olist(X28744))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28744),tc_List_Olist(X28744)),X28743),X28742)),c_List_Olexord(X28744,X28741))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk321_4(X28741,X28742,X28743,X28744)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28744)),X28743)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28744)),X28742))))
        | hAPP(hAPP(c_List_Otake(X28744),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28744)),X28743)),X28742) = X28743
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28744),tc_List_Olist(X28744))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28744),tc_List_Olist(X28744)),X28743),X28742)),c_List_Olexord(X28744,X28741))) )
      & ( hAPP(hAPP(c_List_Otake(X28744),esk321_4(X28741,X28742,X28743,X28744)),X28743) = hAPP(hAPP(c_List_Otake(X28744),esk321_4(X28741,X28742,X28743,X28744)),X28742)
        | hAPP(hAPP(c_List_Otake(X28744),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28744)),X28743)),X28742) = X28743
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28744),tc_List_Olist(X28744))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28744),tc_List_Olist(X28744)),X28743),X28742)),c_List_Olexord(X28744,X28741))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X28744,X28744)),hAPP(hAPP(c_Product__Type_OPair(X28744,X28744),hAPP(hAPP(c_List_Onth(X28744),X28743),esk321_4(X28741,X28742,X28743,X28744))),hAPP(hAPP(c_List_Onth(X28744),X28742),esk321_4(X28741,X28742,X28743,X28744)))),X28741))
        | hAPP(hAPP(c_List_Otake(X28744),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28744)),X28743)),X28742) = X28743
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28744),tc_List_Olist(X28744))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28744),tc_List_Olist(X28744)),X28743),X28742)),c_List_Olexord(X28744,X28741))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28749)),X28748)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28749)),X28747)))
        | hAPP(hAPP(c_List_Otake(X28749),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28749)),X28748)),X28747) != X28748
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28749),tc_List_Olist(X28749))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28749),tc_List_Olist(X28749)),X28748),X28747)),c_List_Olexord(X28749,X28746))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X28750),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28749)),X28748)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28749)),X28747))))
        | hAPP(hAPP(c_List_Otake(X28749),X28750),X28748) != hAPP(hAPP(c_List_Otake(X28749),X28750),X28747)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28749,X28749)),hAPP(hAPP(c_Product__Type_OPair(X28749,X28749),hAPP(hAPP(c_List_Onth(X28749),X28748),X28750)),hAPP(hAPP(c_List_Onth(X28749),X28747),X28750))),X28746))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28749),tc_List_Olist(X28749))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28749),tc_List_Olist(X28749)),X28748),X28747)),c_List_Olexord(X28749,X28746))) ) ),
    inference(distribute,[status(thm)],[inference(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_6375,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_5351]) ).

fof(i_0_6376,plain,
    ! [X27694,X27695,X27696,X27697] : hAPP(c_Set_OCollect(tc_prod(X27697,X27696)),hAPP(c_Product__Type_Oprod_Oprod__case(X27697,X27696,tc_HOL_Obool),hAPP(hAPP(c_COMBS(X27697,tc_fun(X27696,tc_HOL_Obool),tc_fun(X27696,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X27696,tc_HOL_Obool),tc_fun(X27696,tc_HOL_Obool)),X27697),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X27696)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27697),c_fconj),X27695))),X27694))) = hAPP(hAPP(c_Product__Type_OSigma(X27697,X27696),hAPP(c_Set_OCollect(X27697),X27695)),hAPP(hAPP(c_COMBB(tc_fun(X27696,tc_HOL_Obool),tc_fun(X27696,tc_HOL_Obool),X27697),c_Set_OCollect(X27696)),X27694)),
    inference(variable_rename,[status(thm)],[fact_SetCompr__Sigma__eq]) ).

fof(i_0_6377,plain,
    ! [X27678,X27679] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X27679))
      | 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)),X27679))),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,X27678))))) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__less])]) ).

fof(i_0_6378,plain,
    ! [X30355,X30356,X30357,X30358] : c_Hilbert__Choice_OEps(tc_prod(X30358,X30357),hAPP(c_Product__Type_Oprod_Oprod__case(X30358,X30357,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X30358,tc_fun(X30357,tc_HOL_Obool),tc_fun(X30357,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X30357,tc_HOL_Obool),tc_fun(X30357,tc_HOL_Obool)),X30358),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X30357)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X30358),c_fconj),hAPP(c_fequal,X30356)))),hAPP(c_fequal,X30355)))) = hAPP(hAPP(c_Product__Type_OPair(X30358,X30357),X30356),X30355),
    inference(variable_rename,[status(thm)],[fact_Eps__split__eq]) ).

fof(i_0_6379,plain,
    ! [X27014,X27015,X27016,X27017] : c_HOL_OThe(tc_prod(X27017,X27016),hAPP(c_Product__Type_Oprod_Oprod__case(X27017,X27016,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X27017,tc_fun(X27016,tc_HOL_Obool),tc_fun(X27016,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X27016,tc_HOL_Obool),tc_fun(X27016,tc_HOL_Obool)),X27017),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X27016)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27017),c_fconj),hAPP(c_fequal,X27015)))),hAPP(c_fequal,X27014)))) = hAPP(hAPP(c_Product__Type_OPair(X27017,X27016),X27015),X27014),
    inference(variable_rename,[status(thm)],[fact_The__split__eq]) ).

cnf(i_0_6380,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_5340]) ).

fof(i_0_6381,plain,
    ! [X26182,X26183,X26184,X26185,X26186,X26187] :
      ( ~ class_Groups_Ocomm__monoid__add(X26187)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26186,X26187),hAPP(hAPP(c_COMBC(X26186,tc_fun(X26185,tc_HOL_Obool),X26187),hAPP(hAPP(c_COMBB(tc_fun(X26185,X26187),tc_fun(tc_fun(X26185,tc_HOL_Obool),X26187),X26186),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26185,X26187)),X26184)),X26183)),X26182) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26185,X26187),hAPP(hAPP(c_COMBC(X26185,tc_fun(X26186,tc_HOL_Obool),X26187),hAPP(hAPP(c_COMBB(tc_fun(X26186,X26187),tc_fun(tc_fun(X26186,tc_HOL_Obool),X26187),X26185),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26186,X26187)),hAPP(c_COMBC(X26186,X26185,X26187),X26184))),X26182)),X26183) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__commute])]) ).

fof(i_0_6382,plain,
    ! [X27690,X27691,X27692,X27693] : hAPP(c_Set_OCollect(tc_prod(X27693,X27692)),hAPP(c_Product__Type_Oprod_Oprod__case(X27693,X27692,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X27693,tc_fun(X27692,tc_HOL_Obool),tc_fun(X27692,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X27692,tc_HOL_Obool),tc_fun(X27692,tc_HOL_Obool)),X27693),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X27692)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27693),c_fconj),X27691))),X27690))) = hAPP(hAPP(c_Product__Type_OSigma(X27693,X27692),hAPP(c_Set_OCollect(X27693),X27691)),hAPP(c_COMBK(tc_fun(X27692,tc_HOL_Obool),X27693),hAPP(c_Set_OCollect(X27692),X27690))),
    inference(variable_rename,[status(thm)],[fact_Collect__split]) ).

fof(i_0_6383,plain,
    ! [X24909,X24910,X24911,X24912] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24912),X24911))
      | hAPP(c_Set_Oimage(X24912,X24910,X24909),X24911) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(X24910,tc_HOL_Obool),X24912,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24910,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X24912,tc_fun(X24910,tc_HOL_Obool),tc_fun(X24910,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X24910,tc_fun(tc_fun(X24910,tc_HOL_Obool),tc_fun(X24910,tc_HOL_Obool)),X24912),c_Set_Oinsert(X24910)),X24909)),c_Orderings_Obot__class_Obot(tc_fun(X24910,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(X24910,tc_HOL_Obool))),X24911) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__eq__fold__image])]) ).

cnf(i_0_6384,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_5352]) ).

fof(i_0_6385,plain,
    ! [X24590,X24591,X24592,X24593] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24593),X24592))
      | ~ hBOOL(hAPP(hAPP(c_member(X24593),X24591),X24592))
      | ~ hBOOL(hAPP(hAPP(c_member(X24593),X24590),X24592))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X24593),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24593,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24593,tc_HOL_Obool)),X24592),hAPP(hAPP(c_Set_Oinsert(X24593),X24591),c_Orderings_Obot__class_Obot(tc_fun(X24593,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(X24593),X24590),c_Orderings_Obot__class_Obot(tc_fun(X24593,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X24593),X24592))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Diff2__less])]) ).

cnf(i_0_6386,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_5353]) ).

fof(i_0_6387,plain,
    ! [X25309,X25310] : c_Relation_OId__on(X25310,X25309) = hAPP(c_Product__Type_Oprod_Oprod__case(X25310,X25310,tc_HOL_Obool),hAPP(hAPP(c_COMBS(X25310,tc_HOL_Obool,tc_fun(X25310,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25310,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(X25310,tc_HOL_Obool)),X25310),c_COMBC(X25310,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25310,tc_HOL_Obool),tc_fun(X25310,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X25310),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X25310),c_fconj)),c_fequal))),X25309)),
    inference(variable_rename,[status(thm)],[fact_Id__on__def_H]) ).

fof(i_0_6388,plain,
    ! [X27894] : c_Int_Oint__ge__less__than(X27894) = 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),X27894)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
    inference(variable_rename,[status(thm)],[fact_int__ge__less__than__def]) ).

fof(i_0_6389,plain,
    ! [X30320,X30321,X30322,X30323,X30324,X30325,X30326,X30327,X30328] : hAPP(hAPP(c_Product__Type_Oscomp(X30328,X30327,X30326,X30325),hAPP(hAPP(c_Product__Type_Oscomp(X30328,X30324,X30323,tc_prod(X30327,X30326)),X30322),X30321)),X30320) = hAPP(hAPP(c_Product__Type_Oscomp(X30328,X30324,X30323,X30325),X30322),hAPP(hAPP(c_COMBC(X30324,tc_fun(X30327,tc_fun(X30326,X30325)),tc_fun(X30323,X30325)),hAPP(hAPP(c_COMBB(tc_fun(X30323,tc_prod(X30327,X30326)),tc_fun(tc_fun(X30327,tc_fun(X30326,X30325)),tc_fun(X30323,X30325)),X30324),c_Product__Type_Oscomp(X30323,X30327,X30326,X30325)),X30321)),X30320)),
    inference(variable_rename,[status(thm)],[fact_scomp__scomp]) ).

fof(i_0_6390,plain,
    ! [X22784,X22785,X22786,X22787] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X22787),X22786))
      | ~ 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)),X22785),X22787)),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)),X22784),X22786)),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)),X22785),X22784)),X22786)),c_FunDef_Omax__weak)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wmax__insertI])]) ).

fof(i_0_6391,plain,
    ! [X22763,X22764,X22765,X22766] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X22766),X22765))
      | ~ 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)),X22764),X22766)),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)),X22763),X22765)),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)),X22764),X22763)),X22765)),c_FunDef_Omax__strict)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smax__insertI])]) ).

cnf(i_0_6392,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_5325]) ).

cnf(i_0_6393,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_5326]) ).

fof(i_0_6394,plain,
    ! [X31495,X31496,X31497,X31498,X31499] :
      ( ~ class_Orderings_Olinorder(X31499)
      | c_List_Olinorder__class_Osorted(X31499,hAPP(hAPP(c_List_Omap(X31498,X31499),X31497),hAPP(c_List_Ofilter(X31498,hAPP(hAPP(c_COMBC(X31498,X31499,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X31499,tc_fun(X31499,tc_HOL_Obool),X31498),c_fequal),X31497)),hAPP(X31496,X31495))),X31495))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__map__same])]) ).

fof(i_0_6395,plain,
    ! [X28604,X28605,X28606,X28607,X28608] :
      ( ( X28605 = hAPP(hAPP(c_List_Olist_OCons(X28608),esk313_5(X28604,X28605,X28606,X28607,X28608)),esk314_5(X28604,X28605,X28606,X28607,X28608))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28608),tc_List_Olist(X28608))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28608),tc_List_Olist(X28608)),hAPP(hAPP(c_List_Olist_OCons(X28608),X28607),X28606)),X28605)),c_List_Olistrel(X28608,X28604))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X28608,X28608)),hAPP(hAPP(c_Product__Type_OPair(X28608,X28608),X28607),esk313_5(X28604,X28605,X28606,X28607,X28608))),X28604))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28608),tc_List_Olist(X28608))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28608),tc_List_Olist(X28608)),hAPP(hAPP(c_List_Olist_OCons(X28608),X28607),X28606)),X28605)),c_List_Olistrel(X28608,X28604))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28608),tc_List_Olist(X28608))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28608),tc_List_Olist(X28608)),X28606),esk314_5(X28604,X28605,X28606,X28607,X28608))),c_List_Olistrel(X28608,X28604)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28608),tc_List_Olist(X28608))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28608),tc_List_Olist(X28608)),hAPP(hAPP(c_List_Olist_OCons(X28608),X28607),X28606)),X28605)),c_List_Olistrel(X28608,X28604))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5354])])])]) ).

cnf(i_0_6396,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_5355]) ).

fof(i_0_6397,plain,
    ! [X18017,X18018,X18019,X18020,X18021] :
      ( ~ c_Hoare__Mirabelle_Ohoare__derivs(X18021,X18020,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X18021)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X18021),c_Hoare__Mirabelle_Opeek__and(X18021,X18019,X18018)),X18017),X18019)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X18021),tc_HOL_Obool))))
      | c_Hoare__Mirabelle_Ohoare__derivs(X18021,X18020,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X18021)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X18021),X18019),c_Com_Ocom_OWhile(X18018,X18017)),c_Hoare__Mirabelle_Opeek__and(X18021,X18019,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),X18018)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X18021),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Loop])]) ).

cnf(i_0_6398,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_5356]) ).

fof(i_0_6399,plain,
    ! [X32667,X32668,X32669,X32670,X32671,X32673,X32674,X32675,X32676,X32678] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X32670),X32669))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X32670,tc_HOL_Obool),tc_fun(X32670,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X32670,tc_HOL_Obool),tc_fun(X32670,tc_HOL_Obool)),X32669),X32668)),c_Wellfounded_Omax__ext(X32670,X32667))) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X32670),X32668))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X32670,tc_HOL_Obool),tc_fun(X32670,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X32670,tc_HOL_Obool),tc_fun(X32670,tc_HOL_Obool)),X32669),X32668)),c_Wellfounded_Omax__ext(X32670,X32667))) )
      & ( X32668 != c_Orderings_Obot__class_Obot(tc_fun(X32670,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X32670,tc_HOL_Obool),tc_fun(X32670,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X32670,tc_HOL_Obool),tc_fun(X32670,tc_HOL_Obool)),X32669),X32668)),c_Wellfounded_Omax__ext(X32670,X32667))) )
      & ( hBOOL(hAPP(hAPP(c_member(X32670),esk467_5(X32667,X32668,X32669,X32670,X32671)),X32668))
        | ~ hBOOL(hAPP(hAPP(c_member(X32670),X32671),X32669))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X32670,tc_HOL_Obool),tc_fun(X32670,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X32670,tc_HOL_Obool),tc_fun(X32670,tc_HOL_Obool)),X32669),X32668)),c_Wellfounded_Omax__ext(X32670,X32667))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X32670,X32670)),hAPP(hAPP(c_Product__Type_OPair(X32670,X32670),X32671),esk467_5(X32667,X32668,X32669,X32670,X32671))),X32667))
        | ~ hBOOL(hAPP(hAPP(c_member(X32670),X32671),X32669))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X32670,tc_HOL_Obool),tc_fun(X32670,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X32670,tc_HOL_Obool),tc_fun(X32670,tc_HOL_Obool)),X32669),X32668)),c_Wellfounded_Omax__ext(X32670,X32667))) )
      & ( hBOOL(hAPP(hAPP(c_member(X32676),esk468_4(X32673,X32674,X32675,X32676)),X32675))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32676),X32675))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32676),X32674))
        | X32674 = c_Orderings_Obot__class_Obot(tc_fun(X32676,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X32676,tc_HOL_Obool),tc_fun(X32676,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X32676,tc_HOL_Obool),tc_fun(X32676,tc_HOL_Obool)),X32675),X32674)),c_Wellfounded_Omax__ext(X32676,X32673))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X32676),X32678),X32674))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32676,X32676)),hAPP(hAPP(c_Product__Type_OPair(X32676,X32676),esk468_4(X32673,X32674,X32675,X32676)),X32678)),X32673))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32676),X32675))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32676),X32674))
        | X32674 = c_Orderings_Obot__class_Obot(tc_fun(X32676,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X32676,tc_HOL_Obool),tc_fun(X32676,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X32676,tc_HOL_Obool),tc_fun(X32676,tc_HOL_Obool)),X32675),X32674)),c_Wellfounded_Omax__ext(X32676,X32673))) ) ),
    inference(distribute,[status(thm)],[inference(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_6400,plain,
    ! [X28217,X28218,X28219] :
      ( ( ~ c_Wellfounded_Owf(X28219,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28219,X28219),tc_HOL_Obool)),X28218),X28217))
        | c_Wellfounded_Owf(X28219,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28219,X28219),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28219,X28219),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X28219,X28219,X28219),X28218),X28218)),hAPP(hAPP(c_Relation_Orel__comp(X28219,X28219,X28219),X28217),X28218))),X28217)) )
      & ( ~ c_Wellfounded_Owf(X28219,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28219,X28219),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28219,X28219),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X28219,X28219,X28219),X28218),X28218)),hAPP(hAPP(c_Relation_Orel__comp(X28219,X28219,X28219),X28217),X28218))),X28217))
        | c_Wellfounded_Owf(X28219,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28219,X28219),tc_HOL_Obool)),X28218),X28217)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__union__merge])]) ).

fof(i_0_6401,plain,
    ! [X27582,X27583,X27584,X27585,X27586,X27587,X27588,X27589,X27590,X27591] :
      ( hAPP(c_Set_Oimage(X27591,X27590,X27589),X27588) != X27587
      | hAPP(c_Set_Oimage(X27586,X27585,X27584),X27583) != X27582
      | hAPP(c_Set_Oimage(tc_prod(X27591,X27586),tc_prod(X27590,X27585),c_Product__Type_Omap__pair(X27591,X27590,X27586,X27585,X27589,X27584)),hAPP(hAPP(c_Product__Type_OSigma(X27591,X27586),X27588),hAPP(c_COMBK(tc_fun(X27586,tc_HOL_Obool),X27591),X27583))) = hAPP(hAPP(c_Product__Type_OSigma(X27590,X27585),X27587),hAPP(c_COMBK(tc_fun(X27585,tc_HOL_Obool),X27590),X27582)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__pair__surj__on])]) ).

fof(i_0_6402,plain,
    ! [X22780,X22781,X22782,X22783] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X22783),X22782))
      | ~ 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)),X22783),X22781)),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)),X22782),X22780)),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)),X22782),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X22781),X22780))),c_FunDef_Omin__weak)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wmin__insertI])]) ).

fof(i_0_6403,plain,
    ! [X22767,X22768,X22769,X22770] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X22770),X22769))
      | ~ 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)),X22770),X22768)),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)),X22769),X22767)),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)),X22769),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X22768),X22767))),c_FunDef_Omin__strict)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smin__insertI])]) ).

fof(i_0_6404,plain,
    ! [X26979,X26980,X26981,X26982,X26983] :
      ( ( hAPP(hAPP(c_Set_Oinsert(X26983),X26981),X26980) = hAPP(hAPP(c_Set_Oinsert(X26983),esk260_5(X26979,X26980,X26981,X26982,X26983)),esk261_5(X26979,X26980,X26981,X26982,X26983))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X26983,X26982,hAPP(hAPP(c_Set_Oinsert(X26983),X26981),X26980)),X26979)) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X26983,X26983,X26982,esk260_5(X26979,X26980,X26981,X26982,X26983),esk261_5(X26979,X26980,X26981,X26982,X26983)),X26979))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X26983,X26982,hAPP(hAPP(c_Set_Oinsert(X26983),X26981),X26980)),X26979)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X26983),esk260_5(X26979,X26980,X26981,X26982,X26983)),esk261_5(X26979,X26980,X26981,X26982,X26983)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X26983,X26982,hAPP(hAPP(c_Set_Oinsert(X26983),X26981),X26980)),X26979)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__fold1SetE])])])]) ).

fof(i_0_6405,plain,
    ! [X26965,X26966,X26967,X26968,X26969,X26972,X26973,X26974,X26975,X26976,X26977,X26978] :
      ( ( hAPP(hAPP(c_Set_Oinsert(X26969),X26967),X26966) = hAPP(hAPP(c_Set_Oinsert(X26969),esk258_5(X26965,X26966,X26967,X26968,X26969)),esk259_5(X26965,X26966,X26967,X26968,X26969))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X26969,X26968,hAPP(hAPP(c_Set_Oinsert(X26969),X26967),X26966)),X26965)) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X26969,X26969,X26968,esk258_5(X26965,X26966,X26967,X26968,X26969),esk259_5(X26965,X26966,X26967,X26968,X26969)),X26965))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X26969,X26968,hAPP(hAPP(c_Set_Oinsert(X26969),X26967),X26966)),X26965)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X26969),esk258_5(X26965,X26966,X26967,X26968,X26969)),esk259_5(X26965,X26966,X26967,X26968,X26969)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X26969,X26968,hAPP(hAPP(c_Set_Oinsert(X26969),X26967),X26966)),X26965)) )
      & ( hAPP(hAPP(c_Set_Oinsert(X26976),X26974),X26973) != hAPP(hAPP(c_Set_Oinsert(X26976),X26977),X26978)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X26976,X26976,X26975,X26977,X26978),X26972))
        | hBOOL(hAPP(hAPP(c_member(X26976),X26977),X26978))
        | hBOOL(hAPP(c_Finite__Set_Ofold1Set(X26976,X26975,hAPP(hAPP(c_Set_Oinsert(X26976),X26974),X26973)),X26972)) ) ),
    inference(distribute,[status(thm)],[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_5357])])])])])]) ).

fof(i_0_6406,plain,
    ! [X29198,X29199,X29200,X29201,X29204,X29205,X29206,X29207,X29208,X29209] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29201,X29201)),hAPP(hAPP(c_Product__Type_OPair(X29201,X29201),hAPP(hAPP(c_List_Onth(X29201),X29200),esk328_4(X29198,X29199,X29200,X29201))),esk327_4(X29198,X29199,X29200,X29201))),X29198))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29201),tc_List_Olist(X29201))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29201),tc_List_Olist(X29201)),X29200),X29199)),c_List_Olistrel1(X29201,X29198))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk328_4(X29198,X29199,X29200,X29201)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29201)),X29200)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29201),tc_List_Olist(X29201))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29201),tc_List_Olist(X29201)),X29200),X29199)),c_List_Olistrel1(X29201,X29198))) )
      & ( X29199 = hAPP(hAPP(c_List_Olist__update(X29201,X29200),esk328_4(X29198,X29199,X29200,X29201)),esk327_4(X29198,X29199,X29200,X29201))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29201),tc_List_Olist(X29201))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29201),tc_List_Olist(X29201)),X29200),X29199)),c_List_Olistrel1(X29201,X29198))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29207,X29207)),hAPP(hAPP(c_Product__Type_OPair(X29207,X29207),hAPP(hAPP(c_List_Onth(X29207),X29206),X29209)),X29208)),X29204))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29209),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29207)),X29206)))
        | X29205 != hAPP(hAPP(c_List_Olist__update(X29207,X29206),X29209),X29208)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29207),tc_List_Olist(X29207))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29207),tc_List_Olist(X29207)),X29206),X29205)),c_List_Olistrel1(X29207,X29204))) ) ),
    inference(distribute,[status(thm)],[inference(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_6407,plain,
    ! [X27485,X27486,X27487,X27488,X27489,X27490] :
      ( hAPP(c_Set_Oimage(X27490,X27489,X27488),c_Orderings_Otop__class_Otop(tc_fun(X27490,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X27489,tc_HOL_Obool))
      | hAPP(c_Set_Oimage(X27487,X27486,X27485),c_Orderings_Otop__class_Otop(tc_fun(X27487,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X27486,tc_HOL_Obool))
      | hAPP(c_Set_Oimage(tc_prod(X27490,X27487),tc_prod(X27489,X27486),c_Product__Type_Omap__pair(X27490,X27489,X27487,X27486,X27488,X27485)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X27490,X27487),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X27489,X27486),tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__pair__surj])]) ).

fof(i_0_6408,plain,
    ! [X32911,X32912,X32913] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32913),X32912))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X32913,tc_HOL_Obool)),X32911),X32912) = hAPP(hAPP(c_Finite__Set_Ofold(X32913,tc_fun(X32913,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X32913,tc_HOL_Obool),tc_fun(tc_fun(X32913,tc_HOL_Obool),tc_fun(X32913,tc_HOL_Obool)),X32913),hAPP(c_COMBC(tc_fun(X32913,tc_HOL_Obool),tc_fun(X32913,tc_HOL_Obool),tc_fun(X32913,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(X32913,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(X32913,tc_fun(X32913,tc_HOL_Obool),tc_fun(X32913,tc_HOL_Obool)),c_Set_Oinsert(X32913)),c_Orderings_Obot__class_Obot(tc_fun(X32913,tc_HOL_Obool))))),X32911),X32912) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__fold__remove])]) ).

cnf(i_0_6409,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_5341]) ).

cnf(i_0_6410,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_5342]) ).

cnf(i_0_6411,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_5358]) ).

cnf(i_0_6412,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_5359]) ).

cnf(i_0_6413,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_5360]) ).

fof(i_0_6414,plain,
    ! [X27508,X27509,X27510,X27511,X27512,X27513,X27514] : hAPP(c_Product__Type_Ofst(X27514,X27513),hAPP(c_Product__Type_Omap__pair(X27512,X27514,X27511,X27513,X27510,X27509),X27508)) = hAPP(X27510,hAPP(c_Product__Type_Ofst(X27512,X27511),X27508)),
    inference(variable_rename,[status(thm)],[fact_fst__map__pair]) ).

fof(i_0_6415,plain,
    ! [X27526,X27527,X27528,X27529,X27530,X27531,X27532] : hAPP(c_Product__Type_Osnd(X27532,X27531),hAPP(c_Product__Type_Omap__pair(X27530,X27532,X27529,X27531,X27528,X27527),X27526)) = hAPP(X27527,hAPP(c_Product__Type_Osnd(X27530,X27529),X27526)),
    inference(variable_rename,[status(thm)],[fact_snd__prod__fun]) ).

cnf(i_0_6416,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_5361]) ).

cnf(i_0_6417,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_5362]) ).

fof(i_0_6418,plain,
    ! [X29549,X29550,X29551,X29552] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29552,X29552)),hAPP(hAPP(c_Product__Type_OPair(X29552,X29552),esk344_4(X29549,X29550,X29551,X29552)),esk345_4(X29549,X29550,X29551,X29552))),X29551))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29552),tc_List_Olist(X29552))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29552),tc_List_Olist(X29552)),X29550),X29549)),c_List_Olexord(X29552,X29551)))
        | X29550 = X29549
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29552),tc_List_Olist(X29552))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29552),tc_List_Olist(X29552)),X29549),X29550)),c_List_Olexord(X29552,X29551))) )
      & ( esk344_4(X29549,X29550,X29551,X29552) != esk345_4(X29549,X29550,X29551,X29552)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29552),tc_List_Olist(X29552))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29552),tc_List_Olist(X29552)),X29550),X29549)),c_List_Olexord(X29552,X29551)))
        | X29550 = X29549
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29552),tc_List_Olist(X29552))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29552),tc_List_Olist(X29552)),X29549),X29550)),c_List_Olexord(X29552,X29551))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29552,X29552)),hAPP(hAPP(c_Product__Type_OPair(X29552,X29552),esk345_4(X29549,X29550,X29551,X29552)),esk344_4(X29549,X29550,X29551,X29552))),X29551))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29552),tc_List_Olist(X29552))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29552),tc_List_Olist(X29552)),X29550),X29549)),c_List_Olexord(X29552,X29551)))
        | X29550 = X29549
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29552),tc_List_Olist(X29552))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29552),tc_List_Olist(X29552)),X29549),X29550)),c_List_Olexord(X29552,X29551))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__linear])])])]) ).

fof(i_0_6419,plain,
    ! [X23339,X23340,X23341,X23342] : 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),X23342),X23341)),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),X23340),X23339)),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),X23342),X23340)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23341),X23339))),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_6420,plain,
    ! [X25284,X25285] : c_Relation_OId__on(X25285,X25284) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25285,tc_fun(tc_prod(X25285,X25285),tc_HOL_Obool)),X25284),hAPP(hAPP(c_COMBC(X25285,tc_fun(tc_prod(X25285,X25285),tc_HOL_Obool),tc_fun(tc_prod(X25285,X25285),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_prod(X25285,X25285),tc_fun(tc_fun(tc_prod(X25285,X25285),tc_HOL_Obool),tc_fun(tc_prod(X25285,X25285),tc_HOL_Obool)),X25285),c_Set_Oinsert(tc_prod(X25285,X25285))),hAPP(hAPP(c_COMBS(X25285,X25285,tc_prod(X25285,X25285)),c_Product__Type_OPair(X25285,X25285)),c_COMBI(X25285)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X25285,X25285),tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_Id__on__def]) ).

cnf(i_0_6421,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_5363]) ).

fof(i_0_6422,plain,
    ! [X33372,X33373,X33374] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X33374,X33374,hAPP(hAPP(c_COMBB(tc_fun(X33374,tc_HOL_Obool),tc_fun(X33374,tc_HOL_Obool),X33374),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X33374),c_fNot)),c_fequal)),X33373),X33372))
        | X33373 != X33372 )
      & ( X33373 = X33372
        | hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X33374,X33374,hAPP(hAPP(c_COMBB(tc_fun(X33374,tc_HOL_Obool),tc_fun(X33374,tc_HOL_Obool),X33374),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X33374),c_fNot)),c_fequal)),X33373),X33372)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_conversep__noteq])]) ).

cnf(i_0_6423,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_5364]) ).

cnf(i_0_6424,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_5365]) ).

fof(i_0_6425,plain,
    ! [X29790,X29791,X29792,X29793,X29794,X29795,X29796,X29797] : hAPP(hAPP(c_List_Omap(tc_prod(X29797,X29796),X29795),X29794),hAPP(hAPP(c_List_Ozip(X29797,X29796),hAPP(hAPP(c_List_Omap(X29793,X29797),X29792),X29791)),X29790)) = hAPP(hAPP(c_List_Omap(tc_prod(X29793,X29796),X29795),hAPP(c_Product__Type_Oprod_Oprod__case(X29793,X29796,X29795),hAPP(hAPP(c_COMBB(tc_fun(X29796,tc_prod(X29797,X29796)),tc_fun(X29796,X29795),X29793),hAPP(c_COMBB(tc_prod(X29797,X29796),X29795,X29796),X29794)),hAPP(hAPP(c_COMBB(X29797,tc_fun(X29796,tc_prod(X29797,X29796)),X29793),c_Product__Type_OPair(X29797,X29796)),X29792)))),hAPP(hAPP(c_List_Ozip(X29793,X29796),X29791),X29790)),
    inference(variable_rename,[status(thm)],[fact_map__zip__map]) ).

fof(i_0_6426,plain,
    ! [X31995,X31996,X31997,X31998] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X31997,X31998)),X31996),X31995))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X31997,X31998)),X31996),X31995))
        | ~ class_Orderings_Oorder(X31998)
        | ~ class_Enum_Oenum(X31997) )
      & ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X31997),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X31997),c_fNot),hAPP(hAPP(c_COMBS(X31997,X31998,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X31998,tc_fun(X31998,tc_HOL_Obool),X31997),c_fequal),X31996)),X31995))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X31997,X31998)),X31996),X31995))
        | ~ class_Orderings_Oorder(X31998)
        | ~ class_Enum_Oenum(X31997) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X31997,X31998)),X31996),X31995))
        | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X31997),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X31997),c_fNot),hAPP(hAPP(c_COMBS(X31997,X31998,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X31998,tc_fun(X31998,tc_HOL_Obool),X31997),c_fequal),X31996)),X31995))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X31997,X31998)),X31996),X31995))
        | ~ class_Orderings_Oorder(X31998)
        | ~ class_Enum_Oenum(X31997) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__fun_I2_J])])]) ).

fof(i_0_6427,plain,
    ! [X28409,X28410,X28411,X28412] : c_List_Osublist(X28412,hAPP(hAPP(c_List_Olist_OCons(X28412),X28411),X28410),X28409) = hAPP(hAPP(c_List_Oappend(X28412),hAPP(hAPP(hAPP(c_If(tc_List_Olist(X28412)),hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X28409)),hAPP(hAPP(c_List_Olist_OCons(X28412),X28411),c_List_Olist_ONil(X28412))),c_List_Olist_ONil(X28412))),c_List_Osublist(X28412,X28410,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)),X28409)))),
    inference(variable_rename,[status(thm)],[fact_sublist__Cons]) ).

cnf(i_0_6428,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_5366]) ).

fof(i_0_6429,plain,
    ! [X31601,X31602,X31603,X31604] :
      ( ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X31604),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X31604))),X31603)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31602),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31604))),c_List_Otranspose(X31604,X31603))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31601),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31604))),hAPP(c_List_Ofilter(tc_List_Olist(X31604),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X31604)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31602)),c_Nat_Osize__class_Osize(tc_List_Olist(X31604)))),X31603))))
      | hAPP(hAPP(c_List_Onth(X31604),hAPP(hAPP(c_List_Onth(tc_List_Olist(X31604)),c_List_Otranspose(X31604,X31603)),X31602)),X31601) = hAPP(hAPP(c_List_Onth(X31604),hAPP(hAPP(c_List_Onth(tc_List_Olist(X31604)),X31603),X31601)),X31602) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__nth__transpose__sorted])]) ).

cnf(i_0_6430,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_5346]) ).

cnf(i_0_6431,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_5367]) ).

cnf(i_0_6432,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_5368]) ).

cnf(i_0_6433,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_5369]) ).

cnf(i_0_6434,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_5370]) ).

cnf(i_0_6435,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_5348]) ).

cnf(i_0_6436,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_5371]) ).

cnf(i_0_6437,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_5372]) ).

cnf(i_0_6438,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_5373]) ).

fof(i_0_6439,plain,
    ! [X29996,X29997,X29998,X29999,X30000,X30002] :
      ( ( hBOOL(hAPP(hAPP(c_member(X29999),esk355_5(X29996,X29997,X29998,X29999,X30000)),X29998))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X30000),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29999,X30000),X29998),X29997)),X29996))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X30000)
        | ~ class_Orderings_Olinorder(X30000) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X30000),hAPP(X29997,esk355_5(X29996,X29997,X29998,X29999,X30000))),X29996))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X30000),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29999,X30000),X29998),X29997)),X29996))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X30000)
        | ~ class_Orderings_Olinorder(X30000) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X29999),X30002),X29998))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X30000),hAPP(X29997,X30002)),X29996))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X30000),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29999,X30000),X29998),X29997)),X29996))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X30000)
        | ~ class_Orderings_Olinorder(X30000) ) ),
    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_6440,plain,
    ! [X24953,X24954,X24955,X24956,X24957,X24959,X24960,X24961,X24962,X24963,X24964,X24965,X24968] :
      ( ( hBOOL(hAPP(hAPP(c_member(X24957),esk150_5(X24953,X24954,X24955,X24956,X24957)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24956,tc_fun(X24957,tc_HOL_Obool)),X24955),X24954)))
        | ~ hBOOL(hAPP(hAPP(c_member(X24956),X24959),X24955))
        | ~ hBOOL(hAPP(hAPP(c_member(X24957),X24960),hAPP(X24954,X24959)))
        | hBOOL(hAPP(X24953,X24960)) )
      & ( ~ hBOOL(hAPP(X24953,esk150_5(X24953,X24954,X24955,X24956,X24957)))
        | ~ hBOOL(hAPP(hAPP(c_member(X24956),X24959),X24955))
        | ~ hBOOL(hAPP(hAPP(c_member(X24957),X24960),hAPP(X24954,X24959)))
        | hBOOL(hAPP(X24953,X24960)) )
      & ( hBOOL(hAPP(hAPP(c_member(X24964),esk151_5(X24961,X24962,X24963,X24964,X24965)),X24963))
        | ~ hBOOL(hAPP(hAPP(c_member(X24965),X24968),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24964,tc_fun(X24965,tc_HOL_Obool)),X24963),X24962)))
        | hBOOL(hAPP(X24961,X24968)) )
      & ( hBOOL(hAPP(hAPP(c_member(X24965),esk152_5(X24961,X24962,X24963,X24964,X24965)),hAPP(X24962,esk151_5(X24961,X24962,X24963,X24964,X24965))))
        | ~ hBOOL(hAPP(hAPP(c_member(X24965),X24968),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24964,tc_fun(X24965,tc_HOL_Obool)),X24963),X24962)))
        | hBOOL(hAPP(X24961,X24968)) )
      & ( ~ hBOOL(hAPP(X24961,esk152_5(X24961,X24962,X24963,X24964,X24965)))
        | ~ hBOOL(hAPP(hAPP(c_member(X24965),X24968),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24964,tc_fun(X24965,tc_HOL_Obool)),X24963),X24962)))
        | hBOOL(hAPP(X24961,X24968)) ) ),
    inference(distribute,[status(thm)],[inference(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_6441,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_6442,plain,
    ! [X23097,X23098,X23099,X23100,X23101,X23102] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X23102,tc_HOL_Obool),tc_fun(X23102,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X23102,tc_HOL_Obool),tc_fun(X23102,tc_HOL_Obool)),X23101),X23100)),c_Wellfounded_Omax__ext(X23102,X23099)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X23102,tc_HOL_Obool),tc_fun(X23102,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X23102,tc_HOL_Obool),tc_fun(X23102,tc_HOL_Obool)),X23098),X23097)),c_Wellfounded_Omax__ext(X23102,X23099)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X23102,tc_HOL_Obool),tc_fun(X23102,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X23102,tc_HOL_Obool),tc_fun(X23102,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23102,tc_HOL_Obool)),X23101),X23098)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23102,tc_HOL_Obool)),X23100),X23097))),c_Wellfounded_Omax__ext(X23102,X23099))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__ext__additive])]) ).

fof(i_0_6443,plain,
    ! [X27478,X27479,X27480,X27481,X27482] :
      ( ( hBOOL(hAPP(hAPP(c_member(X27482),esk281_5(X27478,X27479,X27480,X27481,X27482)),X27479))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27482,X27481)),X27480),hAPP(hAPP(c_Product__Type_OSigma(X27482,X27481),X27479),X27478))) )
      & ( hBOOL(hAPP(hAPP(c_member(X27481),esk282_5(X27478,X27479,X27480,X27481,X27482)),hAPP(X27478,esk281_5(X27478,X27479,X27480,X27481,X27482))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27482,X27481)),X27480),hAPP(hAPP(c_Product__Type_OSigma(X27482,X27481),X27479),X27478))) )
      & ( X27480 = hAPP(hAPP(c_Product__Type_OPair(X27482,X27481),esk281_5(X27478,X27479,X27480,X27481,X27482)),esk282_5(X27478,X27479,X27480,X27481,X27482))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27482,X27481)),X27480),hAPP(hAPP(c_Product__Type_OSigma(X27482,X27481),X27479),X27478))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SigmaE])])])]) ).

fof(i_0_6444,plain,
    ! [X29734,X29735,X29736,X29737,X29738,X29739,X29740] : hAPP(c_List_Ofoldl(X29740,X29739,X29738,X29737),hAPP(hAPP(c_List_Omap(X29736,X29739),X29735),X29734)) = hAPP(c_List_Ofoldl(X29740,X29736,hAPP(hAPP(c_COMBC(X29740,tc_fun(X29736,X29739),tc_fun(X29736,X29740)),hAPP(hAPP(c_COMBB(tc_fun(X29739,X29740),tc_fun(tc_fun(X29736,X29739),tc_fun(X29736,X29740)),X29740),c_COMBB(X29739,X29740,X29736)),X29738)),X29735),X29737),X29734),
    inference(variable_rename,[status(thm)],[fact_foldl__map]) ).

fof(i_0_6445,plain,
    ! [X27998,X27999,X28000,X28001,X28002,X28003,X28004] : hAPP(hAPP(c_Relation_Orel__comp(X28004,X28003,X28002),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X28001,tc_fun(tc_prod(X28004,X28003),tc_HOL_Obool)),X28000),X27999)),X27998) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X28001,tc_fun(tc_prod(X28004,X28002),tc_HOL_Obool)),X28000),hAPP(hAPP(c_COMBC(X28001,tc_fun(tc_prod(X28003,X28002),tc_HOL_Obool),tc_fun(tc_prod(X28004,X28002),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X28004,X28003),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X28003,X28002),tc_HOL_Obool),tc_fun(tc_prod(X28004,X28002),tc_HOL_Obool)),X28001),c_Relation_Orel__comp(X28004,X28003,X28002)),X27999)),X27998)),
    inference(variable_rename,[status(thm)],[fact_rel__comp__UNION__distrib2]) ).

fof(i_0_6446,plain,
    ! [X21694,X21695] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21695),c_Int_OPls))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21694)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21695)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21694) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21695),c_Int_OPls))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21694)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21695)) = 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),X21694),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21695)))),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_5374])]) ).

cnf(i_0_6447,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_5375]) ).

fof(i_0_6448,plain,
    ! [X27716,X27717,X27718] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X27718),hAPP(c_Set_OCollect(X27718),X27717)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27718),hAPP(c_Set_OCollect(X27718),hAPP(hAPP(c_COMBS(X27718,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27718),c_fdisj),X27717)),X27716)))) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X27718),hAPP(c_Set_OCollect(X27718),X27716)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27718),hAPP(c_Set_OCollect(X27718),hAPP(hAPP(c_COMBS(X27718,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27718),c_fdisj),X27717)),X27716)))) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27718),hAPP(c_Set_OCollect(X27718),X27717)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27718),hAPP(c_Set_OCollect(X27718),X27716)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X27718),hAPP(c_Set_OCollect(X27718),hAPP(hAPP(c_COMBS(X27718,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27718),c_fdisj),X27717)),X27716)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Collect__disjI])])]) ).

fof(i_0_6449,plain,
    ! [X34068,X34069,X34070,X34071,X34072] :
      ( ( hBOOL(hAPP(hAPP(c_member(X34071),esk557_5(X34068,X34069,X34070,X34071,X34072)),hAPP(c_Set_Oimage(X34072,X34071,X34070),c_Orderings_Otop__class_Otop(tc_fun(X34072,tc_HOL_Obool)))))
        | hBOOL(hAPP(X34069,X34068))
        | ~ c_Fun_Oinj__on(X34072,X34071,X34070,c_Orderings_Otop__class_Otop(tc_fun(X34072,tc_HOL_Obool))) )
      & ( ~ hBOOL(hAPP(X34069,hAPP(c_Hilbert__Choice_Oinv__into(X34072,X34071,c_Orderings_Otop__class_Otop(tc_fun(X34072,tc_HOL_Obool)),X34070),esk557_5(X34068,X34069,X34070,X34071,X34072))))
        | hBOOL(hAPP(X34069,X34068))
        | ~ c_Fun_Oinj__on(X34072,X34071,X34070,c_Orderings_Otop__class_Otop(tc_fun(X34072,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_6450,plain,
    ! [X32664,X32665,X32666] :
      ( ( ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(X32665,X32666)),X32664))
        | hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X32665),hAPP(hAPP(c_COMBB(tc_fun(X32666,tc_HOL_Obool),tc_HOL_Obool,X32665),c_Enum_Oenum__class_Oenum__all(X32666)),hAPP(hAPP(c_COMBB(tc_fun(X32666,tc_prod(X32665,X32666)),tc_fun(X32666,tc_HOL_Obool),X32665),hAPP(c_COMBB(tc_prod(X32665,X32666),tc_HOL_Obool,X32666),X32664)),c_Product__Type_OPair(X32665,X32666)))))
        | ~ class_Enum_Oenum(X32666)
        | ~ class_Enum_Oenum(X32665) )
      & ( ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X32665),hAPP(hAPP(c_COMBB(tc_fun(X32666,tc_HOL_Obool),tc_HOL_Obool,X32665),c_Enum_Oenum__class_Oenum__all(X32666)),hAPP(hAPP(c_COMBB(tc_fun(X32666,tc_prod(X32665,X32666)),tc_fun(X32666,tc_HOL_Obool),X32665),hAPP(c_COMBB(tc_prod(X32665,X32666),tc_HOL_Obool,X32666),X32664)),c_Product__Type_OPair(X32665,X32666)))))
        | hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(X32665,X32666)),X32664))
        | ~ class_Enum_Oenum(X32666)
        | ~ class_Enum_Oenum(X32665) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_enum__all__prod__def])])]) ).

fof(i_0_6451,plain,
    ! [X32004,X32005,X32006] :
      ( ( ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(X32005,X32006)),X32004))
        | hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X32005),hAPP(hAPP(c_COMBB(tc_fun(X32006,tc_HOL_Obool),tc_HOL_Obool,X32005),c_Enum_Oenum__class_Oenum__ex(X32006)),hAPP(hAPP(c_COMBB(tc_fun(X32006,tc_prod(X32005,X32006)),tc_fun(X32006,tc_HOL_Obool),X32005),hAPP(c_COMBB(tc_prod(X32005,X32006),tc_HOL_Obool,X32006),X32004)),c_Product__Type_OPair(X32005,X32006)))))
        | ~ class_Enum_Oenum(X32006)
        | ~ class_Enum_Oenum(X32005) )
      & ( ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X32005),hAPP(hAPP(c_COMBB(tc_fun(X32006,tc_HOL_Obool),tc_HOL_Obool,X32005),c_Enum_Oenum__class_Oenum__ex(X32006)),hAPP(hAPP(c_COMBB(tc_fun(X32006,tc_prod(X32005,X32006)),tc_fun(X32006,tc_HOL_Obool),X32005),hAPP(c_COMBB(tc_prod(X32005,X32006),tc_HOL_Obool,X32006),X32004)),c_Product__Type_OPair(X32005,X32006)))))
        | hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(X32005,X32006)),X32004))
        | ~ class_Enum_Oenum(X32006)
        | ~ class_Enum_Oenum(X32005) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_enum__ex__prod__def])])]) ).

fof(i_0_6452,plain,
    ! [X30535,X30536,X30537,X30538] :
      ( ( hBOOL(hAPP(c_List_Olistsp(X30538,X30537),X30535))
        | ~ hBOOL(hAPP(c_List_Olistsp(X30538,hAPP(hAPP(c_COMBS(X30538,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X30538),c_fconj),X30537)),X30536)),X30535)) )
      & ( hBOOL(hAPP(c_List_Olistsp(X30538,X30536),X30535))
        | ~ hBOOL(hAPP(c_List_Olistsp(X30538,hAPP(hAPP(c_COMBS(X30538,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X30538),c_fconj),X30537)),X30536)),X30535)) )
      & ( ~ hBOOL(hAPP(c_List_Olistsp(X30538,X30537),X30535))
        | ~ hBOOL(hAPP(c_List_Olistsp(X30538,X30536),X30535))
        | hBOOL(hAPP(c_List_Olistsp(X30538,hAPP(hAPP(c_COMBS(X30538,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X30538),c_fconj),X30537)),X30536)),X30535)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsp__conj__eq])])]) ).

fof(i_0_6453,plain,
    ! [X21749,X21750] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X21750))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X21749)),hAPP(c_Int_Onat,X21750)) = hAPP(c_Int_Onat,X21749) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,X21750))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X21749)),hAPP(c_Int_Onat,X21750)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X21749),X21750)),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_5376])]) ).

cnf(i_0_6454,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_5377]) ).

fof(i_0_6455,plain,
    ! [X26623,X26624,X26625,X26626,X26627] :
      ( ~ class_Groups_Oab__semigroup__mult(X26627)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X26627,X26627,c_Groups_Otimes__class_Otimes(X26627),X26626,X26625),X26624))
      | ~ hBOOL(hAPP(hAPP(c_member(X26627),X26623),X26625))
      | hBOOL(hAPP(hAPP(c_member(X26627),X26626),X26625))
      | hBOOL(hAPP(c_Finite__Set_Ofold__graph(X26627,X26627,c_Groups_Otimes__class_Otimes(X26627),X26623,hAPP(hAPP(c_Set_Oinsert(X26627),X26626),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26627,tc_HOL_Obool)),X26625),hAPP(hAPP(c_Set_Oinsert(X26627),X26623),c_Orderings_Obot__class_Obot(tc_fun(X26627,tc_HOL_Obool)))))),X26624)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5378])]) ).

fof(i_0_6456,plain,
    ! [X30494,X30495,X30496,X30497] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X30497)),X30496),c_List_Olists(X30497,X30495)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X30497)),X30496),c_List_Olists(X30497,X30494)))
      | hBOOL(hAPP(c_List_Olistsp(X30497,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X30497,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X30497,tc_fun(X30497,tc_HOL_Obool),tc_HOL_Obool),c_member(X30497)),X30495)),hAPP(hAPP(c_COMBC(X30497,tc_fun(X30497,tc_HOL_Obool),tc_HOL_Obool),c_member(X30497)),X30494))),X30496)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lists__IntI])]) ).

fof(i_0_6457,plain,
    ! [X24933,X24934,X24935,X24936,X24937,X24938,X24939,X24940,X24941,X24942] :
      ( ~ c_Equiv__Relations_Oequiv(X24942,X24941,X24940)
      | ~ c_Equiv__Relations_Oequiv(X24939,X24938,X24937)
      | ~ c_Equiv__Relations_Ocongruent2(X24942,X24939,tc_fun(X24936,tc_HOL_Obool),X24940,X24937,X24935)
      | ~ hBOOL(hAPP(hAPP(c_member(X24942),X24934),X24941))
      | ~ hBOOL(hAPP(hAPP(c_member(X24939),X24933),X24938))
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24942,tc_fun(X24936,tc_HOL_Obool)),hAPP(c_Relation_OImage(X24942,X24942,X24940),hAPP(hAPP(c_Set_Oinsert(X24942),X24934),c_Orderings_Obot__class_Obot(tc_fun(X24942,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(X24939,tc_fun(X24936,tc_HOL_Obool)),tc_fun(X24936,tc_HOL_Obool),X24942),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24939,tc_fun(X24936,tc_HOL_Obool)),hAPP(c_Relation_OImage(X24939,X24939,X24937),hAPP(hAPP(c_Set_Oinsert(X24939),X24933),c_Orderings_Obot__class_Obot(tc_fun(X24939,tc_HOL_Obool)))))),X24935)) = hAPP(hAPP(X24935,X24934),X24933) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__equiv__class2])]) ).

fof(i_0_6458,plain,
    ! [X27905,X27906,X27907] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27907)),c_List_Osublist(X27907,X27906,X27905)) = 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(X27907)),X27906)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X27905)))),
    inference(variable_rename,[status(thm)],[fact_length__sublist]) ).

cnf(i_0_6459,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_5379]) ).

fof(i_0_6460,plain,
    ! [X31140,X31141,X31142] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31142)),hAPP(c_List_Ofilter(X31142,X31141),X31140)) = 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(X31142)),X31140)))),hAPP(hAPP(c_COMBB(X31142,tc_HOL_Obool,tc_Nat_Onat),X31141),hAPP(c_List_Onth(X31142),X31140))))),
    inference(variable_rename,[status(thm)],[fact_length__filter__conv__card]) ).

fof(i_0_6461,plain,
    ! [X24880,X24881,X24882,X24883,X24884] :
      ( ~ class_Groups_Ocomm__monoid__mult(X24884)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24883),X24882))
      | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X24884,X24883,c_Groups_Otimes__class_Otimes(X24884)),hAPP(hAPP(c_COMBS(X24883,X24884,X24884),hAPP(hAPP(c_COMBB(X24884,tc_fun(X24884,X24884),X24883),c_Groups_Otimes__class_Otimes(X24884)),X24881)),X24880)),c_Groups_Oone__class_Oone(X24884)),X24882) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24884),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X24884,X24883,c_Groups_Otimes__class_Otimes(X24884)),X24881),c_Groups_Oone__class_Oone(X24884)),X24882)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X24884,X24883,c_Groups_Otimes__class_Otimes(X24884)),X24880),c_Groups_Oone__class_Oone(X24884)),X24882)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__image__distrib])]) ).

fof(i_0_6462,plain,
    ! [X28499,X28500,X28501,X28502,X28503,X28504] :
      ( ( X28503 = X28501
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28504),tc_List_Olist(X28504))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28504),tc_List_Olist(X28504)),X28503),X28501)),c_List_Olistrel1(X28504,X28499)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28504),tc_List_Olist(X28504))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28504),tc_List_Olist(X28504)),hAPP(hAPP(c_List_Oappend(X28504),X28503),hAPP(hAPP(c_List_Olist_OCons(X28504),X28502),c_List_Olist_ONil(X28504)))),hAPP(hAPP(c_List_Oappend(X28504),X28501),hAPP(hAPP(c_List_Olist_OCons(X28504),X28500),c_List_Olist_ONil(X28504))))),c_List_Olistrel1(X28504,X28499))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X28504,X28504)),hAPP(hAPP(c_Product__Type_OPair(X28504,X28504),X28502),X28500)),X28499))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28504),tc_List_Olist(X28504))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28504),tc_List_Olist(X28504)),X28503),X28501)),c_List_Olistrel1(X28504,X28499)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28504),tc_List_Olist(X28504))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28504),tc_List_Olist(X28504)),hAPP(hAPP(c_List_Oappend(X28504),X28503),hAPP(hAPP(c_List_Olist_OCons(X28504),X28502),c_List_Olist_ONil(X28504)))),hAPP(hAPP(c_List_Oappend(X28504),X28501),hAPP(hAPP(c_List_Olist_OCons(X28504),X28500),c_List_Olist_ONil(X28504))))),c_List_Olistrel1(X28504,X28499))) )
      & ( X28503 = X28501
        | X28502 = X28500
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28504),tc_List_Olist(X28504))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28504),tc_List_Olist(X28504)),hAPP(hAPP(c_List_Oappend(X28504),X28503),hAPP(hAPP(c_List_Olist_OCons(X28504),X28502),c_List_Olist_ONil(X28504)))),hAPP(hAPP(c_List_Oappend(X28504),X28501),hAPP(hAPP(c_List_Olist_OCons(X28504),X28500),c_List_Olist_ONil(X28504))))),c_List_Olistrel1(X28504,X28499))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X28504,X28504)),hAPP(hAPP(c_Product__Type_OPair(X28504,X28504),X28502),X28500)),X28499))
        | X28502 = X28500
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28504),tc_List_Olist(X28504))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28504),tc_List_Olist(X28504)),hAPP(hAPP(c_List_Oappend(X28504),X28503),hAPP(hAPP(c_List_Olist_OCons(X28504),X28502),c_List_Olist_ONil(X28504)))),hAPP(hAPP(c_List_Oappend(X28504),X28501),hAPP(hAPP(c_List_Olist_OCons(X28504),X28500),c_List_Olist_ONil(X28504))))),c_List_Olistrel1(X28504,X28499))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28504),tc_List_Olist(X28504))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28504),tc_List_Olist(X28504)),X28503),X28501)),c_List_Olistrel1(X28504,X28499)))
        | X28502 != X28500
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28504),tc_List_Olist(X28504))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28504),tc_List_Olist(X28504)),hAPP(hAPP(c_List_Oappend(X28504),X28503),hAPP(hAPP(c_List_Olist_OCons(X28504),X28502),c_List_Olist_ONil(X28504)))),hAPP(hAPP(c_List_Oappend(X28504),X28501),hAPP(hAPP(c_List_Olist_OCons(X28504),X28500),c_List_Olist_ONil(X28504))))),c_List_Olistrel1(X28504,X28499))) )
      & ( X28503 != X28501
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28504,X28504)),hAPP(hAPP(c_Product__Type_OPair(X28504,X28504),X28502),X28500)),X28499))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28504),tc_List_Olist(X28504))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28504),tc_List_Olist(X28504)),hAPP(hAPP(c_List_Oappend(X28504),X28503),hAPP(hAPP(c_List_Olist_OCons(X28504),X28502),c_List_Olist_ONil(X28504)))),hAPP(hAPP(c_List_Oappend(X28504),X28501),hAPP(hAPP(c_List_Olist_OCons(X28504),X28500),c_List_Olist_ONil(X28504))))),c_List_Olistrel1(X28504,X28499))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_snoc__listrel1__snoc__iff])])]) ).

fof(i_0_6463,plain,
    ! [X30678,X30679,X30680,X30681,X30682,X30683,X30684] :
      ( ( ~ c_List_Olist__all2(X30684,X30683,X30682,X30681,hAPP(hAPP(c_List_Omap(X30680,X30683),X30679),X30678))
        | c_List_Olist__all2(X30684,X30680,hAPP(hAPP(c_COMBC(X30684,tc_fun(X30680,X30683),tc_fun(X30680,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X30683,tc_HOL_Obool),tc_fun(tc_fun(X30680,X30683),tc_fun(X30680,tc_HOL_Obool)),X30684),c_COMBB(X30683,tc_HOL_Obool,X30680)),X30682)),X30679),X30681,X30678) )
      & ( ~ c_List_Olist__all2(X30684,X30680,hAPP(hAPP(c_COMBC(X30684,tc_fun(X30680,X30683),tc_fun(X30680,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X30683,tc_HOL_Obool),tc_fun(tc_fun(X30680,X30683),tc_fun(X30680,tc_HOL_Obool)),X30684),c_COMBB(X30683,tc_HOL_Obool,X30680)),X30682)),X30679),X30681,X30678)
        | c_List_Olist__all2(X30684,X30683,X30682,X30681,hAPP(hAPP(c_List_Omap(X30680,X30683),X30679),X30678)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__map2])]) ).

fof(i_0_6464,plain,
    ! [X26856,X26857,X26858,X26859] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X26859,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk251_4(X26856,X26857,X26858,X26859))),X26858) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X26859,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),esk251_4(X26856,X26857,X26858,X26859)),X26857))),X26856)
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X26859,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X26858) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X26859,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X26856) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__finite2__eq])])]) ).

fof(i_0_6465,plain,
    ! [X26916,X26917,X26918,X26919,X26921] :
      ( ( hBOOL(hAPP(hAPP(c_member(X26919),esk257_4(X26916,X26917,X26918,X26919)),X26918))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X26919,tc_HOL_Obool),tc_fun(X26919,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X26919,tc_HOL_Obool),tc_fun(X26919,tc_HOL_Obool)),X26918),X26917)),c_Wellfounded_Omax__ext(X26919,X26916)))
        | X26917 = c_Orderings_Obot__class_Obot(tc_fun(X26919,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26919),X26917))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26919),X26918)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X26919),X26921),X26917))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X26919,X26919)),hAPP(hAPP(c_Product__Type_OPair(X26919,X26919),esk257_4(X26916,X26917,X26918,X26919)),X26921)),X26916))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X26919,tc_HOL_Obool),tc_fun(X26919,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X26919,tc_HOL_Obool),tc_fun(X26919,tc_HOL_Obool)),X26918),X26917)),c_Wellfounded_Omax__ext(X26919,X26916)))
        | X26917 = c_Orderings_Obot__class_Obot(tc_fun(X26919,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26919),X26917))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26919),X26918)) ) ),
    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_6466,plain,
    ! [X28133,X28134,X28135,X28136,X28137,X28138,X28139,X28141,X28142,X28143,X28144,X28145,X28146,X28147,X28148] :
      ( ( hBOOL(hAPP(hAPP(X28136,X28134),esk296_4(X28133,X28134,X28135,X28136)))
        | ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X28139,X28138,X28137,X28136,X28135),X28134),X28133)) )
      & ( hBOOL(hAPP(hAPP(X28135,esk296_4(X28133,X28134,X28135,X28136)),X28133))
        | ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X28139,X28138,X28137,X28136,X28135),X28134),X28133)) )
      & ( ~ hBOOL(hAPP(hAPP(X28144,X28142),X28145))
        | ~ hBOOL(hAPP(hAPP(X28143,X28145),X28141))
        | hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X28148,X28147,X28146,X28144,X28143),X28142),X28141)) ) ),
    inference(distribute,[status(thm)],[inference(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_6467,plain,
    ! [X32707,X32708,X32709] :
      ( ~ c_Wellfounded_Owf(X32709,X32708)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32709,X32709)),hAPP(hAPP(c_Product__Type_OPair(X32709,X32709),hAPP(X32707,hAPP(c_Nat_OSuc,esk475_3(X32707,X32708,X32709)))),hAPP(X32707,esk475_3(X32707,X32708,X32709)))),X32708)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__no__infinite__down__chainE])])]) ).

fof(i_0_6468,plain,
    ! [X28220,X28221,X28222,X28224,X28225,X28227] :
      ( ( ~ c_Wellfounded_Owf(X28221,X28220)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28221,X28221)),hAPP(hAPP(c_Product__Type_OPair(X28221,X28221),hAPP(X28222,hAPP(c_Nat_OSuc,esk300_3(X28220,X28221,X28222)))),hAPP(X28222,esk300_3(X28220,X28221,X28222)))),X28220)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X28225,X28225)),hAPP(hAPP(c_Product__Type_OPair(X28225,X28225),hAPP(esk301_2(X28224,X28225),hAPP(c_Nat_OSuc,X28227))),hAPP(esk301_2(X28224,X28225),X28227))),X28224))
        | c_Wellfounded_Owf(X28225,X28224) ) ),
    inference(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_6469,plain,
    ! [X25011,X25012,X25013,X25014,X25015,X25016,X25017,X25018,X25019] :
      ( ~ c_Equiv__Relations_Oequiv(X25019,X25018,X25017)
      | ~ c_Equiv__Relations_Oequiv(X25016,X25015,X25014)
      | ~ c_Equiv__Relations_Ocongruent2(X25019,X25016,tc_fun(X25013,tc_HOL_Obool),X25017,X25014,X25012)
      | ~ hBOOL(hAPP(hAPP(c_member(X25016),X25011),X25015))
      | c_Equiv__Relations_Ocongruent(X25019,tc_fun(X25013,tc_HOL_Obool),X25017,hAPP(hAPP(c_COMBB(tc_fun(X25016,tc_fun(X25013,tc_HOL_Obool)),tc_fun(X25013,tc_HOL_Obool),X25019),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25016,tc_fun(X25013,tc_HOL_Obool)),hAPP(c_Relation_OImage(X25016,X25016,X25014),hAPP(hAPP(c_Set_Oinsert(X25016),X25011),c_Orderings_Obot__class_Obot(tc_fun(X25016,tc_HOL_Obool)))))),X25012)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_congruent2__implies__congruent__UN])]) ).

cnf(i_0_6470,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_5380]) ).

cnf(i_0_6471,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_5381]) ).

fof(i_0_6472,plain,
    ! [X26833,X26834,X26835,X26836,X26837,X26838,X26839] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X26839,X26838,X26837,X26836,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26839,tc_HOL_Obool)),X26835),hAPP(hAPP(c_Set_Oinsert(X26839),X26834),c_Orderings_Obot__class_Obot(tc_fun(X26839,tc_HOL_Obool))))),X26833))
      | ~ hBOOL(hAPP(hAPP(c_member(X26839),X26834),X26835))
      | hBOOL(hAPP(c_Finite__Set_Ofold__graph(X26839,X26838,X26837,X26836,X26835),hAPP(hAPP(X26837,X26834),X26833))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Diff1__fold__graph])]) ).

fof(i_0_6473,plain,
    ! [X26568,X26569,X26570,X26571,X26572] :
      ( ( hBOOL(hAPP(hAPP(c_member(X26571),esk237_5(X26568,X26569,X26570,X26571,X26572)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26571,tc_HOL_Obool)),X26570),X26569)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26572),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26571,X26572),X26568),X26569)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26571,X26572),X26568),X26570)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26571,tc_HOL_Obool)),X26569),X26570))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26571),X26570))
        | ~ class_Groups_Ocomm__monoid__add(X26572)
        | ~ class_Groups_Oordered__ab__semigroup__add(X26572) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26572),c_Groups_Ozero__class_Ozero(X26572)),hAPP(X26568,esk237_5(X26568,X26569,X26570,X26571,X26572))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26572),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26571,X26572),X26568),X26569)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26571,X26572),X26568),X26570)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26571,tc_HOL_Obool)),X26569),X26570))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26571),X26570))
        | ~ class_Groups_Ocomm__monoid__add(X26572)
        | ~ class_Groups_Oordered__ab__semigroup__add(X26572) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__mono3])])])]) ).

fof(i_0_6474,plain,
    ! [X26454,X26455,X26456,X26457,X26458] :
      ( ( hBOOL(hAPP(hAPP(c_member(X26457),esk227_5(X26454,X26455,X26456,X26457,X26458)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26457,tc_HOL_Obool)),X26456),X26455)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26458),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26457,X26458),X26454),X26455)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26457,X26458),X26454),X26456)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26457,tc_HOL_Obool)),X26455),X26456))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26457),X26456))
        | ~ class_Groups_Oordered__comm__monoid__add(X26458) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26458),c_Groups_Ozero__class_Ozero(X26458)),hAPP(X26454,esk227_5(X26454,X26455,X26456,X26457,X26458))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26458),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26457,X26458),X26454),X26455)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26457,X26458),X26454),X26456)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26457,tc_HOL_Obool)),X26455),X26456))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26457),X26456))
        | ~ class_Groups_Oordered__comm__monoid__add(X26458) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__mono2])])])]) ).

fof(i_0_6475,plain,
    ! [X29842,X29843,X29844,X29845] :
      ( ( ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29845,tc_fun(X29844,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X29845,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X29844,tc_HOL_Obool),tc_fun(X29844,tc_HOL_Obool),X29845),hAPP(c_COMBC(X29844,tc_fun(X29844,tc_HOL_Obool),tc_HOL_Obool),c_member(X29844))),X29843)),X29842))
        | hBOOL(hAPP(hAPP(c_member(X29844),X29842),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29845,tc_fun(X29844,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X29845,tc_HOL_Obool))),X29843))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X29844),X29842),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29845,tc_fun(X29844,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X29845,tc_HOL_Obool))),X29843)))
        | hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29845,tc_fun(X29844,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X29845,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X29844,tc_HOL_Obool),tc_fun(X29844,tc_HOL_Obool),X29845),hAPP(c_COMBC(X29844,tc_fun(X29844,tc_HOL_Obool),tc_HOL_Obool),c_member(X29844))),X29843)),X29842)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF__INT__eq])]) ).

fof(i_0_6476,plain,
    ! [X26758,X26759,X26760,X26761] :
      ( ( ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26761,tc_fun(X26760,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X26761,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X26760,tc_HOL_Obool),tc_fun(X26760,tc_HOL_Obool),X26761),hAPP(c_COMBC(X26760,tc_fun(X26760,tc_HOL_Obool),tc_HOL_Obool),c_member(X26760))),X26759)),X26758))
        | hBOOL(hAPP(hAPP(c_member(X26760),X26758),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26761,tc_fun(X26760,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X26761,tc_HOL_Obool))),X26759))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X26760),X26758),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26761,tc_fun(X26760,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X26761,tc_HOL_Obool))),X26759)))
        | hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26761,tc_fun(X26760,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X26761,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X26760,tc_HOL_Obool),tc_fun(X26760,tc_HOL_Obool),X26761),hAPP(c_COMBC(X26760,tc_fun(X26760,tc_HOL_Obool),tc_HOL_Obool),c_member(X26760))),X26759)),X26758)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUP__UN__eq])]) ).

fof(i_0_6477,plain,
    ! [X20069,X20070,X20071,X20072,X20073,X20074] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20074),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20074),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20074),X20073),X20072)),X20071)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20074),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20074),X20070),X20072)),X20069)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20074),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20074),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20074),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20074),X20073),X20070)),X20072)),X20071)),X20069))
        | ~ class_Rings_Oordered__ring(X20074) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20074),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20074),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20074),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20074),X20073),X20070)),X20072)),X20071)),X20069))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20074),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20074),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20074),X20073),X20072)),X20071)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20074),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20074),X20070),X20072)),X20069)))
        | ~ class_Rings_Oordered__ring(X20074) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__iff1])])]) ).

fof(i_0_6478,plain,
    ! [X20075,X20076,X20077,X20078,X20079,X20080] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20080),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20080),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20080),X20079),X20078)),X20077)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20080),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20080),X20076),X20078)),X20075)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20080),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20080),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20080),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20080),X20079),X20076)),X20078)),X20077)),X20075))
        | ~ class_Rings_Oordered__ring(X20080) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20080),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20080),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20080),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20080),X20079),X20076)),X20078)),X20077)),X20075))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20080),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20080),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20080),X20079),X20078)),X20077)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20080),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20080),X20076),X20078)),X20075)))
        | ~ class_Rings_Oordered__ring(X20080) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__iff1])])]) ).

cnf(i_0_6479,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_5382]) ).

fof(i_0_6480,plain,
    ! [X21635,X21636,X21637,X21638,X21639,X21640,X21641] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X21641),X21640),X21639))
      | ~ c_Nitpick_Ofold__graph_H(X21641,X21638,X21637,X21636,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X21641,tc_HOL_Obool)),X21639),hAPP(hAPP(c_Set_Oinsert(X21641),X21640),c_Orderings_Obot__class_Obot(tc_fun(X21641,tc_HOL_Obool)))),X21635)
      | c_Nitpick_Ofold__graph_H(X21641,X21638,X21637,X21636,X21639,hAPP(hAPP(X21637,X21640),X21635)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__graph_H_Ointros_I2_J])]) ).

fof(i_0_6481,plain,
    ! [X29818,X29819,X29820,X29821,X29822,X29823,X29824,X29825,X29826,X29827,X29828] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29822,tc_HOL_Obool)),X29821),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29820,tc_fun(X29822,tc_HOL_Obool)),X29819),X29818)))
        | ~ hBOOL(hAPP(hAPP(c_member(X29820),X29823),X29819))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29822,tc_HOL_Obool)),X29821),hAPP(X29818,X29823))) )
      & ( hBOOL(hAPP(hAPP(c_member(X29826),esk351_5(X29824,X29825,X29826,X29827,X29828)),X29825))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29828,tc_HOL_Obool)),X29827),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29826,tc_fun(X29828,tc_HOL_Obool)),X29825),X29824))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29828,tc_HOL_Obool)),X29827),hAPP(X29824,esk351_5(X29824,X29825,X29826,X29827,X29828))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29828,tc_HOL_Obool)),X29827),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29826,tc_fun(X29828,tc_HOL_Obool)),X29825),X29824))) ) ),
    inference(distribute,[status(thm)],[inference(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_6482,plain,
    ! [X33562,X33563,X33564,X33565,X33566] :
      ( ( hBOOL(hAPP(hAPP(c_member(X33566),esk520_5(X33562,X33563,X33564,X33565,X33566)),X33565))
        | c_Relation_Orefl__on(X33564,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X33566,tc_fun(X33564,tc_HOL_Obool)),X33565),X33563),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X33566,tc_fun(tc_prod(X33564,X33564),tc_HOL_Obool)),X33565),X33562)) )
      & ( ~ c_Relation_Orefl__on(X33564,hAPP(X33563,esk520_5(X33562,X33563,X33564,X33565,X33566)),hAPP(X33562,esk520_5(X33562,X33563,X33564,X33565,X33566)))
        | c_Relation_Orefl__on(X33564,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X33566,tc_fun(X33564,tc_HOL_Obool)),X33565),X33563),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X33566,tc_fun(tc_prod(X33564,X33564),tc_HOL_Obool)),X33565),X33562)) ) ),
    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_6483,plain,
    ! [X22115,X22116,X22117,X22118] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22118,X22117),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22116),X22115)))
      | hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22118),X22117),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,X22115),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22116)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22116)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,X22115),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),X22117),X22115))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zminus1__lemma])]) ).

cnf(i_0_6484,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_5383]) ).

fof(i_0_6485,plain,
    ! [X30015,X30016,X30017,X30018,X30019,X30020,X30021,X30022,X30023,X30024,X30025] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X30019),X30018),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30017,tc_fun(X30019,tc_HOL_Obool)),X30016),X30015)))
        | ~ hBOOL(hAPP(hAPP(c_member(X30017),X30020),X30016))
        | hBOOL(hAPP(hAPP(c_member(X30019),X30018),hAPP(X30015,X30020))) )
      & ( hBOOL(hAPP(hAPP(c_member(X30023),esk356_5(X30021,X30022,X30023,X30024,X30025)),X30022))
        | hBOOL(hAPP(hAPP(c_member(X30025),X30024),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30023,tc_fun(X30025,tc_HOL_Obool)),X30022),X30021))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X30025),X30024),hAPP(X30021,esk356_5(X30021,X30022,X30023,X30024,X30025))))
        | hBOOL(hAPP(hAPP(c_member(X30025),X30024),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30023,tc_fun(X30025,tc_HOL_Obool)),X30022),X30021))) ) ),
    inference(distribute,[status(thm)],[inference(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_6486,plain,
    ! [X27421,X27422,X27423,X27424,X27425,X27426] : hAPP(c_Set_Ovimage(X27426,tc_prod(X27425,X27424),X27423),hAPP(hAPP(c_Product__Type_OSigma(X27425,X27424),X27422),hAPP(c_COMBK(tc_fun(X27424,tc_HOL_Obool),X27425),X27421))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27426,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X27426,X27425,hAPP(c_Fun_Ocomp(tc_prod(X27425,X27424),X27425,X27426,c_Product__Type_Ofst(X27425,X27424)),X27423)),X27422)),hAPP(c_Set_Ovimage(X27426,X27424,hAPP(c_Fun_Ocomp(tc_prod(X27425,X27424),X27424,X27426,c_Product__Type_Osnd(X27425,X27424)),X27423)),X27421)),
    inference(variable_rename,[status(thm)],[fact_vimage__Times]) ).

fof(i_0_6487,plain,
    ! [X33545,X33546] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X33546)),X33545) = c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(X33546,tc_Lazy__Sequence_Olazy__sequence(X33546)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(X33546,tc_Lazy__Sequence_Olazy__sequence(X33546),tc_Nat_Onat),hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X33546),tc_Nat_Onat),X33546),hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(X33546),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(X33546)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X33546)))),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(c_Lazy__Sequence_Oyield(X33546),X33545)),
    inference(variable_rename,[status(thm)],[fact_size__code]) ).

fof(i_0_6488,plain,
    ! [X22517,X22518,X22519,X22520,X22521,X22522,X22523,X22524] :
      ( ( X22522 = X22520
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X22524,X22524)),hAPP(hAPP(c_Product__Type_OPair(X22524,X22524),X22522),X22520)),X22518))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X22524,X22523),tc_prod(X22524,X22523))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X22524,X22523),tc_prod(X22524,X22523)),hAPP(hAPP(c_Product__Type_OPair(X22524,X22523),X22522),X22521)),hAPP(hAPP(c_Product__Type_OPair(X22524,X22523),X22520),X22519))),c_Wellfounded_Olex__prod(X22524,X22523,X22518,X22517))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X22523,X22523)),hAPP(hAPP(c_Product__Type_OPair(X22523,X22523),X22521),X22519)),X22517))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X22524,X22524)),hAPP(hAPP(c_Product__Type_OPair(X22524,X22524),X22522),X22520)),X22518))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X22524,X22523),tc_prod(X22524,X22523))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X22524,X22523),tc_prod(X22524,X22523)),hAPP(hAPP(c_Product__Type_OPair(X22524,X22523),X22522),X22521)),hAPP(hAPP(c_Product__Type_OPair(X22524,X22523),X22520),X22519))),c_Wellfounded_Olex__prod(X22524,X22523,X22518,X22517))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X22524,X22524)),hAPP(hAPP(c_Product__Type_OPair(X22524,X22524),X22522),X22520)),X22518))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X22524,X22523),tc_prod(X22524,X22523))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X22524,X22523),tc_prod(X22524,X22523)),hAPP(hAPP(c_Product__Type_OPair(X22524,X22523),X22522),X22521)),hAPP(hAPP(c_Product__Type_OPair(X22524,X22523),X22520),X22519))),c_Wellfounded_Olex__prod(X22524,X22523,X22518,X22517))) )
      & ( X22522 != X22520
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X22523,X22523)),hAPP(hAPP(c_Product__Type_OPair(X22523,X22523),X22521),X22519)),X22517))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X22524,X22523),tc_prod(X22524,X22523))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X22524,X22523),tc_prod(X22524,X22523)),hAPP(hAPP(c_Product__Type_OPair(X22524,X22523),X22522),X22521)),hAPP(hAPP(c_Product__Type_OPair(X22524,X22523),X22520),X22519))),c_Wellfounded_Olex__prod(X22524,X22523,X22518,X22517))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__lex__prod])])]) ).

fof(i_0_6489,plain,
    ! [X30217,X30218,X30219,X30220,X30221,X30222,X30223,X30224,X30225,X30226,X30227] :
      ( ( ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30221,tc_fun(X30220,tc_HOL_Obool)),X30219),X30218),X30217))
        | ~ hBOOL(hAPP(hAPP(c_member(X30221),X30222),X30219))
        | hBOOL(hAPP(hAPP(X30218,X30222),X30217)) )
      & ( hBOOL(hAPP(hAPP(c_member(X30227),esk357_5(X30223,X30224,X30225,X30226,X30227)),X30225))
        | hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30227,tc_fun(X30226,tc_HOL_Obool)),X30225),X30224),X30223)) )
      & ( ~ hBOOL(hAPP(hAPP(X30224,esk357_5(X30223,X30224,X30225,X30226,X30227)),X30223))
        | hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30227,tc_fun(X30226,tc_HOL_Obool)),X30225),X30224),X30223)) ) ),
    inference(distribute,[status(thm)],[inference(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_6490,plain,
    ! [X27786,X27787] : 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),X27787)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X27786))))),
    inference(variable_rename,[status(thm)],[fact_finite__M__bounded__by__nat]) ).

fof(i_0_6491,plain,
    ! [X20181,X20182,X20183] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20183))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20182),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20181),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),X20181),X20182))),c_Groups_Oone__class_Oone(tc_Int_Oint))),X20183)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_incr__lemma])]) ).

fof(i_0_6492,plain,
    ! [X29830,X29831,X29832,X29833,X29834,X29835] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X29834),X29833),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29832,X29834),X29831),X29830)))
        | ~ hBOOL(hAPP(hAPP(c_member(X29832),X29835),X29831))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X29834),X29833),hAPP(X29830,X29835)))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X29834) )
      & ( hBOOL(hAPP(hAPP(c_member(X29832),esk352_5(X29830,X29831,X29832,X29833,X29834)),X29831))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X29834),X29833),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29832,X29834),X29831),X29830)))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X29834) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X29834),X29833),hAPP(X29830,esk352_5(X29830,X29831,X29832,X29833,X29834))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X29834),X29833),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29832,X29834),X29831),X29830)))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X29834) ) ),
    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_6493,plain,
    ! [X32106,X32107,X32108,X32109,X32110] :
      ( ( hBOOL(hAPP(hAPP(c_member(X32109),esk435_5(X32106,X32107,X32108,X32109,X32110)),hAPP(c_List_Oset(X32109),X32108)))
        | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32109,X32110,X32107),X32106),X32108) = hAPP(hAPP(c_List_Olist_OCons(X32109),X32106),X32108)
        | ~ class_Orderings_Olinorder(X32110) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X32110),hAPP(X32107,X32106)),hAPP(X32107,esk435_5(X32106,X32107,X32108,X32109,X32110))))
        | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32109,X32110,X32107),X32106),X32108) = hAPP(hAPP(c_List_Olist_OCons(X32109),X32106),X32108)
        | ~ class_Orderings_Olinorder(X32110) ) ),
    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_6494,plain,
    ! [X26582,X26583,X26584,X26585,X26586] :
      ( ( hBOOL(hAPP(hAPP(c_member(X26585),esk240_5(X26582,X26583,X26584,X26585,X26586)),X26584))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26585,X26586),X26583),X26584) != c_Groups_Ozero__class_Ozero(X26586)
        | ~ hBOOL(hAPP(hAPP(c_member(X26585),X26582),X26584))
        | hAPP(X26583,X26582) = c_Groups_Ozero__class_Ozero(X26586)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26585),X26584))
        | ~ class_Groups_Oordered__ab__group__add(X26586) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26586),c_Groups_Ozero__class_Ozero(X26586)),hAPP(X26583,esk240_5(X26582,X26583,X26584,X26585,X26586))))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26585,X26586),X26583),X26584) != c_Groups_Ozero__class_Ozero(X26586)
        | ~ hBOOL(hAPP(hAPP(c_member(X26585),X26582),X26584))
        | hAPP(X26583,X26582) = c_Groups_Ozero__class_Ozero(X26586)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26585),X26584))
        | ~ class_Groups_Oordered__ab__group__add(X26586) ) ),
    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_6495,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_5384]) ).

fof(i_0_6496,plain,
    ! [X34049,X34050,X34051,X34052,X34053] : hAPP(c_Hilbert__Choice_Oinv__into(X34053,X34052,X34051,X34050),X34049) = c_Hilbert__Choice_OEps(X34053,hAPP(hAPP(c_COMBS(X34053,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X34053),c_fconj),hAPP(hAPP(c_COMBC(X34053,tc_fun(X34053,tc_HOL_Obool),tc_HOL_Obool),c_member(X34053)),X34051))),hAPP(hAPP(c_COMBC(X34053,X34052,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X34052,tc_fun(X34052,tc_HOL_Obool),X34053),c_fequal),X34050)),X34049))),
    inference(variable_rename,[status(thm)],[fact_inv__into__def]) ).

fof(i_0_6497,plain,
    ! [X27033,X27034,X27035,X27036,X27037] : hAPP(c_Fun_Othe__inv__into(X27037,X27036,X27035,X27034),X27033) = c_HOL_OThe(X27037,hAPP(hAPP(c_COMBS(X27037,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27037),c_fconj),hAPP(hAPP(c_COMBC(X27037,tc_fun(X27037,tc_HOL_Obool),tc_HOL_Obool),c_member(X27037)),X27035))),hAPP(hAPP(c_COMBC(X27037,X27036,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X27036,tc_fun(X27036,tc_HOL_Obool),X27037),c_fequal),X27034)),X27033))),
    inference(variable_rename,[status(thm)],[fact_the__inv__into__def]) ).

cnf(i_0_6498,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_5385]) ).

fof(i_0_6499,plain,
    ! [X28563,X28564,X28565,X28566] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X28566,X28566)),hAPP(hAPP(c_Product__Type_OPair(X28566,X28566),esk309_4(X28563,X28564,X28565,X28566)),esk310_4(X28563,X28564,X28565,X28566))),X28563))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28566),tc_List_Olist(X28566))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28566),tc_List_Olist(X28566)),X28565),X28564)),c_List_Olistrel1(X28566,X28563))) )
      & ( X28565 = hAPP(hAPP(c_List_Oappend(X28566),esk311_4(X28563,X28564,X28565,X28566)),hAPP(hAPP(c_List_Olist_OCons(X28566),esk309_4(X28563,X28564,X28565,X28566)),esk312_4(X28563,X28564,X28565,X28566)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28566),tc_List_Olist(X28566))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28566),tc_List_Olist(X28566)),X28565),X28564)),c_List_Olistrel1(X28566,X28563))) )
      & ( X28564 = hAPP(hAPP(c_List_Oappend(X28566),esk311_4(X28563,X28564,X28565,X28566)),hAPP(hAPP(c_List_Olist_OCons(X28566),esk310_4(X28563,X28564,X28565,X28566)),esk312_4(X28563,X28564,X28565,X28566)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28566),tc_List_Olist(X28566))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28566),tc_List_Olist(X28566)),X28565),X28564)),c_List_Olistrel1(X28566,X28563))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel1E])])])]) ).

fof(i_0_6500,plain,
    ! [X32973,X32974,X32975,X32976,X32977,X32978,X32979] :
      ( ~ c_Finite__Set_Ofun__left__comm(X32979,X32978,X32977)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X32979,X32978,X32977,X32976,X32975),X32974))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X32979,X32978,X32977,X32976,X32975),X32973))
      | X32973 = X32974 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__graph__determ])]) ).

fof(i_0_6501,plain,
    ! [X29690,X29691,X29692,X29693,X29694] :
      ( ~ class_Groups_Oab__group__add(X29694)
      | hAPP(c_List_Omonoid__add__class_Olistsum(X29694),hAPP(hAPP(c_List_Omap(X29693,X29694),hAPP(hAPP(c_COMBS(X29693,X29694,X29694),hAPP(hAPP(c_COMBB(X29694,tc_fun(X29694,X29694),X29693),c_Groups_Ominus__class_Ominus(X29694)),X29692)),X29691)),X29690)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X29694),hAPP(c_List_Omonoid__add__class_Olistsum(X29694),hAPP(hAPP(c_List_Omap(X29693,X29694),X29692),X29690))),hAPP(c_List_Omonoid__add__class_Olistsum(X29694),hAPP(hAPP(c_List_Omap(X29693,X29694),X29691),X29690))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__subtractf])]) ).

fof(i_0_6502,plain,
    ! [X29708,X29709,X29710,X29711,X29712] :
      ( ~ class_Groups_Ocomm__monoid__add(X29712)
      | hAPP(c_List_Omonoid__add__class_Olistsum(X29712),hAPP(hAPP(c_List_Omap(X29711,X29712),hAPP(hAPP(c_COMBS(X29711,X29712,X29712),hAPP(hAPP(c_COMBB(X29712,tc_fun(X29712,X29712),X29711),c_Groups_Oplus__class_Oplus(X29712)),X29710)),X29709)),X29708)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X29712),hAPP(c_List_Omonoid__add__class_Olistsum(X29712),hAPP(hAPP(c_List_Omap(X29711,X29712),X29710),X29708))),hAPP(c_List_Omonoid__add__class_Olistsum(X29712),hAPP(hAPP(c_List_Omap(X29711,X29712),X29709),X29708))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__addf])]) ).

fof(i_0_6503,plain,
    ! [X25528,X25529,X25530,X25531] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X25531,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25530,tc_fun(tc_fun(X25531,tc_HOL_Obool),tc_HOL_Obool)),X25529),hAPP(hAPP(c_COMBB(tc_fun(X25531,tc_HOL_Obool),tc_fun(tc_fun(X25531,tc_HOL_Obool),tc_HOL_Obool),X25530),c_Set_OPow(X25531)),X25528))),hAPP(c_Set_OPow(X25531),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25530,tc_fun(X25531,tc_HOL_Obool)),X25529),X25528)))),
    inference(variable_rename,[status(thm)],[fact_UN__Pow__subset]) ).

fof(i_0_6504,plain,
    ! [X20114,X20115,X20116,X20117,X20118] :
      ( ( ~ 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),X20117),X20116)),X20115)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20118),X20116)),X20114)))
        | 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),X20117),X20118)),X20116)),X20115)),X20114))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20118),X20117)) )
      & ( ~ 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),X20117),X20118)),X20116)),X20115)),X20114))
        | 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),X20117),X20116)),X20115)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20118),X20116)),X20114)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20118),X20117)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__le__add__iff1])])]) ).

fof(i_0_6505,plain,
    ! [X20156,X20157,X20158,X20159,X20160] :
      ( ( ~ 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),X20159),X20158)),X20157)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20160),X20158)),X20156)))
        | 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),X20159),X20160)),X20158)),X20157)),X20156))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20160),X20159)) )
      & ( ~ 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),X20159),X20160)),X20158)),X20157)),X20156))
        | 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),X20159),X20158)),X20157)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20160),X20158)),X20156)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20160),X20159)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__add__iff1])])]) ).

fof(i_0_6506,plain,
    ! [X29703,X29704,X29705,X29706,X29707] :
      ( ~ class_Rings_Osemiring__0(X29707)
      | hAPP(c_List_Omonoid__add__class_Olistsum(X29707),hAPP(hAPP(c_List_Omap(X29706,X29707),hAPP(hAPP(c_COMBC(X29706,X29707,X29707),hAPP(hAPP(c_COMBB(X29707,tc_fun(X29707,X29707),X29706),c_Groups_Otimes__class_Otimes(X29707)),X29705)),X29704)),X29703)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X29707),hAPP(c_List_Omonoid__add__class_Olistsum(X29707),hAPP(hAPP(c_List_Omap(X29706,X29707),X29705),X29703))),X29704) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__mult__const])]) ).

fof(i_0_6507,plain,
    ! [X27895] : c_Int_Oint__ge__less__than2(X27895) = 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),X27895)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
    inference(variable_rename,[status(thm)],[fact_int__ge__less__than2__def]) ).

fof(i_0_6508,plain,
    ! [X25278,X25279,X25280,X25281,X25282] :
      ( ( hBOOL(hAPP(hAPP(c_member(X25281),esk164_5(X25278,X25279,X25280,X25281,X25282)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25281,tc_HOL_Obool)),X25280),X25279)))
        | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X25282,X25281,c_Groups_Otimes__class_Otimes(X25282)),X25278),c_Groups_Oone__class_Oone(X25282)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25281,tc_HOL_Obool)),X25280),X25279)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25282),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X25282,X25281,c_Groups_Otimes__class_Otimes(X25282)),X25278),c_Groups_Oone__class_Oone(X25282)),X25280)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X25282,X25281,c_Groups_Otimes__class_Otimes(X25282)),X25278),c_Groups_Oone__class_Oone(X25282)),X25279))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25281),X25279))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25281),X25280))
        | ~ class_Groups_Ocomm__monoid__mult(X25282) )
      & ( hAPP(X25278,esk164_5(X25278,X25279,X25280,X25281,X25282)) != c_Groups_Oone__class_Oone(X25282)
        | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X25282,X25281,c_Groups_Otimes__class_Otimes(X25282)),X25278),c_Groups_Oone__class_Oone(X25282)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25281,tc_HOL_Obool)),X25280),X25279)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25282),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X25282,X25281,c_Groups_Otimes__class_Otimes(X25282)),X25278),c_Groups_Oone__class_Oone(X25282)),X25280)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X25282,X25281,c_Groups_Otimes__class_Otimes(X25282)),X25278),c_Groups_Oone__class_Oone(X25282)),X25279))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25281),X25279))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25281),X25280))
        | ~ class_Groups_Ocomm__monoid__mult(X25282) ) ),
    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_6509,plain,
    ! [X24004,X24005,X24006,X24007] :
      ( ( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24007,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X24007,tc_fun(X24007,tc_HOL_Obool),tc_HOL_Obool),c_member(X24007)),X24006)),hAPP(hAPP(c_COMBC(X24007,tc_fun(X24007,tc_HOL_Obool),tc_HOL_Obool),c_member(X24007)),X24005)),X24004))
        | hBOOL(hAPP(hAPP(c_member(X24007),X24004),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24007,tc_HOL_Obool)),X24006),X24005))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X24007),X24004),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24007,tc_HOL_Obool)),X24006),X24005)))
        | hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24007,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X24007,tc_fun(X24007,tc_HOL_Obool),tc_HOL_Obool),c_member(X24007)),X24006)),hAPP(hAPP(c_COMBC(X24007,tc_fun(X24007,tc_HOL_Obool),tc_HOL_Obool),c_member(X24007)),X24005)),X24004)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__Int__eq])]) ).

fof(i_0_6510,plain,
    ! [X23054,X23055,X23056,X23057] :
      ( ( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23057,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X23057,tc_fun(X23057,tc_HOL_Obool),tc_HOL_Obool),c_member(X23057)),X23056)),hAPP(hAPP(c_COMBC(X23057,tc_fun(X23057,tc_HOL_Obool),tc_HOL_Obool),c_member(X23057)),X23055)),X23054))
        | hBOOL(hAPP(hAPP(c_member(X23057),X23054),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23057,tc_HOL_Obool)),X23056),X23055))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X23057),X23054),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23057,tc_HOL_Obool)),X23056),X23055)))
        | hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23057,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X23057,tc_fun(X23057,tc_HOL_Obool),tc_HOL_Obool),c_member(X23057)),X23056)),hAPP(hAPP(c_COMBC(X23057,tc_fun(X23057,tc_HOL_Obool),tc_HOL_Obool),c_member(X23057)),X23055)),X23054)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__Un__eq])]) ).

fof(i_0_6511,plain,
    ! [X27734,X27735,X27736] : hAPP(hAPP(c_Set_Oinsert(X27736),X27735),hAPP(c_Set_OCollect(X27736),X27734)) = hAPP(c_Set_OCollect(X27736),hAPP(hAPP(c_COMBS(X27736,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27736),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X27736),c_fNot),hAPP(hAPP(c_COMBC(X27736,X27736,tc_HOL_Obool),c_fequal),X27735)))),X27734)),
    inference(variable_rename,[status(thm)],[fact_insert__Collect]) ).

cnf(i_0_6512,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_5386]) ).

fof(i_0_6513,plain,
    ! [X23710,X23711,X23712,X23713,X23714,X23715] :
      ( ~ c_Equiv__Relations_Oequiv(X23715,X23714,X23713)
      | ~ hBOOL(hAPP(hAPP(c_member(X23715),X23712),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23715,tc_HOL_Obool)),hAPP(c_Relation_OImage(X23715,X23715,X23713),hAPP(hAPP(c_Set_Oinsert(X23715),X23711),c_Orderings_Obot__class_Obot(tc_fun(X23715,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X23715,X23715,X23713),hAPP(hAPP(c_Set_Oinsert(X23715),X23710),c_Orderings_Obot__class_Obot(tc_fun(X23715,tc_HOL_Obool)))))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X23715,X23715)),hAPP(hAPP(c_Product__Type_OPair(X23715,X23715),X23711),X23710)),X23713)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__class__nondisjoint])]) ).

fof(i_0_6514,plain,
    ! [X31944,X31945] : c_List_Omeasures(X31945,X31944) = hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat),X31945),c_List_Olex(tc_Nat_Onat,c_Wellfounded_Oless__than)),hAPP(hAPP(c_COMBC(X31945,tc_List_Olist(tc_fun(X31945,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X31945,tc_Nat_Onat),tc_Nat_Onat),tc_fun(tc_List_Olist(tc_fun(X31945,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),X31945),c_List_Omap(tc_fun(X31945,tc_Nat_Onat),tc_Nat_Onat)),hAPP(c_COMBC(tc_fun(X31945,tc_Nat_Onat),X31945,tc_Nat_Onat),c_COMBI(tc_fun(X31945,tc_Nat_Onat))))),X31944)),
    inference(variable_rename,[status(thm)],[fact_measures__def]) ).

fof(i_0_6515,plain,
    ! [X21891,X21892,X21893,X21894,X21895,X21896,X21897] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X21897,X21896),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X21895),X21894)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X21893,X21896),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X21892),X21891)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X21896))
      | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21897),X21893),X21896),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),X21895),X21892)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21894),X21891)),X21896))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21894),X21891),X21896)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__nat__rel__add1__eq])]) ).

fof(i_0_6516,plain,
    ! [X33678,X33679,X33680,X33681] : c_Random__Sequence_Omap(X33681,X33680,X33679,X33678) = c_Random__Sequence_Obind(X33681,X33680,X33678,hAPP(c_Fun_Ocomp(X33680,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(X33680)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))))),X33681,c_Random__Sequence_Osingle(X33680)),X33679)),
    inference(variable_rename,[status(thm)],[fact_Random__Sequence_Omap__def]) ).

fof(i_0_6517,plain,
    ! [X24784,X24785,X24786,X24787,X24788] :
      ( ( hBOOL(hAPP(hAPP(c_member(X24787),esk144_5(X24784,X24785,X24786,X24787,X24788)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24787,tc_HOL_Obool)),X24786),X24785)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24787,X24788),X24784),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24787,tc_HOL_Obool)),X24786),X24785)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24788),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24788),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24787,X24788),X24784),X24786)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24787,X24788),X24784),X24785))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24787,X24788),X24784),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24787,tc_HOL_Obool)),X24786),X24785)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24787),X24785))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24787),X24786))
        | ~ class_Fields_Ofield(X24788) )
      & ( hAPP(X24784,esk144_5(X24784,X24785,X24786,X24787,X24788)) = c_Groups_Ozero__class_Ozero(X24788)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24787,X24788),X24784),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24787,tc_HOL_Obool)),X24786),X24785)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24788),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24788),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24787,X24788),X24784),X24786)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24787,X24788),X24784),X24785))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24787,X24788),X24784),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24787,tc_HOL_Obool)),X24786),X24785)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24787),X24785))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24787),X24786))
        | ~ class_Fields_Ofield(X24788) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__Un])])])]) ).

fof(i_0_6518,plain,
    ! [X22108,X22109,X22110,X22111,X22112,X22113,X22114] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22114,X22113),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22112),X22111)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22110,X22113),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22109),X22108)))
      | X22113 = 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),X22114),X22110),X22113),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),X22112),X22109)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X22111),X22108)),X22113))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X22111),X22108),X22113)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zadd1__lemma])]) ).

fof(i_0_6519,plain,
    ! [X27270,X27271,X27272,X27273,X27274,X27275] :
      ( ~ class_Groups_Ocomm__monoid__add(X27275)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27274,X27275),hAPP(hAPP(c_COMBC(X27274,tc_fun(X27273,tc_HOL_Obool),X27275),hAPP(hAPP(c_COMBB(tc_fun(X27273,X27275),tc_fun(tc_fun(X27273,tc_HOL_Obool),X27275),X27274),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27273,X27275)),X27272)),X27271)),X27270) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(X27274,X27273),X27275),hAPP(c_Product__Type_Oprod_Oprod__case(X27274,X27273,X27275),X27272)),hAPP(hAPP(c_Product__Type_OSigma(X27274,X27273),X27270),hAPP(c_COMBK(tc_fun(X27273,tc_HOL_Obool),X27274),X27271))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__cartesian__product])]) ).

fof(i_0_6520,plain,
    ! [X27289,X27290,X27291,X27292,X27293,X27294] :
      ( ~ class_Groups_Ocomm__monoid__mult(X27294)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27293,X27294),hAPP(hAPP(c_COMBC(X27293,tc_fun(X27292,tc_HOL_Obool),X27294),hAPP(hAPP(c_COMBB(tc_fun(X27292,X27294),tc_fun(tc_fun(X27292,tc_HOL_Obool),X27294),X27293),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27292,X27294)),X27291)),X27290)),X27289) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(X27293,X27292),X27294),hAPP(c_Product__Type_Oprod_Oprod__case(X27293,X27292,X27294),X27291)),hAPP(hAPP(c_Product__Type_OSigma(X27293,X27292),X27289),hAPP(c_COMBK(tc_fun(X27292,tc_HOL_Obool),X27293),X27290))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__cartesian__product])]) ).

fof(i_0_6521,plain,
    ! [X33116,X33117,X33118,X33119] :
      ( ( X33117 = hAPP(hAPP(c_Product__Type_OPair(X33119,X33118),esk501_4(X33116,X33117,X33118,X33119)),esk500_4(X33116,X33117,X33118,X33119))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X33119,X33118)),X33117),hAPP(c_Relation_Oconverse(X33118,X33119),X33116))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X33118,X33119)),hAPP(hAPP(c_Product__Type_OPair(X33118,X33119),esk500_4(X33116,X33117,X33118,X33119)),esk501_4(X33116,X33117,X33118,X33119))),X33116))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X33119,X33118)),X33117),hAPP(c_Relation_Oconverse(X33118,X33119),X33116))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5387])])])]) ).

fof(i_0_6522,plain,
    ! [X27491,X27492,X27493,X27494,X27495,X27496,X27497,X27498] :
      ( ~ c_Fun_Oinj__on(X27498,X27497,X27496,X27495)
      | ~ c_Fun_Oinj__on(X27494,X27493,X27492,X27491)
      | c_Fun_Oinj__on(tc_prod(X27498,X27494),tc_prod(X27497,X27493),c_Product__Type_Omap__pair(X27498,X27497,X27494,X27493,X27496,X27492),hAPP(hAPP(c_Product__Type_OSigma(X27498,X27494),X27495),hAPP(c_COMBK(tc_fun(X27494,tc_HOL_Obool),X27498),X27491))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__pair__inj__on])]) ).

fof(i_0_6523,plain,
    ! [X21865,X21866,X21867,X21868,X21869] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X21869,X21868),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X21867),X21866)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X21868))
      | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21865),X21869),X21868),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),X21865),X21867)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21865),X21866)),X21868))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21865),X21866),X21868)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__nat__rel__mult1__eq])]) ).

fof(i_0_6524,plain,
    ! [X17861,X17862,X17863,X17864] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17864),hAPP(X17863,X17862)),hAPP(X17863,X17861)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17862),X17861))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17864),hAPP(X17863,esk30_4(X17861,X17862,X17863,X17864))),hAPP(X17863,hAPP(c_Nat_OSuc,esk30_4(X17861,X17862,X17863,X17864)))))
        | ~ class_Orderings_Oorder(X17864) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17862),X17861))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17864),hAPP(X17863,X17862)),hAPP(X17863,X17861)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17864),hAPP(X17863,esk30_4(X17861,X17862,X17863,X17864))),hAPP(X17863,hAPP(c_Nat_OSuc,esk30_4(X17861,X17862,X17863,X17864)))))
        | ~ class_Orderings_Oorder(X17864) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lift__Suc__mono__less__iff])])])]) ).

fof(i_0_6525,plain,
    ! [X17856,X17857,X17858,X17859] :
      ( ~ class_Orderings_Oorder(X17859)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17859),hAPP(X17858,esk29_4(X17856,X17857,X17858,X17859))),hAPP(X17858,hAPP(c_Nat_OSuc,esk29_4(X17856,X17857,X17858,X17859)))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17857),X17856))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17859),hAPP(X17858,X17857)),hAPP(X17858,X17856))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lift__Suc__mono__less])])]) ).

fof(i_0_6526,plain,
    ! [X22125,X22126,X22127,X22128,X22129] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22129,X22128),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22127),X22126)))
      | X22128 = 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),X22125),X22129),X22128),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),X22125),X22127)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22125),X22126)),X22128))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22125),X22126),X22128)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult1__lemma])]) ).

fof(i_0_6527,plain,
    ! [X33380,X33381,X33382,X33383] : c_Lazy__Sequence_Oproduct(X33383,X33382,X33381,X33380) = hAPP(c_Lazy__Sequence_Obind(X33383,tc_prod(X33383,X33382),X33381),hAPP(hAPP(c_COMBB(tc_fun(X33382,tc_Lazy__Sequence_Olazy__sequence(tc_prod(X33383,X33382))),tc_Lazy__Sequence_Olazy__sequence(tc_prod(X33383,X33382)),X33383),c_Lazy__Sequence_Obind(X33382,tc_prod(X33383,X33382),X33380)),hAPP(hAPP(c_COMBB(tc_fun(X33382,tc_prod(X33383,X33382)),tc_fun(X33382,tc_Lazy__Sequence_Olazy__sequence(tc_prod(X33383,X33382))),X33383),hAPP(c_COMBB(tc_prod(X33383,X33382),tc_Lazy__Sequence_Olazy__sequence(tc_prod(X33383,X33382)),X33382),c_Lazy__Sequence_Osingle(tc_prod(X33383,X33382)))),c_Product__Type_OPair(X33383,X33382)))),
    inference(variable_rename,[status(thm)],[fact_]) ).

fof(i_0_6528,plain,
    ! [X26450,X26451,X26452,X26453] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X26452),X26451))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26453),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X26453,X26453),hAPP(hAPP(c_COMBB(X26453,tc_fun(X26453,X26453),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(X26453)),X26450)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X26453,tc_Nat_Onat),X26450),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,X26452,X26451)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X26453),hAPP(X26450,X26452)),hAPP(X26450,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26451),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | ~ class_Groups_Oab__group__add(X26453) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X26452),X26451))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26453),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X26453,X26453),hAPP(hAPP(c_COMBB(X26453,tc_fun(X26453,X26453),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(X26453)),X26450)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X26453,tc_Nat_Onat),X26450),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,X26452,X26451)) = c_Groups_Ozero__class_Ozero(X26453)
        | ~ class_Groups_Oab__group__add(X26453) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5388])])]) ).

fof(i_0_6529,plain,
    ! [X27442,X27443,X27444,X27445] :
      ( c_Fun_Oinj__on(X27445,tc_prod(X27444,X27445),esk275_4(X27442,X27443,X27444,X27445),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27444,tc_fun(X27445,tc_HOL_Obool)),X27443),X27442))
      & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27444,X27445),tc_HOL_Obool)),hAPP(c_Set_Oimage(X27445,tc_prod(X27444,X27445),esk275_4(X27442,X27443,X27444,X27445)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27444,tc_fun(X27445,tc_HOL_Obool)),X27443),X27442))),hAPP(hAPP(c_Product__Type_OSigma(X27444,X27445),X27443),X27442))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[fact_Ex__inj__on__UNION__Sigma])]) ).

fof(i_0_6530,plain,
    ! [X26820,X26821,X26822,X26823,X26824] :
      ( ~ class_Groups_Oab__semigroup__mult(X26824)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X26824,X26824,c_Groups_Otimes__class_Otimes(X26824),X26823,X26822),X26821))
      | hBOOL(hAPP(hAPP(c_member(X26824),X26823),X26822))
      | hBOOL(hAPP(c_Finite__Set_Ofold__graph(X26824,X26824,c_Groups_Otimes__class_Otimes(X26824),X26820,hAPP(hAPP(c_Set_Oinsert(X26824),X26823),X26822)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26824),X26820),X26821))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5389])]) ).

fof(i_0_6531,plain,
    ! [X31270,X31271,X31272,X31273] : hAPP(hAPP(c_List_Omap(tc_prod(X31273,tc_Nat_Onat),X31273),c_Product__Type_Ofst(X31273,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X31273,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(X31273,tc_Nat_Onat)),X31272),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(X31273,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(X31273,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(X31273,tc_Nat_Onat),X31271),X31270))) = hAPP(hAPP(c_List_Omap(tc_prod(X31273,tc_Nat_Onat),X31273),c_Product__Type_Ofst(X31273,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X31273,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(X31273,tc_Nat_Onat)),X31272),c_Product__Type_Osnd(X31273,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(X31273,tc_Nat_Onat),X31271),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),X31270)))),
    inference(variable_rename,[status(thm)],[fact_sublist__shift__lemma__Suc]) ).

fof(i_0_6532,plain,
    ! [X27539,X27540,X27541,X27542,X27543,X27544] : hAPP(c_Fun_Ocomp(tc_prod(X27544,X27543),X27544,tc_prod(X27542,X27541),c_Product__Type_Ofst(X27544,X27543)),c_Product__Type_Omap__pair(X27542,X27544,X27541,X27543,X27540,X27539)) = hAPP(c_Fun_Ocomp(X27542,X27544,tc_prod(X27542,X27541),X27540),c_Product__Type_Ofst(X27542,X27541)),
    inference(variable_rename,[status(thm)],[fact_fst__comp__map__pair]) ).

fof(i_0_6533,plain,
    ! [X27533,X27534,X27535,X27536,X27537,X27538] : hAPP(c_Fun_Ocomp(tc_prod(X27538,X27537),X27537,tc_prod(X27536,X27535),c_Product__Type_Osnd(X27538,X27537)),c_Product__Type_Omap__pair(X27536,X27538,X27535,X27537,X27534,X27533)) = hAPP(c_Fun_Ocomp(X27535,X27537,tc_prod(X27536,X27535),X27533),c_Product__Type_Osnd(X27536,X27535)),
    inference(variable_rename,[status(thm)],[fact_snd__comp__map__pair]) ).

fof(i_0_6534,plain,
    ! [X30009,X30010,X30011,X30012,X30013,X30014] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30014,tc_fun(X30013,tc_HOL_Obool)),X30012),hAPP(hAPP(c_COMBC(X30014,tc_fun(X30011,tc_fun(X30013,tc_HOL_Obool)),tc_fun(X30013,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X30011,tc_HOL_Obool),tc_fun(tc_fun(X30011,tc_fun(X30013,tc_HOL_Obool)),tc_fun(X30013,tc_HOL_Obool)),X30014),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30011,tc_fun(X30013,tc_HOL_Obool))),X30010)),X30009)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30011,tc_fun(X30013,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X30014,tc_fun(X30011,tc_HOL_Obool)),X30012),X30010)),X30009),
    inference(variable_rename,[status(thm)],[fact_INT__extend__simps_I9_J]) ).

fof(i_0_6535,plain,
    ! [X24989,X24990,X24991,X24992,X24993,X24994] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24994,tc_fun(X24993,tc_HOL_Obool)),X24992),hAPP(hAPP(c_COMBC(X24994,tc_fun(X24991,tc_fun(X24993,tc_HOL_Obool)),tc_fun(X24993,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X24991,tc_HOL_Obool),tc_fun(tc_fun(X24991,tc_fun(X24993,tc_HOL_Obool)),tc_fun(X24993,tc_HOL_Obool)),X24994),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24991,tc_fun(X24993,tc_HOL_Obool))),X24990)),X24989)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24991,tc_fun(X24993,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24994,tc_fun(X24991,tc_HOL_Obool)),X24992),X24990)),X24989),
    inference(variable_rename,[status(thm)],[fact_UN__extend__simps_I9_J]) ).

fof(i_0_6536,plain,
    ! [X30003,X30004,X30005,X30006,X30007,X30008] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30008,tc_fun(X30007,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X30006,tc_fun(X30008,tc_HOL_Obool)),X30005),X30004)),X30003) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30006,tc_fun(X30007,tc_HOL_Obool)),X30005),hAPP(hAPP(c_COMBC(X30006,tc_fun(X30008,tc_fun(X30007,tc_HOL_Obool)),tc_fun(X30007,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X30008,tc_HOL_Obool),tc_fun(tc_fun(X30008,tc_fun(X30007,tc_HOL_Obool)),tc_fun(X30007,tc_HOL_Obool)),X30006),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30008,tc_fun(X30007,tc_HOL_Obool))),X30004)),X30003)),
    inference(variable_rename,[status(thm)],[fact_INT__simps_I9_J]) ).

fof(i_0_6537,plain,
    ! [X24983,X24984,X24985,X24986,X24987,X24988] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24988,tc_fun(X24987,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24986,tc_fun(X24988,tc_HOL_Obool)),X24985),X24984)),X24983) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24986,tc_fun(X24987,tc_HOL_Obool)),X24985),hAPP(hAPP(c_COMBC(X24986,tc_fun(X24988,tc_fun(X24987,tc_HOL_Obool)),tc_fun(X24987,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X24988,tc_HOL_Obool),tc_fun(tc_fun(X24988,tc_fun(X24987,tc_HOL_Obool)),tc_fun(X24987,tc_HOL_Obool)),X24986),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24988,tc_fun(X24987,tc_HOL_Obool))),X24984)),X24983)),
    inference(variable_rename,[status(thm)],[fact_UN__simps_I9_J]) ).

fof(i_0_6538,plain,
    ! [X24977,X24978,X24979,X24980,X24981,X24982] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24982,tc_fun(X24981,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24980,tc_fun(X24982,tc_HOL_Obool)),X24979),X24978)),X24977) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24980,tc_fun(X24981,tc_HOL_Obool)),X24979),hAPP(hAPP(c_COMBC(X24980,tc_fun(X24982,tc_fun(X24981,tc_HOL_Obool)),tc_fun(X24981,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X24982,tc_HOL_Obool),tc_fun(tc_fun(X24982,tc_fun(X24981,tc_HOL_Obool)),tc_fun(X24981,tc_HOL_Obool)),X24980),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24982,tc_fun(X24981,tc_HOL_Obool))),X24978)),X24977)),
    inference(variable_rename,[status(thm)],[fact_UN__UN__flatten]) ).

fof(i_0_6539,plain,
    ! [X26751,X26752,X26753,X26754,X26755,X26756,X26757] :
      ( hBOOL(hAPP(hAPP(c_member(X26757),X26756),X26755))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X26757,X26754,X26753,X26752,X26755),X26751))
      | hBOOL(hAPP(c_Finite__Set_Ofold__graph(X26757,X26754,X26753,X26752,hAPP(hAPP(c_Set_Oinsert(X26757),X26756),X26755)),hAPP(hAPP(X26753,X26756),X26751))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5390])]) ).

fof(i_0_6540,plain,
    ! [X33232,X33233] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk513_2(X33232,X33233)),hAPP(X33233,esk513_2(X33232,X33233))))
      | 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)),X33233)),X33232)))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__less__ub])])]) ).

fof(i_0_6541,plain,
    ! [X24995,X24996,X24997,X24998,X24999,X25000,X25001,X25002,X25003,X25004] :
      ( ~ c_Equiv__Relations_Ocongruent2(X25004,X25003,X25002,X25001,X25000,X24999)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X25004,X25004)),hAPP(hAPP(c_Product__Type_OPair(X25004,X25004),X24998),X24997)),X25001))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X25003,X25003)),hAPP(hAPP(c_Product__Type_OPair(X25003,X25003),X24996),X24995)),X25000))
      | hAPP(hAPP(X24999,X24998),X24996) = hAPP(hAPP(X24999,X24997),X24995) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_congruent2D])]) ).

fof(i_0_6542,plain,
    ! [X33106,X33107,X33108,X33109,X33110] :
      ( ( hBOOL(hAPP(hAPP(c_member(X33110),esk498_5(X33106,X33107,X33108,X33109,X33110)),X33109))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X33110,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X33110,tc_HOL_Obool)),X33109),hAPP(c_Set_OCollect(X33110),X33107))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X33110,tc_HOL_Obool)),X33108),hAPP(c_Set_OCollect(X33110),X33106))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X33110,tc_HOL_Obool)),X33109),X33108)) )
      & ( hBOOL(hAPP(X33107,esk498_5(X33106,X33107,X33108,X33109,X33110)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X33110,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X33110,tc_HOL_Obool)),X33109),hAPP(c_Set_OCollect(X33110),X33107))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X33110,tc_HOL_Obool)),X33108),hAPP(c_Set_OCollect(X33110),X33106))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X33110,tc_HOL_Obool)),X33109),X33108)) )
      & ( ~ hBOOL(hAPP(X33106,esk498_5(X33106,X33107,X33108,X33109,X33110)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X33110,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X33110,tc_HOL_Obool)),X33109),hAPP(c_Set_OCollect(X33110),X33107))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X33110,tc_HOL_Obool)),X33108),hAPP(c_Set_OCollect(X33110),X33106))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X33110,tc_HOL_Obool)),X33109),X33108)) ) ),
    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_6543,plain,
    ! [X26874,X26875,X26876] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26876,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X26876,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk252_3(X26874,X26875,X26876))),X26875)),X26874))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26876,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X26876,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X26875)),X26874)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__finite__subset])])]) ).

fof(i_0_6544,plain,
    ! [X27769,X27770,X27771] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27771,tc_HOL_Obool)),X27770),X27769) = hAPP(c_Set_OCollect(X27771),hAPP(hAPP(c_COMBS(X27771,tc_HOL_Obool,tc_HOL_Obool),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_COMBB(tc_HOL_Obool,tc_HOL_Obool,X27771),c_fNot),hAPP(hAPP(c_COMBC(X27771,tc_fun(X27771,tc_HOL_Obool),tc_HOL_Obool),c_member(X27771)),X27769)))),
    inference(variable_rename,[status(thm)],[fact_set__diff__eq]) ).

fof(i_0_6545,plain,
    ! [X27685,X27686,X27687] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27687),hAPP(c_Set_OCollect(X27687),X27686)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X27687),hAPP(c_Set_OCollect(X27687),hAPP(hAPP(c_COMBS(X27687,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27687),c_fconj),X27686)),X27685)))) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27687),hAPP(c_Set_OCollect(X27687),X27685)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X27687),hAPP(c_Set_OCollect(X27687),hAPP(hAPP(c_COMBS(X27687,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27687),c_fconj),X27686)),X27685)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Collect__conjI])])]) ).

fof(i_0_6546,plain,
    ! [X26825,X26826] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X26826,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(X26826,tc_HOL_Obool)),tc_fun(X26826,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_fun(X26826,tc_HOL_Obool)),tc_fun(X26826,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X26826,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),X26825)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X26826,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X26825),
    inference(variable_rename,[status(thm)],[fact_UN__UN__finite__eq]) ).

cnf(i_0_6547,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk460_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_5391]) ).

cnf(i_0_6548,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk459_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_5392]) ).

fof(i_0_6549,plain,
    ! [X27515,X27516,X27517,X27518,X27519,X27520,X27521,X27522] : hAPP(c_Product__Type_Omap__pair(X27522,X27521,X27520,X27519,X27518,X27517),hAPP(hAPP(c_Product__Type_OPair(X27522,X27520),X27516),X27515)) = hAPP(hAPP(c_Product__Type_OPair(X27521,X27519),hAPP(X27518,X27516)),hAPP(X27517,X27515)),
    inference(variable_rename,[status(thm)],[fact_map__pair__simp]) ).

cnf(i_0_6550,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_5393]) ).

cnf(i_0_6551,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_5394]) ).

fof(i_0_6552,plain,
    ! [X30751,X30752,X30753,X30754,X30755] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30755,X30754)),esk366_5(X30751,X30752,X30753,X30754,X30755)),hAPP(c_List_Oset(tc_prod(X30755,X30754)),hAPP(hAPP(c_List_Ozip(X30755,X30754),X30753),X30752))))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30755)),X30753) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30754)),X30752)
        | c_List_Olist__all2(X30755,X30754,X30751,X30753,X30752) )
      & ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X30755,X30754,tc_HOL_Obool),X30751),esk366_5(X30751,X30752,X30753,X30754,X30755)))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30755)),X30753) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30754)),X30752)
        | c_List_Olist__all2(X30755,X30754,X30751,X30753,X30752) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2I])])])]) ).

fof(i_0_6553,plain,
    ! [X30610,X30611,X30612,X30613,X30614,X30615,X30616,X30617,X30618,X30619,X30620] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30614)),X30611) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30613)),X30610)
        | ~ c_List_Olist__all2(X30614,X30613,X30612,X30611,X30610) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30614,X30613)),X30615),hAPP(c_List_Oset(tc_prod(X30614,X30613)),hAPP(hAPP(c_List_Ozip(X30614,X30613),X30611),X30610))))
        | hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X30614,X30613,tc_HOL_Obool),X30612),X30615))
        | ~ c_List_Olist__all2(X30614,X30613,X30612,X30611,X30610) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30620,X30619)),esk364_5(X30616,X30617,X30618,X30619,X30620)),hAPP(c_List_Oset(tc_prod(X30620,X30619)),hAPP(hAPP(c_List_Ozip(X30620,X30619),X30617),X30616))))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30620)),X30617) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30619)),X30616)
        | c_List_Olist__all2(X30620,X30619,X30618,X30617,X30616) )
      & ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X30620,X30619,tc_HOL_Obool),X30618),esk364_5(X30616,X30617,X30618,X30619,X30620)))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30620)),X30617) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30619)),X30616)
        | c_List_Olist__all2(X30620,X30619,X30618,X30617,X30616) ) ),
    inference(distribute,[status(thm)],[inference(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_6554,plain,
    ! [X27523,X27524,X27525] : hAPP(c_Product__Type_Omap__pair(X27525,X27525,X27524,X27524,c_COMBI(X27525),c_COMBI(X27524)),X27523) = X27523,
    inference(variable_rename,[status(thm)],[fact_map__pair__ident]) ).

fof(i_0_6555,plain,
    ! [X24107,X24108,X24109,X24110,X24111,X24112,X24113,X24114] :
      ( ~ c_Finite__Set_Ofolding__image__simple(X24114,X24113,X24112,X24111,X24110,X24109)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24113),X24108))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24113),X24107))
      | hAPP(hAPP(X24112,hAPP(X24109,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24113,tc_HOL_Obool)),X24108),X24107))),hAPP(X24109,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24113,tc_HOL_Obool)),X24108),X24107))) = hAPP(hAPP(X24112,hAPP(X24109,X24108)),hAPP(X24109,X24107)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Ounion__inter])]) ).

fof(i_0_6556,plain,
    ! [X26527,X26528,X26529,X26530,X26531] :
      ( ( hBOOL(hAPP(hAPP(c_member(X26530),esk236_5(X26527,X26528,X26529,X26530,X26531)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26530,tc_HOL_Obool)),X26529),X26528)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26530,X26531),X26527),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26530,tc_HOL_Obool)),X26529),X26528)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26531),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26530,X26531),X26527),X26529)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26530,X26531),X26527),X26528))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26530),X26528))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26530),X26529))
        | ~ class_Groups_Ocomm__monoid__add(X26531) )
      & ( hAPP(X26527,esk236_5(X26527,X26528,X26529,X26530,X26531)) != c_Groups_Ozero__class_Ozero(X26531)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26530,X26531),X26527),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26530,tc_HOL_Obool)),X26529),X26528)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26531),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26530,X26531),X26527),X26529)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26530,X26531),X26527),X26528))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26530),X26528))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26530),X26529))
        | ~ class_Groups_Ocomm__monoid__add(X26531) ) ),
    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_6557,plain,
    ! [X26466,X26467,X26468,X26469,X26470] :
      ( ( hBOOL(hAPP(hAPP(c_member(X26469),esk229_5(X26466,X26467,X26468,X26469,X26470)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26469,tc_HOL_Obool)),X26468),X26467)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26469,X26470),X26466),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26469,tc_HOL_Obool)),X26468),X26467)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26470),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26469,X26470),X26466),X26468)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26469,X26470),X26466),X26467))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26469),X26467))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26469),X26468))
        | ~ class_Groups_Ocomm__monoid__add(X26470) )
      & ( hAPP(X26466,esk229_5(X26466,X26467,X26468,X26469,X26470)) != c_Groups_Ozero__class_Ozero(X26470)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26469,X26470),X26466),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26469,tc_HOL_Obool)),X26468),X26467)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26470),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26469,X26470),X26466),X26468)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26469,X26470),X26466),X26467))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26469),X26467))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26469),X26468))
        | ~ class_Groups_Ocomm__monoid__add(X26470) ) ),
    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_6558,plain,
    ! [X24800,X24801,X24802,X24803,X24804] :
      ( ( hBOOL(hAPP(hAPP(c_member(X24803),esk146_5(X24800,X24801,X24802,X24803,X24804)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24803,tc_HOL_Obool)),X24802),X24801)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24803,X24804),X24800),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24803,tc_HOL_Obool)),X24802),X24801)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24804),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24803,X24804),X24800),X24802)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24803,X24804),X24800),X24801))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24803),X24801))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24803),X24802))
        | ~ class_Groups_Ocomm__monoid__mult(X24804) )
      & ( hAPP(X24800,esk146_5(X24800,X24801,X24802,X24803,X24804)) != c_Groups_Oone__class_Oone(X24804)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24803,X24804),X24800),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24803,tc_HOL_Obool)),X24802),X24801)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24804),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24803,X24804),X24800),X24802)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24803,X24804),X24800),X24801))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24803),X24801))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24803),X24802))
        | ~ class_Groups_Ocomm__monoid__mult(X24804) ) ),
    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_6559,plain,
    ! [X24794,X24795,X24796,X24797,X24798] :
      ( ( hBOOL(hAPP(hAPP(c_member(X24797),esk145_5(X24794,X24795,X24796,X24797,X24798)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24797,tc_HOL_Obool)),X24796),X24795)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24797,X24798),X24794),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24797,tc_HOL_Obool)),X24796),X24795)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24798),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24797,X24798),X24794),X24796)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24797,X24798),X24794),X24795))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24797),X24795))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24797),X24796))
        | ~ class_Groups_Ocomm__monoid__mult(X24798) )
      & ( hAPP(X24794,esk145_5(X24794,X24795,X24796,X24797,X24798)) != c_Groups_Oone__class_Oone(X24798)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24797,X24798),X24794),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24797,tc_HOL_Obool)),X24796),X24795)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24798),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24797,X24798),X24794),X24796)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24797,X24798),X24794),X24795))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24797),X24795))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24797),X24796))
        | ~ class_Groups_Ocomm__monoid__mult(X24798) ) ),
    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_6560,plain,
    ! [X27816,X27817,X27818,X27819] : hAPP(c_Relation_OImage(X27819,X27818,X27817),hAPP(hAPP(c_Set_Oinsert(X27819),X27816),c_Orderings_Obot__class_Obot(tc_fun(X27819,tc_HOL_Obool)))) = hAPP(c_Set_OCollect(X27818),hAPP(hAPP(c_COMBC(X27818,tc_fun(tc_prod(X27819,X27818),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X27819,X27818),tc_fun(tc_fun(tc_prod(X27819,X27818),tc_HOL_Obool),tc_HOL_Obool),X27818),c_member(tc_prod(X27819,X27818))),hAPP(c_Product__Type_OPair(X27819,X27818),X27816))),X27817)),
    inference(variable_rename,[status(thm)],[fact_Image__singleton]) ).

fof(i_0_6561,plain,
    ! [X33202,X33203,X33204,X33205] :
      ( ( ~ hBOOL(hAPP(X33204,X33203))
        | c_List_Olist__all(X33205,hAPP(hAPP(c_COMBS(X33205,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X33205),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X33205),c_fNot),X33204))),hAPP(c_fequal,X33203)),X33202)
        | ~ c_List_Olist__ex1(X33205,X33204,hAPP(hAPP(c_List_Olist_OCons(X33205),X33203),X33202)) )
      & ( hBOOL(hAPP(X33204,X33203))
        | c_List_Olist__ex1(X33205,X33204,X33202)
        | ~ c_List_Olist__ex1(X33205,X33204,hAPP(hAPP(c_List_Olist_OCons(X33205),X33203),X33202)) )
      & ( ~ hBOOL(hAPP(X33204,X33203))
        | hBOOL(hAPP(X33204,X33203))
        | c_List_Olist__ex1(X33205,X33204,hAPP(hAPP(c_List_Olist_OCons(X33205),X33203),X33202)) )
      & ( ~ c_List_Olist__ex1(X33205,X33204,X33202)
        | hBOOL(hAPP(X33204,X33203))
        | c_List_Olist__ex1(X33205,X33204,hAPP(hAPP(c_List_Olist_OCons(X33205),X33203),X33202)) )
      & ( ~ hBOOL(hAPP(X33204,X33203))
        | ~ c_List_Olist__all(X33205,hAPP(hAPP(c_COMBS(X33205,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X33205),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X33205),c_fNot),X33204))),hAPP(c_fequal,X33203)),X33202)
        | c_List_Olist__ex1(X33205,X33204,hAPP(hAPP(c_List_Olist_OCons(X33205),X33203),X33202)) )
      & ( ~ c_List_Olist__ex1(X33205,X33204,X33202)
        | ~ c_List_Olist__all(X33205,hAPP(hAPP(c_COMBS(X33205,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X33205),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X33205),c_fNot),X33204))),hAPP(c_fequal,X33203)),X33202)
        | c_List_Olist__ex1(X33205,X33204,hAPP(hAPP(c_List_Olist_OCons(X33205),X33203),X33202)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5395])])]) ).

cnf(i_0_6562,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_5396]) ).

fof(i_0_6563,plain,
    ! [X23584,X23585,X23586,X23587,X23588,X23589,X23590,X23591] :
      ( ~ c_Finite__Set_Ofolding__image__simple(X23591,X23590,X23589,X23588,X23587,X23586)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23590),X23585))
      | ~ hBOOL(hAPP(hAPP(c_member(X23590),X23584),X23585))
      | hAPP(X23586,X23585) = hAPP(hAPP(X23589,hAPP(X23587,X23584)),hAPP(X23586,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23590,tc_HOL_Obool)),X23585),hAPP(hAPP(c_Set_Oinsert(X23590),X23584),c_Orderings_Obot__class_Obot(tc_fun(X23590,tc_HOL_Obool)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Oremove])]) ).

fof(i_0_6564,plain,
    ! [X23173,X23174,X23175,X23176,X23177,X23179,X23180,X23181,X23182,X23183,X23184] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23175,tc_HOL_Obool)),esk107_5(X23173,X23174,X23175,X23176,X23177)),X23173))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23177,tc_HOL_Obool)),X23176),hAPP(c_Set_Oimage(X23175,X23177,X23174),X23173))) )
      & ( X23176 = hAPP(c_Set_Oimage(X23175,X23177,X23174),esk107_5(X23173,X23174,X23175,X23176,X23177))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23177,tc_HOL_Obool)),X23176),hAPP(c_Set_Oimage(X23175,X23177,X23174),X23173))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23181,tc_HOL_Obool)),X23184),X23179))
        | X23182 != hAPP(c_Set_Oimage(X23181,X23183,X23180),X23184)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23183,tc_HOL_Obool)),X23182),hAPP(c_Set_Oimage(X23181,X23183,X23180),X23179))) ) ),
    inference(distribute,[status(thm)],[inference(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_6565,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_5397]) ).

fof(i_0_6566,plain,
    ! [X25034,X25035,X25036,X25037,X25038,X25040,X25041,X25042,X25043,X25044,X25045] :
      ( ( hBOOL(hAPP(hAPP(c_member(X25036),esk155_5(X25034,X25035,X25036,X25037,X25038)),X25035))
        | ~ hBOOL(hAPP(hAPP(c_member(X25038),X25037),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25036,tc_fun(X25038,tc_HOL_Obool)),X25035),X25034))) )
      & ( hBOOL(hAPP(hAPP(c_member(X25038),X25037),hAPP(X25034,esk155_5(X25034,X25035,X25036,X25037,X25038))))
        | ~ hBOOL(hAPP(hAPP(c_member(X25038),X25037),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25036,tc_fun(X25038,tc_HOL_Obool)),X25035),X25034))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X25042),X25045),X25041))
        | ~ hBOOL(hAPP(hAPP(c_member(X25044),X25043),hAPP(X25040,X25045)))
        | hBOOL(hAPP(hAPP(c_member(X25044),X25043),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25042,tc_fun(X25044,tc_HOL_Obool)),X25041),X25040))) ) ),
    inference(distribute,[status(thm)],[inference(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_6567,plain,
    ! [X23679,X23680,X23681,X23682,X23683,X23684,X23685,X23686] :
      ( ~ c_Finite__Set_Ofolding__image__simple(X23686,X23685,X23684,X23683,X23682,X23681)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23685),X23680))
      | hAPP(X23681,hAPP(hAPP(c_Set_Oinsert(X23685),X23679),X23680)) = hAPP(hAPP(X23684,hAPP(X23682,X23679)),hAPP(X23681,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23685,tc_HOL_Obool)),X23680),hAPP(hAPP(c_Set_Oinsert(X23685),X23679),c_Orderings_Obot__class_Obot(tc_fun(X23685,tc_HOL_Obool)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Oinsert__remove])]) ).

fof(i_0_6568,plain,
    ! [X34058,X34059,X34060,X34061,X34062,X34063,X34064] :
      ( ~ c_Fun_Oinj__on(X34064,X34063,X34062,hAPP(c_Set_Oimage(X34061,X34064,X34060),X34059))
      | ~ c_Fun_Oinj__on(X34061,X34064,X34060,X34059)
      | ~ hBOOL(hAPP(hAPP(c_member(X34063),X34058),hAPP(c_Set_Oimage(X34064,X34063,X34062),hAPP(c_Set_Oimage(X34061,X34064,X34060),X34059))))
      | hAPP(c_Hilbert__Choice_Oinv__into(X34061,X34063,X34059,hAPP(c_Fun_Ocomp(X34064,X34063,X34061,X34062),X34060)),X34058) = hAPP(hAPP(c_Fun_Ocomp(X34064,X34061,X34063,c_Hilbert__Choice_Oinv__into(X34061,X34064,X34059,X34060)),c_Hilbert__Choice_Oinv__into(X34064,X34063,hAPP(c_Set_Oimage(X34061,X34064,X34060),X34059),X34062)),X34058) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__comp])]) ).

fof(i_0_6569,plain,
    ! [X26015,X26016,X26017,X26018,X26019,X26020,X26021] :
      ( ~ c_Fun_Oinj__on(X26021,X26020,X26019,hAPP(c_Set_Oimage(X26018,X26021,X26017),X26016))
      | ~ c_Fun_Oinj__on(X26018,X26021,X26017,X26016)
      | ~ hBOOL(hAPP(hAPP(c_member(X26020),X26015),hAPP(c_Set_Oimage(X26021,X26020,X26019),hAPP(c_Set_Oimage(X26018,X26021,X26017),X26016))))
      | hAPP(c_Fun_Othe__inv__into(X26018,X26020,X26016,hAPP(c_Fun_Ocomp(X26021,X26020,X26018,X26019),X26017)),X26015) = hAPP(hAPP(c_Fun_Ocomp(X26021,X26018,X26020,c_Fun_Othe__inv__into(X26018,X26021,X26016,X26017)),c_Fun_Othe__inv__into(X26021,X26020,hAPP(c_Set_Oimage(X26018,X26021,X26017),X26016),X26019)),X26015) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_the__inv__into__comp])]) ).

cnf(i_0_6570,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_5398]) ).

fof(i_0_6571,plain,
    ! [X26605,X26606,X26607,X26608,X26609] :
      ( ( hBOOL(hAPP(hAPP(c_member(X26608),esk244_5(X26605,X26606,X26607,X26608,X26609)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26608,tc_HOL_Obool)),X26607),X26606)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26608,X26609),X26605),X26607) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26608,X26609),X26605),X26606)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26608,tc_HOL_Obool)),X26606),X26607))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26608),X26607))
        | ~ class_Groups_Ocomm__monoid__add(X26609) )
      & ( hAPP(X26605,esk244_5(X26605,X26606,X26607,X26608,X26609)) != c_Groups_Ozero__class_Ozero(X26609)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26608,X26609),X26605),X26607) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26608,X26609),X26605),X26606)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26608,tc_HOL_Obool)),X26606),X26607))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26608),X26607))
        | ~ class_Groups_Ocomm__monoid__add(X26609) ) ),
    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_6572,plain,
    ! [X26599,X26600,X26601,X26602,X26603] :
      ( ( hBOOL(hAPP(hAPP(c_member(X26602),esk243_5(X26599,X26600,X26601,X26602,X26603)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26602,tc_HOL_Obool)),X26601),X26600)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26602,X26603),X26599),X26600) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26602,X26603),X26599),X26601)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26602,tc_HOL_Obool)),X26600),X26601))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26602),X26601))
        | ~ class_Groups_Ocomm__monoid__add(X26603) )
      & ( hAPP(X26599,esk243_5(X26599,X26600,X26601,X26602,X26603)) != c_Groups_Ozero__class_Ozero(X26603)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26602,X26603),X26599),X26600) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26602,X26603),X26599),X26601)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26602,tc_HOL_Obool)),X26600),X26601))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26602),X26601))
        | ~ class_Groups_Ocomm__monoid__add(X26603) ) ),
    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_6573,plain,
    ! [X25404,X25405,X25406,X25407,X25408] :
      ( ( hBOOL(hAPP(hAPP(c_member(X25407),esk180_5(X25404,X25405,X25406,X25407,X25408)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25407,tc_HOL_Obool)),X25406),X25405)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25407,X25408),X25404),X25405) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25407,X25408),X25404),X25406)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25407,tc_HOL_Obool)),X25405),X25406))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25407),X25406))
        | ~ class_Groups_Ocomm__monoid__mult(X25408) )
      & ( hAPP(X25404,esk180_5(X25404,X25405,X25406,X25407,X25408)) != c_Groups_Oone__class_Oone(X25408)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25407,X25408),X25404),X25405) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25407,X25408),X25404),X25406)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25407,tc_HOL_Obool)),X25405),X25406))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25407),X25406))
        | ~ class_Groups_Ocomm__monoid__mult(X25408) ) ),
    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_6574,plain,
    ! [X25398,X25399,X25400,X25401,X25402] :
      ( ( hBOOL(hAPP(hAPP(c_member(X25401),esk179_5(X25398,X25399,X25400,X25401,X25402)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25401,tc_HOL_Obool)),X25400),X25399)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25401,X25402),X25398),X25400) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25401,X25402),X25398),X25399)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25401,tc_HOL_Obool)),X25399),X25400))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25401),X25400))
        | ~ class_Groups_Ocomm__monoid__mult(X25402) )
      & ( hAPP(X25398,esk179_5(X25398,X25399,X25400,X25401,X25402)) != c_Groups_Oone__class_Oone(X25402)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25401,X25402),X25398),X25400) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25401,X25402),X25398),X25399)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25401,tc_HOL_Obool)),X25399),X25400))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25401),X25400))
        | ~ class_Groups_Ocomm__monoid__mult(X25402) ) ),
    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_6575,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_5380]) ).

cnf(i_0_6576,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_5381]) ).

fof(i_0_6577,plain,
    ! [X24851,X24852,X24853,X24854,X24855,X24857,X24858,X24859,X24860,X24861,X24862] :
      ( ( hBOOL(hAPP(hAPP(c_member(X24855),esk149_5(X24851,X24852,X24853,X24854,X24855)),X24853))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24855,tc_fun(X24854,tc_HOL_Obool)),X24853),X24852),X24851)) )
      & ( hBOOL(hAPP(hAPP(X24852,esk149_5(X24851,X24852,X24853,X24854,X24855)),X24851))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24855,tc_fun(X24854,tc_HOL_Obool)),X24853),X24852),X24851)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X24861),X24862),X24859))
        | ~ hBOOL(hAPP(hAPP(X24858,X24862),X24857))
        | hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24861,tc_fun(X24860,tc_HOL_Obool)),X24859),X24858),X24857)) ) ),
    inference(distribute,[status(thm)],[inference(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_6578,plain,
    ! [X32649,X32650,X32651,X32652] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X32651,X32652)),X32650),X32649))
        | hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X32651),hAPP(hAPP(c_COMBS(X32651,X32652,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X32652,tc_fun(X32652,tc_HOL_Obool),X32651),c_Orderings_Oord__class_Oless__eq(X32652)),X32650)),X32649)))
        | ~ class_Orderings_Oorder(X32652)
        | ~ class_Enum_Oenum(X32651) )
      & ( ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X32651),hAPP(hAPP(c_COMBS(X32651,X32652,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X32652,tc_fun(X32652,tc_HOL_Obool),X32651),c_Orderings_Oord__class_Oless__eq(X32652)),X32650)),X32649)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X32651,X32652)),X32650),X32649))
        | ~ class_Orderings_Oorder(X32652)
        | ~ class_Enum_Oenum(X32651) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__fun_I1_J])])]) ).

fof(i_0_6579,plain,
    ! [X32115,X32116,X32117] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32117,X32117)),X32116),c_Transitive__Closure_Ortrancl(X32117,X32115)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X32117,X32117)),X32116),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(X32117,X32117),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(X32117,X32117),tc_HOL_Obool),tc_fun(tc_prod(X32117,X32117),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(X32117,X32117),tc_HOL_Obool)),X32115)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__imp__UN__rel__pow])]) ).

fof(i_0_6580,plain,
    ! [X31057,X31058,X31059,X31060,X31061] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31061,tc_fun(X31060,tc_HOL_Obool)),X31059),hAPP(hAPP(c_COMBS(X31061,tc_fun(X31060,tc_HOL_Obool),tc_fun(X31060,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X31060,tc_HOL_Obool),tc_fun(tc_fun(X31060,tc_HOL_Obool),tc_fun(X31060,tc_HOL_Obool)),X31061),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31060,tc_HOL_Obool))),X31058)),X31057)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31060,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X31060,tc_HOL_Obool),hAPP(c_Set_Oimage(X31061,tc_fun(X31060,tc_HOL_Obool),X31058),X31059))),c_Complete__Lattice_OInf__class_OInf(tc_fun(X31060,tc_HOL_Obool),hAPP(c_Set_Oimage(X31061,tc_fun(X31060,tc_HOL_Obool),X31057),X31059))),
    inference(variable_rename,[status(thm)],[fact_Int__Inter__image]) ).

fof(i_0_6581,plain,
    ! [X30925,X30926,X30927,X30928,X30929] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X30929,tc_fun(X30928,tc_HOL_Obool)),X30927),hAPP(hAPP(c_COMBS(X30929,tc_fun(X30928,tc_HOL_Obool),tc_fun(X30928,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X30928,tc_HOL_Obool),tc_fun(tc_fun(X30928,tc_HOL_Obool),tc_fun(X30928,tc_HOL_Obool)),X30929),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X30928,tc_HOL_Obool))),X30926)),X30925)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X30928,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X30928,tc_HOL_Obool),hAPP(c_Set_Oimage(X30929,tc_fun(X30928,tc_HOL_Obool),X30926),X30927))),c_Complete__Lattice_OSup__class_OSup(tc_fun(X30928,tc_HOL_Obool),hAPP(c_Set_Oimage(X30929,tc_fun(X30928,tc_HOL_Obool),X30925),X30927))),
    inference(variable_rename,[status(thm)],[fact_Un__Union__image]) ).

fof(i_0_6582,plain,
    ! [X28387,X28388,X28389,X28390,X28391,X28392,X28393] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28393,X28393)),hAPP(hAPP(c_Product__Type_OPair(X28393,X28393),X28392),X28391)),X28390))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28393),tc_List_Olist(X28393))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28393),tc_List_Olist(X28393)),hAPP(hAPP(c_List_Oappend(X28393),X28389),hAPP(hAPP(c_List_Olist_OCons(X28393),X28392),X28388))),hAPP(hAPP(c_List_Oappend(X28393),X28389),hAPP(hAPP(c_List_Olist_OCons(X28393),X28391),X28387)))),c_List_Olexord(X28393,X28390))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__append__left__rightI])]) ).

fof(i_0_6583,plain,
    ! [X22775,X22776,X22777,X22778] :
      ( ( ~ 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),X22778),X22777)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X22776),X22775))),c_Int_Ointrel))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22778),X22775) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22776),X22777) )
      & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22778),X22775) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22776),X22777)
        | 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),X22778),X22777)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X22776),X22775))),c_Int_Ointrel)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_intrel__iff])]) ).

fof(i_0_6584,plain,
    ! [X22731,X22732,X22733,X22734,X22735,X22736,X22737] :
      ( ~ hBOOL(hAPP(X22737,X22736))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X22735,X22735)),hAPP(hAPP(c_Product__Type_OPair(X22735,X22735),X22734),X22733)),hAPP(X22732,X22736)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X22731,X22735),tc_prod(X22731,X22735))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X22731,X22735),tc_prod(X22731,X22735)),hAPP(hAPP(c_Product__Type_OPair(X22731,X22735),X22736),X22734)),hAPP(hAPP(c_Product__Type_OPair(X22731,X22735),X22736),X22733))),c_Recdef_Osame__fst(X22731,X22735,X22737,X22732))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_same__fstI])]) ).

fof(i_0_6585,plain,
    ! [X25027,X25028,X25029,X25030,X25031,X25033] :
      ( ( hBOOL(hAPP(hAPP(c_member(X25029),esk154_5(X25027,X25028,X25029,X25030,X25031)),X25028))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25031),X25030),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25029,X25031),X25028),X25027)))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X25031)
        | ~ class_Orderings_Olinorder(X25031) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25031),X25030),hAPP(X25027,esk154_5(X25027,X25028,X25029,X25030,X25031))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25031),X25030),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25029,X25031),X25028),X25027)))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X25031)
        | ~ class_Orderings_Olinorder(X25031) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X25029),X25033),X25028))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25031),X25030),hAPP(X25027,X25033)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25031),X25030),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25029,X25031),X25028),X25027)))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X25031)
        | ~ class_Orderings_Olinorder(X25031) ) ),
    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_6586,plain,
    ! [X22001,X22002,X22003,X22004,X22005,X22006,X22007,X22008] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X22008,X22007,X22006),X22005),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X22004,X22003,tc_prod(X22008,X22007)),X22002),X22001)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X22004,X22003,X22006),hAPP(hAPP(c_COMBB(tc_fun(X22003,tc_prod(X22008,X22007)),tc_fun(X22003,X22006),X22004),hAPP(c_COMBB(tc_prod(X22008,X22007),X22006,X22003),hAPP(c_Product__Type_Oprod_Oprod__case(X22008,X22007,X22006),X22005))),X22002)),X22001),
    inference(variable_rename,[status(thm)],[fact_split__twice]) ).

cnf(i_0_6587,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_5399]) ).

cnf(i_0_6588,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_5400]) ).

cnf(i_0_6589,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_5401]) ).

fof(i_0_6590,plain,
    ! [X26159,X26160,X26161,X26162] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X26162),esk226_4(X26159,X26160,X26161,X26162)))
        | hBOOL(hAPP(X26159,X26161))
        | ~ hBOOL(hAPP(X26159,c_Orderings_Obot__class_Obot(tc_fun(X26162,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26162,tc_HOL_Obool)),X26161),X26160))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26162),X26161)) )
      & ( hBOOL(hAPP(hAPP(c_member(X26162),esk225_4(X26159,X26160,X26161,X26162)),X26160))
        | hBOOL(hAPP(X26159,X26161))
        | ~ hBOOL(hAPP(X26159,c_Orderings_Obot__class_Obot(tc_fun(X26162,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26162,tc_HOL_Obool)),X26161),X26160))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26162),X26161)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X26162),esk225_4(X26159,X26160,X26161,X26162)),esk226_4(X26159,X26160,X26161,X26162)))
        | hBOOL(hAPP(X26159,X26161))
        | ~ hBOOL(hAPP(X26159,c_Orderings_Obot__class_Obot(tc_fun(X26162,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26162,tc_HOL_Obool)),X26161),X26160))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26162),X26161)) )
      & ( hBOOL(hAPP(X26159,esk226_4(X26159,X26160,X26161,X26162)))
        | hBOOL(hAPP(X26159,X26161))
        | ~ hBOOL(hAPP(X26159,c_Orderings_Obot__class_Obot(tc_fun(X26162,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26162,tc_HOL_Obool)),X26161),X26160))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26162),X26161)) )
      & ( ~ hBOOL(hAPP(X26159,hAPP(hAPP(c_Set_Oinsert(X26162),esk225_4(X26159,X26160,X26161,X26162)),esk226_4(X26159,X26160,X26161,X26162))))
        | hBOOL(hAPP(X26159,X26161))
        | ~ hBOOL(hAPP(X26159,c_Orderings_Obot__class_Obot(tc_fun(X26162,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26162,tc_HOL_Obool)),X26161),X26160))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26162),X26161)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5402])])])]) ).

fof(i_0_6591,plain,
    ! [X29586,X29587,X29588,X29589] :
      ( ( hBOOL(hAPP(hAPP(c_member(X29589),esk349_4(X29586,X29587,X29588,X29589)),hAPP(c_List_Oset(X29589),X29588)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(X29589,X29587,X29588)),c_List_Olist_Olist__size(X29589,X29586,X29588))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X29587,esk349_4(X29586,X29587,X29588,X29589))),hAPP(X29586,esk349_4(X29586,X29587,X29588,X29589))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(X29589,X29587,X29588)),c_List_Olist_Olist__size(X29589,X29586,X29588))) ) ),
    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_6592,plain,
    ! [X27856,X27857] : c_Fun_Oinj__on(tc_fun(X27857,X27856),tc_fun(tc_prod(X27857,X27856),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X27857,X27856),tc_HOL_Obool),tc_fun(tc_prod(X27857,X27856),tc_HOL_Obool),tc_fun(X27857,X27856)),c_Set_OCollect(tc_prod(X27857,X27856))),hAPP(hAPP(c_COMBB(tc_fun(X27857,tc_fun(X27856,tc_HOL_Obool)),tc_fun(tc_prod(X27857,X27856),tc_HOL_Obool),tc_fun(X27857,X27856)),c_Product__Type_Oprod_Oprod__case(X27857,X27856,tc_HOL_Obool)),hAPP(c_COMBB(X27856,tc_fun(X27856,tc_HOL_Obool),X27857),hAPP(c_COMBC(X27856,X27856,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X27857,X27856),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_inj__graph]) ).

cnf(i_0_6593,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_6594,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_5403]) ).

cnf(i_0_6595,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_6596,plain,
    ! [X31846,X31847,X31848,X31849,X31850] :
      ( ( hBOOL(hAPP(hAPP(c_member(X31849),esk399_5(X31846,X31847,X31848,X31849,X31850)),hAPP(c_List_Oset(X31849),X31848)))
        | hAPP(c_List_Omonoid__add__class_Olistsum(X31850),hAPP(hAPP(c_List_Omap(X31849,X31850),X31846),hAPP(c_List_Ofilter(X31849,X31847),X31848))) = hAPP(c_List_Omonoid__add__class_Olistsum(X31850),hAPP(hAPP(c_List_Omap(X31849,X31850),X31846),X31848))
        | ~ class_Groups_Omonoid__add(X31850) )
      & ( ~ hBOOL(hAPP(X31847,esk399_5(X31846,X31847,X31848,X31849,X31850)))
        | hAPP(c_List_Omonoid__add__class_Olistsum(X31850),hAPP(hAPP(c_List_Omap(X31849,X31850),X31846),hAPP(c_List_Ofilter(X31849,X31847),X31848))) = hAPP(c_List_Omonoid__add__class_Olistsum(X31850),hAPP(hAPP(c_List_Omap(X31849,X31850),X31846),X31848))
        | ~ class_Groups_Omonoid__add(X31850) )
      & ( hAPP(X31846,esk399_5(X31846,X31847,X31848,X31849,X31850)) != c_Groups_Ozero__class_Ozero(X31850)
        | hAPP(c_List_Omonoid__add__class_Olistsum(X31850),hAPP(hAPP(c_List_Omap(X31849,X31850),X31846),hAPP(c_List_Ofilter(X31849,X31847),X31848))) = hAPP(c_List_Omonoid__add__class_Olistsum(X31850),hAPP(hAPP(c_List_Omap(X31849,X31850),X31846),X31848))
        | ~ class_Groups_Omonoid__add(X31850) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5404])])])]) ).

cnf(i_0_6597,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_5405]) ).

cnf(i_0_6598,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_5406]) ).

fof(i_0_6599,plain,
    ! [X33752,X33753,X33754,X33755,X33756,X33758,X33759,X33760,X33761,X33763] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X33755),X33753))
        | ~ c_Wellfounded_Omax__extp(X33755,X33754,X33753,X33752) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X33755),X33752))
        | ~ c_Wellfounded_Omax__extp(X33755,X33754,X33753,X33752) )
      & ( X33752 != c_Orderings_Obot__class_Obot(tc_fun(X33755,tc_HOL_Obool))
        | ~ c_Wellfounded_Omax__extp(X33755,X33754,X33753,X33752) )
      & ( hBOOL(hAPP(hAPP(c_member(X33755),esk541_5(X33752,X33753,X33754,X33755,X33756)),X33752))
        | ~ hBOOL(hAPP(hAPP(c_member(X33755),X33756),X33753))
        | ~ c_Wellfounded_Omax__extp(X33755,X33754,X33753,X33752) )
      & ( hBOOL(hAPP(hAPP(X33754,X33756),esk541_5(X33752,X33753,X33754,X33755,X33756)))
        | ~ hBOOL(hAPP(hAPP(c_member(X33755),X33756),X33753))
        | ~ c_Wellfounded_Omax__extp(X33755,X33754,X33753,X33752) )
      & ( hBOOL(hAPP(hAPP(c_member(X33761),esk542_4(X33758,X33759,X33760,X33761)),X33759))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33761),X33759))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33761),X33758))
        | X33758 = c_Orderings_Obot__class_Obot(tc_fun(X33761,tc_HOL_Obool))
        | c_Wellfounded_Omax__extp(X33761,X33760,X33759,X33758) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X33761),X33763),X33758))
        | ~ hBOOL(hAPP(hAPP(X33760,esk542_4(X33758,X33759,X33760,X33761)),X33763))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33761),X33759))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33761),X33758))
        | X33758 = c_Orderings_Obot__class_Obot(tc_fun(X33761,tc_HOL_Obool))
        | c_Wellfounded_Omax__extp(X33761,X33760,X33759,X33758) ) ),
    inference(distribute,[status(thm)],[inference(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_6600,plain,
    ! [X26904,X26905,X26906,X26907,X26908,X26910,X26911,X26912,X26913,X26915] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X26907),X26905))
        | ~ c_Wellfounded_Omax__extp(X26907,X26906,X26905,X26904) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X26907),X26904))
        | ~ c_Wellfounded_Omax__extp(X26907,X26906,X26905,X26904) )
      & ( X26904 != c_Orderings_Obot__class_Obot(tc_fun(X26907,tc_HOL_Obool))
        | ~ c_Wellfounded_Omax__extp(X26907,X26906,X26905,X26904) )
      & ( hBOOL(hAPP(hAPP(c_member(X26907),esk255_5(X26904,X26905,X26906,X26907,X26908)),X26904))
        | ~ hBOOL(hAPP(hAPP(c_member(X26907),X26908),X26905))
        | ~ c_Wellfounded_Omax__extp(X26907,X26906,X26905,X26904) )
      & ( hBOOL(hAPP(hAPP(X26906,X26908),esk255_5(X26904,X26905,X26906,X26907,X26908)))
        | ~ hBOOL(hAPP(hAPP(c_member(X26907),X26908),X26905))
        | ~ c_Wellfounded_Omax__extp(X26907,X26906,X26905,X26904) )
      & ( hBOOL(hAPP(hAPP(c_member(X26913),esk256_4(X26910,X26911,X26912,X26913)),X26911))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26913),X26911))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26913),X26910))
        | X26910 = c_Orderings_Obot__class_Obot(tc_fun(X26913,tc_HOL_Obool))
        | c_Wellfounded_Omax__extp(X26913,X26912,X26911,X26910) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X26913),X26915),X26910))
        | ~ hBOOL(hAPP(hAPP(X26912,esk256_4(X26910,X26911,X26912,X26913)),X26915))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26913),X26911))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26913),X26910))
        | X26910 = c_Orderings_Obot__class_Obot(tc_fun(X26913,tc_HOL_Obool))
        | c_Wellfounded_Omax__extp(X26913,X26912,X26911,X26910) ) ),
    inference(distribute,[status(thm)],[inference(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_6601,plain,
    ! [X27756,X27757,X27758] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27758,tc_HOL_Obool)),X27757),X27756) = hAPP(c_Set_OCollect(X27758),hAPP(hAPP(c_COMBS(X27758,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27758),c_fconj),hAPP(hAPP(c_COMBC(X27758,tc_fun(X27758,tc_HOL_Obool),tc_HOL_Obool),c_member(X27758)),X27757))),hAPP(hAPP(c_COMBC(X27758,tc_fun(X27758,tc_HOL_Obool),tc_HOL_Obool),c_member(X27758)),X27756))),
    inference(variable_rename,[status(thm)],[fact_Int__def]) ).

fof(i_0_6602,plain,
    ! [X27749,X27750,X27751] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27751,tc_HOL_Obool)),X27750),X27749) = hAPP(c_Set_OCollect(X27751),hAPP(hAPP(c_COMBS(X27751,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27751),c_fdisj),hAPP(hAPP(c_COMBC(X27751,tc_fun(X27751,tc_HOL_Obool),tc_HOL_Obool),c_member(X27751)),X27750))),hAPP(hAPP(c_COMBC(X27751,tc_fun(X27751,tc_HOL_Obool),tc_HOL_Obool),c_member(X27751)),X27749))),
    inference(variable_rename,[status(thm)],[fact_Un__def]) ).

fof(i_0_6603,plain,
    ! [X24124,X24125,X24126,X24127,X24128,X24129,X24130,X24131] :
      ( ~ c_Finite__Set_Ofolding__image__simple(X24131,X24130,X24129,X24128,X24127,X24126)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24130),X24125))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24130),X24124))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24130,tc_HOL_Obool)),X24125),X24124) != c_Orderings_Obot__class_Obot(tc_fun(X24130,tc_HOL_Obool))
      | hAPP(X24126,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24130,tc_HOL_Obool)),X24125),X24124)) = hAPP(hAPP(X24129,hAPP(X24126,X24125)),hAPP(X24126,X24124)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Ounion__disjoint])]) ).

cnf(i_0_6604,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_5407]) ).

fof(i_0_6605,plain,
    ! [X20063,X20064,X20065,X20066,X20067,X20068] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20068),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20068),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20068),X20067),X20066)),X20065)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20068),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20068),X20064),X20066)),X20063)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20068),X20065),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20068),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20068),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20068),X20064),X20067)),X20066)),X20063)))
        | ~ class_Rings_Oordered__ring(X20068) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20068),X20065),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20068),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20068),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20068),X20064),X20067)),X20066)),X20063)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20068),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20068),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20068),X20067),X20066)),X20065)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20068),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20068),X20064),X20066)),X20063)))
        | ~ class_Rings_Oordered__ring(X20068) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__iff2])])]) ).

fof(i_0_6606,plain,
    ! [X20081,X20082,X20083,X20084,X20085,X20086] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20086),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20086),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20086),X20085),X20084)),X20083)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20086),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20086),X20082),X20084)),X20081)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20086),X20083),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20086),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20086),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20086),X20082),X20085)),X20084)),X20081)))
        | ~ class_Rings_Oordered__ring(X20086) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20086),X20083),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20086),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20086),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20086),X20082),X20085)),X20084)),X20081)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20086),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20086),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20086),X20085),X20084)),X20083)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20086),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20086),X20082),X20084)),X20081)))
        | ~ class_Rings_Oordered__ring(X20086) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__iff2])])]) ).

fof(i_0_6607,plain,
    ! [X30042,X30043,X30044,X30045,X30046,X30047] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X30047,tc_HOL_Obool)),hAPP(c_Relation_OImage(X30046,X30047,X30045),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30044,tc_fun(X30046,tc_HOL_Obool)),X30043),X30042))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30044,tc_fun(X30047,tc_HOL_Obool)),X30043),hAPP(hAPP(c_COMBB(tc_fun(X30046,tc_HOL_Obool),tc_fun(X30047,tc_HOL_Obool),X30044),c_Relation_OImage(X30046,X30047,X30045)),X30042)))),
    inference(variable_rename,[status(thm)],[fact_Image__INT__subset]) ).

fof(i_0_6608,plain,
    ! [X33095,X33096,X33097,X33098,X33099,X33100,X33101,X33102] :
      ( ~ c_Finite__Set_Ofolding__image__simple__idem(X33102,X33101,X33100,X33099,X33098,X33097)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33101),X33096))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X33101,tc_HOL_Obool)),X33095),X33096))
      | hAPP(hAPP(X33100,hAPP(X33097,X33095)),hAPP(X33097,X33096)) = hAPP(X33097,X33096) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Osubset__idem])]) ).

fof(i_0_6609,plain,
    ! [X18455,X18456,X18457,X18458,X18459] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18457,X18458)),X18456),X18455))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18458),hAPP(X18456,X18459)),hAPP(X18455,X18459)))
        | ~ class_Orderings_Oord(X18458) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18458),hAPP(X18456,esk39_4(X18455,X18456,X18457,X18458))),hAPP(X18455,esk39_4(X18455,X18456,X18457,X18458))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18457,X18458)),X18456),X18455))
        | ~ class_Orderings_Oord(X18458) ) ),
    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_6610,plain,
    ! [X24863,X24864,X24865,X24866,X24867,X24868,X24869] :
      ( ~ c_Finite__Set_Ofolding__image__simple(X24869,X24868,X24867,X24866,X24865,X24864)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24868),X24863))
      | hAPP(X24864,X24863) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X24869,X24868,X24867),X24865),X24866),X24863) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Oeq__fold__g])]) ).

fof(i_0_6611,plain,
    ! [X29754,X29755,X29756,X29757,X29758,X29759,X29760,X29761,X29762,X29763,X29764] :
      ( ( hAPP(hAPP(c_List_Omap(X29758,X29757),X29756),X29755) != hAPP(hAPP(c_List_Omap(X29758,X29757),X29754),X29755)
        | ~ hBOOL(hAPP(hAPP(c_member(X29758),X29759),hAPP(c_List_Oset(X29758),X29755)))
        | hAPP(X29756,X29759) = hAPP(X29754,X29759) )
      & ( hBOOL(hAPP(hAPP(c_member(X29764),esk350_5(X29760,X29761,X29762,X29763,X29764)),hAPP(c_List_Oset(X29764),X29761)))
        | hAPP(hAPP(c_List_Omap(X29764,X29763),X29762),X29761) = hAPP(hAPP(c_List_Omap(X29764,X29763),X29760),X29761) )
      & ( hAPP(X29762,esk350_5(X29760,X29761,X29762,X29763,X29764)) != hAPP(X29760,esk350_5(X29760,X29761,X29762,X29763,X29764))
        | hAPP(hAPP(c_List_Omap(X29764,X29763),X29762),X29761) = hAPP(hAPP(c_List_Omap(X29764,X29763),X29760),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_map__eq__conv])])])])])]) ).

fof(i_0_6612,plain,
    ! [X28098,X28099,X28100,X28101,X28102,X28103,X28104,X28105] :
      ( ~ hBOOL(hAPP(hAPP(X28105,X28104),X28103))
      | ~ hBOOL(hAPP(hAPP(X28102,X28103),X28101))
      | hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X28100,X28099,X28098,X28105,X28102),X28104),X28101)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__comp_Ointros])]) ).

fof(i_0_6613,plain,
    ! [X33064,X33065,X33066,X33067,X33068,X33069,X33070,X33071] :
      ( ~ c_Finite__Set_Ofolding__image__simple__idem(X33071,X33070,X33069,X33068,X33067,X33066)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33070),X33065))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33070),X33064))
      | hAPP(X33066,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X33070,tc_HOL_Obool)),X33065),X33064)) = hAPP(hAPP(X33069,hAPP(X33066,X33065)),hAPP(X33066,X33064)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Ounion__idem])]) ).

fof(i_0_6614,plain,
    ! [X24945,X24946,X24947,X24948,X24949,X24950,X24951,X24952] :
      ( ~ c_Equiv__Relations_Oequiv(X24952,X24951,X24950)
      | ~ c_Equiv__Relations_Ocongruent2(X24952,X24949,X24948,X24950,X24947,X24946)
      | ~ hBOOL(hAPP(hAPP(c_member(X24952),X24945),X24951))
      | c_Equiv__Relations_Ocongruent(X24949,X24948,X24947,hAPP(X24946,X24945)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_congruent2__implies__congruent])]) ).

fof(i_0_6615,plain,
    ! [X28165,X28166,X28167,X28168,X28169,X28172,X28173,X28174,X28175,X28176,X28177,X28178] :
      ( ( hAPP(hAPP(c_List_Oappend(X28169),X28168),esk298_5(X28165,X28166,X28167,X28168,X28169)) = X28166
        | X28168 = hAPP(hAPP(c_List_Oappend(X28169),X28166),esk297_5(X28165,X28166,X28167,X28168,X28169))
        | hAPP(hAPP(c_List_Oappend(X28169),X28168),X28167) != hAPP(hAPP(c_List_Oappend(X28169),X28166),X28165) )
      & ( X28167 = hAPP(hAPP(c_List_Oappend(X28169),esk298_5(X28165,X28166,X28167,X28168,X28169)),X28165)
        | X28168 = hAPP(hAPP(c_List_Oappend(X28169),X28166),esk297_5(X28165,X28166,X28167,X28168,X28169))
        | hAPP(hAPP(c_List_Oappend(X28169),X28168),X28167) != hAPP(hAPP(c_List_Oappend(X28169),X28166),X28165) )
      & ( hAPP(hAPP(c_List_Oappend(X28169),X28168),esk298_5(X28165,X28166,X28167,X28168,X28169)) = X28166
        | hAPP(hAPP(c_List_Oappend(X28169),esk297_5(X28165,X28166,X28167,X28168,X28169)),X28167) = X28165
        | hAPP(hAPP(c_List_Oappend(X28169),X28168),X28167) != hAPP(hAPP(c_List_Oappend(X28169),X28166),X28165) )
      & ( X28167 = hAPP(hAPP(c_List_Oappend(X28169),esk298_5(X28165,X28166,X28167,X28168,X28169)),X28165)
        | hAPP(hAPP(c_List_Oappend(X28169),esk297_5(X28165,X28166,X28167,X28168,X28169)),X28167) = X28165
        | hAPP(hAPP(c_List_Oappend(X28169),X28168),X28167) != hAPP(hAPP(c_List_Oappend(X28169),X28166),X28165) )
      & ( X28175 != hAPP(hAPP(c_List_Oappend(X28176),X28173),X28177)
        | hAPP(hAPP(c_List_Oappend(X28176),X28177),X28174) != X28172
        | hAPP(hAPP(c_List_Oappend(X28176),X28175),X28174) = hAPP(hAPP(c_List_Oappend(X28176),X28173),X28172) )
      & ( hAPP(hAPP(c_List_Oappend(X28176),X28175),X28178) != X28173
        | X28174 != hAPP(hAPP(c_List_Oappend(X28176),X28178),X28172)
        | hAPP(hAPP(c_List_Oappend(X28176),X28175),X28174) = hAPP(hAPP(c_List_Oappend(X28176),X28173),X28172) ) ),
    inference(distribute,[status(thm)],[inference(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_6616,plain,
    ! [X23655,X23656,X23657,X23658,X23659,X23660,X23661,X23662] :
      ( ~ c_Finite__Set_Ofolding__image__simple(X23662,X23661,X23660,X23659,X23658,X23657)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23661),X23656))
      | hBOOL(hAPP(hAPP(c_member(X23661),X23655),X23656))
      | hAPP(X23657,hAPP(hAPP(c_Set_Oinsert(X23661),X23655),X23656)) = hAPP(hAPP(X23660,hAPP(X23658,X23655)),hAPP(X23657,X23656)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5408])]) ).

fof(i_0_6617,plain,
    ! [X25943,X25944,X25945,X25946,X25947] :
      ( ( ~ c_Fun_Oinj__on(X25946,X25944,X25947,X25945)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25944,tc_HOL_Obool)),hAPP(c_Set_Oimage(X25946,X25944,X25947),X25945)),X25943))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X25946),X25945)),hAPP(c_Finite__Set_Ocard(X25944),X25943)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25944),X25943))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25946),X25945)) )
      & ( c_Fun_Oinj__on(X25946,X25944,esk221_4(X25943,X25944,X25945,X25946),X25945)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X25946),X25945)),hAPP(c_Finite__Set_Ocard(X25944),X25943)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25944),X25943))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25946),X25945)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25944,tc_HOL_Obool)),hAPP(c_Set_Oimage(X25946,X25944,esk221_4(X25943,X25944,X25945,X25946)),X25945)),X25943))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X25946),X25945)),hAPP(c_Finite__Set_Ocard(X25944),X25943)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25944),X25943))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25946),X25945)) ) ),
    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_6618,plain,
    ! [X33079,X33080,X33081,X33082,X33083,X33084,X33085,X33086] :
      ( ~ c_Finite__Set_Ofolding__image__simple__idem(X33086,X33085,X33084,X33083,X33082,X33081)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33085),X33080))
      | ~ hBOOL(hAPP(hAPP(c_member(X33085),X33079),X33080))
      | hAPP(hAPP(X33084,hAPP(X33082,X33079)),hAPP(X33081,X33080)) = hAPP(X33081,X33080) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Oin__idem])]) ).

fof(i_0_6619,plain,
    ! [X30741,X30742,X30743] : c_Enum_Osublists(X30743,hAPP(hAPP(c_List_Olist_OCons(X30743),X30742),X30741)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(X30743)),tc_List_Olist(tc_List_Olist(X30743))),c_Enum_Osublists(X30743,X30741)),hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(X30743)),tc_List_Olist(tc_List_Olist(X30743)),tc_List_Olist(tc_List_Olist(X30743))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(X30743)),tc_fun(tc_List_Olist(tc_List_Olist(X30743)),tc_List_Olist(tc_List_Olist(X30743))),tc_List_Olist(tc_List_Olist(X30743))),c_List_Oappend(tc_List_Olist(X30743))),hAPP(c_List_Omap(tc_List_Olist(X30743),tc_List_Olist(X30743)),hAPP(c_List_Olist_OCons(X30743),X30742)))),c_COMBI(tc_List_Olist(tc_List_Olist(X30743))))),
    inference(variable_rename,[status(thm)],[fact_sublists_Osimps_I2_J]) ).

fof(i_0_6620,plain,
    ! [X33087,X33088,X33089,X33090,X33091,X33092,X33093,X33094] :
      ( ~ c_Finite__Set_Ofolding__image__simple__idem(X33094,X33093,X33092,X33091,X33090,X33089)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33093),X33088))
      | hAPP(X33089,hAPP(hAPP(c_Set_Oinsert(X33093),X33087),X33088)) = hAPP(hAPP(X33092,hAPP(X33090,X33087)),hAPP(X33089,X33088)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Oinsert__idem])]) ).

fof(i_0_6621,plain,
    ! [X29935,X29936,X29937,X29938,X29939] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29939,tc_fun(X29938,tc_HOL_Obool)),X29937),hAPP(hAPP(c_COMBS(X29939,tc_fun(X29938,tc_HOL_Obool),tc_fun(X29938,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29938,tc_HOL_Obool),tc_fun(tc_fun(X29938,tc_HOL_Obool),tc_fun(X29938,tc_HOL_Obool)),X29939),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29938,tc_HOL_Obool))),X29936)),X29935)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29938,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29939,tc_fun(X29938,tc_HOL_Obool)),X29937),X29936)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29939,tc_fun(X29938,tc_HOL_Obool)),X29937),X29935)),
    inference(variable_rename,[status(thm)],[fact_INT__Int__distrib]) ).

fof(i_0_6622,plain,
    ! [X25107,X25108,X25109,X25110,X25111] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25111,tc_fun(X25110,tc_HOL_Obool)),X25109),hAPP(hAPP(c_COMBS(X25111,tc_fun(X25110,tc_HOL_Obool),tc_fun(X25110,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25110,tc_HOL_Obool),tc_fun(tc_fun(X25110,tc_HOL_Obool),tc_fun(X25110,tc_HOL_Obool)),X25111),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25110,tc_HOL_Obool))),X25108)),X25107)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25110,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25111,tc_fun(X25110,tc_HOL_Obool)),X25109),X25108)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25111,tc_fun(X25110,tc_HOL_Obool)),X25109),X25107)),
    inference(variable_rename,[status(thm)],[fact_UN__Un__distrib]) ).

fof(i_0_6623,plain,
    ! [X23617,X23618,X23619,X23620,X23621,X23622] :
      ( ~ c_Finite__Set_Ofolding__image__simple(X23622,X23621,X23620,X23619,X23618,X23617)
      | hAPP(X23617,c_Orderings_Obot__class_Obot(tc_fun(X23621,tc_HOL_Obool))) = X23619 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Oempty])]) ).

fof(i_0_6624,plain,
    ! [X33072,X33073,X33074,X33075,X33076,X33077,X33078] :
      ( ~ c_Finite__Set_Ofolding__image__simple__idem(X33078,X33077,X33076,X33075,X33074,X33073)
      | hAPP(hAPP(X33076,X33072),X33072) = X33072 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Oidem])]) ).

fof(i_0_6625,plain,
    ! [X23524] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X23524))
      | X23524 = 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))),X23524)),c_FunDef_Omax__strict)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smax__emptyI])]) ).

fof(i_0_6626,plain,
    ! [X31248,X31249,X31250] : hAPP(c_List_Oset(X31250),hAPP(c_List_Ofilter(X31250,X31249),X31248)) = hAPP(c_Set_OCollect(X31250),hAPP(hAPP(c_COMBS(X31250,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X31250),c_fconj),hAPP(hAPP(c_COMBC(X31250,tc_fun(X31250,tc_HOL_Obool),tc_HOL_Obool),c_member(X31250)),hAPP(c_List_Oset(X31250),X31248)))),X31249)),
    inference(variable_rename,[status(thm)],[fact_set__filter]) ).

fof(i_0_6627,plain,
    ! [X26595,X26596,X26597] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(X26597,esk242_3(X26595,X26596,X26597))),hAPP(X26596,esk242_3(X26595,X26596,X26597))))
      | 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),X26596),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X26595))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X26597),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X26595))) = 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)),X26596)),X26597)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X26595)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__diff__distrib])])]) ).

fof(i_0_6628,plain,
    ! [X25999,X26000,X26001,X26002,X26003,X26005] :
      ( ( ~ c_Fun_Oinj__on(X26001,X26000,X26003,X26002)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26000,tc_HOL_Obool)),hAPP(c_Set_Oimage(X26001,X26000,X26003),X26002)),X25999))
        | hAPP(c_Set_Oimage(X26000,X26001,esk222_4(X25999,X26000,X26001,X26002)),X25999) = X26002
        | X26002 = c_Orderings_Obot__class_Obot(tc_fun(X26001,tc_HOL_Obool)) )
      & ( c_Fun_Oinj__on(X26001,X26000,esk223_4(X25999,X26000,X26001,X26002),X26002)
        | hAPP(c_Set_Oimage(X26000,X26001,X26005),X25999) != X26002
        | X26002 = c_Orderings_Obot__class_Obot(tc_fun(X26001,tc_HOL_Obool)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26000,tc_HOL_Obool)),hAPP(c_Set_Oimage(X26001,X26000,esk223_4(X25999,X26000,X26001,X26002)),X26002)),X25999))
        | hAPP(c_Set_Oimage(X26000,X26001,X26005),X25999) != X26002
        | X26002 = c_Orderings_Obot__class_Obot(tc_fun(X26001,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_6629,plain,
    ! [X28331,X28332,X28333,X28334] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X28334),X28333),hAPP(c_Relation_ORange(X28332,X28334),X28331)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28332,X28334)),hAPP(hAPP(c_Product__Type_OPair(X28332,X28334),esk305_4(X28331,X28332,X28333,X28334)),X28333)),X28331)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5409])])]) ).

fof(i_0_6630,plain,
    ! [X28278,X28279,X28280,X28281,X28283,X28284,X28285,X28286,X28287] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X28281),X28280),hAPP(c_Relation_ORange(X28279,X28281),X28278)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X28279,X28281)),hAPP(hAPP(c_Product__Type_OPair(X28279,X28281),esk303_4(X28278,X28279,X28280,X28281)),X28280)),X28278)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28284,X28286)),hAPP(hAPP(c_Product__Type_OPair(X28284,X28286),X28287),X28285)),X28283))
        | hBOOL(hAPP(hAPP(c_member(X28286),X28285),hAPP(c_Relation_ORange(X28284,X28286),X28283))) ) ),
    inference(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_6631,plain,
    ! [X23465] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X23465))
      | 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))),X23465)),c_FunDef_Omax__weak)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wmax__emptyI])]) ).

fof(i_0_6632,plain,
    ! [X30156,X30157,X30158,X30159,X30160] :
      ( ( X30160 != c_Orderings_Obot__class_Obot(tc_fun(X30159,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30159,tc_fun(X30158,tc_HOL_Obool)),X30160),hAPP(hAPP(c_COMBC(X30159,tc_fun(X30158,tc_HOL_Obool),tc_fun(X30158,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X30158,tc_HOL_Obool),tc_fun(tc_fun(X30158,tc_HOL_Obool),tc_fun(X30158,tc_HOL_Obool)),X30159),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X30158,tc_HOL_Obool))),X30157)),X30156)) = c_Orderings_Otop__class_Otop(tc_fun(X30158,tc_HOL_Obool)) )
      & ( X30160 = c_Orderings_Obot__class_Obot(tc_fun(X30159,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30159,tc_fun(X30158,tc_HOL_Obool)),X30160),hAPP(hAPP(c_COMBC(X30159,tc_fun(X30158,tc_HOL_Obool),tc_fun(X30158,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X30158,tc_HOL_Obool),tc_fun(tc_fun(X30158,tc_HOL_Obool),tc_fun(X30158,tc_HOL_Obool)),X30159),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X30158,tc_HOL_Obool))),X30157)),X30156)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X30158,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30159,tc_fun(X30158,tc_HOL_Obool)),X30160),X30157)),X30156) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__simps_I1_J])]) ).

fof(i_0_6633,plain,
    ! [X30171,X30172,X30173,X30174,X30175] :
      ( ( X30175 != c_Orderings_Obot__class_Obot(tc_fun(X30174,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30174,tc_fun(X30173,tc_HOL_Obool)),X30175),hAPP(hAPP(c_COMBC(X30174,tc_fun(X30173,tc_HOL_Obool),tc_fun(X30173,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X30173,tc_HOL_Obool),tc_fun(tc_fun(X30173,tc_HOL_Obool),tc_fun(X30173,tc_HOL_Obool)),X30174),c_Groups_Ominus__class_Ominus(tc_fun(X30173,tc_HOL_Obool))),X30172)),X30171)) = c_Orderings_Otop__class_Otop(tc_fun(X30173,tc_HOL_Obool)) )
      & ( X30175 = c_Orderings_Obot__class_Obot(tc_fun(X30174,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30174,tc_fun(X30173,tc_HOL_Obool)),X30175),hAPP(hAPP(c_COMBC(X30174,tc_fun(X30173,tc_HOL_Obool),tc_fun(X30173,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X30173,tc_HOL_Obool),tc_fun(tc_fun(X30173,tc_HOL_Obool),tc_fun(X30173,tc_HOL_Obool)),X30174),c_Groups_Ominus__class_Ominus(tc_fun(X30173,tc_HOL_Obool))),X30172)),X30171)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X30173,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30174,tc_fun(X30173,tc_HOL_Obool)),X30175),X30172)),X30171) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__simps_I3_J])]) ).

fof(i_0_6634,plain,
    ! [X25213,X25214,X25215,X25216,X25217] :
      ( ( X25217 != c_Orderings_Obot__class_Obot(tc_fun(X25216,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25216,tc_fun(X25215,tc_HOL_Obool)),X25217),hAPP(hAPP(c_COMBC(X25216,tc_fun(X25215,tc_HOL_Obool),tc_fun(X25215,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25215,tc_HOL_Obool),tc_fun(tc_fun(X25215,tc_HOL_Obool),tc_fun(X25215,tc_HOL_Obool)),X25216),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25215,tc_HOL_Obool))),X25214)),X25213)) = c_Orderings_Obot__class_Obot(tc_fun(X25215,tc_HOL_Obool)) )
      & ( X25217 = c_Orderings_Obot__class_Obot(tc_fun(X25216,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25216,tc_fun(X25215,tc_HOL_Obool)),X25217),hAPP(hAPP(c_COMBC(X25216,tc_fun(X25215,tc_HOL_Obool),tc_fun(X25215,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25215,tc_HOL_Obool),tc_fun(tc_fun(X25215,tc_HOL_Obool),tc_fun(X25215,tc_HOL_Obool)),X25216),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25215,tc_HOL_Obool))),X25214)),X25213)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25215,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25216,tc_fun(X25215,tc_HOL_Obool)),X25217),X25214)),X25213) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__simps_I2_J])]) ).

fof(i_0_6635,plain,
    ! [X29925,X29926,X29927,X29928,X29929] :
      ( ( X29929 != c_Orderings_Obot__class_Obot(tc_fun(X29928,tc_HOL_Obool))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29927,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29928,tc_fun(X29927,tc_HOL_Obool)),X29929),X29926)),X29925) = X29925 )
      & ( X29929 = c_Orderings_Obot__class_Obot(tc_fun(X29928,tc_HOL_Obool))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29927,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29928,tc_fun(X29927,tc_HOL_Obool)),X29929),X29926)),X29925) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29928,tc_fun(X29927,tc_HOL_Obool)),X29929),hAPP(hAPP(c_COMBC(X29928,tc_fun(X29927,tc_HOL_Obool),tc_fun(X29927,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29927,tc_HOL_Obool),tc_fun(tc_fun(X29927,tc_HOL_Obool),tc_fun(X29927,tc_HOL_Obool)),X29928),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29927,tc_HOL_Obool))),X29926)),X29925)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I1_J])]) ).

fof(i_0_6636,plain,
    ! [X25203,X25204,X25205,X25206,X25207] :
      ( ( X25207 != c_Orderings_Obot__class_Obot(tc_fun(X25206,tc_HOL_Obool))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25205,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25206,tc_fun(X25205,tc_HOL_Obool)),X25207),X25204)),X25203) = X25203 )
      & ( X25207 = c_Orderings_Obot__class_Obot(tc_fun(X25206,tc_HOL_Obool))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25205,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25206,tc_fun(X25205,tc_HOL_Obool)),X25207),X25204)),X25203) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25206,tc_fun(X25205,tc_HOL_Obool)),X25207),hAPP(hAPP(c_COMBC(X25206,tc_fun(X25205,tc_HOL_Obool),tc_fun(X25205,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25205,tc_HOL_Obool),tc_fun(tc_fun(X25205,tc_HOL_Obool),tc_fun(X25205,tc_HOL_Obool)),X25206),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25205,tc_HOL_Obool))),X25204)),X25203)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I2_J])]) ).

fof(i_0_6637,plain,
    ! [X30166,X30167,X30168,X30169,X30170] :
      ( ( X30170 != c_Orderings_Obot__class_Obot(tc_fun(X30169,tc_HOL_Obool))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X30168,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30169,tc_fun(X30168,tc_HOL_Obool)),X30170),X30167)),X30166) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X30168,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X30168,tc_HOL_Obool))),X30166) )
      & ( X30170 = c_Orderings_Obot__class_Obot(tc_fun(X30169,tc_HOL_Obool))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X30168,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30169,tc_fun(X30168,tc_HOL_Obool)),X30170),X30167)),X30166) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30169,tc_fun(X30168,tc_HOL_Obool)),X30170),hAPP(hAPP(c_COMBC(X30169,tc_fun(X30168,tc_HOL_Obool),tc_fun(X30168,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X30168,tc_HOL_Obool),tc_fun(tc_fun(X30168,tc_HOL_Obool),tc_fun(X30168,tc_HOL_Obool)),X30169),c_Groups_Ominus__class_Ominus(tc_fun(X30168,tc_HOL_Obool))),X30167)),X30166)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I3_J])]) ).

fof(i_0_6638,plain,
    ! [X29962,X29963,X29964,X29965,X29966] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29966,tc_fun(X29965,tc_HOL_Obool)),X29964),hAPP(hAPP(c_COMBC(X29966,tc_fun(X29965,tc_HOL_Obool),tc_fun(X29965,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29965,tc_HOL_Obool),tc_fun(tc_fun(X29965,tc_HOL_Obool),tc_fun(X29965,tc_HOL_Obool)),X29966),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X29965,tc_HOL_Obool))),X29963)),X29962)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X29965,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29966,tc_fun(X29965,tc_HOL_Obool)),X29964),X29963)),X29962),
    inference(variable_rename,[status(thm)],[fact_INT__simps_I6_J]) ).

fof(i_0_6639,plain,
    ! [X25122,X25123,X25124,X25125,X25126] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25126,tc_fun(X25125,tc_HOL_Obool)),X25124),hAPP(hAPP(c_COMBC(X25126,tc_fun(X25125,tc_HOL_Obool),tc_fun(X25125,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25125,tc_HOL_Obool),tc_fun(tc_fun(X25125,tc_HOL_Obool),tc_fun(X25125,tc_HOL_Obool)),X25126),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25125,tc_HOL_Obool))),X25123)),X25122)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25125,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25126,tc_fun(X25125,tc_HOL_Obool)),X25124),X25123)),X25122),
    inference(variable_rename,[status(thm)],[fact_UN__simps_I4_J]) ).

fof(i_0_6640,plain,
    ! [X25155,X25156,X25157,X25158,X25159] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25159,tc_fun(X25158,tc_HOL_Obool)),X25157),hAPP(hAPP(c_COMBC(X25159,tc_fun(X25158,tc_HOL_Obool),tc_fun(X25158,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25158,tc_HOL_Obool),tc_fun(tc_fun(X25158,tc_HOL_Obool),tc_fun(X25158,tc_HOL_Obool)),X25159),c_Groups_Ominus__class_Ominus(tc_fun(X25158,tc_HOL_Obool))),X25156)),X25155)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25158,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25159,tc_fun(X25158,tc_HOL_Obool)),X25157),X25156)),X25155),
    inference(variable_rename,[status(thm)],[fact_UN__simps_I6_J]) ).

fof(i_0_6641,plain,
    ! [X25137,X25138,X25139,X25140,X25141] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25141,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25140,tc_fun(X25141,tc_HOL_Obool)),X25139),X25138)),X25137) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25140,tc_fun(X25141,tc_HOL_Obool)),X25139),hAPP(hAPP(c_COMBC(X25140,tc_fun(X25141,tc_HOL_Obool),tc_fun(X25141,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25141,tc_HOL_Obool),tc_fun(tc_fun(X25141,tc_HOL_Obool),tc_fun(X25141,tc_HOL_Obool)),X25140),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25141,tc_HOL_Obool))),X25138)),X25137)),
    inference(variable_rename,[status(thm)],[fact_UN__extend__simps_I4_J]) ).

fof(i_0_6642,plain,
    ! [X29947,X29948,X29949,X29950,X29951] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X29951,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29950,tc_fun(X29951,tc_HOL_Obool)),X29949),X29948)),X29947) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29950,tc_fun(X29951,tc_HOL_Obool)),X29949),hAPP(hAPP(c_COMBC(X29950,tc_fun(X29951,tc_HOL_Obool),tc_fun(X29951,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29951,tc_HOL_Obool),tc_fun(tc_fun(X29951,tc_HOL_Obool),tc_fun(X29951,tc_HOL_Obool)),X29950),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X29951,tc_HOL_Obool))),X29948)),X29947)),
    inference(variable_rename,[status(thm)],[fact_INT__extend__simps_I6_J]) ).

fof(i_0_6643,plain,
    ! [X25160,X25161,X25162,X25163,X25164] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25164,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25163,tc_fun(X25164,tc_HOL_Obool)),X25162),X25161)),X25160) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25163,tc_fun(X25164,tc_HOL_Obool)),X25162),hAPP(hAPP(c_COMBC(X25163,tc_fun(X25164,tc_HOL_Obool),tc_fun(X25164,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25164,tc_HOL_Obool),tc_fun(tc_fun(X25164,tc_HOL_Obool),tc_fun(X25164,tc_HOL_Obool)),X25163),c_Groups_Ominus__class_Ominus(tc_fun(X25164,tc_HOL_Obool))),X25161)),X25160)),
    inference(variable_rename,[status(thm)],[fact_UN__extend__simps_I6_J]) ).

fof(i_0_6644,plain,
    ! [X28070,X28071,X28072,X28073,X28074,X28075,X28076,X28077] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28077,X28076),tc_HOL_Obool)),X28075),hAPP(hAPP(c_Product__Type_OSigma(X28077,X28076),X28074),hAPP(c_COMBK(tc_fun(X28076,tc_HOL_Obool),X28077),X28073))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28076,X28072),tc_HOL_Obool)),X28071),hAPP(hAPP(c_Product__Type_OSigma(X28076,X28072),X28073),hAPP(c_COMBK(tc_fun(X28072,tc_HOL_Obool),X28076),X28070))))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28077,X28072),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X28077,X28076,X28072),X28075),X28071)),hAPP(hAPP(c_Product__Type_OSigma(X28077,X28072),X28074),hAPP(c_COMBK(tc_fun(X28072,tc_HOL_Obool),X28077),X28070)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__comp__subset__Sigma])]) ).

fof(i_0_6645,plain,
    ! [X28539,X28540,X28541,X28542,X28543,X28544] :
      ( ( X28543 = X28541
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X28544,X28544)),hAPP(hAPP(c_Product__Type_OPair(X28544,X28544),X28543),X28541)),X28539))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28544),tc_List_Olist(X28544))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28544),tc_List_Olist(X28544)),hAPP(hAPP(c_List_Olist_OCons(X28544),X28543),X28542)),hAPP(hAPP(c_List_Olist_OCons(X28544),X28541),X28540))),c_List_Olistrel1(X28544,X28539))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28544),tc_List_Olist(X28544))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28544),tc_List_Olist(X28544)),X28542),X28540)),c_List_Olistrel1(X28544,X28539)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X28544,X28544)),hAPP(hAPP(c_Product__Type_OPair(X28544,X28544),X28543),X28541)),X28539))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28544),tc_List_Olist(X28544))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28544),tc_List_Olist(X28544)),hAPP(hAPP(c_List_Olist_OCons(X28544),X28543),X28542)),hAPP(hAPP(c_List_Olist_OCons(X28544),X28541),X28540))),c_List_Olistrel1(X28544,X28539))) )
      & ( X28543 = X28541
        | X28542 = X28540
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28544),tc_List_Olist(X28544))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28544),tc_List_Olist(X28544)),hAPP(hAPP(c_List_Olist_OCons(X28544),X28543),X28542)),hAPP(hAPP(c_List_Olist_OCons(X28544),X28541),X28540))),c_List_Olistrel1(X28544,X28539))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28544),tc_List_Olist(X28544))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28544),tc_List_Olist(X28544)),X28542),X28540)),c_List_Olistrel1(X28544,X28539)))
        | X28542 = X28540
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28544),tc_List_Olist(X28544))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28544),tc_List_Olist(X28544)),hAPP(hAPP(c_List_Olist_OCons(X28544),X28543),X28542)),hAPP(hAPP(c_List_Olist_OCons(X28544),X28541),X28540))),c_List_Olistrel1(X28544,X28539))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28544,X28544)),hAPP(hAPP(c_Product__Type_OPair(X28544,X28544),X28543),X28541)),X28539))
        | X28542 != X28540
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28544),tc_List_Olist(X28544))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28544),tc_List_Olist(X28544)),hAPP(hAPP(c_List_Olist_OCons(X28544),X28543),X28542)),hAPP(hAPP(c_List_Olist_OCons(X28544),X28541),X28540))),c_List_Olistrel1(X28544,X28539))) )
      & ( X28543 != X28541
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28544),tc_List_Olist(X28544))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28544),tc_List_Olist(X28544)),X28542),X28540)),c_List_Olistrel1(X28544,X28539)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28544),tc_List_Olist(X28544))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28544),tc_List_Olist(X28544)),hAPP(hAPP(c_List_Olist_OCons(X28544),X28543),X28542)),hAPP(hAPP(c_List_Olist_OCons(X28544),X28541),X28540))),c_List_Olistrel1(X28544,X28539))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cons__listrel1__Cons])])]) ).

fof(i_0_6646,plain,
    ! [X28381,X28382,X28383,X28384,X28385,X28386] :
      ( ( X28385 = X28383
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X28386,X28386)),hAPP(hAPP(c_Product__Type_OPair(X28386,X28386),X28385),X28383)),X28381))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28386),tc_List_Olist(X28386))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28386),tc_List_Olist(X28386)),hAPP(hAPP(c_List_Olist_OCons(X28386),X28385),X28384)),hAPP(hAPP(c_List_Olist_OCons(X28386),X28383),X28382))),c_List_Olexord(X28386,X28381))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28386),tc_List_Olist(X28386))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28386),tc_List_Olist(X28386)),X28384),X28382)),c_List_Olexord(X28386,X28381)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X28386,X28386)),hAPP(hAPP(c_Product__Type_OPair(X28386,X28386),X28385),X28383)),X28381))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28386),tc_List_Olist(X28386))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28386),tc_List_Olist(X28386)),hAPP(hAPP(c_List_Olist_OCons(X28386),X28385),X28384)),hAPP(hAPP(c_List_Olist_OCons(X28386),X28383),X28382))),c_List_Olexord(X28386,X28381))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28386,X28386)),hAPP(hAPP(c_Product__Type_OPair(X28386,X28386),X28385),X28383)),X28381))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28386),tc_List_Olist(X28386))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28386),tc_List_Olist(X28386)),hAPP(hAPP(c_List_Olist_OCons(X28386),X28385),X28384)),hAPP(hAPP(c_List_Olist_OCons(X28386),X28383),X28382))),c_List_Olexord(X28386,X28381))) )
      & ( X28385 != X28383
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28386),tc_List_Olist(X28386))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28386),tc_List_Olist(X28386)),X28384),X28382)),c_List_Olexord(X28386,X28381)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28386),tc_List_Olist(X28386))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28386),tc_List_Olist(X28386)),hAPP(hAPP(c_List_Olist_OCons(X28386),X28385),X28384)),hAPP(hAPP(c_List_Olist_OCons(X28386),X28383),X28382))),c_List_Olexord(X28386,X28381))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__cons__cons])])]) ).

fof(i_0_6647,plain,
    ! [X28350,X28351,X28352,X28353,X28354,X28355] :
      ( ( X28354 = X28352
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X28355,X28355)),hAPP(hAPP(c_Product__Type_OPair(X28355,X28355),X28354),X28352)),X28350))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28355),tc_List_Olist(X28355))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28355),tc_List_Olist(X28355)),hAPP(hAPP(c_List_Olist_OCons(X28355),X28354),X28353)),hAPP(hAPP(c_List_Olist_OCons(X28355),X28352),X28351))),c_List_Olex(X28355,X28350))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28355),tc_List_Olist(X28355))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28355),tc_List_Olist(X28355)),X28353),X28351)),c_List_Olex(X28355,X28350)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X28355,X28355)),hAPP(hAPP(c_Product__Type_OPair(X28355,X28355),X28354),X28352)),X28350))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28355),tc_List_Olist(X28355))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28355),tc_List_Olist(X28355)),hAPP(hAPP(c_List_Olist_OCons(X28355),X28354),X28353)),hAPP(hAPP(c_List_Olist_OCons(X28355),X28352),X28351))),c_List_Olex(X28355,X28350))) )
      & ( X28354 = X28352
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28355)),X28353) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28355)),X28351)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28355),tc_List_Olist(X28355))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28355),tc_List_Olist(X28355)),hAPP(hAPP(c_List_Olist_OCons(X28355),X28354),X28353)),hAPP(hAPP(c_List_Olist_OCons(X28355),X28352),X28351))),c_List_Olex(X28355,X28350))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28355),tc_List_Olist(X28355))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28355),tc_List_Olist(X28355)),X28353),X28351)),c_List_Olex(X28355,X28350)))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28355)),X28353) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28355)),X28351)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28355),tc_List_Olist(X28355))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28355),tc_List_Olist(X28355)),hAPP(hAPP(c_List_Olist_OCons(X28355),X28354),X28353)),hAPP(hAPP(c_List_Olist_OCons(X28355),X28352),X28351))),c_List_Olex(X28355,X28350))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28355,X28355)),hAPP(hAPP(c_Product__Type_OPair(X28355,X28355),X28354),X28352)),X28350))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28355)),X28353) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28355)),X28351)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28355),tc_List_Olist(X28355))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28355),tc_List_Olist(X28355)),hAPP(hAPP(c_List_Olist_OCons(X28355),X28354),X28353)),hAPP(hAPP(c_List_Olist_OCons(X28355),X28352),X28351))),c_List_Olex(X28355,X28350))) )
      & ( X28354 != X28352
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28355),tc_List_Olist(X28355))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28355),tc_List_Olist(X28355)),X28353),X28351)),c_List_Olex(X28355,X28350)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28355),tc_List_Olist(X28355))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28355),tc_List_Olist(X28355)),hAPP(hAPP(c_List_Olist_OCons(X28355),X28354),X28353)),hAPP(hAPP(c_List_Olist_OCons(X28355),X28352),X28351))),c_List_Olex(X28355,X28350))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cons__in__lex])])]) ).

fof(i_0_6648,plain,
    ! [X27321,X27322,X27323,X27324,X27325] : hAPP(hAPP(c_Product__Type_OSigma(X27325,X27324),X27323),hAPP(hAPP(c_COMBS(X27325,tc_fun(X27324,tc_HOL_Obool),tc_fun(X27324,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27324,tc_HOL_Obool),tc_fun(tc_fun(X27324,tc_HOL_Obool),tc_fun(X27324,tc_HOL_Obool)),X27325),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27324,tc_HOL_Obool))),X27322)),X27321)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X27325,X27324),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X27325,X27324),X27323),X27322)),hAPP(hAPP(c_Product__Type_OSigma(X27325,X27324),X27323),X27321)),
    inference(variable_rename,[status(thm)],[fact_Sigma__Int__distrib2]) ).

fof(i_0_6649,plain,
    ! [X27295,X27296,X27297,X27298,X27299] : hAPP(hAPP(c_Product__Type_OSigma(X27299,X27298),X27297),hAPP(hAPP(c_COMBS(X27299,tc_fun(X27298,tc_HOL_Obool),tc_fun(X27298,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27298,tc_HOL_Obool),tc_fun(tc_fun(X27298,tc_HOL_Obool),tc_fun(X27298,tc_HOL_Obool)),X27299),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27298,tc_HOL_Obool))),X27296)),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),X27297),X27296)),hAPP(hAPP(c_Product__Type_OSigma(X27299,X27298),X27297),X27295)),
    inference(variable_rename,[status(thm)],[fact_Sigma__Un__distrib2]) ).

fof(i_0_6650,plain,
    ! [X27338,X27339,X27340,X27341,X27342] : hAPP(hAPP(c_Product__Type_OSigma(X27342,X27341),X27340),hAPP(hAPP(c_COMBS(X27342,tc_fun(X27341,tc_HOL_Obool),tc_fun(X27341,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27341,tc_HOL_Obool),tc_fun(tc_fun(X27341,tc_HOL_Obool),tc_fun(X27341,tc_HOL_Obool)),X27342),c_Groups_Ominus__class_Ominus(tc_fun(X27341,tc_HOL_Obool))),X27339)),X27338)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X27342,X27341),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X27342,X27341),X27340),X27339)),hAPP(hAPP(c_Product__Type_OSigma(X27342,X27341),X27340),X27338)),
    inference(variable_rename,[status(thm)],[fact_Sigma__Diff__distrib2]) ).

fof(i_0_6651,plain,
    ! [X20423,X20424,X20425,X20426,X20427] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X20427)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20427),hAPP(c_Groups_Oabs__class_Oabs(X20427),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20427),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20427),X20426),X20425)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20427),X20424),X20423)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20427),hAPP(c_Groups_Oabs__class_Oabs(X20427),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20427),X20426),X20424))),hAPP(c_Groups_Oabs__class_Oabs(X20427),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20427),X20425),X20423))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__diff__triangle__ineq])]) ).

fof(i_0_6652,plain,
    ! [X20129,X20130,X20131,X20132,X20133] :
      ( ( ~ 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),X20133),X20131)),X20130)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20132),X20131)),X20129)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20130),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),X20132),X20133)),X20131)),X20129)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20133),X20132)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20130),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),X20132),X20133)),X20131)),X20129)))
        | 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),X20133),X20131)),X20130)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20132),X20131)),X20129)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20133),X20132)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__le__add__iff2])])]) ).

fof(i_0_6653,plain,
    ! [X20161,X20162,X20163,X20164,X20165] :
      ( ( ~ 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),X20165),X20163)),X20162)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20164),X20163)),X20161)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20162),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),X20164),X20165)),X20163)),X20161)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20165),X20164)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20162),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),X20164),X20165)),X20163)),X20161)))
        | 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),X20165),X20163)),X20162)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20164),X20163)),X20161)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20165),X20164)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__add__iff2])])]) ).

fof(i_0_6654,plain,
    ! [X26031,X26032,X26033,X26034,X26035,X26036,X26037,X26038] :
      ( ~ c_Finite__Set_Ofolding__image(X26038,X26037,X26036,X26035,X26034)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26037),X26033))
      | hAPP(hAPP(X26034,hAPP(hAPP(c_COMBS(X26037,X26038,X26038),hAPP(hAPP(c_COMBB(X26038,tc_fun(X26038,X26038),X26037),X26036),X26032)),X26031)),X26033) = hAPP(hAPP(X26036,hAPP(hAPP(X26034,X26032),X26033)),hAPP(hAPP(X26034,X26031),X26033)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image_Odistrib])]) ).

cnf(i_0_6655,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_5410]) ).

fof(i_0_6656,plain,
    ! [X24904,X24905,X24906,X24907,X24908] :
      ( ~ class_Groups_Ocomm__monoid__mult(X24908)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24907),X24906))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24907),X24905))
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24908),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X24908,X24907,c_Groups_Otimes__class_Otimes(X24908)),X24904),c_Groups_Oone__class_Oone(X24908)),X24906)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X24908,X24907,c_Groups_Otimes__class_Otimes(X24908)),X24904),c_Groups_Oone__class_Oone(X24908)),X24905)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24908),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X24908,X24907,c_Groups_Otimes__class_Otimes(X24908)),X24904),c_Groups_Oone__class_Oone(X24908)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24907,tc_HOL_Obool)),X24906),X24905))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X24908,X24907,c_Groups_Otimes__class_Otimes(X24908)),X24904),c_Groups_Oone__class_Oone(X24908)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24907,tc_HOL_Obool)),X24906),X24905))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__image__Un__Int])]) ).

fof(i_0_6657,plain,
    ! [X26519,X26520,X26521] : 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),X26521)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),X26520))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X26519))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X26519),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26521),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26521),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X26519),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X26520)))),
    inference(variable_rename,[status(thm)],[fact_arith__series__nat]) ).

fof(i_0_6658,plain,
    ! [X23970,X23971,X23972,X23973] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23973,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23973,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23973,tc_HOL_Obool)),X23972),X23971)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23973,tc_HOL_Obool)),X23971),X23970))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23973,tc_HOL_Obool)),X23970),X23972)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23973,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23973,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23973,tc_HOL_Obool)),X23972),X23971)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23973,tc_HOL_Obool)),X23971),X23970))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23973,tc_HOL_Obool)),X23970),X23972)),
    inference(variable_rename,[status(thm)],[fact_Un__Int__crazy]) ).

fof(i_0_6659,plain,
    ! [X32215,X32216,X32217,X32218,X32219,X32220] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32220,X32220)),hAPP(hAPP(c_Product__Type_OPair(X32220,X32220),X32219),X32218)),c_Transitive__Closure_Ortrancl(X32220,X32217)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32220),tc_List_Olist(X32220))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32220),tc_List_Olist(X32220)),X32216),X32215)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X32220),c_List_Olistrel1(X32220,X32217))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32220),tc_List_Olist(X32220))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32220),tc_List_Olist(X32220)),hAPP(hAPP(c_List_Olist_OCons(X32220),X32219),X32216)),hAPP(hAPP(c_List_Olist_OCons(X32220),X32218),X32215))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X32220),c_List_Olistrel1(X32220,X32217)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__listrel1__ConsI2])]) ).

fof(i_0_6660,plain,
    ! [X23243,X23244,X23245,X23246,X23247] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23247,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23247,tc_HOL_Obool)),hAPP(c_Set_Oimage(X23246,X23247,X23245),X23244)),hAPP(c_Set_Oimage(X23246,X23247,X23245),X23243))),hAPP(c_Set_Oimage(X23246,X23247,X23245),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23246,tc_HOL_Obool)),X23244),X23243)))),
    inference(variable_rename,[status(thm)],[fact_image__diff__subset]) ).

cnf(i_0_6661,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_5411]) ).

cnf(i_0_6662,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_5412]) ).

fof(i_0_6663,plain,
    ! [X27865] : hAPP(c_Set_OCollect(tc_Nat_Onat),X27865) = 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),X27865),c_Int_Onat)))),
    inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J]) ).

fof(i_0_6664,plain,
    ! [X28305,X28306] : c_List_Olenlex(X28306,X28305) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(X28306)),tc_List_Olist(X28306)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(X28306),c_Wellfounded_Oless__than,c_List_Olex(X28306,X28305))),hAPP(hAPP(c_COMBS(tc_List_Olist(X28306),tc_List_Olist(X28306),tc_prod(tc_Nat_Onat,tc_List_Olist(X28306))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(X28306),tc_prod(tc_Nat_Onat,tc_List_Olist(X28306))),tc_List_Olist(X28306)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(X28306))),c_Nat_Osize__class_Osize(tc_List_Olist(X28306)))),c_COMBI(tc_List_Olist(X28306)))),
    inference(variable_rename,[status(thm)],[fact_lenlex__def]) ).

fof(i_0_6665,plain,
    ! [X27642,X27643,X27644] :
      ( ( hBOOL(hAPP(hAPP(c_member(X27644),esk287_3(X27642,X27643,X27644)),X27642))
        | c_Relation_Orefl__on(X27644,X27642,X27643)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27644,X27644),tc_HOL_Obool)),X27643),hAPP(hAPP(c_Product__Type_OSigma(X27644,X27644),X27642),hAPP(c_COMBK(tc_fun(X27644,tc_HOL_Obool),X27644),X27642)))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27644,X27644)),hAPP(hAPP(c_Product__Type_OPair(X27644,X27644),esk287_3(X27642,X27643,X27644)),esk287_3(X27642,X27643,X27644))),X27643))
        | c_Relation_Orefl__on(X27644,X27642,X27643)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27644,X27644),tc_HOL_Obool)),X27643),hAPP(hAPP(c_Product__Type_OSigma(X27644,X27644),X27642),hAPP(c_COMBK(tc_fun(X27644,tc_HOL_Obool),X27644),X27642)))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__onI])])])]) ).

fof(i_0_6666,plain,
    ! [X27602,X27603,X27604,X27605,X27606,X27607,X27608] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27604,X27604),tc_HOL_Obool)),X27602),hAPP(hAPP(c_Product__Type_OSigma(X27604,X27604),X27603),hAPP(c_COMBK(tc_fun(X27604,tc_HOL_Obool),X27604),X27603))))
        | ~ c_Relation_Orefl__on(X27604,X27603,X27602) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X27604),X27605),X27603))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X27604,X27604)),hAPP(hAPP(c_Product__Type_OPair(X27604,X27604),X27605),X27605)),X27602))
        | ~ c_Relation_Orefl__on(X27604,X27603,X27602) )
      & ( hBOOL(hAPP(hAPP(c_member(X27608),esk285_3(X27606,X27607,X27608)),X27607))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27608,X27608),tc_HOL_Obool)),X27606),hAPP(hAPP(c_Product__Type_OSigma(X27608,X27608),X27607),hAPP(c_COMBK(tc_fun(X27608,tc_HOL_Obool),X27608),X27607))))
        | c_Relation_Orefl__on(X27608,X27607,X27606) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27608,X27608)),hAPP(hAPP(c_Product__Type_OPair(X27608,X27608),esk285_3(X27606,X27607,X27608)),esk285_3(X27606,X27607,X27608))),X27606))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27608,X27608),tc_HOL_Obool)),X27606),hAPP(hAPP(c_Product__Type_OSigma(X27608,X27608),X27607),hAPP(c_COMBK(tc_fun(X27608,tc_HOL_Obool),X27608),X27607))))
        | c_Relation_Orefl__on(X27608,X27607,X27606) ) ),
    inference(distribute,[status(thm)],[inference(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_6667,plain,
    ! [X27746,X27747,X27748] : hAPP(hAPP(c_Set_Oinsert(X27748),X27747),X27746) = hAPP(c_Set_OCollect(X27748),hAPP(hAPP(c_COMBS(X27748,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27748),c_fdisj),hAPP(hAPP(c_COMBC(X27748,X27748,tc_HOL_Obool),c_fequal),X27747))),hAPP(hAPP(c_COMBC(X27748,tc_fun(X27748,tc_HOL_Obool),tc_HOL_Obool),c_member(X27748)),X27746))),
    inference(variable_rename,[status(thm)],[fact_insert__compr]) ).

fof(i_0_6668,plain,
    ! [X27743,X27744,X27745] : hAPP(hAPP(c_Set_Oinsert(X27745),X27744),X27743) = hAPP(c_Set_OCollect(X27745),hAPP(hAPP(c_COMBS(X27745,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27745),c_fdisj),hAPP(hAPP(c_COMBC(X27745,X27745,tc_HOL_Obool),c_fequal),X27744))),hAPP(hAPP(c_COMBC(X27745,tc_fun(X27745,tc_HOL_Obool),tc_HOL_Obool),c_member(X27745)),X27743))),
    inference(variable_rename,[status(thm)],[fact_insert__compr__raw]) ).

cnf(i_0_6669,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk459_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_5392]) ).

fof(i_0_6670,plain,
    ! [X28594,X28595,X28596,X28597,X28598,X28599] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28599,X28599)),hAPP(hAPP(c_Product__Type_OPair(X28599,X28599),X28598),X28597)),X28596))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28599),tc_List_Olist(X28599))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28599),tc_List_Olist(X28599)),X28595),X28594)),c_List_Olistrel(X28599,X28596)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28599),tc_List_Olist(X28599))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28599),tc_List_Olist(X28599)),hAPP(hAPP(c_List_Olist_OCons(X28599),X28598),X28595)),hAPP(hAPP(c_List_Olist_OCons(X28599),X28597),X28594))),c_List_Olistrel(X28599,X28596))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel_OCons])]) ).

cnf(i_0_6671,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk460_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_5391]) ).

fof(i_0_6672,plain,
    ! [X26846,X26847,X26848,X26849,X26850] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X26850,X26850,X26849,X26848,X26847),X26846))
      | hBOOL(hAPP(hAPP(c_member(X26850),X26848),X26847))
      | hBOOL(hAPP(c_Finite__Set_Ofold1Set(X26850,X26849,hAPP(hAPP(c_Set_Oinsert(X26850),X26848),X26847)),X26846)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5413])]) ).

cnf(i_0_6673,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_5414]) ).

cnf(i_0_6674,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_5415]) ).

cnf(i_0_6675,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_5416]) ).

fof(i_0_6676,plain,
    ! [X22779] :
      ( X22779 = 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)),X22779),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_6677,plain,
    ! [X23336,X23337] : 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),X23337),X23336)),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),X23336),X23337)),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_6678,plain,
    ! [X22788] : 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)),X22788),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_6679,plain,
    ! [X32988,X32989,X32990,X32991,X32992,X32993] :
      ( ~ c_Finite__Set_Ofun__left__comm(X32993,X32992,X32991)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X32993,X32992,X32991,X32990,X32989),X32988))
      | hAPP(hAPP(c_Finite__Set_Ofold(X32993,X32992,X32991),X32990),X32989) = X32988 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__equality])]) ).

fof(i_0_6680,plain,
    ! [X26668,X26669,X26670,X26671,X26672] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X26672,X26671,X26670,X26669,c_Orderings_Obot__class_Obot(tc_fun(X26672,tc_HOL_Obool))),X26668))
      | X26668 = X26669 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_empty__fold__graphE])]) ).

fof(i_0_6681,plain,
    ! [X23457,X23458,X23459,X23460,X23461] :
      ( ~ c_Equiv__Relations_Oequiv(X23461,X23460,X23459)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23461,tc_HOL_Obool)),hAPP(c_Relation_OImage(X23461,X23461,X23459),hAPP(hAPP(c_Set_Oinsert(X23461),X23458),c_Orderings_Obot__class_Obot(tc_fun(X23461,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X23461,X23461,X23459),hAPP(hAPP(c_Set_Oinsert(X23461),X23457),c_Orderings_Obot__class_Obot(tc_fun(X23461,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(X23461),X23458),X23460))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X23461,X23461)),hAPP(hAPP(c_Product__Type_OPair(X23461,X23461),X23457),X23458)),X23459)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__equiv__class])]) ).

fof(i_0_6682,plain,
    ! [X16973,X16974,X16975,X16976,X16977] :
      ( ~ c_Hoare__Mirabelle_Ohoare__derivs(X16977,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X16977)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X16977),X16976),hAPP(c_Com_Ocom_OBODY,X16975)),X16974)),X16973),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X16977)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X16977),X16976),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X16975))),X16974)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X16977),tc_HOL_Obool))))
      | c_Hoare__Mirabelle_Ohoare__derivs(X16977,X16973,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X16977)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X16977),X16976),hAPP(c_Com_Ocom_OBODY,X16975)),X16974)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X16977),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_BodyN])]) ).

fof(i_0_6683,plain,
    ! [X24199,X24200,X24201,X24202,X24203,X24204] :
      ( ( hBOOL(hAPP(hAPP(X24202,X24200),X24203))
        | ~ hBOOL(hAPP(hAPP(c_member(X24204),X24203),c_SetInterval_Oord_OatLeastLessThan(X24204,X24202,X24201,X24200,X24199))) )
      & ( hBOOL(hAPP(hAPP(X24201,X24203),X24199))
        | ~ hBOOL(hAPP(hAPP(c_member(X24204),X24203),c_SetInterval_Oord_OatLeastLessThan(X24204,X24202,X24201,X24200,X24199))) )
      & ( ~ hBOOL(hAPP(hAPP(X24202,X24200),X24203))
        | ~ hBOOL(hAPP(hAPP(X24201,X24203),X24199))
        | hBOOL(hAPP(hAPP(c_member(X24204),X24203),c_SetInterval_Oord_OatLeastLessThan(X24204,X24202,X24201,X24200,X24199))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OatLeastLessThan__iff])])]) ).

fof(i_0_6684,plain,
    ! [X24193,X24194,X24195,X24196,X24197,X24198] :
      ( ( hBOOL(hAPP(hAPP(X24195,X24194),X24197))
        | ~ hBOOL(hAPP(hAPP(c_member(X24198),X24197),c_SetInterval_Oord_OgreaterThanAtMost(X24198,X24196,X24195,X24194,X24193))) )
      & ( hBOOL(hAPP(hAPP(X24196,X24197),X24193))
        | ~ hBOOL(hAPP(hAPP(c_member(X24198),X24197),c_SetInterval_Oord_OgreaterThanAtMost(X24198,X24196,X24195,X24194,X24193))) )
      & ( ~ hBOOL(hAPP(hAPP(X24195,X24194),X24197))
        | ~ hBOOL(hAPP(hAPP(X24196,X24197),X24193))
        | hBOOL(hAPP(hAPP(c_member(X24198),X24197),c_SetInterval_Oord_OgreaterThanAtMost(X24198,X24196,X24195,X24194,X24193))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OgreaterThanAtMost__iff])])]) ).

fof(i_0_6685,plain,
    ! [X26631,X26632,X26633,X26634,X26635] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk247_5(X26631,X26632,X26633,X26634,X26635)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X26635),X26632),X26634) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X26635),X26631),X26633)
        | ~ c_Nat__Transfer_Onat__set(X26633)
        | X26634 != X26633
        | ~ class_Groups_Ocomm__monoid__add(X26635)
        | ~ class_Groups_Ocomm__monoid__mult(X26635) )
      & ( hAPP(X26632,esk247_5(X26631,X26632,X26633,X26634,X26635)) != hAPP(X26631,esk247_5(X26631,X26632,X26633,X26634,X26635))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X26635),X26632),X26634) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X26635),X26631),X26633)
        | ~ c_Nat__Transfer_Onat__set(X26633)
        | X26634 != X26633
        | ~ class_Groups_Ocomm__monoid__add(X26635)
        | ~ class_Groups_Ocomm__monoid__mult(X26635) ) ),
    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_6686,plain,
    ! [X26617,X26618,X26619,X26620,X26621] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk246_5(X26617,X26618,X26619,X26620,X26621)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X26621),X26618),X26620) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X26621),X26617),X26619)
        | ~ c_Nat__Transfer_Onat__set(X26619)
        | X26620 != X26619
        | ~ class_Groups_Ocomm__monoid__add(X26621)
        | ~ class_Groups_Ocomm__monoid__mult(X26621) )
      & ( hAPP(X26618,esk246_5(X26617,X26618,X26619,X26620,X26621)) != hAPP(X26617,esk246_5(X26617,X26618,X26619,X26620,X26621))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X26621),X26618),X26620) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X26621),X26617),X26619)
        | ~ c_Nat__Transfer_Onat__set(X26619)
        | X26620 != X26619
        | ~ class_Groups_Ocomm__monoid__add(X26621)
        | ~ class_Groups_Ocomm__monoid__mult(X26621) ) ),
    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_6687,plain,
    ! [X31276,X31277] : c_Random_Oselect__weight(X31277,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,X31277),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,X31277,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X31277,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,X31277)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),X31276)) = c_Random_Oselect__weight(X31277,X31276),
    inference(variable_rename,[status(thm)],[fact_select__weigth__drop__zero]) ).

fof(i_0_6688,plain,
    ! [X31274,X31275] : c_Random_Opick(X31275,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,X31275),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,X31275,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X31275,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,X31275)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),X31274)) = c_Random_Opick(X31275,X31274),
    inference(variable_rename,[status(thm)],[fact_pick__drop__zero]) ).

cnf(i_0_6689,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_6690,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_6691,plain,
    ! [X34123,X34124,X34125,X34126,X34127] :
      ( ~ c_Fun_Obij__betw(X34127,X34126,X34125,c_Orderings_Otop__class_Otop(tc_fun(X34127,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X34126,tc_HOL_Obool)))
      | ~ c_Fun_Obij__betw(X34124,X34127,X34123,c_Orderings_Otop__class_Otop(tc_fun(X34124,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X34127,tc_HOL_Obool)))
      | c_Hilbert__Choice_Oinv__into(X34124,X34126,c_Orderings_Otop__class_Otop(tc_fun(X34124,tc_HOL_Obool)),hAPP(c_Fun_Ocomp(X34127,X34126,X34124,X34125),X34123)) = hAPP(c_Fun_Ocomp(X34127,X34124,X34126,c_Hilbert__Choice_Oinv__into(X34124,X34127,c_Orderings_Otop__class_Otop(tc_fun(X34124,tc_HOL_Obool)),X34123)),c_Hilbert__Choice_Oinv__into(X34127,X34126,c_Orderings_Otop__class_Otop(tc_fun(X34127,tc_HOL_Obool)),X34125)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_o__inv__distrib])]) ).

cnf(i_0_6692,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_5417]) ).

cnf(i_0_6693,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_5418]) ).

fof(i_0_6694,plain,
    ! [X30938,X30939,X30940,X30941] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X30941,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X30941,X30940),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X30941,X30940),tc_HOL_Obool)),X30939),X30938))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X30941,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X30941,X30940),X30939)),hAPP(c_Relation_ODomain(X30941,X30940),X30938)))),
    inference(variable_rename,[status(thm)],[fact_Domain__Int__subset]) ).

fof(i_0_6695,plain,
    ! [X28293,X28294,X28295,X28296] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28296,tc_HOL_Obool)),hAPP(c_Relation_ORange(X28295,X28296),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X28295,X28296),tc_HOL_Obool)),X28294),X28293))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X28296,tc_HOL_Obool)),hAPP(c_Relation_ORange(X28295,X28296),X28294)),hAPP(c_Relation_ORange(X28295,X28296),X28293)))),
    inference(variable_rename,[status(thm)],[fact_Range__Int__subset]) ).

fof(i_0_6696,plain,
    ! [X26249,X26250,X26251,X26252,X26253] :
      ( ~ class_Groups_Ocomm__monoid__add(X26253)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26252),X26251))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26252,X26253),hAPP(hAPP(c_COMBS(X26252,X26253,X26253),hAPP(hAPP(c_COMBB(X26253,tc_fun(X26253,X26253),X26252),c_Groups_Oplus__class_Oplus(X26253)),X26250)),X26249)),X26251) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26253),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26252,X26253),X26250),X26251)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26252,X26253),X26249),X26251)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum_Odistrib])]) ).

fof(i_0_6697,plain,
    ! [X24711,X24712,X24713,X24714,X24715] :
      ( ~ class_Fields_Ofield__inverse__zero(X24715)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24714),X24713))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24714,X24715),hAPP(hAPP(c_COMBS(X24714,X24715,X24715),hAPP(hAPP(c_COMBB(X24715,tc_fun(X24715,X24715),X24714),c_Rings_Oinverse__class_Odivide(X24715)),X24712)),X24711)),X24713) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24715),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24714,X24715),X24712),X24713)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24714,X24715),X24711),X24713)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__dividef])]) ).

fof(i_0_6698,plain,
    ! [X24706,X24707,X24708,X24709,X24710] :
      ( ~ class_Groups_Ocomm__monoid__mult(X24710)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24709),X24708))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24709,X24710),hAPP(hAPP(c_COMBS(X24709,X24710,X24710),hAPP(hAPP(c_COMBB(X24710,tc_fun(X24710,X24710),X24709),c_Groups_Otimes__class_Otimes(X24710)),X24707)),X24706)),X24708) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24710),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24709,X24710),X24707),X24708)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24709,X24710),X24706),X24708)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod_Odistrib])]) ).

fof(i_0_6699,plain,
    ! [X26686,X26687,X26688,X26689,X26690,X26691] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X26691,X26690,X26689,X26688,X26687),X26686))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X26691),X26687)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__graph__imp__finite])]) ).

fof(i_0_6700,plain,
    ! [X29296,X29297] : hAPP(c_List_Orotate1(X29297),X29296) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(X29297),X29297,c_List_Olist_ONil(X29297),hAPP(hAPP(c_COMBB(tc_List_Olist(X29297),tc_fun(tc_List_Olist(X29297),tc_List_Olist(X29297)),X29297),hAPP(c_COMBC(tc_List_Olist(X29297),tc_List_Olist(X29297),tc_List_Olist(X29297)),c_List_Oappend(X29297))),hAPP(hAPP(c_COMBC(X29297,tc_List_Olist(X29297),tc_List_Olist(X29297)),c_List_Olist_OCons(X29297)),c_List_Olist_ONil(X29297)))),X29296),
    inference(variable_rename,[status(thm)],[fact_rotate1__def]) ).

fof(i_0_6701,plain,
    ! [X26230,X26231,X26232,X26233,X26234] :
      ( ~ class_Groups_Oab__group__add(X26234)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26233,X26234),hAPP(hAPP(c_COMBS(X26233,X26234,X26234),hAPP(hAPP(c_COMBB(X26234,tc_fun(X26234,X26234),X26233),c_Groups_Ominus__class_Ominus(X26234)),X26232)),X26231)),X26230) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X26234),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26233,X26234),X26232),X26230)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26233,X26234),X26231),X26230)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__subtractf])]) ).

fof(i_0_6702,plain,
    ! [X26216,X26217,X26218,X26219,X26220] :
      ( ~ class_Groups_Ocomm__monoid__add(X26220)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26219,X26220),hAPP(hAPP(c_COMBS(X26219,X26220,X26220),hAPP(hAPP(c_COMBB(X26220,tc_fun(X26220,X26220),X26219),c_Groups_Oplus__class_Oplus(X26220)),X26218)),X26217)),X26216) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26220),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26219,X26220),X26218),X26216)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26219,X26220),X26217),X26216)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__addf])]) ).

fof(i_0_6703,plain,
    ! [X24649,X24650,X24651,X24652,X24653] :
      ( ~ class_Groups_Ocomm__monoid__mult(X24653)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24652,X24653),hAPP(hAPP(c_COMBS(X24652,X24653,X24653),hAPP(hAPP(c_COMBB(X24653,tc_fun(X24653,X24653),X24652),c_Groups_Otimes__class_Otimes(X24653)),X24651)),X24650)),X24649) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24653),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24652,X24653),X24651),X24649)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24652,X24653),X24650),X24649)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__timesf])]) ).

fof(i_0_6704,plain,
    ! [X21904,X21905,X21906,X21907,X21908] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X21908,X21907),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X21906),X21905)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X21907))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X21904))
      | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X21908,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21907),X21904)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X21906),X21904)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21907),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21906,X21904))),X21905)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__nat__rel__mult2__eq])]) ).

fof(i_0_6705,plain,
    ! [X30578,X30579,X30580] : c_List_Olistsp(X30580,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X30580,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X30580,tc_fun(X30580,tc_HOL_Obool),tc_HOL_Obool),c_member(X30580)),X30579)),hAPP(hAPP(c_COMBC(X30580,tc_fun(X30580,tc_HOL_Obool),tc_HOL_Obool),c_member(X30580)),X30578))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X30580),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_List_Olist(X30580),tc_fun(tc_List_Olist(X30580),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(X30580))),c_List_Olists(X30580,X30579))),hAPP(hAPP(c_COMBC(tc_List_Olist(X30580),tc_fun(tc_List_Olist(X30580),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(X30580))),c_List_Olists(X30580,X30578))),
    inference(variable_rename,[status(thm)],[fact_lists__Int__eq]) ).

fof(i_0_6706,plain,
    ! [X30318,X30319] : c_Random_Oselect__weight(X30319,X30318) = 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(X30319,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,X30319),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X30319)),X30318)))),hAPP(hAPP(c_COMBB(X30319,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X30319,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(X30319,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Opick(X30319,X30318))),
    inference(variable_rename,[status(thm)],[fact_select__weight__def]) ).

fof(i_0_6707,plain,
    ! [X27411,X27412,X27413,X27414,X27415,X27416] : hAPP(hAPP(c_Product__Type_OSigma(X27416,X27415),hAPP(hAPP(c_Set_Oinsert(X27416),X27414),X27413)),hAPP(c_COMBK(tc_fun(X27415,tc_HOL_Obool),X27416),hAPP(hAPP(c_Set_Oinsert(X27415),X27412),X27411))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(X27416,X27415)),hAPP(hAPP(c_Product__Type_OPair(X27416,X27415),X27414),X27412)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X27416,X27415),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X27416,X27415),X27413),hAPP(c_COMBK(tc_fun(X27415,tc_HOL_Obool),X27416),hAPP(hAPP(c_Set_Oinsert(X27415),X27412),X27411)))),hAPP(hAPP(c_Product__Type_OSigma(X27416,X27415),hAPP(hAPP(c_Set_Oinsert(X27416),X27414),X27413)),hAPP(c_COMBK(tc_fun(X27415,tc_HOL_Obool),X27416),X27411)))),
    inference(variable_rename,[status(thm)],[fact_insert__times__insert]) ).

fof(i_0_6708,plain,
    ! [X26225,X26226,X26227,X26228,X26229] :
      ( ~ class_Fields_Ofield(X26229)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X26229),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26228,X26229),X26227),X26226)),X26225) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26228,X26229),hAPP(hAPP(c_COMBC(X26228,X26229,X26229),hAPP(hAPP(c_COMBB(X26229,tc_fun(X26229,X26229),X26228),c_Rings_Oinverse__class_Odivide(X26229)),X26227)),X26225)),X26226) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__divide__distrib])]) ).

fof(i_0_6709,plain,
    ! [X26204,X26205,X26206,X26207,X26208] :
      ( ~ class_Rings_Osemiring__0(X26208)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26208),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26207,X26208),X26206),X26205)),X26204) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26207,X26208),hAPP(hAPP(c_COMBC(X26207,X26208,X26208),hAPP(hAPP(c_COMBB(X26208,tc_fun(X26208,X26208),X26207),c_Groups_Otimes__class_Otimes(X26208)),X26206)),X26204)),X26205) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__left__distrib])]) ).

fof(i_0_6710,plain,
    ! [X22026,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)))
      | X22029 = 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)),X22026))
      | hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22030,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22029),X22026)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X22028),X22026)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22029),c_Divides_Odiv__class_Omod(tc_Int_Oint,X22028,X22026))),X22027)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult2__lemma])]) ).

fof(i_0_6711,plain,
    ! [X32221,X32222,X32223,X32224,X32225] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32225),tc_List_Olist(X32225))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32225),tc_List_Olist(X32225)),X32224),X32223)),c_List_Olistrel(X32225,c_Transitive__Closure_Ortrancl(X32225,X32222))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32225),tc_List_Olist(X32225))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32225),tc_List_Olist(X32225)),X32223),X32221)),c_List_Olistrel(X32225,c_Transitive__Closure_Ortrancl(X32225,X32222))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32225),tc_List_Olist(X32225))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32225),tc_List_Olist(X32225)),X32224),X32221)),c_List_Olistrel(X32225,c_Transitive__Closure_Ortrancl(X32225,X32222)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__rtrancl__trans])]) ).

cnf(i_0_6712,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_5419]) ).

cnf(i_0_6713,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_5420]) ).

fof(i_0_6714,plain,
    ! [X22312,X22313,X22314] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22314,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X22314,tc_fun(X22314,tc_HOL_Obool),tc_HOL_Obool),c_member(X22314)),X22313)),hAPP(hAPP(c_COMBC(X22314,tc_fun(X22314,tc_HOL_Obool),tc_HOL_Obool),c_member(X22314)),X22312)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22314,tc_HOL_Obool)),X22313),X22312)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22314,tc_HOL_Obool)),X22313),X22312))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22314,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X22314,tc_fun(X22314,tc_HOL_Obool),tc_HOL_Obool),c_member(X22314)),X22313)),hAPP(hAPP(c_COMBC(X22314,tc_fun(X22314,tc_HOL_Obool),tc_HOL_Obool),c_member(X22314)),X22312))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__subset__eq])]) ).

cnf(i_0_6715,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_5421]) ).

cnf(i_0_6716,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_5422]) ).

fof(i_0_6717,plain,
    ! [X28237,X28238,X28239,X28240] :
      ( ~ c_FunDef_Oreduction__pair(X28240,X28239)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28240,X28240),tc_HOL_Obool)),X28238),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X28240,X28240),tc_HOL_Obool),tc_fun(tc_prod(X28240,X28240),tc_HOL_Obool)),X28239)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28240,X28240),tc_HOL_Obool)),X28237),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(X28240,X28240),tc_HOL_Obool),tc_fun(tc_prod(X28240,X28240),tc_HOL_Obool)),X28239)))
      | ~ c_Wellfounded_Owf(X28240,X28237)
      | c_Wellfounded_Owf(X28240,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28240,X28240),tc_HOL_Obool)),X28238),X28237)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_reduction__pair__lemma])]) ).

fof(i_0_6718,plain,
    ! [X30935,X30936,X30937] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X30937,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X30937,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X30937,tc_HOL_Obool),tc_HOL_Obool)),X30936),X30935))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X30937,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X30937,tc_HOL_Obool),X30936)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X30937,tc_HOL_Obool),X30935)))),
    inference(variable_rename,[status(thm)],[fact_Union__Int__subset]) ).

fof(i_0_6719,plain,
    ! [X23392,X23393,X23394,X23395,X23396,X23397,X23398] :
      ( X23398 = X23397
      | c_Fun_Ofun__upd(X23396,X23395,c_Fun_Ofun__upd(X23396,X23395,X23394,X23398,X23393),X23397,X23392) = c_Fun_Ofun__upd(X23396,X23395,c_Fun_Ofun__upd(X23396,X23395,X23394,X23397,X23392),X23398,X23393) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__upd__twist])]) ).

fof(i_0_6720,plain,
    ! [X32506,X32507,X32508,X32509,X32510] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X32510,tc_HOL_Obool)),hAPP(c_Relation_OImage(X32509,X32510,X32508),X32507)),X32506))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X32509,tc_HOL_Obool)),X32507),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X32509,tc_HOL_Obool)),hAPP(c_Relation_OImage(X32510,X32509,hAPP(c_Relation_Oconverse(X32509,X32510),X32508)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X32510,tc_HOL_Obool)),X32506))))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X32509,tc_HOL_Obool)),X32507),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X32509,tc_HOL_Obool)),hAPP(c_Relation_OImage(X32510,X32509,hAPP(c_Relation_Oconverse(X32509,X32510),X32508)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X32510,tc_HOL_Obool)),X32506)))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X32510,tc_HOL_Obool)),hAPP(c_Relation_OImage(X32509,X32510,X32508),X32507)),X32506)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Image__subset__eq])]) ).

cnf(i_0_6721,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_5423]) ).

cnf(i_0_6722,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_5424]) ).

fof(i_0_6723,plain,
    ! [X24923,X24924,X24925,X24926] : hAPP(c_Set_Oimage(X24926,X24925,X24924),X24923) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24926,tc_fun(X24925,tc_HOL_Obool)),X24923),hAPP(hAPP(c_COMBC(X24926,tc_fun(X24925,tc_HOL_Obool),tc_fun(X24925,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X24925,tc_fun(tc_fun(X24925,tc_HOL_Obool),tc_fun(X24925,tc_HOL_Obool)),X24926),c_Set_Oinsert(X24925)),X24924)),c_Orderings_Obot__class_Obot(tc_fun(X24925,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_image__eq__UN]) ).

fof(i_0_6724,plain,
    ! [X27766,X27767,X27768] :
      ( ( ~ hBOOL(hAPP(X27768,X27767))
        | hAPP(c_Set_OCollect(X27766),hAPP(hAPP(c_COMBS(X27766,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27766),c_fconj),hAPP(hAPP(c_COMBC(X27766,X27766,tc_HOL_Obool),c_fequal),X27767))),X27768)) = hAPP(hAPP(c_Set_Oinsert(X27766),X27767),c_Orderings_Obot__class_Obot(tc_fun(X27766,tc_HOL_Obool))) )
      & ( hBOOL(hAPP(X27768,X27767))
        | hAPP(c_Set_OCollect(X27766),hAPP(hAPP(c_COMBS(X27766,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27766),c_fconj),hAPP(hAPP(c_COMBC(X27766,X27766,tc_HOL_Obool),c_fequal),X27767))),X27768)) = c_Orderings_Obot__class_Obot(tc_fun(X27766,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5425])]) ).

fof(i_0_6725,plain,
    ! [X32246,X32247,X32248,X32249,X32250] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32250),tc_List_Olist(X32250))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32250),tc_List_Olist(X32250)),X32249),X32248)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X32250),c_List_Olistrel1(X32250,X32247))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32250),tc_List_Olist(X32250))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32250),tc_List_Olist(X32250)),hAPP(hAPP(c_List_Olist_OCons(X32250),X32246),X32249)),hAPP(hAPP(c_List_Olist_OCons(X32250),X32246),X32248))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X32250),c_List_Olistrel1(X32250,X32247)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__listrel1__ConsI1])]) ).

fof(i_0_6726,plain,
    ! [X22759,X22760,X22761,X22762] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22762),X22761))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22760),X22759))
      | 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),X22762),X22760)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X22761),X22759))),c_FunDef_Opair__leq)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pair__leqI2])]) ).

fof(i_0_6727,plain,
    ! [X22739,X22740,X22741,X22742] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22742),X22741))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22740),X22739))
      | 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),X22742),X22740)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X22741),X22739))),c_FunDef_Opair__less)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pair__lessI2])]) ).

fof(i_0_6728,plain,
    ! [X32178,X32179,X32180] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X32180,X32180),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X32180,X32180),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X32180,X32179)),c_Transitive__Closure_Ortrancl(X32180,X32178))),c_Transitive__Closure_Ortrancl(X32180,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X32180,X32180),tc_HOL_Obool)),X32179),X32178)))),
    inference(variable_rename,[status(thm)],[fact_rtrancl__Un__subset]) ).

fof(i_0_6729,plain,
    ! [X33770,X33771,X33772,X33773,X33774] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33774),tc_List_Olist(X33774))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33774),tc_List_Olist(X33774)),X33773),X33772)),c_List_Olexord(X33774,X33771)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33774),tc_List_Olist(X33774))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33774),tc_List_Olist(X33774)),X33772),X33770)),c_List_Olexord(X33774,X33771)))
      | ~ c_Relation_Otrans(X33774,X33771)
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X33774),tc_List_Olist(X33774))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X33774),tc_List_Olist(X33774)),X33773),X33770)),c_List_Olexord(X33774,X33771))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__trans])]) ).

fof(i_0_6730,plain,
    ! [X24085,X24086,X24087,X24088,X24089] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24089,tc_HOL_Obool)),hAPP(c_Relation_OImage(X24088,X24089,X24087),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24088,tc_HOL_Obool)),X24086),X24085))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24089,tc_HOL_Obool)),hAPP(c_Relation_OImage(X24088,X24089,X24087),X24086)),hAPP(c_Relation_OImage(X24088,X24089,X24087),X24085)))),
    inference(variable_rename,[status(thm)],[fact_Image__Int__subset]) ).

fof(i_0_6731,plain,
    ! [X24053,X24054,X24055,X24056,X24057] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24057,tc_HOL_Obool)),hAPP(c_Set_Oimage(X24056,X24057,X24055),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24056,tc_HOL_Obool)),X24054),X24053))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24057,tc_HOL_Obool)),hAPP(c_Set_Oimage(X24056,X24057,X24055),X24054)),hAPP(c_Set_Oimage(X24056,X24057,X24055),X24053)))),
    inference(variable_rename,[status(thm)],[fact_image__Int__subset]) ).

fof(i_0_6732,plain,
    ! [X33103,X33104] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk497_2(X33103,X33104)))
        | 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)))),X33104)) = 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)))),X33103)) )
      & ( ~ hBOOL(hAPP(X33104,esk497_2(X33103,X33104)))
        | ~ hBOOL(hAPP(X33103,esk497_2(X33103,X33104)))
        | 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)))),X33104)) = 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)))),X33103)) )
      & ( hBOOL(hAPP(X33104,esk497_2(X33103,X33104)))
        | hBOOL(hAPP(X33103,esk497_2(X33103,X33104)))
        | 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)))),X33104)) = 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)))),X33103)) ) ),
    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_6733,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_5426]) ).

fof(i_0_6734,plain,
    ! [X22771,X22772,X22773,X22774] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22774),X22773))
      | 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),X22774),X22772)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X22773),X22771))),c_FunDef_Opair__leq)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pair__leqI1])]) ).

fof(i_0_6735,plain,
    ! [X22755,X22756,X22757,X22758] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22758),X22757))
      | 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),X22758),X22756)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X22757),X22755))),c_FunDef_Opair__less)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pair__lessI1])]) ).

fof(i_0_6736,plain,
    ! [X28960,X28961] : c_List_Olists(X28961,X28960) = hAPP(c_Set_OCollect(tc_List_Olist(X28961)),hAPP(hAPP(c_COMBC(tc_List_Olist(X28961),tc_fun(X28961,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X28961,tc_HOL_Obool),tc_fun(tc_fun(X28961,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X28961)),c_Orderings_Oord__class_Oless__eq(tc_fun(X28961,tc_HOL_Obool))),c_List_Oset(X28961))),X28960)),
    inference(variable_rename,[status(thm)],[fact_lists__eq__set]) ).

fof(i_0_6737,plain,
    ! [X23348,X23349,X23350,X23351,X23352,X23353] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X23353),X23352),X23351))
        | hAPP(c_Set_Oimage(X23353,X23350,c_Fun_Ofun__upd(X23353,X23350,X23349,X23352,X23348)),X23351) = hAPP(hAPP(c_Set_Oinsert(X23350),X23348),hAPP(c_Set_Oimage(X23353,X23350,X23349),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23353,tc_HOL_Obool)),X23351),hAPP(hAPP(c_Set_Oinsert(X23353),X23352),c_Orderings_Obot__class_Obot(tc_fun(X23353,tc_HOL_Obool)))))) )
      & ( hBOOL(hAPP(hAPP(c_member(X23353),X23352),X23351))
        | hAPP(c_Set_Oimage(X23353,X23350,c_Fun_Ofun__upd(X23353,X23350,X23349,X23352,X23348)),X23351) = hAPP(c_Set_Oimage(X23353,X23350,X23349),X23351) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5427])]) ).

fof(i_0_6738,plain,
    ! [X28533,X28534,X28535,X28536,X28537,X28538] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28538),tc_List_Olist(X28538))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28538),tc_List_Olist(X28538)),X28537),X28536)),c_List_Olistrel1(X28538,X28535)))
        | X28534 != X28533
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28538),tc_List_Olist(X28538))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28538),tc_List_Olist(X28538)),hAPP(hAPP(c_List_Oappend(X28538),X28537),X28534)),hAPP(hAPP(c_List_Oappend(X28538),X28536),X28533))),c_List_Olistrel1(X28538,X28535))) )
      & ( X28537 != X28536
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28538),tc_List_Olist(X28538))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28538),tc_List_Olist(X28538)),X28534),X28533)),c_List_Olistrel1(X28538,X28535)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28538),tc_List_Olist(X28538))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28538),tc_List_Olist(X28538)),hAPP(hAPP(c_List_Oappend(X28538),X28537),X28534)),hAPP(hAPP(c_List_Oappend(X28538),X28536),X28533))),c_List_Olistrel1(X28538,X28535))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__listrel1I])])]) ).

fof(i_0_6739,plain,
    ! [X28518,X28519,X28520,X28521,X28522] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28522),tc_List_Olist(X28522))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28522),tc_List_Olist(X28522)),X28521),X28520)),c_List_Olistrel1(X28522,X28519)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28522),tc_List_Olist(X28522))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28522),tc_List_Olist(X28522)),hAPP(hAPP(c_List_Olist_OCons(X28522),X28518),X28521)),hAPP(hAPP(c_List_Olist_OCons(X28522),X28518),X28520))),c_List_Olistrel1(X28522,X28519))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel1I2])]) ).

fof(i_0_6740,plain,
    ! [X28397,X28398,X28399,X28400,X28401] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28401),tc_List_Olist(X28401))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28401),tc_List_Olist(X28401)),X28400),X28399)),c_List_Olexord(X28401,X28398)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28401),tc_List_Olist(X28401))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28401),tc_List_Olist(X28401)),hAPP(hAPP(c_List_Oappend(X28401),X28397),X28400)),hAPP(hAPP(c_List_Oappend(X28401),X28397),X28399))),c_List_Olexord(X28401,X28398))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__append__leftI])]) ).

cnf(i_0_6741,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_5428]) ).

fof(i_0_6742,plain,
    ! [X27858] : 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)))),X27858))),
    inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J]) ).

fof(i_0_6743,plain,
    ! [X29784,X29785,X29786,X29787,X29788,X29789] : hAPP(hAPP(c_List_Ozip(X29789,X29788),hAPP(hAPP(c_List_Omap(X29787,X29789),X29786),X29785)),X29784) = hAPP(hAPP(c_List_Omap(tc_prod(X29787,X29788),tc_prod(X29789,X29788)),hAPP(c_Product__Type_Oprod_Oprod__case(X29787,X29788,tc_prod(X29789,X29788)),hAPP(hAPP(c_COMBB(X29789,tc_fun(X29788,tc_prod(X29789,X29788)),X29787),c_Product__Type_OPair(X29789,X29788)),X29786))),hAPP(hAPP(c_List_Ozip(X29787,X29788),X29785),X29784)),
    inference(variable_rename,[status(thm)],[fact_zip__map1]) ).

fof(i_0_6744,plain,
    ! [X22791,X22792,X22793] : c_Wellfounded_Omlex__prod(X22793,X22792,X22791) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,X22793),X22793),c_Wellfounded_Olex__prod(tc_Nat_Onat,X22793,c_Wellfounded_Oless__than,X22791)),hAPP(hAPP(c_COMBS(X22793,X22793,tc_prod(tc_Nat_Onat,X22793)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X22793,tc_prod(tc_Nat_Onat,X22793)),X22793),c_Product__Type_OPair(tc_Nat_Onat,X22793)),X22792)),c_COMBI(X22793))),
    inference(variable_rename,[status(thm)],[fact_mlex__prod__def]) ).

fof(i_0_6745,plain,
    ! [X25412,X25413,X25414] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X25414),esk182_3(X25412,X25413,X25414)))
        | hBOOL(hAPP(X25412,c_Orderings_Obot__class_Obot(tc_fun(X25414,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(X25412,X25413))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25414),X25413)) )
      & ( hBOOL(hAPP(hAPP(c_member(X25414),esk181_3(X25412,X25413,X25414)),esk182_3(X25412,X25413,X25414)))
        | hBOOL(hAPP(X25412,c_Orderings_Obot__class_Obot(tc_fun(X25414,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(X25412,X25413))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25414),X25413)) )
      & ( hBOOL(hAPP(X25412,esk182_3(X25412,X25413,X25414)))
        | hBOOL(hAPP(X25412,c_Orderings_Obot__class_Obot(tc_fun(X25414,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(X25412,X25413))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25414),X25413)) )
      & ( ~ hBOOL(hAPP(X25412,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25414,tc_HOL_Obool)),esk182_3(X25412,X25413,X25414)),hAPP(hAPP(c_Set_Oinsert(X25414),esk181_3(X25412,X25413,X25414)),c_Orderings_Obot__class_Obot(tc_fun(X25414,tc_HOL_Obool))))))
        | hBOOL(hAPP(X25412,c_Orderings_Obot__class_Obot(tc_fun(X25414,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(X25412,X25413))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25414),X25413)) ) ),
    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_6746,plain,
    ! [X27383,X27384,X27385,X27386,X27387,X27388] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27385,X27388),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X27385,X27388),X27384),hAPP(c_COMBK(tc_fun(X27388,tc_HOL_Obool),X27385),X27386))),hAPP(hAPP(c_Product__Type_OSigma(X27385,X27388),X27383),hAPP(c_COMBK(tc_fun(X27388,tc_HOL_Obool),X27385),X27386))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27385,tc_HOL_Obool)),X27384),X27383))
        | ~ hBOOL(hAPP(hAPP(c_member(X27388),X27387),X27386)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27385,tc_HOL_Obool)),X27384),X27383))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27385,X27388),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X27385,X27388),X27384),hAPP(c_COMBK(tc_fun(X27388,tc_HOL_Obool),X27385),X27386))),hAPP(hAPP(c_Product__Type_OSigma(X27385,X27388),X27383),hAPP(c_COMBK(tc_fun(X27388,tc_HOL_Obool),X27385),X27386))))
        | ~ hBOOL(hAPP(hAPP(c_member(X27388),X27387),X27386)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Times__subset__cancel2])])]) ).

cnf(i_0_6747,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_5429]) ).

fof(i_0_6748,plain,
    ! [X21919,X21920,X21921,X21922,X21923,X21924] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X21924,X21924)),hAPP(hAPP(c_Product__Type_OPair(X21924,X21924),X21923),X21922)),X21921))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X21924,X21924)),hAPP(hAPP(c_Product__Type_OPair(X21924,X21924),X21922),X21920)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X21924,X21924),tc_HOL_Obool),X21919),X21921)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X21924,X21924)),hAPP(hAPP(c_Product__Type_OPair(X21924,X21924),X21923),X21920)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X21924,X21924),tc_HOL_Obool),hAPP(c_Nat_OSuc,X21919)),X21921))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__pow__Suc__I2])]) ).

fof(i_0_6749,plain,
    ! [X21925,X21926,X21927,X21928,X21929,X21930] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X21930,X21930)),hAPP(hAPP(c_Product__Type_OPair(X21930,X21930),X21929),X21928)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X21930,X21930),tc_HOL_Obool),X21927),X21926)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X21930,X21930)),hAPP(hAPP(c_Product__Type_OPair(X21930,X21930),X21928),X21925)),X21926))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X21930,X21930)),hAPP(hAPP(c_Product__Type_OPair(X21930,X21930),X21929),X21925)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X21930,X21930),tc_HOL_Obool),hAPP(c_Nat_OSuc,X21927)),X21926))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__pow__Suc__I])]) ).

fof(i_0_6750,plain,
    ! [X25493,X25494,X25495,X25496,X25497] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25497,tc_HOL_Obool)),hAPP(c_Set_Oimage(X25496,X25497,X25495),X25494)),X25493))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X25497,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_fun(X25496,tc_HOL_Obool),tc_fun(X25497,tc_HOL_Obool),c_Set_Oimage(X25496,X25497,X25495)),hAPP(c_Set_OPow(X25496),X25494))),hAPP(c_Set_OPow(X25497),X25493))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__Pow__mono])]) ).

fof(i_0_6751,plain,
    ! [X22132,X22133] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22132),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | c_Nitpick_Onorm__frac(X22133,X22132) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22133),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22132))
        | ~ 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),X22133),X22132))) )
      & ( X22133 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Nitpick_Onorm__frac(X22133,X22132) = 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),X22132),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),X22133),X22132))) )
      & ( X22132 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Nitpick_Onorm__frac(X22133,X22132) = 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),X22132),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),X22133),X22132))) )
      & ( X22133 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | X22132 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Nitpick_Onorm__frac(X22133,X22132) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X22133),X22132)),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),X22133))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X22132)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22132),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),X22133),X22132))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5430])])]) ).

cnf(i_0_6752,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_5431]) ).

fof(i_0_6753,plain,
    ! [X30313,X30314,X30315] :
      ( ~ 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,X30315),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X30315)),X30314))))
      | hBOOL(hAPP(hAPP(c_member(X30315),hAPP(c_Product__Type_Ofst(X30315,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect__weight(X30315,X30314),X30313))),hAPP(c_List_Oset(X30315),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X30315),X30315),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X30315)),X30314)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_select__weight__member])]) ).

fof(i_0_6754,plain,
    ! [X26167,X26168,X26169,X26170] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X26170)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26170),hAPP(c_Groups_Oabs__class_Oabs(X26170),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26169,X26170),X26168),X26167))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26169,X26170),hAPP(hAPP(c_COMBB(X26170,X26170,X26169),c_Groups_Oabs__class_Oabs(X26170)),X26168)),X26167))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__abs])]) ).

fof(i_0_6755,plain,
    ! [X31278,X31279,X31280] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X31280,tc_HOL_Obool)),hAPP(c_List_Oset(X31280),X31279)),hAPP(hAPP(c_Set_Oinsert(X31280),X31278),c_Orderings_Obot__class_Obot(tc_fun(X31280,tc_HOL_Obool)))) = hAPP(c_List_Oset(X31280),hAPP(c_List_Ofilter(X31280,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X31280),c_fNot),hAPP(hAPP(c_COMBC(X31280,X31280,tc_HOL_Obool),c_fequal),X31278))),X31279)),
    inference(variable_rename,[status(thm)],[fact_set__minus__filter__out]) ).

fof(i_0_6756,plain,
    ! [X31155,X31156,X31157,X31158] : hAPP(c_List_Ofilter(X31158,X31157),hAPP(c_List_Ofilter(X31158,X31156),X31155)) = hAPP(c_List_Ofilter(X31158,hAPP(hAPP(c_COMBS(X31158,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X31158),c_fconj),X31156)),X31157)),X31155),
    inference(variable_rename,[status(thm)],[fact_filter__filter]) ).

fof(i_0_6757,plain,
    ! [X30942,X30943,X30944,X30945] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X30945,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X30945,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X30945,X30944),X30943)),hAPP(c_Relation_ODomain(X30945,X30944),X30942))),hAPP(c_Relation_ODomain(X30945,X30944),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X30945,X30944),tc_HOL_Obool)),X30943),X30942)))),
    inference(variable_rename,[status(thm)],[fact_Domain__Diff__subset]) ).

fof(i_0_6758,plain,
    ! [X28297,X28298,X28299,X28300] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28300,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X28300,tc_HOL_Obool)),hAPP(c_Relation_ORange(X28299,X28300),X28298)),hAPP(c_Relation_ORange(X28299,X28300),X28297))),hAPP(c_Relation_ORange(X28299,X28300),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X28299,X28300),tc_HOL_Obool)),X28298),X28297)))),
    inference(variable_rename,[status(thm)],[fact_Range__Diff__subset]) ).

fof(i_0_6759,plain,
    ! [X20704,X20705,X20706,X20707] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X20707),X20705),X20704))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X20707,tc_HOL_Obool)),X20706),X20704))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X20707,tc_HOL_Obool)),X20706),hAPP(hAPP(c_Set_Oinsert(X20707),X20705),X20704))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X20707),X20705),X20706))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X20707,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20707,tc_HOL_Obool)),X20706),hAPP(hAPP(c_Set_Oinsert(X20707),X20705),c_Orderings_Obot__class_Obot(tc_fun(X20707,tc_HOL_Obool))))),X20704))
        | hBOOL(hAPP(hAPP(c_member(X20707),X20705),X20704))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X20707,tc_HOL_Obool)),X20706),hAPP(hAPP(c_Set_Oinsert(X20707),X20705),X20704))) )
      & ( hBOOL(hAPP(hAPP(c_member(X20707),X20705),X20706))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20707,tc_HOL_Obool)),X20706),X20704))
        | hBOOL(hAPP(hAPP(c_member(X20707),X20705),X20704))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X20707,tc_HOL_Obool)),X20706),hAPP(hAPP(c_Set_Oinsert(X20707),X20705),X20704))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X20707),X20705),X20704))
        | hBOOL(hAPP(hAPP(c_member(X20707),X20705),X20704))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X20707,tc_HOL_Obool)),X20706),hAPP(hAPP(c_Set_Oinsert(X20707),X20705),X20704))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X20707),X20705),X20706))
        | hBOOL(hAPP(hAPP(c_member(X20707),X20705),X20706))
        | hBOOL(hAPP(hAPP(c_member(X20707),X20705),X20704))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X20707,tc_HOL_Obool)),X20706),hAPP(hAPP(c_Set_Oinsert(X20707),X20705),X20704))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20707,tc_HOL_Obool)),X20706),X20704))
        | hBOOL(hAPP(hAPP(c_member(X20707),X20705),X20706))
        | hBOOL(hAPP(hAPP(c_member(X20707),X20705),X20704))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X20707,tc_HOL_Obool)),X20706),hAPP(hAPP(c_Set_Oinsert(X20707),X20705),X20704))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X20707),X20705),X20706))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X20707,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20707,tc_HOL_Obool)),X20706),hAPP(hAPP(c_Set_Oinsert(X20707),X20705),c_Orderings_Obot__class_Obot(tc_fun(X20707,tc_HOL_Obool))))),X20704))
        | hBOOL(hAPP(hAPP(c_member(X20707),X20705),X20704))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X20707,tc_HOL_Obool)),X20706),hAPP(hAPP(c_Set_Oinsert(X20707),X20705),X20704))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20707,tc_HOL_Obool)),X20706),X20704))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X20707,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20707,tc_HOL_Obool)),X20706),hAPP(hAPP(c_Set_Oinsert(X20707),X20705),c_Orderings_Obot__class_Obot(tc_fun(X20707,tc_HOL_Obool))))),X20704))
        | hBOOL(hAPP(hAPP(c_member(X20707),X20705),X20704))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X20707,tc_HOL_Obool)),X20706),hAPP(hAPP(c_Set_Oinsert(X20707),X20705),X20704))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X20707),X20705),X20704))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X20707,tc_HOL_Obool)),X20706),X20704))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X20707,tc_HOL_Obool)),X20706),hAPP(hAPP(c_Set_Oinsert(X20707),X20705),X20704))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X20707),X20705),X20706))
        | hBOOL(hAPP(hAPP(c_member(X20707),X20705),X20706))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X20707,tc_HOL_Obool)),X20706),X20704))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X20707,tc_HOL_Obool)),X20706),hAPP(hAPP(c_Set_Oinsert(X20707),X20705),X20704))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20707,tc_HOL_Obool)),X20706),X20704))
        | hBOOL(hAPP(hAPP(c_member(X20707),X20705),X20706))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X20707,tc_HOL_Obool)),X20706),X20704))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X20707,tc_HOL_Obool)),X20706),hAPP(hAPP(c_Set_Oinsert(X20707),X20705),X20704))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X20707),X20705),X20706))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X20707,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20707,tc_HOL_Obool)),X20706),hAPP(hAPP(c_Set_Oinsert(X20707),X20705),c_Orderings_Obot__class_Obot(tc_fun(X20707,tc_HOL_Obool))))),X20704))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X20707,tc_HOL_Obool)),X20706),X20704))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X20707,tc_HOL_Obool)),X20706),hAPP(hAPP(c_Set_Oinsert(X20707),X20705),X20704))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20707,tc_HOL_Obool)),X20706),X20704))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X20707,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20707,tc_HOL_Obool)),X20706),hAPP(hAPP(c_Set_Oinsert(X20707),X20705),c_Orderings_Obot__class_Obot(tc_fun(X20707,tc_HOL_Obool))))),X20704))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X20707,tc_HOL_Obool)),X20706),X20704))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X20707,tc_HOL_Obool)),X20706),hAPP(hAPP(c_Set_Oinsert(X20707),X20705),X20704))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5432])])]) ).

fof(i_0_6760,plain,
    ! [X28754,X28755,X28756] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X28756,X28756)),hAPP(hAPP(c_Product__Type_OPair(X28756,X28756),esk322_3(X28754,X28755,X28756)),esk322_3(X28754,X28755,X28756))),X28755))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28756),tc_List_Olist(X28756))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28756),tc_List_Olist(X28756)),X28754),X28754)),c_List_Olexord(X28756,X28755))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5433])])]) ).

fof(i_0_6761,plain,
    ! [X27646] : c_Finite__Set_Ofun__left__comm__idem(X27646,tc_fun(X27646,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X27646,tc_HOL_Obool),tc_fun(tc_fun(X27646,tc_HOL_Obool),tc_fun(X27646,tc_HOL_Obool)),X27646),hAPP(c_COMBC(tc_fun(X27646,tc_HOL_Obool),tc_fun(X27646,tc_HOL_Obool),tc_fun(X27646,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(X27646,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(X27646,tc_fun(X27646,tc_HOL_Obool),tc_fun(X27646,tc_HOL_Obool)),c_Set_Oinsert(X27646)),c_Orderings_Obot__class_Obot(tc_fun(X27646,tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[fact_fun__left__comm__idem__remove]) ).

cnf(i_0_6762,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_5434]) ).

fof(i_0_6763,plain,
    ! [X24594,X24595,X24596] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24596),X24595))
      | ~ hBOOL(hAPP(hAPP(c_member(X24596),X24594),X24595))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X24596),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24596,tc_HOL_Obool)),X24595),hAPP(hAPP(c_Set_Oinsert(X24596),X24594),c_Orderings_Obot__class_Obot(tc_fun(X24596,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X24596),X24595))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Diff1__less])]) ).

fof(i_0_6764,plain,
    ! [X22259,X22260,X22261,X22262,X22263,X22264] : hAPP(hAPP(c_COMBS(tc_prod(X22264,X22263),X22263,X22262),hAPP(hAPP(c_COMBB(X22261,tc_fun(X22263,X22262),tc_prod(X22264,X22263)),X22260),hAPP(hAPP(c_COMBB(X22264,X22261,tc_prod(X22264,X22263)),X22259),c_Product__Type_Ofst(X22264,X22263)))),c_Product__Type_Osnd(X22264,X22263)) = hAPP(c_Product__Type_Oprod_Oprod__case(X22264,X22263,X22262),hAPP(hAPP(c_COMBB(X22261,tc_fun(X22263,X22262),X22264),X22260),X22259)),
    inference(variable_rename,[status(thm)],[fact_split__comp__eq]) ).

fof(i_0_6765,plain,
    ! [X31445,X31446,X31447,X31448,X31449] :
      ( ~ class_Orderings_Olinorder(X31449)
      | ~ hBOOL(hAPP(hAPP(c_member(X31448),X31447),hAPP(c_List_Oset(X31448),X31446)))
      | ~ c_List_Olinorder__class_Osorted(X31449,hAPP(hAPP(c_List_Omap(X31448,X31449),X31445),X31446))
      | hAPP(c_List_Ohd(X31448),hAPP(c_List_Ofilter(X31448,hAPP(hAPP(c_COMBB(X31449,tc_HOL_Obool,X31448),hAPP(c_fequal,hAPP(X31445,X31447))),X31445)),X31446)) != X31447
      | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X31448,X31449,X31445),X31447),c_List_Oremove1(X31448,X31447,X31446)) = X31446 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insort__key__remove1])]) ).

fof(i_0_6766,plain,
    ! [X34153,X34154,X34155,X34156,X34157,X34158,X34159] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X34159,tc_HOL_Obool)),X34158),X34157) != c_Orderings_Obot__class_Obot(tc_fun(X34159,tc_HOL_Obool))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X34156,tc_HOL_Obool)),X34155),X34154) != c_Orderings_Obot__class_Obot(tc_fun(X34156,tc_HOL_Obool))
      | ~ c_Fun_Obij__betw(X34159,X34156,X34153,X34158,X34155)
      | ~ c_Fun_Obij__betw(X34159,X34156,X34153,X34157,X34154)
      | c_Fun_Obij__betw(X34159,X34156,X34153,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X34159,tc_HOL_Obool)),X34158),X34157),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X34156,tc_HOL_Obool)),X34155),X34154)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__betw__Disj__Un])]) ).

fof(i_0_6767,plain,
    ! [X23123,X23124] :
      ( ( 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)),X23124),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)),X23123),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)),X23124),X23123)),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)),X23124),X23123)),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)),X23124),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)),X23123),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_6768,plain,
    ! [X33591,X33592,X33593,X33594] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_fun(X33593,tc_HOL_Obool)),esk524_4(X33591,X33592,X33593,X33594)),X33592))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X33593,X33594),X33591),c_Complete__Lattice_OSup__class_OSup(tc_fun(X33593,tc_HOL_Obool),X33592)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X33593,tc_HOL_Obool),X33594),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X33593,X33594),X33591)),X33592)
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X33593,tc_HOL_Obool)),esk523_4(X33591,X33592,X33593,X33594)),X33592))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X33593,tc_HOL_Obool)),X33592))
        | ~ class_Groups_Ocomm__monoid__add(X33594) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_fun(X33593,tc_HOL_Obool)),esk525_4(X33591,X33592,X33593,X33594)),X33592))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X33593,X33594),X33591),c_Complete__Lattice_OSup__class_OSup(tc_fun(X33593,tc_HOL_Obool),X33592)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X33593,tc_HOL_Obool),X33594),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X33593,X33594),X33591)),X33592)
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X33593,tc_HOL_Obool)),esk523_4(X33591,X33592,X33593,X33594)),X33592))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X33593,tc_HOL_Obool)),X33592))
        | ~ class_Groups_Ocomm__monoid__add(X33594) )
      & ( esk524_4(X33591,X33592,X33593,X33594) != esk525_4(X33591,X33592,X33593,X33594)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X33593,X33594),X33591),c_Complete__Lattice_OSup__class_OSup(tc_fun(X33593,tc_HOL_Obool),X33592)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X33593,tc_HOL_Obool),X33594),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X33593,X33594),X33591)),X33592)
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X33593,tc_HOL_Obool)),esk523_4(X33591,X33592,X33593,X33594)),X33592))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X33593,tc_HOL_Obool)),X33592))
        | ~ class_Groups_Ocomm__monoid__add(X33594) )
      & ( hBOOL(hAPP(hAPP(c_member(X33593),esk526_4(X33591,X33592,X33593,X33594)),esk524_4(X33591,X33592,X33593,X33594)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X33593,X33594),X33591),c_Complete__Lattice_OSup__class_OSup(tc_fun(X33593,tc_HOL_Obool),X33592)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X33593,tc_HOL_Obool),X33594),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X33593,X33594),X33591)),X33592)
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X33593,tc_HOL_Obool)),esk523_4(X33591,X33592,X33593,X33594)),X33592))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X33593,tc_HOL_Obool)),X33592))
        | ~ class_Groups_Ocomm__monoid__add(X33594) )
      & ( hBOOL(hAPP(hAPP(c_member(X33593),esk526_4(X33591,X33592,X33593,X33594)),esk525_4(X33591,X33592,X33593,X33594)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X33593,X33594),X33591),c_Complete__Lattice_OSup__class_OSup(tc_fun(X33593,tc_HOL_Obool),X33592)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X33593,tc_HOL_Obool),X33594),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X33593,X33594),X33591)),X33592)
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X33593,tc_HOL_Obool)),esk523_4(X33591,X33592,X33593,X33594)),X33592))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X33593,tc_HOL_Obool)),X33592))
        | ~ class_Groups_Ocomm__monoid__add(X33594) )
      & ( hAPP(X33591,esk526_4(X33591,X33592,X33593,X33594)) != c_Groups_Ozero__class_Ozero(X33594)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X33593,X33594),X33591),c_Complete__Lattice_OSup__class_OSup(tc_fun(X33593,tc_HOL_Obool),X33592)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X33593,tc_HOL_Obool),X33594),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X33593,X33594),X33591)),X33592)
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X33593,tc_HOL_Obool)),esk523_4(X33591,X33592,X33593,X33594)),X33592))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X33593,tc_HOL_Obool)),X33592))
        | ~ class_Groups_Ocomm__monoid__add(X33594) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_fun(X33593,tc_HOL_Obool)),esk524_4(X33591,X33592,X33593,X33594)),X33592))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X33593,X33594),X33591),c_Complete__Lattice_OSup__class_OSup(tc_fun(X33593,tc_HOL_Obool),X33592)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X33593,tc_HOL_Obool),X33594),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X33593,X33594),X33591)),X33592)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33593),esk523_4(X33591,X33592,X33593,X33594)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X33593,tc_HOL_Obool)),X33592))
        | ~ class_Groups_Ocomm__monoid__add(X33594) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_fun(X33593,tc_HOL_Obool)),esk525_4(X33591,X33592,X33593,X33594)),X33592))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X33593,X33594),X33591),c_Complete__Lattice_OSup__class_OSup(tc_fun(X33593,tc_HOL_Obool),X33592)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X33593,tc_HOL_Obool),X33594),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X33593,X33594),X33591)),X33592)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33593),esk523_4(X33591,X33592,X33593,X33594)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X33593,tc_HOL_Obool)),X33592))
        | ~ class_Groups_Ocomm__monoid__add(X33594) )
      & ( esk524_4(X33591,X33592,X33593,X33594) != esk525_4(X33591,X33592,X33593,X33594)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X33593,X33594),X33591),c_Complete__Lattice_OSup__class_OSup(tc_fun(X33593,tc_HOL_Obool),X33592)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X33593,tc_HOL_Obool),X33594),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X33593,X33594),X33591)),X33592)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33593),esk523_4(X33591,X33592,X33593,X33594)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X33593,tc_HOL_Obool)),X33592))
        | ~ class_Groups_Ocomm__monoid__add(X33594) )
      & ( hBOOL(hAPP(hAPP(c_member(X33593),esk526_4(X33591,X33592,X33593,X33594)),esk524_4(X33591,X33592,X33593,X33594)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X33593,X33594),X33591),c_Complete__Lattice_OSup__class_OSup(tc_fun(X33593,tc_HOL_Obool),X33592)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X33593,tc_HOL_Obool),X33594),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X33593,X33594),X33591)),X33592)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33593),esk523_4(X33591,X33592,X33593,X33594)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X33593,tc_HOL_Obool)),X33592))
        | ~ class_Groups_Ocomm__monoid__add(X33594) )
      & ( hBOOL(hAPP(hAPP(c_member(X33593),esk526_4(X33591,X33592,X33593,X33594)),esk525_4(X33591,X33592,X33593,X33594)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X33593,X33594),X33591),c_Complete__Lattice_OSup__class_OSup(tc_fun(X33593,tc_HOL_Obool),X33592)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X33593,tc_HOL_Obool),X33594),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X33593,X33594),X33591)),X33592)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33593),esk523_4(X33591,X33592,X33593,X33594)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X33593,tc_HOL_Obool)),X33592))
        | ~ class_Groups_Ocomm__monoid__add(X33594) )
      & ( hAPP(X33591,esk526_4(X33591,X33592,X33593,X33594)) != c_Groups_Ozero__class_Ozero(X33594)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X33593,X33594),X33591),c_Complete__Lattice_OSup__class_OSup(tc_fun(X33593,tc_HOL_Obool),X33592)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X33593,tc_HOL_Obool),X33594),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X33593,X33594),X33591)),X33592)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33593),esk523_4(X33591,X33592,X33593,X33594)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X33593,tc_HOL_Obool)),X33592))
        | ~ class_Groups_Ocomm__monoid__add(X33594) ) ),
    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_6769,plain,
    ! [X21648,X21649,X21650,X21651] : c_Nitpick_Ofold__graph_H(X21651,X21650,X21649,X21648,c_Orderings_Obot__class_Obot(tc_fun(X21651,tc_HOL_Obool)),X21648),
    inference(variable_rename,[status(thm)],[fact_fold__graph_H_Ointros_I1_J]) ).

fof(i_0_6770,plain,
    ! [X21644,X21645,X21646,X21647] : c_Nitpick_Ofold__graph_H(X21647,X21646,X21645,X21644,c_Orderings_Obot__class_Obot(tc_fun(X21647,tc_HOL_Obool)),X21644),
    inference(variable_rename,[status(thm)],[fact_fold__graph_H_Oequations_I1_J]) ).

fof(i_0_6771,plain,
    ! [X25933,X25934,X25935,X25936,X25937] :
      ( ( c_Fun_Oinj__on(X25937,X25936,X25935,X25933)
        | ~ c_Fun_Oinj__on(X25937,X25936,X25935,hAPP(hAPP(c_Set_Oinsert(X25937),X25934),X25933)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X25936),hAPP(X25935,X25934)),hAPP(c_Set_Oimage(X25937,X25936,X25935),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25937,tc_HOL_Obool)),X25933),hAPP(hAPP(c_Set_Oinsert(X25937),X25934),c_Orderings_Obot__class_Obot(tc_fun(X25937,tc_HOL_Obool)))))))
        | ~ c_Fun_Oinj__on(X25937,X25936,X25935,hAPP(hAPP(c_Set_Oinsert(X25937),X25934),X25933)) )
      & ( ~ c_Fun_Oinj__on(X25937,X25936,X25935,X25933)
        | hBOOL(hAPP(hAPP(c_member(X25936),hAPP(X25935,X25934)),hAPP(c_Set_Oimage(X25937,X25936,X25935),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25937,tc_HOL_Obool)),X25933),hAPP(hAPP(c_Set_Oinsert(X25937),X25934),c_Orderings_Obot__class_Obot(tc_fun(X25937,tc_HOL_Obool)))))))
        | c_Fun_Oinj__on(X25937,X25936,X25935,hAPP(hAPP(c_Set_Oinsert(X25937),X25934),X25933)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5435])])]) ).

fof(i_0_6772,plain,
    ! [X27939,X27940] : c_Product__Type_Omap__pair(X27940,X27940,X27939,X27939,c_Fun_Oid(X27940),c_Fun_Oid(X27939)) = c_Fun_Oid(tc_prod(X27940,X27939)),
    inference(variable_rename,[status(thm)],[fact_map__pair_Oid]) ).

cnf(i_0_6773,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_5436]) ).

fof(i_0_6774,plain,
    ! [X27941,X27942] : c_Product__Type_Omap__pair(X27942,X27942,X27941,X27941,c_COMBI(X27942),c_COMBI(X27941)) = c_Fun_Oid(tc_prod(X27942,X27941)),
    inference(variable_rename,[status(thm)],[fact_map__pair_Oidentity]) ).

cnf(i_0_6775,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_5437]) ).

fof(i_0_6776,plain,
    ! [X32994,X32995,X32996,X32997,X32998] :
      ( ~ c_Finite__Set_Ofun__left__comm(X32998,X32997,X32996)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32998),X32995))
      | hBOOL(hAPP(c_Finite__Set_Ofold__graph(X32998,X32997,X32996,X32994,X32995),hAPP(hAPP(c_Finite__Set_Ofold(X32998,X32997,X32996),X32994),X32995))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__graph__fold])]) ).

cnf(i_0_6777,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_6778,plain,
    ! [X24581,X24582,X24583] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24583),X24582))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X24583),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24583,tc_HOL_Obool)),X24582),hAPP(hAPP(c_Set_Oinsert(X24583),X24581),c_Orderings_Obot__class_Obot(tc_fun(X24583,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X24583),X24582))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Diff1__le])]) ).

fof(i_0_6779,plain,
    ! [X28036,X28037,X28038,X28039,X28040,X28041,X28042] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28042,X28041),tc_HOL_Obool)),X28040),X28039))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28041,X28038),tc_HOL_Obool)),X28037),X28036))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28042,X28038),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X28042,X28041,X28038),X28040),X28037)),hAPP(hAPP(c_Relation_Orel__comp(X28042,X28041,X28038),X28039),X28036))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__comp__mono])]) ).

fof(i_0_6780,plain,
    ! [X23519,X23520,X23521,X23522,X23523] :
      ( ~ c_Equiv__Relations_Oequiv(X23523,X23522,X23521)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X23523,X23523)),hAPP(hAPP(c_Product__Type_OPair(X23523,X23523),X23520),X23519)),X23521))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23523,tc_HOL_Obool)),hAPP(c_Relation_OImage(X23523,X23523,X23521),hAPP(hAPP(c_Set_Oinsert(X23523),X23520),c_Orderings_Obot__class_Obot(tc_fun(X23523,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X23523,X23523,X23521),hAPP(hAPP(c_Set_Oinsert(X23523),X23519),c_Orderings_Obot__class_Obot(tc_fun(X23523,tc_HOL_Obool)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__class__subset])]) ).

fof(i_0_6781,plain,
    ! [X26079,X26080,X26081,X26082,X26083,X26084] :
      ( ~ c_Fun_Oinj__on(X26084,X26083,X26082,X26081)
      | ~ hBOOL(hAPP(hAPP(c_member(X26083),X26080),hAPP(c_Set_Oimage(X26084,X26083,X26082),X26081)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26084,tc_HOL_Obool)),X26081),X26079))
      | hBOOL(hAPP(hAPP(c_member(X26084),hAPP(c_Fun_Othe__inv__into(X26084,X26083,X26081,X26082),X26080)),X26079)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_the__inv__into__into])]) ).

fof(i_0_6782,plain,
    ! [X26762,X26763,X26764,X26765,X26766] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26766),hAPP(c_Set_Oimage(X26765,X26766,X26764),c_Orderings_Otop__class_Otop(tc_fun(X26765,tc_HOL_Obool)))))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X26763),hAPP(c_Set_Oimage(X26765,X26763,hAPP(hAPP(c_COMBB(X26766,X26763,X26765),X26762),X26764)),c_Orderings_Otop__class_Otop(tc_fun(X26765,tc_HOL_Obool))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__range__imageI])]) ).

fof(i_0_6783,plain,
    ! [X31062,X31063,X31064] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X31064,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X31064,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X31064,tc_HOL_Obool),X31063)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X31064,tc_HOL_Obool),X31062))),c_Complete__Lattice_OInf__class_OInf(tc_fun(X31064,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X31064,tc_HOL_Obool),tc_HOL_Obool)),X31063),X31062)))),
    inference(variable_rename,[status(thm)],[fact_Inter__Un__subset]) ).

fof(i_0_6784,plain,
    ! [X28643,X28644,X28645] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28645,X28645),tc_HOL_Obool)),X28644),hAPP(hAPP(c_Product__Type_OSigma(X28645,X28645),X28643),hAPP(c_COMBK(tc_fun(X28645,tc_HOL_Obool),X28645),X28643))))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X28645),tc_List_Olist(X28645)),tc_HOL_Obool)),c_List_Olistrel(X28645,X28644)),hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(X28645),tc_List_Olist(X28645)),c_List_Olists(X28645,X28643)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X28645),tc_HOL_Obool),tc_List_Olist(X28645)),c_List_Olists(X28645,X28643))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__subset])]) ).

fof(i_0_6785,plain,
    ! [X25962,X25963,X25964,X25965,X25966,X25967,X25968] :
      ( ~ class_Groups_Oab__semigroup__mult(X25968)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25967),X25966))
      | ~ c_Fun_Oinj__on(X25967,X25965,X25964,X25966)
      | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X25968,X25965,c_Groups_Otimes__class_Otimes(X25968)),X25963),X25962),hAPP(c_Set_Oimage(X25967,X25965,X25964),X25966)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X25968,X25967,c_Groups_Otimes__class_Otimes(X25968)),hAPP(c_Fun_Ocomp(X25965,X25968,X25967,X25963),X25964)),X25962),X25966) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__image__reindex])]) ).

fof(i_0_6786,plain,
    ! [X19504,X19505,X19506,X19507] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19507))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19506))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19506),X19505))
      | 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),X19505),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19504,X19507))),X19506)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19505),X19507))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult2__lemma__aux4])]) ).

fof(i_0_6787,plain,
    ! [X33047,X33048,X33049,X33050] :
      ( ( hBOOL(hAPP(hAPP(c_member(X33050),esk492_4(X33047,X33048,X33049,X33050)),X33049))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X33050),hAPP(hAPP(c_Finite__Set_Ofold(X33050,X33050,c_Lattices_Osemilattice__sup__class_Osup(X33050)),X33047),X33049)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X33050),X33048),X33047)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33050),X33049))
        | ~ class_Lattices_Osemilattice__sup(X33050) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X33050),esk492_4(X33047,X33048,X33049,X33050)),X33048))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X33050),hAPP(hAPP(c_Finite__Set_Ofold(X33050,X33050,c_Lattices_Osemilattice__sup__class_Osup(X33050)),X33047),X33049)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X33050),X33048),X33047)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33050),X33049))
        | ~ class_Lattices_Osemilattice__sup(X33050) ) ),
    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_6788,plain,
    ! [X33032,X33033,X33034,X33035] :
      ( ( hBOOL(hAPP(hAPP(c_member(X33035),esk489_4(X33032,X33033,X33034,X33035)),X33034))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X33035),hAPP(hAPP(c_Finite__Set_Ofold(X33035,X33035,c_Orderings_Oord__class_Omax(X33035)),X33032),X33034)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X33035),X33033),X33032)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33035),X33034))
        | ~ class_Orderings_Olinorder(X33035) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X33035),esk489_4(X33032,X33033,X33034,X33035)),X33033))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X33035),hAPP(hAPP(c_Finite__Set_Ofold(X33035,X33035,c_Orderings_Oord__class_Omax(X33035)),X33032),X33034)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X33035),X33033),X33032)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33035),X33034))
        | ~ class_Orderings_Olinorder(X33035) ) ),
    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_6789,plain,
    ! [X34160,X34161,X34162,X34163,X34164,X34165,X34166] :
      ( ~ c_Fun_Obij__betw(X34166,X34165,X34164,X34163,X34162)
      | ~ c_Fun_Obij__betw(X34166,X34165,X34164,X34161,X34160)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X34165,tc_HOL_Obool)),X34162),X34160) != c_Orderings_Obot__class_Obot(tc_fun(X34165,tc_HOL_Obool))
      | c_Fun_Obij__betw(X34166,X34165,X34164,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X34166,tc_HOL_Obool)),X34163),X34161),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X34165,tc_HOL_Obool)),X34162),X34160)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__betw__combine])]) ).

cnf(i_0_6790,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_5438]) ).

fof(i_0_6791,plain,
    ! [X20869,X20870,X20871,X20872] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X20872),X20870),X20871))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20872,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20872,tc_HOL_Obool)),X20871),hAPP(hAPP(c_Set_Oinsert(X20872),X20870),c_Orderings_Obot__class_Obot(tc_fun(X20872,tc_HOL_Obool))))),X20869))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20872,tc_HOL_Obool)),X20871),hAPP(hAPP(c_Set_Oinsert(X20872),X20870),X20869))) )
      & ( hBOOL(hAPP(hAPP(c_member(X20872),X20870),X20871))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20872,tc_HOL_Obool)),X20871),X20869))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20872,tc_HOL_Obool)),X20871),hAPP(hAPP(c_Set_Oinsert(X20872),X20870),X20869))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X20872),X20870),X20871))
        | hBOOL(hAPP(hAPP(c_member(X20872),X20870),X20871))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20872,tc_HOL_Obool)),X20871),hAPP(hAPP(c_Set_Oinsert(X20872),X20870),X20869))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20872,tc_HOL_Obool)),X20871),X20869))
        | hBOOL(hAPP(hAPP(c_member(X20872),X20870),X20871))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20872,tc_HOL_Obool)),X20871),hAPP(hAPP(c_Set_Oinsert(X20872),X20870),X20869))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X20872),X20870),X20871))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20872,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20872,tc_HOL_Obool)),X20871),hAPP(hAPP(c_Set_Oinsert(X20872),X20870),c_Orderings_Obot__class_Obot(tc_fun(X20872,tc_HOL_Obool))))),X20869))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20872,tc_HOL_Obool)),X20871),hAPP(hAPP(c_Set_Oinsert(X20872),X20870),X20869))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20872,tc_HOL_Obool)),X20871),X20869))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20872,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20872,tc_HOL_Obool)),X20871),hAPP(hAPP(c_Set_Oinsert(X20872),X20870),c_Orderings_Obot__class_Obot(tc_fun(X20872,tc_HOL_Obool))))),X20869))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20872,tc_HOL_Obool)),X20871),hAPP(hAPP(c_Set_Oinsert(X20872),X20870),X20869))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5439])])]) ).

fof(i_0_6792,plain,
    ! [X28545,X28546,X28547,X28548,X28549] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28549,X28549)),hAPP(hAPP(c_Product__Type_OPair(X28549,X28549),X28548),X28547)),X28546))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28549),tc_List_Olist(X28549))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28549),tc_List_Olist(X28549)),hAPP(hAPP(c_List_Olist_OCons(X28549),X28548),X28545)),hAPP(hAPP(c_List_Olist_OCons(X28549),X28547),X28545))),c_List_Olistrel1(X28549,X28546))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel1I1])]) ).

cnf(i_0_6793,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_5440]) ).

cnf(i_0_6794,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_5441]) ).

fof(i_0_6795,plain,
    ! [X31598,X31599,X31600] :
      ( ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X31600),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X31600))),X31599)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31598),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31600))),X31599)))
      | hAPP(hAPP(c_List_Omap(tc_List_Olist(X31600),X31600),hAPP(hAPP(c_COMBC(tc_List_Olist(X31600),tc_Nat_Onat,X31600),c_List_Onth(X31600)),X31598)),hAPP(c_List_Ofilter(tc_List_Olist(X31600),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X31600)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31598)),c_Nat_Osize__class_Osize(tc_List_Olist(X31600)))),c_List_Otranspose(X31600,X31599))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(X31600)),X31599),X31598) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transpose__column])]) ).

fof(i_0_6796,plain,
    ! [X30352,X30353,X30354] : c_Hilbert__Choice_OEps(tc_prod(X30354,X30353),X30352) = c_Hilbert__Choice_OEps(tc_prod(X30354,X30353),hAPP(c_Product__Type_Oprod_Oprod__case(X30354,X30353,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X30353,tc_prod(X30354,X30353)),tc_fun(X30353,tc_HOL_Obool),X30354),hAPP(c_COMBB(tc_prod(X30354,X30353),tc_HOL_Obool,X30353),X30352)),c_Product__Type_OPair(X30354,X30353)))),
    inference(variable_rename,[status(thm)],[fact_split__paired__Eps]) ).

fof(i_0_6797,plain,
    ! [X27018,X27019,X27020] : c_HOL_OThe(tc_prod(X27020,X27019),X27018) = c_HOL_OThe(tc_prod(X27020,X27019),hAPP(c_Product__Type_Oprod_Oprod__case(X27020,X27019,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X27019,tc_prod(X27020,X27019)),tc_fun(X27019,tc_HOL_Obool),X27020),hAPP(c_COMBB(tc_prod(X27020,X27019),tc_HOL_Obool,X27019),X27018)),c_Product__Type_OPair(X27020,X27019)))),
    inference(variable_rename,[status(thm)],[fact_split__paired__The]) ).

fof(i_0_6798,plain,
    ! [X17029,X17030,X17031,X17032,X17033,X17034,X17035] :
      ( ~ c_Hoare__Mirabelle_Ohoare__derivs(X17035,X17034,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X17035)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17035),X17033),X17032),X17031)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X17035),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(X17035,X17034,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X17035)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17035),X17031),X17030),X17029)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X17035),tc_HOL_Obool))))
      | c_Hoare__Mirabelle_Ohoare__derivs(X17035,X17034,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X17035)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17035),X17033),c_Com_Ocom_OSemi(X17032,X17030)),X17029)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X17035),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Comp])]) ).

fof(i_0_6799,plain,
    ! [X23494,X23495,X23496,X23497,X23498,X23499,X23500,X23501] :
      ( ( ~ c_Relation_Ototal__on(X23496,X23495,X23494)
        | ~ hBOOL(hAPP(hAPP(c_member(X23496),X23497),X23495))
        | ~ hBOOL(hAPP(hAPP(c_member(X23496),X23498),X23495))
        | X23497 = X23498
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X23496,X23496)),hAPP(hAPP(c_Product__Type_OPair(X23496,X23496),X23497),X23498)),X23494))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X23496,X23496)),hAPP(hAPP(c_Product__Type_OPair(X23496,X23496),X23498),X23497)),X23494)) )
      & ( hBOOL(hAPP(hAPP(c_member(X23501),esk115_3(X23499,X23500,X23501)),X23500))
        | c_Relation_Ototal__on(X23501,X23500,X23499) )
      & ( hBOOL(hAPP(hAPP(c_member(X23501),esk116_3(X23499,X23500,X23501)),X23500))
        | c_Relation_Ototal__on(X23501,X23500,X23499) )
      & ( esk115_3(X23499,X23500,X23501) != esk116_3(X23499,X23500,X23501)
        | c_Relation_Ototal__on(X23501,X23500,X23499) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X23501,X23501)),hAPP(hAPP(c_Product__Type_OPair(X23501,X23501),esk115_3(X23499,X23500,X23501)),esk116_3(X23499,X23500,X23501))),X23499))
        | c_Relation_Ototal__on(X23501,X23500,X23499) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X23501,X23501)),hAPP(hAPP(c_Product__Type_OPair(X23501,X23501),esk116_3(X23499,X23500,X23501)),esk115_3(X23499,X23500,X23501))),X23499))
        | c_Relation_Ototal__on(X23501,X23500,X23499) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_total__on__def])])])])])]) ).

fof(i_0_6800,plain,
    ! [X19776,X19777,X19778,X19779] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19779))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19778),X19777))
      | 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),X19777),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19776,X19779))),X19778)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19777),X19779))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__lemma])]) ).

fof(i_0_6801,plain,
    ! [X32566,X32567,X32568,X32569,X32570] :
      ( ~ c_Relation_Osingle__valued(X32570,X32570,X32569)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32570,X32570)),hAPP(hAPP(c_Product__Type_OPair(X32570,X32570),X32568),X32567)),c_Transitive__Closure_Ortrancl(X32570,X32569)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32570,X32570)),hAPP(hAPP(c_Product__Type_OPair(X32570,X32570),X32568),X32566)),c_Transitive__Closure_Ortrancl(X32570,X32569)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X32570,X32570)),hAPP(hAPP(c_Product__Type_OPair(X32570,X32570),X32567),X32566)),c_Transitive__Closure_Ortrancl(X32570,X32569)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X32570,X32570)),hAPP(hAPP(c_Product__Type_OPair(X32570,X32570),X32566),X32567)),c_Transitive__Closure_Ortrancl(X32570,X32569))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_single__valued__confluent])]) ).

fof(i_0_6802,plain,
    ! [X28091,X28092,X28093] :
      ( ~ c_Wellfounded_Owf(X28093,X28092)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28093,X28093),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X28093,X28093,X28093),X28092),X28091)),X28092))
      | c_FunDef_Oreduction__pair(X28093,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(X28093,X28093),tc_HOL_Obool),tc_fun(tc_prod(X28093,X28093),tc_HOL_Obool)),X28092),X28091)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_reduction__pairI])]) ).

fof(i_0_6803,plain,
    ! [X19512,X19513,X19514,X19515] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19515))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19514),X19513))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19513),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),X19514),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19512,X19515))),X19513)),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_6804,plain,
    ! [X30374,X30375] : c_Random_Oselect(X30375,X30374) = 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(X30375,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(X30375)),X30374)))),hAPP(hAPP(c_COMBB(X30375,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X30375,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(X30375,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X30375,tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Onth(X30375),X30374)),c_Code__Numeral_Onat__of))),
    inference(variable_rename,[status(thm)],[fact_select__def]) ).

fof(i_0_6805,plain,
    ! [X21807,X21808] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21808),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | c_Nitpick_Onorm__frac(X21807,X21808) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21807),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21808)) )
      & ( X21807 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Nitpick_Onorm__frac(X21807,X21808) = 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),X21808),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( X21808 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Nitpick_Onorm__frac(X21807,X21808) = 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),X21808),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( X21807 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | X21808 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Nitpick_Onorm__frac(X21807,X21808) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X21807),X21808)),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),X21807))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X21808)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21808),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5442])])]) ).

fof(i_0_6806,plain,
    ! [X23303,X23304,X23305] :
      ( ~ class_Rings_Oring__1(X23305)
      | hAPP(c_Int_Oring__1__class_Oof__int(X23305),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),X23304),X23303)),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(X23305),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X23305),X23304)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X23305),X23303)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int])]) ).

cnf(i_0_6807,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk402_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_5443]) ).

cnf(i_0_6808,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_5444]) ).

cnf(i_0_6809,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_5445]) ).

fof(i_0_6810,plain,
    ! [X20873,X20874,X20875,X20876] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20876,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20876,tc_HOL_Obool)),X20875),hAPP(hAPP(c_Set_Oinsert(X20876),X20874),c_Orderings_Obot__class_Obot(tc_fun(X20876,tc_HOL_Obool))))),X20873))
      | ~ hBOOL(hAPP(hAPP(c_member(X20876),X20874),X20875))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20876,tc_HOL_Obool)),X20875),hAPP(hAPP(c_Set_Oinsert(X20876),X20874),X20873))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__single__insert])]) ).

fof(i_0_6811,plain,
    ! [X23343,X23344] : 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),X23344),X23343)),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),X23344),X23343),
    inference(variable_rename,[status(thm)],[fact_nat]) ).

cnf(i_0_6812,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_5446]) ).

cnf(i_0_6813,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_5447]) ).

cnf(i_0_6814,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_5448]) ).

fof(i_0_6815,plain,
    ! [X25938,X25939,X25940,X25941,X25942] :
      ( ( c_Fun_Oinj__on(X25942,X25941,X25940,X25939)
        | ~ c_Fun_Oinj__on(X25942,X25941,X25940,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25942,tc_HOL_Obool)),X25939),X25938)) )
      & ( c_Fun_Oinj__on(X25942,X25941,X25940,X25938)
        | ~ c_Fun_Oinj__on(X25942,X25941,X25940,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25942,tc_HOL_Obool)),X25939),X25938)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25941,tc_HOL_Obool)),hAPP(c_Set_Oimage(X25942,X25941,X25940),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25942,tc_HOL_Obool)),X25939),X25938))),hAPP(c_Set_Oimage(X25942,X25941,X25940),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25942,tc_HOL_Obool)),X25938),X25939))) = c_Orderings_Obot__class_Obot(tc_fun(X25941,tc_HOL_Obool))
        | ~ c_Fun_Oinj__on(X25942,X25941,X25940,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25942,tc_HOL_Obool)),X25939),X25938)) )
      & ( ~ c_Fun_Oinj__on(X25942,X25941,X25940,X25939)
        | ~ c_Fun_Oinj__on(X25942,X25941,X25940,X25938)
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25941,tc_HOL_Obool)),hAPP(c_Set_Oimage(X25942,X25941,X25940),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25942,tc_HOL_Obool)),X25939),X25938))),hAPP(c_Set_Oimage(X25942,X25941,X25940),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25942,tc_HOL_Obool)),X25938),X25939))) != c_Orderings_Obot__class_Obot(tc_fun(X25941,tc_HOL_Obool))
        | c_Fun_Oinj__on(X25942,X25941,X25940,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25942,tc_HOL_Obool)),X25939),X25938)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__Un])])]) ).

fof(i_0_6816,plain,
    ! [X23570,X23571,X23572] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X23572,tc_HOL_Obool)),X23571),X23570))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X23572,tc_HOL_Obool),tc_fun(X23572,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X23572,tc_HOL_Obool),tc_fun(X23572,tc_HOL_Obool)),X23571),X23570)),c_Wellfounded_Ofinite__psubset(X23572))) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X23572),X23570))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X23572,tc_HOL_Obool),tc_fun(X23572,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X23572,tc_HOL_Obool),tc_fun(X23572,tc_HOL_Obool)),X23571),X23570)),c_Wellfounded_Ofinite__psubset(X23572))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X23572,tc_HOL_Obool)),X23571),X23570))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23572),X23570))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X23572,tc_HOL_Obool),tc_fun(X23572,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X23572,tc_HOL_Obool),tc_fun(X23572,tc_HOL_Obool)),X23571),X23570)),c_Wellfounded_Ofinite__psubset(X23572))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__finite__psubset])])]) ).

fof(i_0_6817,plain,
    ! [X30985,X30986,X30987,X30988] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X30988),X30987),hAPP(c_Relation_ODomain(X30988,X30986),X30985)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X30988,X30986)),hAPP(hAPP(c_Product__Type_OPair(X30988,X30986),X30987),esk375_4(X30985,X30986,X30987,X30988))),X30985)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5449])])]) ).

fof(i_0_6818,plain,
    ! [X30912,X30913,X30914,X30915,X30917,X30918,X30919,X30920,X30921] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X30915),X30914),hAPP(c_Relation_ODomain(X30915,X30913),X30912)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X30915,X30913)),hAPP(hAPP(c_Product__Type_OPair(X30915,X30913),X30914),esk370_4(X30912,X30913,X30914,X30915))),X30912)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30920,X30918)),hAPP(hAPP(c_Product__Type_OPair(X30920,X30918),X30919),X30921)),X30917))
        | hBOOL(hAPP(hAPP(c_member(X30920),X30919),hAPP(c_Relation_ODomain(X30920,X30918),X30917))) ) ),
    inference(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_6819,plain,
    ! [X25448,X25449,X25450] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X25450,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X25450,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X25450),X25449)),hAPP(c_Set_OPow(X25450),X25448))),hAPP(c_Set_OPow(X25450),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25450,tc_HOL_Obool)),X25449),X25448)))),
    inference(variable_rename,[status(thm)],[fact_Un__Pow__subset]) ).

fof(i_0_6820,plain,
    ! [X33961,X33962,X33963,X33964,X33965] :
      ( ~ c_Fun_Oinj__on(X33965,X33964,X33963,c_Orderings_Otop__class_Otop(tc_fun(X33965,tc_HOL_Obool)))
      | hAPP(c_Fun_Ocomp(X33964,X33962,X33965,hAPP(c_Fun_Ocomp(X33965,X33962,X33964,X33961),c_Hilbert__Choice_Oinv__into(X33965,X33964,c_Orderings_Otop__class_Otop(tc_fun(X33965,tc_HOL_Obool)),X33963))),X33963) = X33961 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_o__inv__o__cancel])]) ).

fof(i_0_6821,negated_conjecture,
    ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),v_G),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_1])]) ).

fof(i_0_6822,plain,
    ! [X20119,X20120,X20121,X20122,X20123] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20123),X20122))
      | 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),X20122),X20121)),X20120)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20123),X20121)),X20119)) = 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),X20122),X20123)),X20121)),X20120)),X20119) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__diff__add__eq1])]) ).

cnf(i_0_6823,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_5450]) ).

fof(i_0_6824,plain,
    ! [X30293,X30294,X30295] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X30295),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X30294),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X30294)),X30293))))
      | hBOOL(hAPP(hAPP(c_member(X30294),hAPP(c_Random_Opick(X30294,X30293),X30295)),hAPP(c_List_Oset(X30294),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X30294),X30294),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X30294)),X30293)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pick__member])]) ).

fof(i_0_6825,plain,
    ! [X27990,X27991,X27992,X27993,X27994,X27995,X27996,X27997] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27997,X27996)),hAPP(hAPP(c_Product__Type_OPair(X27997,X27996),X27995),X27994)),X27993))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27996,X27992)),hAPP(hAPP(c_Product__Type_OPair(X27996,X27992),X27994),X27991)),X27990))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X27997,X27992)),hAPP(hAPP(c_Product__Type_OPair(X27997,X27992),X27995),X27991)),hAPP(hAPP(c_Relation_Orel__comp(X27997,X27996,X27992),X27993),X27990))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__compI])]) ).

fof(i_0_6826,plain,
    ! [X31510,X31511,X31512,X31513,X31514] :
      ( ~ class_Orderings_Olinorder(X31514)
      | ~ c_List_Olinorder__class_Osorted(X31514,hAPP(hAPP(c_List_Omap(X31513,X31514),X31512),X31511))
      | c_List_Olinorder__class_Osorted(X31514,hAPP(hAPP(c_List_Omap(X31513,X31514),X31512),c_List_Olinorder__class_Oinsort__insert__key(X31513,X31514,X31512,X31510,X31511))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__insort__insert__key])]) ).

fof(i_0_6827,plain,
    ! [X30627,X30628,X30629,X30630,X30631,X30632,X30633] :
      ( ( c_List_Olist__all2(X30633,X30631,X30629,X30632,X30630)
        | ~ c_List_Olist__all2(X30633,X30631,X30629,hAPP(hAPP(c_List_Oappend(X30633),X30632),X30628),hAPP(hAPP(c_List_Oappend(X30631),X30630),X30627))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30633)),X30632) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30631)),X30630) )
      & ( c_List_Olist__all2(X30633,X30631,X30629,X30628,X30627)
        | ~ c_List_Olist__all2(X30633,X30631,X30629,hAPP(hAPP(c_List_Oappend(X30633),X30632),X30628),hAPP(hAPP(c_List_Oappend(X30631),X30630),X30627))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30633)),X30632) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30631)),X30630) )
      & ( ~ c_List_Olist__all2(X30633,X30631,X30629,X30632,X30630)
        | ~ c_List_Olist__all2(X30633,X30631,X30629,X30628,X30627)
        | c_List_Olist__all2(X30633,X30631,X30629,hAPP(hAPP(c_List_Oappend(X30633),X30632),X30628),hAPP(hAPP(c_List_Oappend(X30631),X30630),X30627))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30633)),X30632) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30631)),X30630) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__append])])]) ).

fof(i_0_6828,plain,
    ! [X22950,X22951,X22952,X22953,X22954,X22957,X22958,X22959,X22960,X22961,X22962] :
      ( ( hBOOL(hAPP(hAPP(c_member(X22953),esk99_4(X22950,X22951,X22952,X22953)),X22951))
        | hBOOL(hAPP(hAPP(c_member(X22953),esk98_4(X22950,X22951,X22952,X22953)),X22952))
        | ~ hBOOL(hAPP(hAPP(c_member(X22953),X22954),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22953,tc_HOL_Obool)),X22952),X22951)))
        | ~ hBOOL(hAPP(X22950,X22954)) )
      & ( hBOOL(hAPP(X22950,esk99_4(X22950,X22951,X22952,X22953)))
        | hBOOL(hAPP(hAPP(c_member(X22953),esk98_4(X22950,X22951,X22952,X22953)),X22952))
        | ~ hBOOL(hAPP(hAPP(c_member(X22953),X22954),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22953,tc_HOL_Obool)),X22952),X22951)))
        | ~ hBOOL(hAPP(X22950,X22954)) )
      & ( hBOOL(hAPP(hAPP(c_member(X22953),esk99_4(X22950,X22951,X22952,X22953)),X22951))
        | hBOOL(hAPP(X22950,esk98_4(X22950,X22951,X22952,X22953)))
        | ~ hBOOL(hAPP(hAPP(c_member(X22953),X22954),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22953,tc_HOL_Obool)),X22952),X22951)))
        | ~ hBOOL(hAPP(X22950,X22954)) )
      & ( hBOOL(hAPP(X22950,esk99_4(X22950,X22951,X22952,X22953)))
        | hBOOL(hAPP(X22950,esk98_4(X22950,X22951,X22952,X22953)))
        | ~ hBOOL(hAPP(hAPP(c_member(X22953),X22954),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22953,tc_HOL_Obool)),X22952),X22951)))
        | ~ hBOOL(hAPP(X22950,X22954)) )
      & ( hBOOL(hAPP(hAPP(c_member(X22960),esk100_4(X22957,X22958,X22959,X22960)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22960,tc_HOL_Obool)),X22959),X22958)))
        | ~ hBOOL(hAPP(hAPP(c_member(X22960),X22961),X22959))
        | ~ hBOOL(hAPP(X22957,X22961)) )
      & ( hBOOL(hAPP(X22957,esk100_4(X22957,X22958,X22959,X22960)))
        | ~ hBOOL(hAPP(hAPP(c_member(X22960),X22961),X22959))
        | ~ hBOOL(hAPP(X22957,X22961)) )
      & ( hBOOL(hAPP(hAPP(c_member(X22960),esk100_4(X22957,X22958,X22959,X22960)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22960,tc_HOL_Obool)),X22959),X22958)))
        | ~ hBOOL(hAPP(hAPP(c_member(X22960),X22962),X22958))
        | ~ hBOOL(hAPP(X22957,X22962)) )
      & ( hBOOL(hAPP(X22957,esk100_4(X22957,X22958,X22959,X22960)))
        | ~ hBOOL(hAPP(hAPP(c_member(X22960),X22962),X22958))
        | ~ hBOOL(hAPP(X22957,X22962)) ) ),
    inference(distribute,[status(thm)],[inference(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_6829,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_5451]) ).

fof(i_0_6830,plain,
    ! [X22964,X22965,X22966,X22967,X22969,X22970,X22971,X22972,X22973,X22974,X22977] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X22967),X22969),X22966))
        | hBOOL(hAPP(X22964,X22969))
        | hBOOL(hAPP(hAPP(c_member(X22967),esk101_4(X22964,X22965,X22966,X22967)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22967,tc_HOL_Obool)),X22966),X22965))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X22967),X22970),X22965))
        | hBOOL(hAPP(X22964,X22970))
        | hBOOL(hAPP(hAPP(c_member(X22967),esk101_4(X22964,X22965,X22966,X22967)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22967,tc_HOL_Obool)),X22966),X22965))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X22967),X22969),X22966))
        | hBOOL(hAPP(X22964,X22969))
        | ~ hBOOL(hAPP(X22964,esk101_4(X22964,X22965,X22966,X22967))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X22967),X22970),X22965))
        | hBOOL(hAPP(X22964,X22970))
        | ~ hBOOL(hAPP(X22964,esk101_4(X22964,X22965,X22966,X22967))) )
      & ( hBOOL(hAPP(hAPP(c_member(X22974),esk103_4(X22971,X22972,X22973,X22974)),X22972))
        | hBOOL(hAPP(hAPP(c_member(X22974),esk102_4(X22971,X22972,X22973,X22974)),X22973))
        | ~ hBOOL(hAPP(hAPP(c_member(X22974),X22977),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22974,tc_HOL_Obool)),X22973),X22972)))
        | hBOOL(hAPP(X22971,X22977)) )
      & ( ~ hBOOL(hAPP(X22971,esk103_4(X22971,X22972,X22973,X22974)))
        | hBOOL(hAPP(hAPP(c_member(X22974),esk102_4(X22971,X22972,X22973,X22974)),X22973))
        | ~ hBOOL(hAPP(hAPP(c_member(X22974),X22977),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22974,tc_HOL_Obool)),X22973),X22972)))
        | hBOOL(hAPP(X22971,X22977)) )
      & ( hBOOL(hAPP(hAPP(c_member(X22974),esk103_4(X22971,X22972,X22973,X22974)),X22972))
        | ~ hBOOL(hAPP(X22971,esk102_4(X22971,X22972,X22973,X22974)))
        | ~ hBOOL(hAPP(hAPP(c_member(X22974),X22977),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22974,tc_HOL_Obool)),X22973),X22972)))
        | hBOOL(hAPP(X22971,X22977)) )
      & ( ~ hBOOL(hAPP(X22971,esk103_4(X22971,X22972,X22973,X22974)))
        | ~ hBOOL(hAPP(X22971,esk102_4(X22971,X22972,X22973,X22974)))
        | ~ hBOOL(hAPP(hAPP(c_member(X22974),X22977),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22974,tc_HOL_Obool)),X22973),X22972)))
        | hBOOL(hAPP(X22971,X22977)) ) ),
    inference(distribute,[status(thm)],[inference(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_6831,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_5452]) ).

cnf(i_0_6832,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_5453]) ).

cnf(i_0_6833,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_5415]) ).

fof(i_0_6834,plain,
    ! [X29674,X29675,X29676,X29677,X29678,X29679,X29680,X29681] :
      ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29681,tc_fun(X29680,tc_fun(X29679,tc_HOL_Obool))),X29678),X29677),X29676),X29675))
      | hBOOL(hAPP(hAPP(hAPP(X29677,X29674),X29676),X29675))
      | ~ hBOOL(hAPP(hAPP(c_member(X29681),X29674),X29678)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5454])]) ).

fof(i_0_6835,plain,
    ! [X29666,X29667,X29668,X29669,X29670,X29671,X29672,X29673] :
      ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29673,tc_fun(X29672,tc_fun(X29671,tc_HOL_Obool))),X29670),X29669),X29668),X29667))
      | ~ hBOOL(hAPP(hAPP(c_member(X29673),X29666),X29670))
      | hBOOL(hAPP(hAPP(hAPP(X29669,X29666),X29668),X29667)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF2__D])]) ).

cnf(i_0_6836,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_5455]) ).

cnf(i_0_6837,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_5456]) ).

cnf(i_0_6838,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_5457]) ).

cnf(i_0_6839,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_5458]) ).

cnf(i_0_6840,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_5415]) ).

cnf(i_0_6841,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_5416]) ).

fof(i_0_6842,plain,
    ! [X30643,X30644,X30645,X30646,X30647,X30648,X30649] :
      ( ~ c_List_Olist__all2(X30649,X30648,X30647,X30646,X30645)
      | ~ c_List_Olist__all2(X30649,X30648,X30647,X30644,X30643)
      | c_List_Olist__all2(X30649,X30648,X30647,hAPP(hAPP(c_List_Oappend(X30649),X30646),X30644),hAPP(hAPP(c_List_Oappend(X30648),X30645),X30643)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__appendI])]) ).

cnf(i_0_6843,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_6844,plain,
    ! [X30131,X30132,X30133,X30134,X30135,X30136] :
      ( hBOOL(hAPP(hAPP(c_member(X30136),X30135),hAPP(c_List_Oset(X30136),X30134)))
      | hAPP(hAPP(c_List_Omap(X30136,X30133),c_Fun_Ofun__upd(X30136,X30133,X30132,X30135,X30131)),X30134) = hAPP(hAPP(c_List_Omap(X30136,X30133),X30132),X30134) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5459])]) ).

fof(i_0_6845,plain,
    ! [X23416,X23417,X23418,X23419,X23420,X23421,X23422] : hAPP(c_Fun_Ocomp(X23422,X23421,X23420,X23419),c_Fun_Ofun__upd(X23420,X23422,X23418,X23417,X23416)) = c_Fun_Ofun__upd(X23420,X23421,hAPP(c_Fun_Ocomp(X23422,X23421,X23420,X23419),X23418),X23417,hAPP(X23419,X23416)),
    inference(variable_rename,[status(thm)],[fact_fun__upd__comp]) ).

cnf(i_0_6846,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_6847,plain,
    ! [X27779,X27780,X27781,X27782] : hAPP(c_Set_Ovimage(X27782,X27781,X27780),X27779) = hAPP(c_Set_OCollect(X27782),hAPP(hAPP(c_COMBC(X27782,tc_fun(X27781,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(X27781,tc_fun(tc_fun(X27781,tc_HOL_Obool),tc_HOL_Obool),X27782),c_member(X27781)),X27780)),X27779)),
    inference(variable_rename,[status(thm)],[fact_vimage__def]) ).

fof(i_0_6848,plain,
    ! [X29179,X29180,X29181,X29182,X29183] : hAPP(hAPP(c_List_Ozip(X29183,X29182),X29181),hAPP(hAPP(c_List_Oappend(X29182),X29180),X29179)) = hAPP(hAPP(c_List_Oappend(tc_prod(X29183,X29182)),hAPP(hAPP(c_List_Ozip(X29183,X29182),hAPP(hAPP(c_List_Otake(X29183),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29182)),X29180)),X29181)),X29180)),hAPP(hAPP(c_List_Ozip(X29183,X29182),hAPP(hAPP(c_List_Odrop(X29183),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29182)),X29180)),X29181)),X29179)),
    inference(variable_rename,[status(thm)],[fact_zip__append2]) ).

fof(i_0_6849,plain,
    ! [X32437,X32438,X32439,X32440] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32440),tc_List_Olist(X32440))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32440),tc_List_Olist(X32440)),X32439),X32438)),c_List_Olistrel1(X32440,hAPP(c_Relation_Oconverse(X32440,X32440),X32437))))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32440),tc_List_Olist(X32440))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32440),tc_List_Olist(X32440)),X32439),X32438)),hAPP(c_Relation_Oconverse(tc_List_Olist(X32440),tc_List_Olist(X32440)),c_List_Olistrel1(X32440,X32437)))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32440),tc_List_Olist(X32440))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32440),tc_List_Olist(X32440)),X32439),X32438)),hAPP(c_Relation_Oconverse(tc_List_Olist(X32440),tc_List_Olist(X32440)),c_List_Olistrel1(X32440,X32437))))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32440),tc_List_Olist(X32440))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32440),tc_List_Olist(X32440)),X32439),X32438)),c_List_Olistrel1(X32440,hAPP(c_Relation_Oconverse(X32440,X32440),X32437)))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__listrel1__converse])]) ).

fof(i_0_6850,plain,
    ! [X28456,X28457,X28458,X28459,X28460,X28462,X28463,X28464,X28465,X28466,X28467] :
      ( ( hAPP(hAPP(c_List_Olist_OCons(X28460),X28459),esk306_5(X28456,X28457,X28458,X28459,X28460)) = X28457
        | X28457 = c_List_Olist_ONil(X28460)
        | hAPP(hAPP(c_List_Olist_OCons(X28460),X28459),X28458) != hAPP(hAPP(c_List_Oappend(X28460),X28457),X28456) )
      & ( X28458 = hAPP(hAPP(c_List_Oappend(X28460),esk306_5(X28456,X28457,X28458,X28459,X28460)),X28456)
        | X28457 = c_List_Olist_ONil(X28460)
        | hAPP(hAPP(c_List_Olist_OCons(X28460),X28459),X28458) != hAPP(hAPP(c_List_Oappend(X28460),X28457),X28456) )
      & ( hAPP(hAPP(c_List_Olist_OCons(X28460),X28459),esk306_5(X28456,X28457,X28458,X28459,X28460)) = X28457
        | hAPP(hAPP(c_List_Olist_OCons(X28460),X28459),X28458) = X28456
        | hAPP(hAPP(c_List_Olist_OCons(X28460),X28459),X28458) != hAPP(hAPP(c_List_Oappend(X28460),X28457),X28456) )
      & ( X28458 = hAPP(hAPP(c_List_Oappend(X28460),esk306_5(X28456,X28457,X28458,X28459,X28460)),X28456)
        | hAPP(hAPP(c_List_Olist_OCons(X28460),X28459),X28458) = X28456
        | hAPP(hAPP(c_List_Olist_OCons(X28460),X28459),X28458) != hAPP(hAPP(c_List_Oappend(X28460),X28457),X28456) )
      & ( X28463 != c_List_Olist_ONil(X28466)
        | hAPP(hAPP(c_List_Olist_OCons(X28466),X28465),X28464) != X28462
        | hAPP(hAPP(c_List_Olist_OCons(X28466),X28465),X28464) = hAPP(hAPP(c_List_Oappend(X28466),X28463),X28462) )
      & ( hAPP(hAPP(c_List_Olist_OCons(X28466),X28465),X28467) != X28463
        | X28464 != hAPP(hAPP(c_List_Oappend(X28466),X28467),X28462)
        | hAPP(hAPP(c_List_Olist_OCons(X28466),X28465),X28464) = hAPP(hAPP(c_List_Oappend(X28466),X28463),X28462) ) ),
    inference(distribute,[status(thm)],[inference(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_6851,plain,
    ! [X28468,X28469,X28470,X28471,X28472,X28474,X28475,X28476,X28477,X28478,X28479] :
      ( ( X28471 = hAPP(hAPP(c_List_Olist_OCons(X28472),X28469),esk307_5(X28468,X28469,X28470,X28471,X28472))
        | X28471 = c_List_Olist_ONil(X28472)
        | hAPP(hAPP(c_List_Oappend(X28472),X28471),X28470) != hAPP(hAPP(c_List_Olist_OCons(X28472),X28469),X28468) )
      & ( hAPP(hAPP(c_List_Oappend(X28472),esk307_5(X28468,X28469,X28470,X28471,X28472)),X28470) = X28468
        | X28471 = c_List_Olist_ONil(X28472)
        | hAPP(hAPP(c_List_Oappend(X28472),X28471),X28470) != hAPP(hAPP(c_List_Olist_OCons(X28472),X28469),X28468) )
      & ( X28471 = hAPP(hAPP(c_List_Olist_OCons(X28472),X28469),esk307_5(X28468,X28469,X28470,X28471,X28472))
        | X28470 = hAPP(hAPP(c_List_Olist_OCons(X28472),X28469),X28468)
        | hAPP(hAPP(c_List_Oappend(X28472),X28471),X28470) != hAPP(hAPP(c_List_Olist_OCons(X28472),X28469),X28468) )
      & ( hAPP(hAPP(c_List_Oappend(X28472),esk307_5(X28468,X28469,X28470,X28471,X28472)),X28470) = X28468
        | X28470 = hAPP(hAPP(c_List_Olist_OCons(X28472),X28469),X28468)
        | hAPP(hAPP(c_List_Oappend(X28472),X28471),X28470) != hAPP(hAPP(c_List_Olist_OCons(X28472),X28469),X28468) )
      & ( X28477 != c_List_Olist_ONil(X28478)
        | X28476 != hAPP(hAPP(c_List_Olist_OCons(X28478),X28475),X28474)
        | hAPP(hAPP(c_List_Oappend(X28478),X28477),X28476) = hAPP(hAPP(c_List_Olist_OCons(X28478),X28475),X28474) )
      & ( X28477 != hAPP(hAPP(c_List_Olist_OCons(X28478),X28475),X28479)
        | hAPP(hAPP(c_List_Oappend(X28478),X28479),X28476) != X28474
        | hAPP(hAPP(c_List_Oappend(X28478),X28477),X28476) = hAPP(hAPP(c_List_Olist_OCons(X28478),X28475),X28474) ) ),
    inference(distribute,[status(thm)],[inference(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_6852,plain,
    ! [X34017,X34018,X34019,X34020,X34021] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X34021),X34020),hAPP(c_Set_Oimage(X34019,X34021,X34018),X34017)))
      | hBOOL(hAPP(hAPP(c_member(X34019),hAPP(c_Hilbert__Choice_Oinv__into(X34019,X34021,X34017,X34018),X34020)),X34017)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__into])]) ).

fof(i_0_6853,plain,
    ! [X24511,X24512] :
      ( ~ class_Orderings_Olinorder(X24512)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24512),X24511))
      | X24511 = c_Orderings_Obot__class_Obot(tc_fun(X24512,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_member(X24512),hAPP(hAPP(c_Orderings_Oord__class_Omin(X24512),esk136_2(X24511,X24512)),esk137_2(X24511,X24512))),hAPP(hAPP(c_Set_Oinsert(X24512),esk136_2(X24511,X24512)),hAPP(hAPP(c_Set_Oinsert(X24512),esk137_2(X24511,X24512)),c_Orderings_Obot__class_Obot(tc_fun(X24512,tc_HOL_Obool))))))
      | hBOOL(hAPP(hAPP(c_member(X24512),c_Big__Operators_Olattice_OInf__fin(X24512,c_Orderings_Oord__class_Omin(X24512),X24511)),X24511)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oclosed])])]) ).

fof(i_0_6854,plain,
    ! [X24467,X24468] :
      ( ~ class_Orderings_Olinorder(X24468)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24468),X24467))
      | X24467 = c_Orderings_Obot__class_Obot(tc_fun(X24468,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_member(X24468),hAPP(hAPP(c_Orderings_Oord__class_Omax(X24468),esk132_2(X24467,X24468)),esk133_2(X24467,X24468))),hAPP(hAPP(c_Set_Oinsert(X24468),esk132_2(X24467,X24468)),hAPP(hAPP(c_Set_Oinsert(X24468),esk133_2(X24467,X24468)),c_Orderings_Obot__class_Obot(tc_fun(X24468,tc_HOL_Obool))))))
      | hBOOL(hAPP(hAPP(c_member(X24468),c_Big__Operators_Olattice_OSup__fin(X24468,c_Orderings_Oord__class_Omax(X24468),X24467)),X24467)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oclosed])])]) ).

fof(i_0_6855,plain,
    ! [X17146,X17147,X17148,X17149,X17150,X17151,X17152,X17153,X17154,X17155,X17156,X17157,X17161] :
      ( ( ~ c_Hoare__Mirabelle_Otriple__valid(X17150,X17149,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17150),X17148),X17147),X17146))
        | ~ hBOOL(hAPP(hAPP(X17148,X17151),X17152))
        | ~ c_Natural_Oevaln(X17147,X17152,X17149,X17153)
        | hBOOL(hAPP(hAPP(X17146,X17151),X17153)) )
      & ( hBOOL(hAPP(hAPP(X17156,esk12_4(X17154,X17155,X17156,X17157)),esk13_4(X17154,X17155,X17156,X17157)))
        | c_Hoare__Mirabelle_Otriple__valid(X17161,X17157,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17161),X17156),X17155),X17154)) )
      & ( c_Natural_Oevaln(X17155,esk13_4(X17154,X17155,X17156,X17157),X17157,esk14_4(X17154,X17155,X17156,X17157))
        | c_Hoare__Mirabelle_Otriple__valid(X17161,X17157,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17161),X17156),X17155),X17154)) )
      & ( ~ hBOOL(hAPP(hAPP(X17154,esk12_4(X17154,X17155,X17156,X17157)),esk14_4(X17154,X17155,X17156,X17157)))
        | c_Hoare__Mirabelle_Otriple__valid(X17161,X17157,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17161),X17156),X17155),X17154)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_triple__valid__def2])])])])])]) ).

fof(i_0_6856,plain,
    ! [X27473,X27474,X27475,X27476] :
      ( ( hBOOL(hAPP(hAPP(c_member(X27476),esk280_4(X27473,X27474,X27475,X27476)),X27475))
        | hAPP(c_Finite__Set_Ocard(tc_prod(X27476,X27474)),hAPP(hAPP(c_Product__Type_OSigma(X27476,X27474),X27475),X27473)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27476,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X27474,tc_HOL_Obool),tc_Nat_Onat,X27476),c_Finite__Set_Ocard(X27474)),X27473)),X27475)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27476),X27475)) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27474),hAPP(X27473,esk280_4(X27473,X27474,X27475,X27476))))
        | hAPP(c_Finite__Set_Ocard(tc_prod(X27476,X27474)),hAPP(hAPP(c_Product__Type_OSigma(X27476,X27474),X27475),X27473)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27476,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X27474,tc_HOL_Obool),tc_Nat_Onat,X27476),c_Finite__Set_Ocard(X27474)),X27473)),X27475)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27476),X27475)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__SigmaI])])])]) ).

fof(i_0_6857,plain,
    ! [X26664,X26665,X26666,X26667] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(X26667,X26666,X26665,X26664,c_Orderings_Obot__class_Obot(tc_fun(X26667,tc_HOL_Obool))),X26664)),
    inference(variable_rename,[status(thm)],[fact_fold__graph_OemptyI]) ).

fof(i_0_6858,plain,
    ! [X26660,X26661,X26662,X26663] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(X26663,X26662,X26661,X26660,c_Orderings_Obot__class_Obot(tc_fun(X26663,tc_HOL_Obool))),X26660)),
    inference(variable_rename,[status(thm)],[fact_fold__graph_Oequations_I1_J]) ).

fof(i_0_6859,plain,
    ! [X28231,X28232,X28233] :
      ( ~ c_Wellfounded_Owf(X28233,X28232)
      | ~ c_Wellfounded_Owf(X28233,X28231)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28233,X28233),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X28233,X28233,X28233),X28232),X28231)),X28232))
      | c_Wellfounded_Owf(X28233,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28233,X28233),tc_HOL_Obool)),X28232),X28231)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__union__compatible])]) ).

fof(i_0_6860,plain,
    ! [X27090,X27091] :
      ( ~ class_Groups_Oab__semigroup__mult(X27091)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27091),X27090))
      | X27090 = c_Orderings_Obot__class_Obot(tc_fun(X27091,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_member(X27091),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27091),esk267_2(X27090,X27091)),esk268_2(X27090,X27091))),hAPP(hAPP(c_Set_Oinsert(X27091),esk267_2(X27090,X27091)),hAPP(hAPP(c_Set_Oinsert(X27091),esk268_2(X27090,X27091)),c_Orderings_Obot__class_Obot(tc_fun(X27091,tc_HOL_Obool))))))
      | hBOOL(hAPP(hAPP(c_member(X27091),hAPP(c_Finite__Set_Ofold1(X27091,c_Groups_Otimes__class_Otimes(X27091)),X27090)),X27090)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1__in])])]) ).

cnf(i_0_6861,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_5460]) ).

fof(i_0_6862,plain,
    ! [X19043,X19044,X19045,X19046,X19047] :
      ( ~ 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),X19047),X19046)),X19045)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19047),X19044)),X19043)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19045))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19045),X19047))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19043),X19047))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19046),X19044)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_unique__quotient__lemma])]) ).

fof(i_0_6863,plain,
    ! [X19054,X19055,X19056,X19057,X19058] :
      ( ~ 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),X19058),X19057)),X19056)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19058),X19055)),X19054)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19054),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19058),X19054))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19058),X19056))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19055),X19057)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_unique__quotient__lemma__neg])]) ).

fof(i_0_6864,plain,
    ! [X30589,X30590,X30591,X30592,X30593] :
      ( ~ class_Orderings_Olinorder(X30593)
      | ~ hBOOL(hAPP(c_List_Odistinct(X30592),X30591))
      | hBOOL(hAPP(c_List_Odistinct(X30592),c_List_Olinorder__class_Oinsort__insert__key(X30592,X30593,X30590,X30589,X30591))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__insort__insert])]) ).

fof(i_0_6865,plain,
    ! [X31320,X31321,X31322] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31322),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31321))),c_List_Otranspose(X31321,X31320))))
      | hAPP(hAPP(c_List_Onth(tc_List_Olist(X31321)),c_List_Otranspose(X31321,X31320)),X31322) = hAPP(hAPP(c_List_Omap(tc_List_Olist(X31321),X31321),hAPP(hAPP(c_COMBC(tc_List_Olist(X31321),tc_Nat_Onat,X31321),c_List_Onth(X31321)),X31322)),hAPP(c_List_Ofilter(tc_List_Olist(X31321),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X31321)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31322)),c_Nat_Osize__class_Osize(tc_List_Olist(X31321)))),X31320)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__transpose])]) ).

fof(i_0_6866,plain,
    ! [X25552,X25553,X25554] :
      ( ( ~ hBOOL(hAPP(c_Predicate_OPowp(X25554,hAPP(hAPP(c_COMBC(X25554,tc_fun(X25554,tc_HOL_Obool),tc_HOL_Obool),c_member(X25554)),X25553)),X25552))
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X25554,tc_HOL_Obool)),X25552),hAPP(c_Set_OPow(X25554),X25553))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X25554,tc_HOL_Obool)),X25552),hAPP(c_Set_OPow(X25554),X25553)))
        | hBOOL(hAPP(c_Predicate_OPowp(X25554,hAPP(hAPP(c_COMBC(X25554,tc_fun(X25554,tc_HOL_Obool),tc_HOL_Obool),c_member(X25554)),X25553)),X25552)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Powp__Pow__eq])]) ).

fof(i_0_6867,plain,
    ! [X25892,X25893,X25894,X25895,X25896,X25897] :
      ( ~ c_Fun_Oinj__on(X25897,X25896,X25895,X25894)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25896,tc_HOL_Obool)),hAPP(c_Set_Oimage(X25897,X25896,X25895),X25894)),X25893))
      | ~ c_Fun_Oinj__on(X25896,X25897,X25892,X25893)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25897,tc_HOL_Obool)),hAPP(c_Set_Oimage(X25896,X25897,X25892),X25893)),X25894))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25897),X25894))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25896),X25893))
      | hAPP(c_Finite__Set_Ocard(X25897),X25894) = hAPP(c_Finite__Set_Ocard(X25896),X25893) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__bij__eq])]) ).

fof(i_0_6868,plain,
    ! [X30366,X30367,X30368] : c_Hilbert__Choice_OEps(tc_prod(X30368,X30367),hAPP(c_Product__Type_Oprod_Oprod__case(X30368,X30367,tc_HOL_Obool),X30366)) = c_Hilbert__Choice_OEps(tc_prod(X30368,X30367),hAPP(hAPP(c_COMBS(tc_prod(X30368,X30367),X30367,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X30368,tc_fun(X30367,tc_HOL_Obool),tc_prod(X30368,X30367)),X30366),c_Product__Type_Ofst(X30368,X30367))),c_Product__Type_Osnd(X30368,X30367))),
    inference(variable_rename,[status(thm)],[fact_Eps__split]) ).

fof(i_0_6869,plain,
    ! [X27077,X27078,X27079] : c_HOL_OThe(tc_prod(X27079,X27078),hAPP(c_Product__Type_Oprod_Oprod__case(X27079,X27078,tc_HOL_Obool),X27077)) = c_HOL_OThe(tc_prod(X27079,X27078),hAPP(hAPP(c_COMBS(tc_prod(X27079,X27078),X27078,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X27079,tc_fun(X27078,tc_HOL_Obool),tc_prod(X27079,X27078)),X27077),c_Product__Type_Ofst(X27079,X27078))),c_Product__Type_Osnd(X27079,X27078))),
    inference(variable_rename,[status(thm)],[fact_The__split]) ).

fof(i_0_6870,plain,
    ! [X31946,X31947,X31948,X31949,X31950] :
      ( ( hAPP(X31947,X31949) = hAPP(X31947,X31948)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X31947,X31949)),hAPP(X31947,X31948)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X31950,X31950)),hAPP(hAPP(c_Product__Type_OPair(X31950,X31950),X31949),X31948)),c_List_Omeasures(X31950,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X31950,tc_Nat_Onat)),X31947),X31946)))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X31950,X31950)),hAPP(hAPP(c_Product__Type_OPair(X31950,X31950),X31949),X31948)),c_List_Omeasures(X31950,X31946)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X31947,X31949)),hAPP(X31947,X31948)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X31950,X31950)),hAPP(hAPP(c_Product__Type_OPair(X31950,X31950),X31949),X31948)),c_List_Omeasures(X31950,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X31950,tc_Nat_Onat)),X31947),X31946)))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X31947,X31949)),hAPP(X31947,X31948)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X31950,X31950)),hAPP(hAPP(c_Product__Type_OPair(X31950,X31950),X31949),X31948)),c_List_Omeasures(X31950,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X31950,tc_Nat_Onat)),X31947),X31946)))) )
      & ( hAPP(X31947,X31949) != hAPP(X31947,X31948)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X31950,X31950)),hAPP(hAPP(c_Product__Type_OPair(X31950,X31950),X31949),X31948)),c_List_Omeasures(X31950,X31946)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X31950,X31950)),hAPP(hAPP(c_Product__Type_OPair(X31950,X31950),X31949),X31948)),c_List_Omeasures(X31950,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X31950,tc_Nat_Onat)),X31947),X31946)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__measures_I2_J])])]) ).

fof(i_0_6871,plain,
    ! [X19739,X19740,X19741,X19742] :
      ( ~ class_Divides_Osemiring__div(X19742)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19742),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19742),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19742),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X19742),X19741),X19740)),X19740)),c_Divides_Odiv__class_Omod(X19742,X19741,X19740))),X19739) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19742),X19741),X19739) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mod__equality])]) ).

fof(i_0_6872,plain,
    ! [X23375,X23376,X23377,X23378,X23379,X23380] : c_Fun_Ofun__upd(X23380,X23379,c_Fun_Ofun__upd(X23380,X23379,X23378,X23377,X23376),X23377,X23375) = c_Fun_Ofun__upd(X23380,X23379,X23378,X23377,X23375),
    inference(variable_rename,[status(thm)],[fact_fun__upd__upd]) ).

fof(i_0_6873,plain,
    ! [X24815,X24816,X24817,X24818,X24819] :
      ( ~ class_Groups_Ocomm__monoid__mult(X24819)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24818),X24817))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24818),X24816))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24818,tc_HOL_Obool)),X24817),X24816) != c_Orderings_Obot__class_Obot(tc_fun(X24818,tc_HOL_Obool))
      | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X24819,X24818,c_Groups_Otimes__class_Otimes(X24819)),X24815),c_Groups_Oone__class_Oone(X24819)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24818,tc_HOL_Obool)),X24817),X24816)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24819),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X24819,X24818,c_Groups_Otimes__class_Otimes(X24819)),X24815),c_Groups_Oone__class_Oone(X24819)),X24817)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X24819,X24818,c_Groups_Otimes__class_Otimes(X24819)),X24815),c_Groups_Oone__class_Oone(X24819)),X24816)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__Un__disjoint])]) ).

cnf(i_0_6874,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_5461]) ).

fof(i_0_6875,plain,
    ! [X30143,X30144,X30145,X30146] :
      ( ~ class_Groups_Oab__group__add(X30146)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X30146),hAPP(c_List_Omonoid__add__class_Olistsum(X30146),hAPP(hAPP(c_List_Omap(X30145,X30146),X30144),X30143))) = hAPP(c_List_Omonoid__add__class_Olistsum(X30146),hAPP(hAPP(c_List_Omap(X30145,X30146),hAPP(c_Fun_Ocomp(X30146,X30146,X30145,c_Groups_Ouminus__class_Ouminus(X30146)),X30144)),X30143)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_uminus__listsum__map])]) ).

fof(i_0_6876,plain,
    ! [X33287,X33288,X33289,X33290] : c_New__Random__Sequence_Oneg__map(X33290,X33289,X33288,X33287) = c_New__Random__Sequence_Oneg__bind(X33290,X33289,X33287,hAPP(c_Fun_Ocomp(X33289,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(X33289)))))),X33290,c_New__Random__Sequence_Oneg__single(X33289)),X33288)),
    inference(variable_rename,[status(thm)],[fact_neg__map__def]) ).

fof(i_0_6877,plain,
    ! [X30575,X30576,X30577] :
      ( ( ~ hBOOL(hAPP(c_List_Olistsp(X30577,hAPP(hAPP(c_COMBC(X30577,tc_fun(X30577,tc_HOL_Obool),tc_HOL_Obool),c_member(X30577)),X30576)),X30575))
        | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X30577)),X30575),c_List_Olists(X30577,X30576))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X30577)),X30575),c_List_Olists(X30577,X30576)))
        | hBOOL(hAPP(c_List_Olistsp(X30577,hAPP(hAPP(c_COMBC(X30577,tc_fun(X30577,tc_HOL_Obool),tc_HOL_Obool),c_member(X30577)),X30576)),X30575)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsp__lists__eq])]) ).

fof(i_0_6878,plain,
    ! [X26171,X26172,X26173,X26174] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X26174)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26174),c_Groups_Ozero__class_Ozero(X26174)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26173,X26174),hAPP(hAPP(c_COMBB(X26174,X26174,X26173),c_Groups_Oabs__class_Oabs(X26174)),X26172)),X26171))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__abs__ge__zero])]) ).

fof(i_0_6879,plain,
    ! [X27839,X27840] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27840),X27839))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X27840,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(X27840,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(X27840,tc_HOL_Obool),tc_fun(X27840,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(X27840,tc_HOL_Obool))),X27839)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Collect__subsets])]) ).

fof(i_0_6880,plain,
    ! [X18997,X18998,X18999] :
      ( ( X18998 = c_Groups_Ozero__class_Ozero(X18999)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18999),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18999),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18999),X18998),X18998)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18999),X18997),X18997))),c_Groups_Ozero__class_Ozero(X18999)))
        | ~ class_Rings_Olinordered__ring__strict(X18999) )
      & ( X18997 = c_Groups_Ozero__class_Ozero(X18999)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18999),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18999),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18999),X18998),X18998)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18999),X18997),X18997))),c_Groups_Ozero__class_Ozero(X18999)))
        | ~ class_Rings_Olinordered__ring__strict(X18999) )
      & ( X18998 != c_Groups_Ozero__class_Ozero(X18999)
        | X18997 != c_Groups_Ozero__class_Ozero(X18999)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18999),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18999),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18999),X18998),X18998)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18999),X18997),X18997))),c_Groups_Ozero__class_Ozero(X18999)))
        | ~ class_Rings_Olinordered__ring__strict(X18999) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__squares__le__zero__iff])])]) ).

fof(i_0_6881,plain,
    ! [X24395,X24396] :
      ( ~ class_Orderings_Olinorder(X24396)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24396),X24395))
      | X24395 = c_Orderings_Obot__class_Obot(tc_fun(X24396,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_member(X24396),hAPP(hAPP(c_Orderings_Oord__class_Omin(X24396),esk130_2(X24395,X24396)),esk131_2(X24395,X24396))),hAPP(hAPP(c_Set_Oinsert(X24396),esk130_2(X24395,X24396)),hAPP(hAPP(c_Set_Oinsert(X24396),esk131_2(X24395,X24396)),c_Orderings_Obot__class_Obot(tc_fun(X24396,tc_HOL_Obool))))))
      | hBOOL(hAPP(hAPP(c_member(X24396),c_Big__Operators_Olinorder__class_OMin(X24396,X24395)),X24395)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Oclosed])])]) ).

fof(i_0_6882,plain,
    ! [X24342,X24343] :
      ( ~ class_Orderings_Olinorder(X24343)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24343),X24342))
      | X24342 = c_Orderings_Obot__class_Obot(tc_fun(X24343,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_member(X24343),hAPP(hAPP(c_Orderings_Oord__class_Omax(X24343),esk124_2(X24342,X24343)),esk125_2(X24342,X24343))),hAPP(hAPP(c_Set_Oinsert(X24343),esk124_2(X24342,X24343)),hAPP(hAPP(c_Set_Oinsert(X24343),esk125_2(X24342,X24343)),c_Orderings_Obot__class_Obot(tc_fun(X24343,tc_HOL_Obool))))))
      | hBOOL(hAPP(hAPP(c_member(X24343),c_Big__Operators_Olinorder__class_OMax(X24343,X24342)),X24342)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Oclosed])])]) ).

fof(i_0_6883,plain,
    ! [X24350,X24351] :
      ( ~ class_Lattices_Olattice(X24351)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24351),X24350))
      | X24350 = c_Orderings_Obot__class_Obot(tc_fun(X24351,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_member(X24351),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24351),esk128_2(X24350,X24351)),esk129_2(X24350,X24351))),hAPP(hAPP(c_Set_Oinsert(X24351),esk128_2(X24350,X24351)),hAPP(hAPP(c_Set_Oinsert(X24351),esk129_2(X24350,X24351)),c_Orderings_Obot__class_Obot(tc_fun(X24351,tc_HOL_Obool))))))
      | hBOOL(hAPP(hAPP(c_member(X24351),c_Big__Operators_Olattice__class_OSup__fin(X24351,X24350)),X24350)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oclosed])])]) ).

fof(i_0_6884,plain,
    ! [X24346,X24347] :
      ( ~ class_Lattices_Olattice(X24347)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24347),X24346))
      | X24346 = c_Orderings_Obot__class_Obot(tc_fun(X24347,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_member(X24347),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24347),esk126_2(X24346,X24347)),esk127_2(X24346,X24347))),hAPP(hAPP(c_Set_Oinsert(X24347),esk126_2(X24346,X24347)),hAPP(hAPP(c_Set_Oinsert(X24347),esk127_2(X24346,X24347)),c_Orderings_Obot__class_Obot(tc_fun(X24347,tc_HOL_Obool))))))
      | hBOOL(hAPP(hAPP(c_member(X24347),c_Big__Operators_Olattice__class_OInf__fin(X24347,X24346)),X24346)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oclosed])])]) ).

fof(i_0_6885,plain,
    ! [X18423,X18424,X18425] :
      ( ~ class_Rings_Olinordered__ring(X18425)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18425),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18425),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18425),X18424),X18424)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18425),X18423),X18423))),c_Groups_Ozero__class_Ozero(X18425))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5462])]) ).

fof(i_0_6886,plain,
    ! [X26007,X26008,X26009,X26010,X26011,X26012,X26013,X26014] :
      ( ~ c_Finite__Set_Ofolding__image(X26014,X26013,X26012,X26011,X26010)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26013),X26009))
      | ~ c_Fun_Oinj__on(X26013,X26013,X26008,X26009)
      | hAPP(hAPP(X26010,X26007),hAPP(c_Set_Oimage(X26013,X26013,X26008),X26009)) = hAPP(hAPP(X26010,hAPP(c_Fun_Ocomp(X26013,X26014,X26013,X26007),X26008)),X26009) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image_Oreindex])]) ).

fof(i_0_6887,plain,
    ! [X31710,X31711,X31712] :
      ( ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X31712),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X31712))),X31711)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31710),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31712))),X31711)))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31712))),hAPP(c_List_Ofilter(tc_List_Olist(X31712),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X31712)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31710)),c_Nat_Osize__class_Osize(tc_List_Olist(X31712)))),c_List_Otranspose(X31712,X31711))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31712)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X31712)),X31711),X31710)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transpose__column__length])]) ).

fof(i_0_6888,plain,
    ! [X23318,X23319,X23320,X23321,X23322,X23323,X23324] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X23324,X23323)),hAPP(hAPP(c_Product__Type_OPair(X23324,X23323),X23322),X23321)),X23320))
      | hBOOL(hAPP(hAPP(c_member(X23319),hAPP(hAPP(X23318,X23322),X23321)),hAPP(c_Set_Oimage(tc_prod(X23324,X23323),X23319,hAPP(c_Product__Type_Oprod_Oprod__case(X23324,X23323,X23319),X23318)),X23320))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pair__imageI])]) ).

fof(i_0_6889,plain,
    ! [X31251,X31252,X31253,X31254,X31255] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31255)),hAPP(c_List_Ofilter(X31255,X31254),hAPP(hAPP(c_List_Omap(X31253,X31255),X31252),X31251))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31253)),hAPP(c_List_Ofilter(X31253,hAPP(c_Fun_Ocomp(X31255,tc_HOL_Obool,X31253,X31254),X31252)),X31251)),
    inference(variable_rename,[status(thm)],[fact_length__filter__map]) ).

cnf(i_0_6890,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_5463]) ).

fof(i_0_6891,plain,
    ! [X32274,X32275,X32276,X32277,X32278] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32278,X32278)),hAPP(hAPP(c_Product__Type_OPair(X32278,X32278),X32277),X32276)),c_Transitive__Closure_Ortrancl(X32278,X32275)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X32278,X32278),tc_HOL_Obool)),X32275),hAPP(hAPP(c_Product__Type_OSigma(X32278,X32278),X32274),hAPP(c_COMBK(tc_fun(X32278,tc_HOL_Obool),X32278),X32274))))
      | X32277 = X32276
      | hBOOL(hAPP(hAPP(c_member(X32278),X32277),X32274)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__subset__Sigma__aux])]) ).

fof(i_0_6892,plain,
    ! [X23125,X23126,X23127,X23128,X23129,X23130] :
      ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23130,tc_fun(X23129,tc_HOL_Obool))),X23128),X23127),X23126),X23125))
      | hBOOL(hAPP(hAPP(X23128,X23126),X23125))
      | hBOOL(hAPP(hAPP(X23127,X23126),X23125)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5464])]) ).

fof(i_0_6893,plain,
    ! [X31149,X31150,X31151] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31151)),hAPP(c_List_Ofilter(X31151,X31150),X31149))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31151)),hAPP(c_List_Ofilter(X31151,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X31151),c_fNot),X31150)),X31149))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31151)),X31149),
    inference(variable_rename,[status(thm)],[fact_sum__length__filter__compl]) ).

fof(i_0_6894,plain,
    ! [X32143,X32144,X32145,X32146,X32147] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32147,X32147)),hAPP(hAPP(c_Product__Type_OPair(X32147,X32147),X32146),X32145)),c_Transitive__Closure_Ortrancl(X32147,X32144)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32147,X32147)),hAPP(hAPP(c_Product__Type_OPair(X32147,X32147),X32145),X32143)),c_Transitive__Closure_Ortrancl(X32147,X32144)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X32147,X32147)),hAPP(hAPP(c_Product__Type_OPair(X32147,X32147),X32146),X32143)),c_Transitive__Closure_Ortrancl(X32147,X32144))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__trans])]) ).

cnf(i_0_6895,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_5465]) ).

cnf(i_0_6896,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_5466]) ).

fof(i_0_6897,plain,
    ! [X19632,X19633,X19634] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19634),X19633)),X19632) = 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),X19634),X19632)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19633),X19632))),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,X19634,X19632)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19633,X19632))),X19632)),
    inference(variable_rename,[status(thm)],[fact_zdiv__zadd1__eq]) ).

fof(i_0_6898,plain,
    ! [X19552,X19553,X19554] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19554),X19553)),X19552) = 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),X19554),X19552)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19553),X19552))),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,X19554,X19552)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19553,X19552))),X19552)),
    inference(variable_rename,[status(thm)],[fact_div__add1__eq]) ).

fof(i_0_6899,plain,
    ! [X24210,X24211,X24212,X24213,X24214,X24215] :
      ( ( hBOOL(hAPP(hAPP(X24213,X24211),X24210))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24215,tc_fun(X24214,tc_HOL_Obool))),X24213),X24212),X24211),X24210)) )
      & ( hBOOL(hAPP(hAPP(X24212,X24211),X24210))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24215,tc_fun(X24214,tc_HOL_Obool))),X24213),X24212),X24211),X24210)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5467])])]) ).

fof(i_0_6900,plain,
    ! [X24228,X24229,X24230,X24231,X24232,X24233] :
      ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24233,tc_fun(X24232,tc_HOL_Obool))),X24231),X24230),X24229),X24228))
      | hBOOL(hAPP(hAPP(X24231,X24229),X24228)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf2D1])]) ).

fof(i_0_6901,plain,
    ! [X24222,X24223,X24224,X24225,X24226,X24227] :
      ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24227,tc_fun(X24226,tc_HOL_Obool))),X24225),X24224),X24223),X24222))
      | hBOOL(hAPP(hAPP(X24224,X24223),X24222)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf2D2])]) ).

cnf(i_0_6902,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),esk388_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_5270]) ).

cnf(i_0_6903,plain,
    ( X2 = X3
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),esk387_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_5271]) ).

fof(i_0_6904,plain,
    ! [X31900,X31901,X31902,X31903] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk404_4(X31900,X31901,X31902,X31903)),X31903))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31903),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31901)),X31900)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31903),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31901)),c_List_OtakeWhile(X31901,X31902,X31900)))) )
      & ( ~ hBOOL(hAPP(X31902,hAPP(hAPP(c_List_Onth(X31901),X31900),esk404_4(X31900,X31901,X31902,X31903))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31903),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31901)),X31900)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31903),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31901)),c_List_OtakeWhile(X31901,X31902,X31900)))) ) ),
    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_6905,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_5468]) ).

cnf(i_0_6906,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_5469]) ).

cnf(i_0_6907,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_5470]) ).

cnf(i_0_6908,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_5471]) ).

fof(i_0_6909,plain,
    ! [X32153,X32154,X32155,X32156,X32157] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32157,X32157)),hAPP(hAPP(c_Product__Type_OPair(X32157,X32157),X32156),X32155)),X32154))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32157,X32157)),hAPP(hAPP(c_Product__Type_OPair(X32157,X32157),X32155),X32153)),c_Transitive__Closure_Ortrancl(X32157,X32154)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X32157,X32157)),hAPP(hAPP(c_Product__Type_OPair(X32157,X32157),X32156),X32153)),c_Transitive__Closure_Ortrancl(X32157,X32154))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_converse__rtrancl__into__rtrancl])]) ).

fof(i_0_6910,plain,
    ! [X32148,X32149,X32150,X32151,X32152] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32152,X32152)),hAPP(hAPP(c_Product__Type_OPair(X32152,X32152),X32151),X32150)),c_Transitive__Closure_Ortrancl(X32152,X32149)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32152,X32152)),hAPP(hAPP(c_Product__Type_OPair(X32152,X32152),X32150),X32148)),X32149))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X32152,X32152)),hAPP(hAPP(c_Product__Type_OPair(X32152,X32152),X32151),X32148)),c_Transitive__Closure_Ortrancl(X32152,X32149))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl_Ortrancl__into__rtrancl])]) ).

fof(i_0_6911,plain,
    ! [X32263,X32264,X32265,X32266] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32266),tc_List_Olist(X32266))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32266),tc_List_Olist(X32266)),X32265),X32264)),c_List_Olistrel(X32266,X32263)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32266),tc_List_Olist(X32266))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32266),tc_List_Olist(X32266)),X32265),X32264)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X32266),c_List_Olistrel1(X32266,X32263)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__listrel1__if__listrel])]) ).

fof(i_0_6912,plain,
    ! [X23592,X23593,X23594,X23595,X23596,X23597,X23598,X23599,X23600,X23601,X23602] :
      ( ~ c_Finite__Set_Ofolding(X23602,X23601,X23600,X23599)
      | hAPP(c_Fun_Ocomp(X23598,X23597,X23596,X23595),hAPP(c_Fun_Ocomp(X23594,X23598,X23596,X23593),X23592)) = hAPP(c_Fun_Ocomp(X23594,X23597,X23596,hAPP(c_Fun_Ocomp(X23598,X23597,X23594,X23595),X23593)),X23592) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__comps_I1_J])]) ).

cnf(i_0_6913,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_5472]) ).

fof(i_0_6914,plain,
    ! [X19059,X19060,X19061,X19062,X19063,X19064] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19064),X19063)),X19062) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19061),X19060)),X19059)
      | ~ 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),X19061),X19060)),X19059)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19062),X19064))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19059))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19061))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19061),X19064))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19060),X19063)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono2__neg__lemma])]) ).

fof(i_0_6915,plain,
    ! [X27864] : 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)))),X27864)) = 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),X27864),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_6916,plain,
    ! [X32259,X32260,X32261,X32262] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32262),tc_List_Olist(X32262))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32262),tc_List_Olist(X32262)),X32261),X32260)),c_List_Olistrel1(X32262,X32259)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32262),tc_List_Olist(X32262))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32262),tc_List_Olist(X32262)),X32261),X32260)),c_List_Olistrel(X32262,c_Transitive__Closure_Ortrancl(X32262,X32259)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__reflcl__if__listrel1])]) ).

fof(i_0_6917,plain,
    ! [X28346,X28347,X28348,X28349] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28349),tc_List_Olist(X28349))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28349),tc_List_Olist(X28349)),X28348),X28347)),c_List_Olexord(X28349,X28346)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28349),tc_List_Olist(X28349))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28349),tc_List_Olist(X28349)),X28348),X28347)),c_List_Olex(X28349,X28346))) )
      & ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28349)),X28348) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28349)),X28347)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28349),tc_List_Olist(X28349))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28349),tc_List_Olist(X28349)),X28348),X28347)),c_List_Olex(X28349,X28346))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28349),tc_List_Olist(X28349))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28349),tc_List_Olist(X28349)),X28348),X28347)),c_List_Olexord(X28349,X28346)))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28349)),X28348) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28349)),X28347)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28349),tc_List_Olist(X28349))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28349),tc_List_Olist(X28349)),X28348),X28347)),c_List_Olex(X28349,X28346))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__lex])])]) ).

fof(i_0_6918,plain,
    ! [X31173,X31174,X31175,X31176,X31177] : hAPP(c_List_Ofilter(X31177,X31176),hAPP(hAPP(c_List_Omap(X31175,X31177),X31174),X31173)) = hAPP(hAPP(c_List_Omap(X31175,X31177),X31174),hAPP(c_List_Ofilter(X31175,hAPP(c_Fun_Ocomp(X31177,tc_HOL_Obool,X31175,X31176),X31174)),X31173)),
    inference(variable_rename,[status(thm)],[fact_filter__map]) ).

fof(i_0_6919,plain,
    ! [X32055,X32056,X32057] :
      ( ( hAPP(X32056,esk424_3(X32055,X32056,X32057)) != hAPP(X32056,esk425_3(X32055,X32056,X32057))
        | c_Wellfounded_OwfP(X32057,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X32055,tc_fun(X32057,tc_fun(X32057,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X32055,tc_HOL_Obool))),X32056))
        | ~ c_Wellfounded_OwfP(X32057,hAPP(X32056,esk423_3(X32055,X32056,X32057))) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X32057,tc_HOL_Obool)),c_Predicate_ODomainP(X32057,X32057,hAPP(X32056,esk424_3(X32055,X32056,X32057)))),c_Predicate_ORangeP(X32057,X32057,hAPP(X32056,esk425_3(X32055,X32056,X32057)))) != c_Orderings_Obot__class_Obot(tc_fun(X32057,tc_HOL_Obool))
        | c_Wellfounded_OwfP(X32057,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X32055,tc_fun(X32057,tc_fun(X32057,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X32055,tc_HOL_Obool))),X32056))
        | ~ c_Wellfounded_OwfP(X32057,hAPP(X32056,esk423_3(X32055,X32056,X32057))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wfP__SUP])])])]) ).

fof(i_0_6920,plain,
    ! [X31267,X31268,X31269] : c_List_Opartition(X31269,X31268,X31267) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X31269),tc_List_Olist(X31269)),hAPP(c_List_Ofilter(X31269,X31268),X31267)),hAPP(c_List_Ofilter(X31269,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,X31269,c_fNot),X31268)),X31267)),
    inference(variable_rename,[status(thm)],[fact_partition__filter__conv]) ).

cnf(i_0_6921,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_5473]) ).

fof(i_0_6922,plain,
    ! [X29544,X29545,X29546] :
      ( ( 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),esk342_3(X29544,X29545,X29546)),esk343_3(X29544,X29545,X29546))))
        | hBOOL(hAPP(hAPP(X29544,X29546),X29545))
        | ~ 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),X29546),X29545))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk342_3(X29544,X29545,X29546)),esk343_3(X29544,X29545,X29546)))
        | hBOOL(hAPP(hAPP(X29544,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk342_3(X29544,X29545,X29546)),c_Groups_Oone__class_Oone(tc_Int_Oint))),esk343_3(X29544,X29545,X29546)))
        | hBOOL(hAPP(hAPP(X29544,X29546),X29545))
        | ~ 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),X29546),X29545))) )
      & ( ~ hBOOL(hAPP(hAPP(X29544,esk342_3(X29544,X29545,X29546)),esk343_3(X29544,X29545,X29546)))
        | hBOOL(hAPP(hAPP(X29544,X29546),X29545))
        | ~ 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),X29546),X29545))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_upto_Opinduct])])])]) ).

fof(i_0_6923,plain,
    ! [X30671,X30672,X30673,X30674,X30675,X30676,X30677] :
      ( ( ~ c_List_Olist__all2(X30677,X30676,X30675,hAPP(hAPP(c_List_Omap(X30674,X30677),X30673),X30672),X30671)
        | c_List_Olist__all2(X30674,X30676,hAPP(hAPP(c_COMBB(X30677,tc_fun(X30676,tc_HOL_Obool),X30674),X30675),X30673),X30672,X30671) )
      & ( ~ c_List_Olist__all2(X30674,X30676,hAPP(hAPP(c_COMBB(X30677,tc_fun(X30676,tc_HOL_Obool),X30674),X30675),X30673),X30672,X30671)
        | c_List_Olist__all2(X30677,X30676,X30675,hAPP(hAPP(c_List_Omap(X30674,X30677),X30673),X30672),X30671) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__map1])]) ).

cnf(i_0_6924,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_5474]) ).

fof(i_0_6925,plain,
    ! [X31934,X31935,X31936,X31937,X31938] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(X31938,X31937)),hAPP(X31938,X31936)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X31935,X31935)),hAPP(hAPP(c_Product__Type_OPair(X31935,X31935),X31937),X31936)),c_List_Omeasures(X31935,X31934)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X31935,X31935)),hAPP(hAPP(c_Product__Type_OPair(X31935,X31935),X31937),X31936)),c_List_Omeasures(X31935,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X31935,tc_Nat_Onat)),X31938),X31934)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_measures__lesseq])]) ).

fof(i_0_6926,plain,
    ! [X33811,X33812,X33813,X33814,X33815,X33816,X33817] :
      ( ( ~ c_Relation_Otrans(X33812,X33811)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X33812,X33812)),hAPP(hAPP(c_Product__Type_OPair(X33812,X33812),X33813),X33814)),X33811))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X33812,X33812)),hAPP(hAPP(c_Product__Type_OPair(X33812,X33812),X33814),X33815)),X33811))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X33812,X33812)),hAPP(hAPP(c_Product__Type_OPair(X33812,X33812),X33813),X33815)),X33811)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X33817,X33817)),hAPP(hAPP(c_Product__Type_OPair(X33817,X33817),esk543_2(X33816,X33817)),esk544_2(X33816,X33817))),X33816))
        | c_Relation_Otrans(X33817,X33816) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X33817,X33817)),hAPP(hAPP(c_Product__Type_OPair(X33817,X33817),esk544_2(X33816,X33817)),esk545_2(X33816,X33817))),X33816))
        | c_Relation_Otrans(X33817,X33816) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X33817,X33817)),hAPP(hAPP(c_Product__Type_OPair(X33817,X33817),esk543_2(X33816,X33817)),esk545_2(X33816,X33817))),X33816))
        | c_Relation_Otrans(X33817,X33816) ) ),
    inference(distribute,[status(thm)],[inference(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_6927,plain,
    ! [X33806,X33807,X33808,X33809,X33810] :
      ( ~ c_Relation_Otrans(X33810,X33809)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X33810,X33810)),hAPP(hAPP(c_Product__Type_OPair(X33810,X33810),X33808),X33807)),X33809))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X33810,X33810)),hAPP(hAPP(c_Product__Type_OPair(X33810,X33810),X33807),X33806)),X33809))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X33810,X33810)),hAPP(hAPP(c_Product__Type_OPair(X33810,X33810),X33808),X33806)),X33809)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transD])]) ).

fof(i_0_6928,plain,
    ! [X20881,X20882] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20882),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20882),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20882),c_Groups_Oone__class_Oone(X20882)),X20881)),X20881)),c_Groups_Ozero__class_Ozero(X20882)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20882),X20881),c_Groups_Ozero__class_Ozero(X20882)))
        | ~ hBOOL(hAPP(hAPP(c_member(X20882),X20881),c_Int_Oring__1__class_OInts(X20882)))
        | ~ class_Rings_Olinordered__idom(X20882) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20882),X20881),c_Groups_Ozero__class_Ozero(X20882)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20882),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20882),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20882),c_Groups_Oone__class_Oone(X20882)),X20881)),X20881)),c_Groups_Ozero__class_Ozero(X20882)))
        | ~ hBOOL(hAPP(hAPP(c_member(X20882),X20881),c_Int_Oring__1__class_OInts(X20882)))
        | ~ class_Rings_Olinordered__idom(X20882) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__odd__less__0])])]) ).

cnf(i_0_6929,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_5475]) ).

fof(i_0_6930,plain,
    ! [X19714,X19715,X19716] : 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),X19716),X19715)),X19715)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19716,X19715))),X19714) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19716),X19714),
    inference(variable_rename,[status(thm)],[fact_zdiv__zmod__equality2]) ).

cnf(i_0_6931,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk426_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_5476]) ).

cnf(i_0_6932,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_5477]) ).

fof(i_0_6933,plain,
    ! [X31771,X31772,X31773] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31773)),c_List_OtakeWhile(X31773,X31772,X31771))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31773)),X31771)))
      | ~ hBOOL(hAPP(X31772,hAPP(hAPP(c_List_Onth(X31773),X31771),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31773)),c_List_OtakeWhile(X31773,X31772,X31771))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5478])]) ).

cnf(i_0_6934,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_5479]) ).

cnf(i_0_6935,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk443_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_5480]) ).

fof(i_0_6936,plain,
    ! [X29638,X29639,X29640,X29641] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X29641)
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29640,X29641),hAPP(c_List_Oset(X29640),X29639)),X29638) = hAPP(c_List_Ofoldl(X29641,X29640,hAPP(c_COMBC(X29640,X29641,X29641),hAPP(hAPP(c_COMBB(X29641,tc_fun(X29641,X29641),X29640),c_Lattices_Osemilattice__inf__class_Oinf(X29641)),X29638)),c_Orderings_Otop__class_Otop(X29641)),X29639) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INFI__set__fold])]) ).

fof(i_0_6937,plain,
    ! [X29484,X29485,X29486,X29487] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X29487)
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X29486,X29487),hAPP(c_List_Oset(X29486),X29485)),X29484) = hAPP(c_List_Ofoldl(X29487,X29486,hAPP(c_COMBC(X29486,X29487,X29487),hAPP(hAPP(c_COMBB(X29487,tc_fun(X29487,X29487),X29486),c_Lattices_Osemilattice__sup__class_Osup(X29487)),X29484)),c_Orderings_Obot__class_Obot(X29487)),X29485) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUPR__set__fold])]) ).

cnf(i_0_6938,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_5481]) ).

fof(i_0_6939,plain,
    ! [X32047,X32048,X32049,X32050] :
      ( ( hBOOL(hAPP(hAPP(c_member(X32050),esk421_4(X32047,X32048,X32049,X32050)),X32049))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X32048),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X32050,tc_fun(X32048,tc_HOL_Obool)),X32049),X32047)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32050),X32049)) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32048),hAPP(X32047,esk421_4(X32047,X32048,X32049,X32050))))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X32048),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X32050,tc_fun(X32048,tc_HOL_Obool)),X32049),X32047)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32050),X32049)) ) ),
    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_6940,plain,
    ! [X24828,X24829,X24830,X24831,X24832] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24829),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24831,tc_fun(X24829,tc_HOL_Obool)),X24830),X24828)))
        | ~ hBOOL(hAPP(hAPP(c_member(X24831),X24832),X24830))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X24829),hAPP(X24828,X24832)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24831),X24830)) )
      & ( hBOOL(hAPP(hAPP(c_member(X24831),esk148_4(X24828,X24829,X24830,X24831)),X24830))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X24829),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24831,tc_fun(X24829,tc_HOL_Obool)),X24830),X24828)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24831),X24830)) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24829),hAPP(X24828,esk148_4(X24828,X24829,X24830,X24831))))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X24829),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24831,tc_fun(X24829,tc_HOL_Obool)),X24830),X24828)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24831),X24830)) ) ),
    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_6941,plain,
    ! [X28005,X28006,X28007,X28008,X28009,X28010,X28011] : hAPP(hAPP(c_Relation_Orel__comp(X28011,X28010,X28009),X28008),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X28007,tc_fun(tc_prod(X28010,X28009),tc_HOL_Obool)),X28006),X28005)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X28007,tc_fun(tc_prod(X28011,X28009),tc_HOL_Obool)),X28006),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X28010,X28009),tc_HOL_Obool),tc_fun(tc_prod(X28011,X28009),tc_HOL_Obool),X28007),hAPP(c_Relation_Orel__comp(X28011,X28010,X28009),X28008)),X28005)),
    inference(variable_rename,[status(thm)],[fact_rel__comp__UNION__distrib]) ).

fof(i_0_6942,plain,
    ! [X18038,X18039,X18040,X18041,X18042,X18043,X18044] : hAPP(c_Fun_Ocomp(X18044,X18043,X18042,X18041),hAPP(c_Fun_Ocomp(X18040,X18044,X18042,X18039),X18038)) = hAPP(c_Fun_Ocomp(X18040,X18043,X18042,hAPP(c_Fun_Ocomp(X18044,X18043,X18040,X18041),X18039)),X18038),
    inference(variable_rename,[status(thm)],[fact_o__assoc]) ).

fof(i_0_6943,plain,
    ! [X26816,X26817,X26818,X26819] :
      ( hAPP(c_Set_Oimage(X26819,X26818,X26817),c_Orderings_Otop__class_Otop(tc_fun(X26819,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X26818,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26818,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X26818,tc_HOL_Obool)),hAPP(c_Set_Oimage(X26819,X26818,X26817),X26816))),hAPP(c_Set_Oimage(X26819,X26818,X26817),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X26819,tc_HOL_Obool)),X26816)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_surj__Compl__image__subset])]) ).

fof(i_0_6944,plain,
    ! [X23073,X23074,X23075,X23076,X23077,X23078] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X23078,X23078)),hAPP(hAPP(c_Product__Type_OPair(X23078,X23078),X23077),X23076)),hAPP(hAPP(c_Relation_Oinv__image(X23075,X23078),X23074),X23073)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X23075,X23075)),hAPP(hAPP(c_Product__Type_OPair(X23075,X23075),hAPP(X23073,X23077)),hAPP(X23073,X23076))),X23074)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X23075,X23075)),hAPP(hAPP(c_Product__Type_OPair(X23075,X23075),hAPP(X23073,X23077)),hAPP(X23073,X23076))),X23074))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X23078,X23078)),hAPP(hAPP(c_Product__Type_OPair(X23078,X23078),X23077),X23076)),hAPP(hAPP(c_Relation_Oinv__image(X23075,X23078),X23074),X23073))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__inv__image])]) ).

fof(i_0_6945,plain,
    ! [X33865,X33866] :
      ( ~ c_Relation_Osym(X33866,X33865)
      | ~ c_Relation_Otrans(X33866,X33865)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X33866,X33866),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X33866,X33866,X33866),hAPP(c_Relation_Oconverse(X33866,X33866),X33865)),X33865)),X33865)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sym__trans__comp__subset])]) ).

fof(i_0_6946,plain,
    ! [X23573,X23574,X23575,X23576,X23577,X23578] :
      ( ~ c_Finite__Set_Ofolding(X23578,X23577,X23576,X23575)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23578),X23574))
      | ~ hBOOL(hAPP(hAPP(c_member(X23578),X23573),X23574))
      | hAPP(X23575,X23574) = hAPP(c_Fun_Ocomp(X23577,X23577,X23577,hAPP(X23575,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23578,tc_HOL_Obool)),X23574),hAPP(hAPP(c_Set_Oinsert(X23578),X23573),c_Orderings_Obot__class_Obot(tc_fun(X23578,tc_HOL_Obool)))))),hAPP(X23576,X23573)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Oremove])]) ).

fof(i_0_6947,plain,
    ! [X27389,X27390,X27391,X27392,X27393,X27394] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27394,X27393),tc_HOL_Obool)),X27392),hAPP(hAPP(c_Product__Type_OSigma(X27394,X27393),X27391),hAPP(c_COMBK(tc_fun(X27393,tc_HOL_Obool),X27394),X27390))))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27393,tc_HOL_Obool)),hAPP(c_Relation_OImage(X27394,X27393,X27392),X27389)),X27390)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Image__subset])]) ).

fof(i_0_6948,plain,
    ! [X29376,X29377,X29378] : hAPP(c_List_Otl(X29378),hAPP(hAPP(c_List_Oappend(X29378),X29377),X29376)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(X29378),X29378,hAPP(c_List_Otl(X29378),X29376),hAPP(c_COMBK(tc_fun(tc_List_Olist(X29378),tc_List_Olist(X29378)),X29378),hAPP(hAPP(c_COMBC(tc_List_Olist(X29378),tc_List_Olist(X29378),tc_List_Olist(X29378)),c_List_Oappend(X29378)),X29376))),X29377),
    inference(variable_rename,[status(thm)],[fact_tl__append]) ).

fof(i_0_6949,plain,
    ! [X33306,X33307,X33308,X33309] : c_New__Random__Sequence_Opos__map(X33309,X33308,X33307,X33306) = c_New__Random__Sequence_Opos__bind(X33309,X33308,X33306,hAPP(c_Fun_Ocomp(X33308,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(X33308))))),X33309,c_New__Random__Sequence_Opos__single(X33308)),X33307)),
    inference(variable_rename,[status(thm)],[fact_pos__map__def]) ).

fof(i_0_6950,plain,
    ! [X26829,X26830,X26831,X26832] :
      ( ~ c_Fun_Oinj__on(X26832,X26831,X26830,c_Orderings_Otop__class_Otop(tc_fun(X26832,tc_HOL_Obool)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26831,tc_HOL_Obool)),hAPP(c_Set_Oimage(X26832,X26831,X26830),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X26832,tc_HOL_Obool)),X26829))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X26831,tc_HOL_Obool)),hAPP(c_Set_Oimage(X26832,X26831,X26830),X26829)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__image__Compl__subset])]) ).

fof(i_0_6951,plain,
    ! [X34142,X34143,X34144] :
      ( ~ c_Fun_Obij__betw(X34144,X34143,X34142,c_Orderings_Otop__class_Otop(tc_fun(X34144,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X34143,tc_HOL_Obool)))
      | c_Fun_Obij__betw(X34143,X34144,c_Hilbert__Choice_Oinv__into(X34144,X34143,c_Orderings_Otop__class_Otop(tc_fun(X34144,tc_HOL_Obool)),X34142),c_Orderings_Otop__class_Otop(tc_fun(X34143,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X34144,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__imp__bij__inv])]) ).

fof(i_0_6952,plain,
    ! [X23687,X23688,X23689,X23690,X23691,X23692] :
      ( ~ c_Finite__Set_Ofolding(X23692,X23691,X23690,X23689)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23692),X23688))
      | hAPP(X23689,hAPP(hAPP(c_Set_Oinsert(X23692),X23687),X23688)) = hAPP(c_Fun_Ocomp(X23691,X23691,X23691,hAPP(X23689,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23692,tc_HOL_Obool)),X23688),hAPP(hAPP(c_Set_Oinsert(X23692),X23687),c_Orderings_Obot__class_Obot(tc_fun(X23692,tc_HOL_Obool)))))),hAPP(X23690,X23687)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Oinsert__remove])]) ).

fof(i_0_6953,plain,
    ! [X30712,X30713,X30714,X30715,X30716,X30717,X30718,X30719] :
      ( ~ c_List_Olist__all2(X30719,X30718,X30717,X30716,X30715)
      | ~ hBOOL(hAPP(hAPP(X30717,X30714),X30713))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30712),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30718)),X30715)))
      | c_List_Olist__all2(X30719,X30718,X30717,hAPP(hAPP(c_List_Olist__update(X30719,X30716),X30712),X30714),hAPP(hAPP(c_List_Olist__update(X30718,X30715),X30712),X30713)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__update__cong2])]) ).

fof(i_0_6954,plain,
    ! [X30720,X30721,X30722,X30723,X30724,X30725,X30726,X30727] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30727),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30726)),X30725)))
      | ~ c_List_Olist__all2(X30726,X30724,X30723,X30725,X30722)
      | ~ hBOOL(hAPP(hAPP(X30723,X30721),X30720))
      | c_List_Olist__all2(X30726,X30724,X30723,hAPP(hAPP(c_List_Olist__update(X30726,X30725),X30727),X30721),hAPP(hAPP(c_List_Olist__update(X30724,X30722),X30727),X30720)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__update__cong])]) ).

fof(i_0_6955,plain,
    ! [X34106,X34107,X34108,X34109] :
      ( ~ c_Fun_Obij__betw(X34109,X34108,X34107,c_Orderings_Otop__class_Otop(tc_fun(X34109,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X34108,tc_HOL_Obool)))
      | hAPP(c_Set_Oimage(X34109,X34108,X34107),hAPP(c_Set_OCollect(X34109),X34106)) = hAPP(c_Set_OCollect(X34108),hAPP(hAPP(c_COMBB(X34109,tc_HOL_Obool,X34108),X34106),c_Hilbert__Choice_Oinv__into(X34109,X34108,c_Orderings_Otop__class_Otop(tc_fun(X34109,tc_HOL_Obool)),X34107))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__image__Collect__eq])]) ).

fof(i_0_6956,plain,
    ! [X29312,X29313,X29314,X29315] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X29315),X29314))
      | hBOOL(hAPP(hAPP(c_member(X29315),X29313),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X29315,tc_HOL_Obool)),hAPP(c_List_Oset(X29315),X29314)),hAPP(hAPP(c_Set_Oinsert(X29315),hAPP(hAPP(c_List_Onth(X29315),X29314),X29312)),c_Orderings_Obot__class_Obot(tc_fun(X29315,tc_HOL_Obool))))))
      | hBOOL(hAPP(c_List_Odistinct(X29315),hAPP(hAPP(c_List_Olist__update(X29315,X29314),X29312),X29313))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5482])]) ).

fof(i_0_6957,plain,
    ! [X25855,X25856,X25857,X25858] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X25858),hAPP(c_Set_Oimage(X25857,X25858,X25856),X25855))),hAPP(c_Finite__Set_Ocard(X25857),X25855)))
      | ~ c_Fun_Oinj__on(X25857,X25858,X25856,X25855) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5483])]) ).

fof(i_0_6958,plain,
    ! [X33227,X33228,X33229,X33230] :
      ( ( hBOOL(hAPP(hAPP(c_member(X33229),esk512_4(X33227,X33228,X33229,X33230)),X33228))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X33230),c_Groups_Ozero__class_Ozero(X33230)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X33229,X33230),X33227),X33228)))
        | ~ class_Rings_Olinordered__semidom(X33230) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X33230),c_Groups_Ozero__class_Ozero(X33230)),hAPP(X33227,esk512_4(X33227,X33228,X33229,X33230))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X33230),c_Groups_Ozero__class_Ozero(X33230)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X33229,X33230),X33227),X33228)))
        | ~ class_Rings_Olinordered__semidom(X33230) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__nonneg])])])]) ).

fof(i_0_6959,plain,
    ! [X33152,X33153,X33154,X33155] :
      ( ( hBOOL(hAPP(hAPP(c_member(X33154),esk505_4(X33152,X33153,X33154,X33155)),X33153))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X33155),c_Groups_Ozero__class_Ozero(X33155)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X33154,X33155),X33152),X33153)))
        | ~ class_Rings_Olinordered__semidom(X33155) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X33155),c_Groups_Ozero__class_Ozero(X33155)),hAPP(X33152,esk505_4(X33152,X33153,X33154,X33155))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X33155),c_Groups_Ozero__class_Ozero(X33155)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X33154,X33155),X33152),X33153)))
        | ~ class_Rings_Olinordered__semidom(X33155) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__pos])])])]) ).

fof(i_0_6960,plain,
    ! [X33339,X33340,X33341,X33342,X33343] : c_Predicate_Oconversep(X33343,X33342,c_Predicate_Opred__comp(X33343,X33341,X33342,X33340,X33339)) = c_Predicate_Opred__comp(X33342,X33341,X33343,c_Predicate_Oconversep(X33341,X33342,X33339),c_Predicate_Oconversep(X33343,X33341,X33340)),
    inference(variable_rename,[status(thm)],[fact_converse__pred__comp]) ).

cnf(i_0_6961,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_5484]) ).

cnf(i_0_6962,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_5465]) ).

fof(i_0_6963,plain,
    ! [X23623,X23624,X23625,X23626,X23627,X23628,X23629,X23630] :
      ( ~ c_Finite__Set_Ofolding(X23630,X23629,X23628,X23627)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23630),X23626))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23630),X23625))
      | hAPP(c_Fun_Ocomp(X23629,X23629,X23624,hAPP(X23627,X23625)),hAPP(c_Fun_Ocomp(X23629,X23629,X23624,hAPP(X23627,X23626)),X23623)) = hAPP(c_Fun_Ocomp(X23629,X23629,X23624,hAPP(X23627,X23626)),hAPP(c_Fun_Ocomp(X23629,X23629,X23624,hAPP(X23627,X23625)),X23623)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__left__comp_H_H])]) ).

fof(i_0_6964,plain,
    ! [X34054,X34055,X34056,X34057] : hAPP(c_Hilbert__Choice_Oinv__into(X34057,X34056,c_Orderings_Otop__class_Otop(tc_fun(X34057,tc_HOL_Obool)),X34055),X34054) = c_Hilbert__Choice_OEps(X34057,hAPP(hAPP(c_COMBC(X34057,X34056,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X34056,tc_fun(X34056,tc_HOL_Obool),X34057),c_fequal),X34055)),X34054)),
    inference(variable_rename,[status(thm)],[fact_inv__def]) ).

fof(i_0_6965,plain,
    ! [X27454,X27455,X27456,X27457] :
      ( ( hBOOL(hAPP(hAPP(c_member(X27457),esk277_4(X27454,X27455,X27456,X27457)),X27456))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X27457,X27455)),hAPP(hAPP(c_Product__Type_OSigma(X27457,X27455),X27456),X27454)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27457),X27456)) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27455),hAPP(X27454,esk277_4(X27454,X27455,X27456,X27457))))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X27457,X27455)),hAPP(hAPP(c_Product__Type_OSigma(X27457,X27455),X27456),X27454)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27457),X27456)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__SigmaI])])])]) ).

fof(i_0_6966,plain,
    ! [X18703,X18704,X18705,X18706,X18707,X18708] :
      ( ~ class_Rings_Olinordered__semiring__1(X18708)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18708),X18707),X18706))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18708),X18705),X18706))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18708),c_Groups_Ozero__class_Ozero(X18708)),X18704))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18708),c_Groups_Ozero__class_Ozero(X18708)),X18703))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18708),X18704),X18703) != c_Groups_Oone__class_Oone(X18708)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18708),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18708),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18708),X18704),X18707)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18708),X18703),X18705))),X18706)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_convex__bound__le])]) ).

fof(i_0_6967,plain,
    ! [X18718,X18719,X18720,X18721,X18722,X18723] :
      ( ~ class_Rings_Olinordered__semiring__1__strict(X18723)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18723),X18722),X18721))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18723),X18720),X18721))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18723),c_Groups_Ozero__class_Ozero(X18723)),X18719))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18723),c_Groups_Ozero__class_Ozero(X18723)),X18718))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18723),X18719),X18718) != c_Groups_Oone__class_Oone(X18723)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18723),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18723),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18723),X18719),X18722)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18723),X18718),X18720))),X18721)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_convex__bound__lt])]) ).

fof(i_0_6968,plain,
    ! [X25561,X25562,X25563,X25564] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk185_4(X25561,X25562,X25563,X25564)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X25563)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25564),X25562))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25564),X25563)),X25562))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25562),c_Groups_Oone__class_Oone(tc_Int_Oint))),X25561))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25563)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk186_4(X25561,X25562,X25563,X25564)),X25561))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25564),X25562))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25564),X25563)),X25562))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25562),c_Groups_Oone__class_Oone(tc_Int_Oint))),X25561))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25563)) )
      & ( X25564 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk186_4(X25561,X25562,X25563,X25564)),esk185_4(X25561,X25562,X25563,X25564))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25564),X25562))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25564),X25563)),X25562))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25562),c_Groups_Oone__class_Oone(tc_Int_Oint))),X25561))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25563)) ) ),
    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_6969,plain,
    ! [X31895,X31896,X31897,X31898] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31898),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31897)),X31896)))
        | c_List_OtakeWhile(X31897,X31895,X31896) = hAPP(hAPP(c_List_Otake(X31897),X31898),X31896)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk403_4(X31895,X31896,X31897,X31898)),X31898)) )
      & ( hBOOL(hAPP(X31895,hAPP(hAPP(c_List_Onth(X31897),X31896),X31898)))
        | c_List_OtakeWhile(X31897,X31895,X31896) = hAPP(hAPP(c_List_Otake(X31897),X31898),X31896)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk403_4(X31895,X31896,X31897,X31898)),X31898)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31898),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31897)),X31896)))
        | c_List_OtakeWhile(X31897,X31895,X31896) = hAPP(hAPP(c_List_Otake(X31897),X31898),X31896)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk403_4(X31895,X31896,X31897,X31898)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31897)),X31896))) )
      & ( hBOOL(hAPP(X31895,hAPP(hAPP(c_List_Onth(X31897),X31896),X31898)))
        | c_List_OtakeWhile(X31897,X31895,X31896) = hAPP(hAPP(c_List_Otake(X31897),X31898),X31896)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk403_4(X31895,X31896,X31897,X31898)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31897)),X31896))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31898),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31897)),X31896)))
        | c_List_OtakeWhile(X31897,X31895,X31896) = hAPP(hAPP(c_List_Otake(X31897),X31898),X31896)
        | ~ hBOOL(hAPP(X31895,hAPP(hAPP(c_List_Onth(X31897),X31896),esk403_4(X31895,X31896,X31897,X31898)))) )
      & ( hBOOL(hAPP(X31895,hAPP(hAPP(c_List_Onth(X31897),X31896),X31898)))
        | c_List_OtakeWhile(X31897,X31895,X31896) = hAPP(hAPP(c_List_Otake(X31897),X31898),X31896)
        | ~ hBOOL(hAPP(X31895,hAPP(hAPP(c_List_Onth(X31897),X31896),esk403_4(X31895,X31896,X31897,X31898)))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5485])])])]) ).

fof(i_0_6970,plain,
    ! [X34100,X34101,X34102,X34103,X34104,X34105] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X34105,X34104,X34103,X34102,c_Lazy__Sequence_Olazy__sequence_OInsert(X34104,X34101,X34100)) = hAPP(hAPP(hAPP(X34102,X34101),X34100),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X34105,X34104,X34103,X34102,X34100)),
    inference(variable_rename,[status(thm)],[fact_lazy__sequence_Orecs_I2_J]) ).

fof(i_0_6971,plain,
    ! [X33746,X33747,X33748,X33749,X33751] :
      ( ( hBOOL(hAPP(hAPP(c_member(X33749),esk540_4(X33746,X33747,X33748,X33749)),X33748))
        | c_Wellfounded_Omax__extp(X33749,X33746,X33748,X33747)
        | X33747 = c_Orderings_Obot__class_Obot(tc_fun(X33749,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33749),X33747))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33749),X33748)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X33749),X33751),X33747))
        | ~ hBOOL(hAPP(hAPP(X33746,esk540_4(X33746,X33747,X33748,X33749)),X33751))
        | c_Wellfounded_Omax__extp(X33749,X33746,X33748,X33747)
        | X33747 = c_Orderings_Obot__class_Obot(tc_fun(X33749,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33749),X33747))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33749),X33748)) ) ),
    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_6972,plain,
    ! [X23637,X23638,X23639,X23640,X23641,X23642,X23643,X23644] :
      ( ~ c_Finite__Set_Ofolding(X23644,X23643,X23642,X23641)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23644),X23640))
      | hAPP(c_Fun_Ocomp(X23643,X23643,X23639,hAPP(X23642,X23638)),hAPP(c_Fun_Ocomp(X23643,X23643,X23639,hAPP(X23641,X23640)),X23637)) = hAPP(c_Fun_Ocomp(X23643,X23643,X23639,hAPP(X23641,X23640)),hAPP(c_Fun_Ocomp(X23643,X23643,X23639,hAPP(X23642,X23638)),X23637)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__left__comp_H])]) ).

fof(i_0_6973,plain,
    ! [X28550,X28551,X28552,X28553,X28554,X28555,X28556,X28557] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28557,X28557)),hAPP(hAPP(c_Product__Type_OPair(X28557,X28557),X28556),X28555)),X28554))
      | X28553 != hAPP(hAPP(c_List_Oappend(X28557),X28552),hAPP(hAPP(c_List_Olist_OCons(X28557),X28556),X28551))
      | X28550 != hAPP(hAPP(c_List_Oappend(X28557),X28552),hAPP(hAPP(c_List_Olist_OCons(X28557),X28555),X28551))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28557),tc_List_Olist(X28557))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28557),tc_List_Olist(X28557)),X28553),X28550)),c_List_Olistrel1(X28557,X28554))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel1I])]) ).

cnf(i_0_6974,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_5486]) ).

fof(i_0_6975,plain,
    ! [X31083,X31084,X31085,X31086] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk382_4(X31083,X31084,X31085,X31086)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31086)),X31085)))
        | ~ hBOOL(hAPP(hAPP(c_member(X31086),X31083),hAPP(c_List_Oset(X31086),X31085)))
        | hBOOL(hAPP(X31084,X31083)) )
      & ( ~ hBOOL(hAPP(X31084,hAPP(hAPP(c_List_Onth(X31086),X31085),esk382_4(X31083,X31084,X31085,X31086))))
        | ~ hBOOL(hAPP(hAPP(c_member(X31086),X31083),hAPP(c_List_Oset(X31086),X31085)))
        | hBOOL(hAPP(X31084,X31083)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_all__nth__imp__all__set])])])]) ).

fof(i_0_6976,plain,
    ! [X33042,X33043,X33044,X33045] :
      ( ( hBOOL(hAPP(hAPP(c_member(X33045),esk491_4(X33042,X33043,X33044,X33045)),X33044))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X33045),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X33045),X33043),X33042)),hAPP(hAPP(c_Finite__Set_Ofold(X33045,X33045,c_Lattices_Osemilattice__inf__class_Oinf(X33045)),X33042),X33044)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33045),X33044))
        | ~ class_Lattices_Osemilattice__inf(X33045) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X33045),X33043),esk491_4(X33042,X33043,X33044,X33045)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X33045),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X33045),X33043),X33042)),hAPP(hAPP(c_Finite__Set_Ofold(X33045,X33045,c_Lattices_Osemilattice__inf__class_Oinf(X33045)),X33042),X33044)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33045),X33044))
        | ~ class_Lattices_Osemilattice__inf(X33045) ) ),
    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_6977,plain,
    ! [X33037,X33038,X33039,X33040] :
      ( ( hBOOL(hAPP(hAPP(c_member(X33040),esk490_4(X33037,X33038,X33039,X33040)),X33039))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X33040),hAPP(hAPP(c_Orderings_Oord__class_Omin(X33040),X33038),X33037)),hAPP(hAPP(c_Finite__Set_Ofold(X33040,X33040,c_Orderings_Oord__class_Omin(X33040)),X33037),X33039)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33040),X33039))
        | ~ class_Orderings_Olinorder(X33040) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X33040),X33038),esk490_4(X33037,X33038,X33039,X33040)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X33040),hAPP(hAPP(c_Orderings_Oord__class_Omin(X33040),X33038),X33037)),hAPP(hAPP(c_Finite__Set_Ofold(X33040,X33040,c_Orderings_Oord__class_Omin(X33040)),X33037),X33039)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33040),X33039))
        | ~ class_Orderings_Olinorder(X33040) ) ),
    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_6978,plain,
    ! [X26261,X26262,X26263,X26264,X26265] :
      ( ~ class_Groups_Ocomm__monoid__add(X26265)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26265),X26264),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26263),X26262)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26261),X26262))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26265),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X26265,tc_Nat_Onat),X26264),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X26262))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X26263),X26261)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__shift__bounds__nat__ivl])]) ).

fof(i_0_6979,plain,
    ! [X32160,X32161,X32162,X32163] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32163,X32163)),X32162),c_Transitive__Closure_Ortrancl(X32163,X32161)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X32163,X32163)),X32162),c_Transitive__Closure_Ortrancl(X32163,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X32163,X32163),tc_HOL_Obool)),X32161),X32160)))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32163,X32163)),X32162),c_Transitive__Closure_Ortrancl(X32163,X32160)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X32163,X32163)),X32162),c_Transitive__Closure_Ortrancl(X32163,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X32163,X32163),tc_HOL_Obool)),X32161),X32160)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__rtrancl__UnI])])]) ).

fof(i_0_6980,plain,
    ! [X23609,X23610,X23611,X23612,X23613,X23614,X23615,X23616] :
      ( ~ c_Finite__Set_Ofolding(X23616,X23615,X23614,X23613)
      | hAPP(c_Fun_Ocomp(X23615,X23615,X23612,hAPP(X23614,X23611)),hAPP(c_Fun_Ocomp(X23615,X23615,X23612,hAPP(X23614,X23610)),X23609)) = hAPP(c_Fun_Ocomp(X23615,X23615,X23612,hAPP(X23614,X23610)),hAPP(c_Fun_Ocomp(X23615,X23615,X23612,hAPP(X23614,X23611)),X23609)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__left__comp])]) ).

cnf(i_0_6981,plain,
    ( c_List_OdropWhile(X4,X1,hAPP(hAPP(c_List_Oappend(X4),X3),X2)) = c_List_OdropWhile(X4,X1,X2)
    | ~ hBOOL(hAPP(X1,esk426_4(X2,X1,X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_5476]) ).

fof(i_0_6982,plain,
    ! [X26784,X26785,X26786,X26787,X26789,X26790] :
      ( ( X26784 = hAPP(X26785,esk248_4(X26784,X26785,X26786,X26787))
        | ~ hBOOL(hAPP(hAPP(c_member(X26786),X26784),hAPP(c_Set_Oimage(X26787,X26786,X26785),c_Orderings_Otop__class_Otop(tc_fun(X26787,tc_HOL_Obool)))))
        | ~ c_Fun_Oinj__on(X26787,X26786,X26785,c_Orderings_Otop__class_Otop(tc_fun(X26787,tc_HOL_Obool))) )
      & ( X26784 != hAPP(X26785,X26789)
        | X26789 = esk248_4(X26784,X26785,X26786,X26787)
        | ~ hBOOL(hAPP(hAPP(c_member(X26786),X26784),hAPP(c_Set_Oimage(X26787,X26786,X26785),c_Orderings_Otop__class_Otop(tc_fun(X26787,tc_HOL_Obool)))))
        | ~ c_Fun_Oinj__on(X26787,X26786,X26785,c_Orderings_Otop__class_Otop(tc_fun(X26787,tc_HOL_Obool))) )
      & ( X26784 = hAPP(X26785,esk249_5(X26784,X26785,X26786,X26787,X26790))
        | X26784 != hAPP(X26785,X26790)
        | hBOOL(hAPP(hAPP(c_member(X26786),X26784),hAPP(c_Set_Oimage(X26787,X26786,X26785),c_Orderings_Otop__class_Otop(tc_fun(X26787,tc_HOL_Obool)))))
        | ~ c_Fun_Oinj__on(X26787,X26786,X26785,c_Orderings_Otop__class_Otop(tc_fun(X26787,tc_HOL_Obool))) )
      & ( esk249_5(X26784,X26785,X26786,X26787,X26790) != X26790
        | X26784 != hAPP(X26785,X26790)
        | hBOOL(hAPP(hAPP(c_member(X26786),X26784),hAPP(c_Set_Oimage(X26787,X26786,X26785),c_Orderings_Otop__class_Otop(tc_fun(X26787,tc_HOL_Obool)))))
        | ~ c_Fun_Oinj__on(X26787,X26786,X26785,c_Orderings_Otop__class_Otop(tc_fun(X26787,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_6983,plain,
    ! [X26377,X26378,X26379,X26380,X26381] :
      ( ~ class_Groups_Oab__group__add(X26381)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26380),X26379))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26380),X26378))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26380,X26381),X26377),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26380,tc_HOL_Obool)),X26379),X26378)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X26381),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26381),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26380,X26381),X26377),X26379)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26380,X26381),X26377),X26378))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26380,X26381),X26377),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26380,tc_HOL_Obool)),X26379),X26378))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__Un])]) ).

fof(i_0_6984,plain,
    ! [X31697,X31698,X31699,X31700] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31700),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31699)),X31698)))
      | hAPP(c_List_Orev(X31699),hAPP(hAPP(c_List_Olist__update(X31699,X31698),X31700),X31697)) = hAPP(hAPP(c_List_Olist__update(X31699,hAPP(c_List_Orev(X31699),X31698)),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(X31699)),X31698)),X31700)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X31697) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__update])]) ).

cnf(i_0_6985,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_5441]) ).

cnf(i_0_6986,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_5440]) ).

fof(i_0_6987,plain,
    ! [X27783,X27784,X27785] : hAPP(c_Set_OCollect(X27785),hAPP(hAPP(c_COMBS(X27785,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27785),c_fimplies),X27784)),X27783)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27785,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X27785,tc_HOL_Obool)),hAPP(c_Set_OCollect(X27785),X27784))),hAPP(c_Set_OCollect(X27785),X27783)),
    inference(variable_rename,[status(thm)],[fact_Collect__imp__eq]) ).

fof(i_0_6988,plain,
    ! [X21602,X21603,X21604,X21605] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21605),c_Groups_Ozero__class_Ozero(X21605)),X21603))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21605),X21604),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21605),hAPP(c_Int_Onumber__class_Onumber__of(X21605),X21602)),X21603)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21605),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21605),X21604),X21603)),hAPP(c_Int_Onumber__class_Onumber__of(X21605),X21602)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21605)
        | ~ class_Int_Onumber(X21605) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21605),X21603),c_Groups_Ozero__class_Ozero(X21605)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21605),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21605),hAPP(c_Int_Onumber__class_Onumber__of(X21605),X21602)),X21603)),X21604))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21605),c_Groups_Ozero__class_Ozero(X21605)),X21603))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21605),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21605),X21604),X21603)),hAPP(c_Int_Onumber__class_Onumber__of(X21605),X21602)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21605)
        | ~ class_Int_Onumber(X21605) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21605),X21603),c_Groups_Ozero__class_Ozero(X21605)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21605),c_Groups_Ozero__class_Ozero(X21605)),hAPP(c_Int_Onumber__class_Onumber__of(X21605),X21602)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21605),c_Groups_Ozero__class_Ozero(X21605)),X21603))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21605),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21605),X21604),X21603)),hAPP(c_Int_Onumber__class_Onumber__of(X21605),X21602)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21605)
        | ~ class_Int_Onumber(X21605) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21605),c_Groups_Ozero__class_Ozero(X21605)),X21603))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21605),c_Groups_Ozero__class_Ozero(X21605)),X21603))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21605),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21605),X21604),X21603)),hAPP(c_Int_Onumber__class_Onumber__of(X21605),X21602)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21605)
        | ~ class_Int_Onumber(X21605) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21605),X21603),c_Groups_Ozero__class_Ozero(X21605)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21605),X21603),c_Groups_Ozero__class_Ozero(X21605)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21605),c_Groups_Ozero__class_Ozero(X21605)),X21603))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21605),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21605),X21604),X21603)),hAPP(c_Int_Onumber__class_Onumber__of(X21605),X21602)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21605)
        | ~ class_Int_Onumber(X21605) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21605),c_Groups_Ozero__class_Ozero(X21605)),hAPP(c_Int_Onumber__class_Onumber__of(X21605),X21602)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21605),X21603),c_Groups_Ozero__class_Ozero(X21605)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21605),c_Groups_Ozero__class_Ozero(X21605)),X21603))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21605),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21605),X21604),X21603)),hAPP(c_Int_Onumber__class_Onumber__of(X21605),X21602)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21605)
        | ~ class_Int_Onumber(X21605) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21605),X21603),c_Groups_Ozero__class_Ozero(X21605)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21605),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21605),hAPP(c_Int_Onumber__class_Onumber__of(X21605),X21602)),X21603)),X21604))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21605),c_Groups_Ozero__class_Ozero(X21605)),X21603))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21605),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21605),X21604),X21603)),hAPP(c_Int_Onumber__class_Onumber__of(X21605),X21602)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21605)
        | ~ class_Int_Onumber(X21605) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21605),c_Groups_Ozero__class_Ozero(X21605)),hAPP(c_Int_Onumber__class_Onumber__of(X21605),X21602)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21605),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21605),hAPP(c_Int_Onumber__class_Onumber__of(X21605),X21602)),X21603)),X21604))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21605),c_Groups_Ozero__class_Ozero(X21605)),X21603))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21605),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21605),X21604),X21603)),hAPP(c_Int_Onumber__class_Onumber__of(X21605),X21602)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21605)
        | ~ class_Int_Onumber(X21605) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21605),c_Groups_Ozero__class_Ozero(X21605)),X21603))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21605),X21604),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21605),hAPP(c_Int_Onumber__class_Onumber__of(X21605),X21602)),X21603)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21605),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21605),X21604),X21603)),hAPP(c_Int_Onumber__class_Onumber__of(X21605),X21602)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21605)
        | ~ class_Int_Onumber(X21605) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21605),X21603),c_Groups_Ozero__class_Ozero(X21605)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21605),X21603),c_Groups_Ozero__class_Ozero(X21605)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21605),X21604),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21605),hAPP(c_Int_Onumber__class_Onumber__of(X21605),X21602)),X21603)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21605),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21605),X21604),X21603)),hAPP(c_Int_Onumber__class_Onumber__of(X21605),X21602)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21605)
        | ~ class_Int_Onumber(X21605) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21605),c_Groups_Ozero__class_Ozero(X21605)),hAPP(c_Int_Onumber__class_Onumber__of(X21605),X21602)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21605),X21603),c_Groups_Ozero__class_Ozero(X21605)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21605),X21604),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21605),hAPP(c_Int_Onumber__class_Onumber__of(X21605),X21602)),X21603)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21605),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21605),X21604),X21603)),hAPP(c_Int_Onumber__class_Onumber__of(X21605),X21602)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21605)
        | ~ class_Int_Onumber(X21605) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21605),X21603),c_Groups_Ozero__class_Ozero(X21605)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21605),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21605),hAPP(c_Int_Onumber__class_Onumber__of(X21605),X21602)),X21603)),X21604))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21605),X21604),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21605),hAPP(c_Int_Onumber__class_Onumber__of(X21605),X21602)),X21603)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21605),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21605),X21604),X21603)),hAPP(c_Int_Onumber__class_Onumber__of(X21605),X21602)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21605)
        | ~ class_Int_Onumber(X21605) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21605),c_Groups_Ozero__class_Ozero(X21605)),hAPP(c_Int_Onumber__class_Onumber__of(X21605),X21602)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21605),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21605),hAPP(c_Int_Onumber__class_Onumber__of(X21605),X21602)),X21603)),X21604))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21605),X21604),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21605),hAPP(c_Int_Onumber__class_Onumber__of(X21605),X21602)),X21603)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21605),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21605),X21604),X21603)),hAPP(c_Int_Onumber__class_Onumber__of(X21605),X21602)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21605)
        | ~ class_Int_Onumber(X21605) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5487])])]) ).

fof(i_0_6989,plain,
    ! [X21584,X21585,X21586,X21587] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21587),c_Groups_Ozero__class_Ozero(X21587)),X21585))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21587),X21586),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21587),hAPP(c_Int_Onumber__class_Onumber__of(X21587),X21584)),X21585)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21587),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21587),X21586),X21585)),hAPP(c_Int_Onumber__class_Onumber__of(X21587),X21584)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21587)
        | ~ class_Int_Onumber(X21587) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21587),X21585),c_Groups_Ozero__class_Ozero(X21587)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21587),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21587),hAPP(c_Int_Onumber__class_Onumber__of(X21587),X21584)),X21585)),X21586))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21587),c_Groups_Ozero__class_Ozero(X21587)),X21585))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21587),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21587),X21586),X21585)),hAPP(c_Int_Onumber__class_Onumber__of(X21587),X21584)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21587)
        | ~ class_Int_Onumber(X21587) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21587),X21585),c_Groups_Ozero__class_Ozero(X21587)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21587),c_Groups_Ozero__class_Ozero(X21587)),hAPP(c_Int_Onumber__class_Onumber__of(X21587),X21584)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21587),c_Groups_Ozero__class_Ozero(X21587)),X21585))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21587),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21587),X21586),X21585)),hAPP(c_Int_Onumber__class_Onumber__of(X21587),X21584)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21587)
        | ~ class_Int_Onumber(X21587) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21587),c_Groups_Ozero__class_Ozero(X21587)),X21585))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21587),c_Groups_Ozero__class_Ozero(X21587)),X21585))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21587),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21587),X21586),X21585)),hAPP(c_Int_Onumber__class_Onumber__of(X21587),X21584)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21587)
        | ~ class_Int_Onumber(X21587) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21587),X21585),c_Groups_Ozero__class_Ozero(X21587)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21587),X21585),c_Groups_Ozero__class_Ozero(X21587)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21587),c_Groups_Ozero__class_Ozero(X21587)),X21585))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21587),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21587),X21586),X21585)),hAPP(c_Int_Onumber__class_Onumber__of(X21587),X21584)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21587)
        | ~ class_Int_Onumber(X21587) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21587),c_Groups_Ozero__class_Ozero(X21587)),hAPP(c_Int_Onumber__class_Onumber__of(X21587),X21584)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21587),X21585),c_Groups_Ozero__class_Ozero(X21587)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21587),c_Groups_Ozero__class_Ozero(X21587)),X21585))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21587),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21587),X21586),X21585)),hAPP(c_Int_Onumber__class_Onumber__of(X21587),X21584)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21587)
        | ~ class_Int_Onumber(X21587) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21587),X21585),c_Groups_Ozero__class_Ozero(X21587)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21587),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21587),hAPP(c_Int_Onumber__class_Onumber__of(X21587),X21584)),X21585)),X21586))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21587),c_Groups_Ozero__class_Ozero(X21587)),X21585))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21587),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21587),X21586),X21585)),hAPP(c_Int_Onumber__class_Onumber__of(X21587),X21584)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21587)
        | ~ class_Int_Onumber(X21587) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21587),c_Groups_Ozero__class_Ozero(X21587)),hAPP(c_Int_Onumber__class_Onumber__of(X21587),X21584)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21587),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21587),hAPP(c_Int_Onumber__class_Onumber__of(X21587),X21584)),X21585)),X21586))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21587),c_Groups_Ozero__class_Ozero(X21587)),X21585))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21587),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21587),X21586),X21585)),hAPP(c_Int_Onumber__class_Onumber__of(X21587),X21584)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21587)
        | ~ class_Int_Onumber(X21587) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21587),c_Groups_Ozero__class_Ozero(X21587)),X21585))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21587),X21586),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21587),hAPP(c_Int_Onumber__class_Onumber__of(X21587),X21584)),X21585)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21587),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21587),X21586),X21585)),hAPP(c_Int_Onumber__class_Onumber__of(X21587),X21584)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21587)
        | ~ class_Int_Onumber(X21587) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21587),X21585),c_Groups_Ozero__class_Ozero(X21587)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21587),X21585),c_Groups_Ozero__class_Ozero(X21587)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21587),X21586),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21587),hAPP(c_Int_Onumber__class_Onumber__of(X21587),X21584)),X21585)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21587),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21587),X21586),X21585)),hAPP(c_Int_Onumber__class_Onumber__of(X21587),X21584)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21587)
        | ~ class_Int_Onumber(X21587) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21587),c_Groups_Ozero__class_Ozero(X21587)),hAPP(c_Int_Onumber__class_Onumber__of(X21587),X21584)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21587),X21585),c_Groups_Ozero__class_Ozero(X21587)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21587),X21586),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21587),hAPP(c_Int_Onumber__class_Onumber__of(X21587),X21584)),X21585)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21587),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21587),X21586),X21585)),hAPP(c_Int_Onumber__class_Onumber__of(X21587),X21584)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21587)
        | ~ class_Int_Onumber(X21587) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21587),X21585),c_Groups_Ozero__class_Ozero(X21587)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21587),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21587),hAPP(c_Int_Onumber__class_Onumber__of(X21587),X21584)),X21585)),X21586))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21587),X21586),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21587),hAPP(c_Int_Onumber__class_Onumber__of(X21587),X21584)),X21585)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21587),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21587),X21586),X21585)),hAPP(c_Int_Onumber__class_Onumber__of(X21587),X21584)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21587)
        | ~ class_Int_Onumber(X21587) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21587),c_Groups_Ozero__class_Ozero(X21587)),hAPP(c_Int_Onumber__class_Onumber__of(X21587),X21584)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21587),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21587),hAPP(c_Int_Onumber__class_Onumber__of(X21587),X21584)),X21585)),X21586))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21587),X21586),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21587),hAPP(c_Int_Onumber__class_Onumber__of(X21587),X21584)),X21585)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21587),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21587),X21586),X21585)),hAPP(c_Int_Onumber__class_Onumber__of(X21587),X21584)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21587)
        | ~ class_Int_Onumber(X21587) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5488])])]) ).

fof(i_0_6990,plain,
    ! [X32554,X32555,X32556,X32557,X32558,X32559,X32560,X32561,X32562] :
      ( ( ~ c_Relation_Osingle__valued(X32556,X32555,X32554)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32556,X32555)),hAPP(hAPP(c_Product__Type_OPair(X32556,X32555),X32557),X32558)),X32554))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32556,X32555)),hAPP(hAPP(c_Product__Type_OPair(X32556,X32555),X32557),X32559)),X32554))
        | X32558 = X32559 )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X32562,X32561)),hAPP(hAPP(c_Product__Type_OPair(X32562,X32561),esk445_3(X32560,X32561,X32562)),esk446_3(X32560,X32561,X32562))),X32560))
        | c_Relation_Osingle__valued(X32562,X32561,X32560) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X32562,X32561)),hAPP(hAPP(c_Product__Type_OPair(X32562,X32561),esk445_3(X32560,X32561,X32562)),esk447_3(X32560,X32561,X32562))),X32560))
        | c_Relation_Osingle__valued(X32562,X32561,X32560) )
      & ( esk446_3(X32560,X32561,X32562) != esk447_3(X32560,X32561,X32562)
        | c_Relation_Osingle__valued(X32562,X32561,X32560) ) ),
    inference(distribute,[status(thm)],[inference(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_6991,plain,
    ! [X21606,X21607,X21608,X21609] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21609),c_Groups_Ozero__class_Ozero(X21609)),X21606))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21609),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21609),hAPP(c_Int_Onumber__class_Onumber__of(X21609),X21608)),X21606)),X21607))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21609),hAPP(c_Int_Onumber__class_Onumber__of(X21609),X21608)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21609),X21607),X21606)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21609)
        | ~ class_Int_Onumber(X21609) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21609),X21606),c_Groups_Ozero__class_Ozero(X21609)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21609),X21607),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21609),hAPP(c_Int_Onumber__class_Onumber__of(X21609),X21608)),X21606)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21609),c_Groups_Ozero__class_Ozero(X21609)),X21606))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21609),hAPP(c_Int_Onumber__class_Onumber__of(X21609),X21608)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21609),X21607),X21606)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21609)
        | ~ class_Int_Onumber(X21609) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21609),X21606),c_Groups_Ozero__class_Ozero(X21609)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21609),hAPP(c_Int_Onumber__class_Onumber__of(X21609),X21608)),c_Groups_Ozero__class_Ozero(X21609)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21609),c_Groups_Ozero__class_Ozero(X21609)),X21606))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21609),hAPP(c_Int_Onumber__class_Onumber__of(X21609),X21608)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21609),X21607),X21606)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21609)
        | ~ class_Int_Onumber(X21609) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21609),c_Groups_Ozero__class_Ozero(X21609)),X21606))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21609),c_Groups_Ozero__class_Ozero(X21609)),X21606))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21609),hAPP(c_Int_Onumber__class_Onumber__of(X21609),X21608)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21609),X21607),X21606)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21609)
        | ~ class_Int_Onumber(X21609) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21609),X21606),c_Groups_Ozero__class_Ozero(X21609)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21609),X21606),c_Groups_Ozero__class_Ozero(X21609)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21609),c_Groups_Ozero__class_Ozero(X21609)),X21606))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21609),hAPP(c_Int_Onumber__class_Onumber__of(X21609),X21608)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21609),X21607),X21606)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21609)
        | ~ class_Int_Onumber(X21609) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21609),hAPP(c_Int_Onumber__class_Onumber__of(X21609),X21608)),c_Groups_Ozero__class_Ozero(X21609)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21609),X21606),c_Groups_Ozero__class_Ozero(X21609)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21609),c_Groups_Ozero__class_Ozero(X21609)),X21606))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21609),hAPP(c_Int_Onumber__class_Onumber__of(X21609),X21608)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21609),X21607),X21606)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21609)
        | ~ class_Int_Onumber(X21609) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21609),X21606),c_Groups_Ozero__class_Ozero(X21609)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21609),X21607),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21609),hAPP(c_Int_Onumber__class_Onumber__of(X21609),X21608)),X21606)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21609),c_Groups_Ozero__class_Ozero(X21609)),X21606))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21609),hAPP(c_Int_Onumber__class_Onumber__of(X21609),X21608)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21609),X21607),X21606)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21609)
        | ~ class_Int_Onumber(X21609) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21609),hAPP(c_Int_Onumber__class_Onumber__of(X21609),X21608)),c_Groups_Ozero__class_Ozero(X21609)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21609),X21607),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21609),hAPP(c_Int_Onumber__class_Onumber__of(X21609),X21608)),X21606)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21609),c_Groups_Ozero__class_Ozero(X21609)),X21606))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21609),hAPP(c_Int_Onumber__class_Onumber__of(X21609),X21608)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21609),X21607),X21606)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21609)
        | ~ class_Int_Onumber(X21609) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21609),c_Groups_Ozero__class_Ozero(X21609)),X21606))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21609),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21609),hAPP(c_Int_Onumber__class_Onumber__of(X21609),X21608)),X21606)),X21607))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21609),hAPP(c_Int_Onumber__class_Onumber__of(X21609),X21608)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21609),X21607),X21606)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21609)
        | ~ class_Int_Onumber(X21609) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21609),X21606),c_Groups_Ozero__class_Ozero(X21609)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21609),X21606),c_Groups_Ozero__class_Ozero(X21609)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21609),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21609),hAPP(c_Int_Onumber__class_Onumber__of(X21609),X21608)),X21606)),X21607))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21609),hAPP(c_Int_Onumber__class_Onumber__of(X21609),X21608)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21609),X21607),X21606)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21609)
        | ~ class_Int_Onumber(X21609) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21609),hAPP(c_Int_Onumber__class_Onumber__of(X21609),X21608)),c_Groups_Ozero__class_Ozero(X21609)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21609),X21606),c_Groups_Ozero__class_Ozero(X21609)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21609),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21609),hAPP(c_Int_Onumber__class_Onumber__of(X21609),X21608)),X21606)),X21607))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21609),hAPP(c_Int_Onumber__class_Onumber__of(X21609),X21608)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21609),X21607),X21606)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21609)
        | ~ class_Int_Onumber(X21609) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21609),X21606),c_Groups_Ozero__class_Ozero(X21609)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21609),X21607),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21609),hAPP(c_Int_Onumber__class_Onumber__of(X21609),X21608)),X21606)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21609),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21609),hAPP(c_Int_Onumber__class_Onumber__of(X21609),X21608)),X21606)),X21607))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21609),hAPP(c_Int_Onumber__class_Onumber__of(X21609),X21608)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21609),X21607),X21606)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21609)
        | ~ class_Int_Onumber(X21609) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21609),hAPP(c_Int_Onumber__class_Onumber__of(X21609),X21608)),c_Groups_Ozero__class_Ozero(X21609)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21609),X21607),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21609),hAPP(c_Int_Onumber__class_Onumber__of(X21609),X21608)),X21606)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21609),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21609),hAPP(c_Int_Onumber__class_Onumber__of(X21609),X21608)),X21606)),X21607))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21609),hAPP(c_Int_Onumber__class_Onumber__of(X21609),X21608)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21609),X21607),X21606)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21609)
        | ~ class_Int_Onumber(X21609) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5489])])]) ).

fof(i_0_6992,plain,
    ! [X21580,X21581,X21582,X21583] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21583),c_Groups_Ozero__class_Ozero(X21583)),X21580))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21583),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21583),hAPP(c_Int_Onumber__class_Onumber__of(X21583),X21582)),X21580)),X21581))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21583),hAPP(c_Int_Onumber__class_Onumber__of(X21583),X21582)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21583),X21581),X21580)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21583)
        | ~ class_Int_Onumber(X21583) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21583),X21580),c_Groups_Ozero__class_Ozero(X21583)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21583),X21581),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21583),hAPP(c_Int_Onumber__class_Onumber__of(X21583),X21582)),X21580)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21583),c_Groups_Ozero__class_Ozero(X21583)),X21580))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21583),hAPP(c_Int_Onumber__class_Onumber__of(X21583),X21582)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21583),X21581),X21580)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21583)
        | ~ class_Int_Onumber(X21583) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21583),X21580),c_Groups_Ozero__class_Ozero(X21583)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21583),hAPP(c_Int_Onumber__class_Onumber__of(X21583),X21582)),c_Groups_Ozero__class_Ozero(X21583)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21583),c_Groups_Ozero__class_Ozero(X21583)),X21580))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21583),hAPP(c_Int_Onumber__class_Onumber__of(X21583),X21582)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21583),X21581),X21580)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21583)
        | ~ class_Int_Onumber(X21583) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21583),c_Groups_Ozero__class_Ozero(X21583)),X21580))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21583),c_Groups_Ozero__class_Ozero(X21583)),X21580))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21583),hAPP(c_Int_Onumber__class_Onumber__of(X21583),X21582)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21583),X21581),X21580)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21583)
        | ~ class_Int_Onumber(X21583) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21583),X21580),c_Groups_Ozero__class_Ozero(X21583)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21583),X21580),c_Groups_Ozero__class_Ozero(X21583)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21583),c_Groups_Ozero__class_Ozero(X21583)),X21580))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21583),hAPP(c_Int_Onumber__class_Onumber__of(X21583),X21582)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21583),X21581),X21580)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21583)
        | ~ class_Int_Onumber(X21583) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21583),hAPP(c_Int_Onumber__class_Onumber__of(X21583),X21582)),c_Groups_Ozero__class_Ozero(X21583)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21583),X21580),c_Groups_Ozero__class_Ozero(X21583)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21583),c_Groups_Ozero__class_Ozero(X21583)),X21580))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21583),hAPP(c_Int_Onumber__class_Onumber__of(X21583),X21582)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21583),X21581),X21580)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21583)
        | ~ class_Int_Onumber(X21583) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21583),X21580),c_Groups_Ozero__class_Ozero(X21583)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21583),X21581),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21583),hAPP(c_Int_Onumber__class_Onumber__of(X21583),X21582)),X21580)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21583),c_Groups_Ozero__class_Ozero(X21583)),X21580))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21583),hAPP(c_Int_Onumber__class_Onumber__of(X21583),X21582)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21583),X21581),X21580)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21583)
        | ~ class_Int_Onumber(X21583) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21583),hAPP(c_Int_Onumber__class_Onumber__of(X21583),X21582)),c_Groups_Ozero__class_Ozero(X21583)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21583),X21581),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21583),hAPP(c_Int_Onumber__class_Onumber__of(X21583),X21582)),X21580)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21583),c_Groups_Ozero__class_Ozero(X21583)),X21580))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21583),hAPP(c_Int_Onumber__class_Onumber__of(X21583),X21582)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21583),X21581),X21580)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21583)
        | ~ class_Int_Onumber(X21583) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21583),c_Groups_Ozero__class_Ozero(X21583)),X21580))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21583),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21583),hAPP(c_Int_Onumber__class_Onumber__of(X21583),X21582)),X21580)),X21581))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21583),hAPP(c_Int_Onumber__class_Onumber__of(X21583),X21582)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21583),X21581),X21580)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21583)
        | ~ class_Int_Onumber(X21583) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21583),X21580),c_Groups_Ozero__class_Ozero(X21583)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21583),X21580),c_Groups_Ozero__class_Ozero(X21583)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21583),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21583),hAPP(c_Int_Onumber__class_Onumber__of(X21583),X21582)),X21580)),X21581))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21583),hAPP(c_Int_Onumber__class_Onumber__of(X21583),X21582)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21583),X21581),X21580)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21583)
        | ~ class_Int_Onumber(X21583) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21583),hAPP(c_Int_Onumber__class_Onumber__of(X21583),X21582)),c_Groups_Ozero__class_Ozero(X21583)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21583),X21580),c_Groups_Ozero__class_Ozero(X21583)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21583),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21583),hAPP(c_Int_Onumber__class_Onumber__of(X21583),X21582)),X21580)),X21581))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21583),hAPP(c_Int_Onumber__class_Onumber__of(X21583),X21582)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21583),X21581),X21580)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21583)
        | ~ class_Int_Onumber(X21583) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21583),X21580),c_Groups_Ozero__class_Ozero(X21583)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21583),X21581),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21583),hAPP(c_Int_Onumber__class_Onumber__of(X21583),X21582)),X21580)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21583),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21583),hAPP(c_Int_Onumber__class_Onumber__of(X21583),X21582)),X21580)),X21581))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21583),hAPP(c_Int_Onumber__class_Onumber__of(X21583),X21582)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21583),X21581),X21580)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21583)
        | ~ class_Int_Onumber(X21583) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21583),hAPP(c_Int_Onumber__class_Onumber__of(X21583),X21582)),c_Groups_Ozero__class_Ozero(X21583)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21583),X21581),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21583),hAPP(c_Int_Onumber__class_Onumber__of(X21583),X21582)),X21580)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21583),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21583),hAPP(c_Int_Onumber__class_Onumber__of(X21583),X21582)),X21580)),X21581))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21583),hAPP(c_Int_Onumber__class_Onumber__of(X21583),X21582)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21583),X21581),X21580)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21583)
        | ~ class_Int_Onumber(X21583) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5490])])]) ).

fof(i_0_6993,plain,
    ! [X22319,X22320,X22321,X22322,X22323] : c_Product__Type_Oprod_Oprod__size(X22323,X22322,X22321,X22320,X22319) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X22321,hAPP(c_Product__Type_Ofst(X22323,X22322),X22319))),hAPP(X22320,hAPP(c_Product__Type_Osnd(X22323,X22322),X22319)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[fact_prod__size__simp]) ).

fof(i_0_6994,plain,
    ! [X26270,X26271,X26272,X26273,X26274] :
      ( ~ class_Groups_Ocomm__monoid__add(X26274)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26274),X26273),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26272),X26271),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26270),X26271))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26274),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X26274,tc_Nat_Onat),X26273),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X26271))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X26272,X26270)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__shift__bounds__cl__nat__ivl])]) ).

fof(i_0_6995,plain,
    ! [X25555,X25556,X25557,X25558] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk183_4(X25555,X25556,X25557,X25558)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X25557)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25556),X25558))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25556),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X25558),X25557)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X25556),c_Groups_Oone__class_Oone(tc_Int_Oint))),X25555))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25557)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk184_4(X25555,X25556,X25557,X25558)),X25555))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25556),X25558))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25556),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X25558),X25557)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X25556),c_Groups_Oone__class_Oone(tc_Int_Oint))),X25555))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25557)) )
      & ( X25558 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk184_4(X25555,X25556,X25557,X25558)),esk183_4(X25555,X25556,X25557,X25558))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25556),X25558))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25556),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X25558),X25557)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X25556),c_Groups_Oone__class_Oone(tc_Int_Oint))),X25555))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25557)) ) ),
    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_6996,plain,
    ! [X27417,X27418,X27419,X27420] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27420),X27419))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27420,X27420),tc_HOL_Obool)),X27418),hAPP(hAPP(c_Product__Type_OSigma(X27420,X27420),X27419),hAPP(c_COMBK(tc_fun(X27420,tc_HOL_Obool),X27420),X27419))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X27420,tc_HOL_Obool)),X27417),hAPP(hAPP(c_Equiv__Relations_Oquotient(X27420),X27419),X27418)))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X27420),X27417)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__equiv__class])]) ).

fof(i_0_6997,plain,
    ! [X25859,X25860,X25861,X25862,X25863,X25864] :
      ( ~ c_Fun_Oinj__on(X25864,X25863,X25862,X25861)
      | hBOOL(hAPP(hAPP(c_member(X25863),X25860),hAPP(c_Set_Oimage(X25864,X25863,X25862),X25861)))
      | c_Fun_Oinj__on(X25864,X25863,c_Fun_Ofun__upd(X25864,X25863,X25862,X25859,X25860),X25861) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5491])]) ).

fof(i_0_6998,plain,
    ! [X24153,X24154,X24155,X24156,X24157,X24158,X24159] :
      ( ~ c_Equiv__Relations_Oequiv(X24159,X24158,X24157)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X24159,tc_HOL_Obool)),X24156),hAPP(hAPP(c_Equiv__Relations_Oquotient(X24159),X24158),X24157)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X24159,tc_HOL_Obool)),X24155),hAPP(hAPP(c_Equiv__Relations_Oquotient(X24159),X24158),X24157)))
      | ~ hBOOL(hAPP(hAPP(c_member(X24159),X24154),X24156))
      | ~ hBOOL(hAPP(hAPP(c_member(X24159),X24153),X24155))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X24159,X24159)),hAPP(hAPP(c_Product__Type_OPair(X24159,X24159),X24154),X24153)),X24157))
      | X24156 = X24155 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_quotient__eqI])]) ).

fof(i_0_6999,plain,
    ! [X24146,X24147,X24148,X24149,X24150,X24151,X24152] :
      ( ( X24149 != X24148
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X24152,X24152)),hAPP(hAPP(c_Product__Type_OPair(X24152,X24152),X24147),X24146)),X24150))
        | ~ hBOOL(hAPP(hAPP(c_member(X24152),X24146),X24148))
        | ~ hBOOL(hAPP(hAPP(c_member(X24152),X24147),X24149))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X24152,tc_HOL_Obool)),X24148),hAPP(hAPP(c_Equiv__Relations_Oquotient(X24152),X24151),X24150)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X24152,tc_HOL_Obool)),X24149),hAPP(hAPP(c_Equiv__Relations_Oquotient(X24152),X24151),X24150)))
        | ~ c_Equiv__Relations_Oequiv(X24152,X24151,X24150) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X24152,X24152)),hAPP(hAPP(c_Product__Type_OPair(X24152,X24152),X24147),X24146)),X24150))
        | X24149 = X24148
        | ~ hBOOL(hAPP(hAPP(c_member(X24152),X24146),X24148))
        | ~ hBOOL(hAPP(hAPP(c_member(X24152),X24147),X24149))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X24152,tc_HOL_Obool)),X24148),hAPP(hAPP(c_Equiv__Relations_Oquotient(X24152),X24151),X24150)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X24152,tc_HOL_Obool)),X24149),hAPP(hAPP(c_Equiv__Relations_Oquotient(X24152),X24151),X24150)))
        | ~ c_Equiv__Relations_Oequiv(X24152,X24151,X24150) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_quotient__eq__iff])])]) ).

fof(i_0_7000,plain,
    ! [X19807,X19808,X19809] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19809),c_Groups_Ozero__class_Ozero(X19809)),esk63_3(X19807,X19808,X19809)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19809),X19808),X19807))
        | ~ class_Fields_Olinordered__field__inverse__zero(X19809) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19809),esk63_3(X19807,X19808,X19809)),c_Groups_Oone__class_Oone(X19809)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19809),X19808),X19807))
        | ~ class_Fields_Olinordered__field__inverse__zero(X19809) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19809),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19809),esk63_3(X19807,X19808,X19809)),X19808)),X19807))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19809),X19808),X19807))
        | ~ class_Fields_Olinordered__field__inverse__zero(X19809) ) ),
    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_7001,plain,
    ! [X33504,X33505] : c_Predicate_Opred__comp(X33505,X33505,X33505,c_fequal,c_Predicate_Opred__comp(X33505,X33505,X33505,X33504,c_fequal)) = X33504,
    inference(variable_rename,[status(thm)],[fact_eq__comp__r]) ).

fof(i_0_7002,plain,
    ! [X27220,X27221,X27222,X27223] : hAPP(c_Set_Ovimage(X27223,X27222,X27221),X27220) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27222,tc_fun(X27223,tc_HOL_Obool)),X27220),hAPP(hAPP(c_COMBB(tc_fun(X27222,tc_HOL_Obool),tc_fun(X27223,tc_HOL_Obool),X27222),c_Set_Ovimage(X27223,X27222,X27221)),hAPP(hAPP(c_COMBC(X27222,tc_fun(X27222,tc_HOL_Obool),tc_fun(X27222,tc_HOL_Obool)),c_Set_Oinsert(X27222)),c_Orderings_Obot__class_Obot(tc_fun(X27222,tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[fact_vimage__eq__UN]) ).

fof(i_0_7003,plain,
    ! [X24876,X24877,X24878,X24879] : hAPP(c_Relation_OImage(X24879,X24878,X24877),X24876) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24879,tc_fun(X24878,tc_HOL_Obool)),X24876),hAPP(hAPP(c_COMBB(tc_fun(X24879,tc_HOL_Obool),tc_fun(X24878,tc_HOL_Obool),X24879),c_Relation_OImage(X24879,X24878,X24877)),hAPP(hAPP(c_COMBC(X24879,tc_fun(X24879,tc_HOL_Obool),tc_fun(X24879,tc_HOL_Obool)),c_Set_Oinsert(X24879)),c_Orderings_Obot__class_Obot(tc_fun(X24879,tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[fact_Image__eq__UN]) ).

fof(i_0_7004,plain,
    ! [X24012,X24013,X24014,X24015] :
      ( ~ class_Lattices_Olattice(X24015)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24015),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24015),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24015),X24014),X24013)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24015),X24014),X24012))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24015),X24014),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24015),X24013),X24012)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distrib__inf__le])]) ).

fof(i_0_7005,plain,
    ! [X22696,X22697,X22698,X22699] :
      ( ~ class_Orderings_Olinorder(X22699)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22699),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22699),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22699),X22698),X22697)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22699),X22698),X22696))),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22699),X22698),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22699),X22697),X22696)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Odistrib__inf__le])]) ).

fof(i_0_7006,plain,
    ! [X34134,X34135,X34136,X34137,X34138] :
      ( ~ c_Fun_Obij__betw(X34138,X34137,X34136,X34135,X34134)
      | c_Fun_Obij__betw(X34137,X34138,c_Hilbert__Choice_Oinv__into(X34138,X34137,X34135,X34136),X34134,X34135) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__betw__inv__into])]) ).

fof(i_0_7007,plain,
    ! [X34192,X34193,X34194,X34195,X34196] :
      ( ~ c_Fun_Obij__betw(X34196,X34195,X34194,X34193,X34192)
      | c_Fun_Obij__betw(X34195,X34196,c_Fun_Othe__inv__into(X34196,X34195,X34193,X34194),X34192,X34193) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__betw__the__inv__into])]) ).

fof(i_0_7008,plain,
    ! [X34128,X34129,X34130,X34131,X34132,X34133] :
      ( ~ c_Fun_Obij__betw(X34133,X34132,X34131,X34130,X34129)
      | ~ hBOOL(hAPP(hAPP(c_member(X34133),X34128),X34130))
      | hAPP(c_Hilbert__Choice_Oinv__into(X34132,X34133,X34129,c_Hilbert__Choice_Oinv__into(X34133,X34132,X34130,X34131)),X34128) = hAPP(X34131,X34128) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__inv__into__eq])]) ).

fof(i_0_7009,plain,
    ! [X25259,X25260,X25261,X25262,X25263,X25264,X25265,X25266] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X25266),X25265),X25264))
      | ~ hBOOL(hAPP(hAPP(hAPP(X25263,X25265),X25262),X25261))
      | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25266,tc_fun(X25260,tc_fun(X25259,tc_HOL_Obool))),X25264),X25263),X25262),X25261)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUP2__I])]) ).

fof(i_0_7010,plain,
    ! [X22060,X22061,X22062,X22063,X22064,X22065,X22066] :
      ( ~ hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X22066,X22065,tc_fun(X22064,tc_HOL_Obool)),X22063),hAPP(hAPP(c_Product__Type_OPair(X22066,X22065),X22062),X22061)),X22060))
      | hBOOL(hAPP(hAPP(hAPP(X22063,X22062),X22061),X22060)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_splitD_H])]) ).

fof(i_0_7011,plain,
    ! [X28049,X28050,X28051,X28052,X28053,X28054] : hAPP(hAPP(c_Relation_Orel__comp(X28054,X28053,X28052),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28054,X28053),tc_HOL_Obool)),X28051),X28050)),X28049) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28054,X28052),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X28054,X28053,X28052),X28051),X28049)),hAPP(hAPP(c_Relation_Orel__comp(X28054,X28053,X28052),X28050),X28049)),
    inference(variable_rename,[status(thm)],[fact_rel__comp__distrib2]) ).

fof(i_0_7012,plain,
    ! [X32855,X32856,X32857,X32858,X32859] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X32859)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32858),X32857))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X32859),X32856),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X32858,X32859),X32857),X32855)) = hAPP(hAPP(c_Finite__Set_Ofold(X32858,X32859,hAPP(hAPP(c_COMBB(X32859,tc_fun(X32859,X32859),X32858),c_Lattices_Osemilattice__inf__class_Oinf(X32859)),X32855)),X32856),X32857) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__INFI__fold__inf])]) ).

fof(i_0_7013,plain,
    ! [X32850,X32851,X32852,X32853,X32854] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X32854)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32853),X32852))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X32854),X32851),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X32853,X32854),X32852),X32850)) = hAPP(hAPP(c_Finite__Set_Ofold(X32853,X32854,hAPP(hAPP(c_COMBB(X32854,tc_fun(X32854,X32854),X32853),c_Lattices_Osemilattice__sup__class_Osup(X32854)),X32850)),X32851),X32852) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__SUPR__fold__sup])]) ).

fof(i_0_7014,plain,
    ! [X26512,X26513,X26514,X26515] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26515),X26514))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26515),X26513))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26515,tc_Nat_Onat),X26512),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26515,tc_HOL_Obool)),X26514),X26513)) = 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(X26515,tc_Nat_Onat),X26512),X26514)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26515,tc_Nat_Onat),X26512),X26513))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26515,tc_Nat_Onat),X26512),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26515,tc_HOL_Obool)),X26514),X26513))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__Un__nat])]) ).

fof(i_0_7015,plain,
    ! [X27772,X27773] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27773),hAPP(c_Set_OCollect(X27773),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X27773),c_fNot),X27772))))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X27773),c_Orderings_Otop__class_Otop(tc_fun(X27773,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27773),hAPP(c_Set_OCollect(X27773),X27772))) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27773),c_Orderings_Otop__class_Otop(tc_fun(X27773,tc_HOL_Obool))))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X27773),hAPP(c_Set_OCollect(X27773),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X27773),c_fNot),X27772))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27773),hAPP(c_Set_OCollect(X27773),X27772))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Collect__not])])]) ).

fof(i_0_7016,plain,
    ! [X19508,X19509,X19510,X19511] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19511))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19510),X19509))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19509),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),X19510),X19511)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19510),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19508,X19511))),X19509))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult2__lemma__aux1])]) ).

fof(i_0_7017,plain,
    ! [X20134,X20135,X20136,X20137,X20138] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20138),X20137))
      | 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),X20138),X20136)),X20135)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20137),X20136)),X20134)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20135),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),X20137),X20138)),X20136)),X20134)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__diff__add__eq2])]) ).

fof(i_0_7018,plain,
    ! [X26221,X26222,X26223,X26224] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X26224)
      | hAPP(c_Groups_Oabs__class_Oabs(X26224),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26223,X26224),hAPP(hAPP(c_COMBB(X26224,X26224,X26223),c_Groups_Oabs__class_Oabs(X26224)),X26222)),X26221)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26223,X26224),hAPP(hAPP(c_COMBB(X26224,X26224,X26223),c_Groups_Oabs__class_Oabs(X26224)),X26222)),X26221) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__setsum__abs])]) ).

fof(i_0_7019,plain,
    ! [X26801,X26802,X26803,X26804,X26805] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26804,tc_HOL_Obool)),hAPP(c_Set_Oimage(X26805,X26804,X26803),X26802)),hAPP(c_Set_Oimage(X26805,X26804,X26803),X26801)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26805,tc_HOL_Obool)),X26802),X26801))
        | ~ c_Fun_Oinj__on(X26805,X26804,X26803,c_Orderings_Otop__class_Otop(tc_fun(X26805,tc_HOL_Obool))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26805,tc_HOL_Obool)),X26802),X26801))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26804,tc_HOL_Obool)),hAPP(c_Set_Oimage(X26805,X26804,X26803),X26802)),hAPP(c_Set_Oimage(X26805,X26804,X26803),X26801)))
        | ~ c_Fun_Oinj__on(X26805,X26804,X26803,c_Orderings_Otop__class_Otop(tc_fun(X26805,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_7020,plain,
    ( hBOOL(hAPP(c_List_Odistinct(X1),c_List_Oconcat(X1,X2)))
    | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk408_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),esk409_2(X2,X1))),hAPP(c_List_Oset(X1),esk410_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_5492]) ).

fof(i_0_7021,plain,
    ! [X21519,X21520,X21521] :
      ( ~ class_Fields_Olinordered__field(X21521)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21521),X21520),X21519))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21521),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21521),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21521),X21520),X21519)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21521),c_Groups_Oone__class_Oone(X21521)),c_Groups_Oone__class_Oone(X21521)))),X21519)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gt__half__sum])]) ).

fof(i_0_7022,plain,
    ! [X34022,X34023,X34024,X34025,X34026,X34027] :
      ( hAPP(c_Hilbert__Choice_Oinv__into(X34027,X34026,X34025,X34024),X34023) != hAPP(c_Hilbert__Choice_Oinv__into(X34027,X34026,X34025,X34024),X34022)
      | ~ hBOOL(hAPP(hAPP(c_member(X34026),X34023),hAPP(c_Set_Oimage(X34027,X34026,X34024),X34025)))
      | ~ hBOOL(hAPP(hAPP(c_member(X34026),X34022),hAPP(c_Set_Oimage(X34027,X34026,X34024),X34025)))
      | X34023 = X34022 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__injective])]) ).

fof(i_0_7023,plain,
    ! [X30656,X30657,X30658,X30659,X30660,X30661,X30662] :
      ( ( hBOOL(hAPP(hAPP(X30660,X30659),X30657))
        | ~ c_List_Olist__all2(X30662,X30661,X30660,hAPP(hAPP(c_List_Olist_OCons(X30662),X30659),X30658),hAPP(hAPP(c_List_Olist_OCons(X30661),X30657),X30656)) )
      & ( c_List_Olist__all2(X30662,X30661,X30660,X30658,X30656)
        | ~ c_List_Olist__all2(X30662,X30661,X30660,hAPP(hAPP(c_List_Olist_OCons(X30662),X30659),X30658),hAPP(hAPP(c_List_Olist_OCons(X30661),X30657),X30656)) )
      & ( ~ hBOOL(hAPP(hAPP(X30660,X30659),X30657))
        | ~ c_List_Olist__all2(X30662,X30661,X30660,X30658,X30656)
        | c_List_Olist__all2(X30662,X30661,X30660,hAPP(hAPP(c_List_Olist_OCons(X30662),X30659),X30658),hAPP(hAPP(c_List_Olist_OCons(X30661),X30657),X30656)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__Cons])])]) ).

fof(i_0_7024,plain,
    ! [X19040,X19041,X19042] :
      ( ~ 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),X19042),X19041)),X19040)),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)),X19040))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19042))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19041),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_7025,plain,
    ! [X27763,X27764,X27765] :
      ( ( ~ hBOOL(hAPP(X27765,X27764))
        | hAPP(c_Set_OCollect(X27763),hAPP(hAPP(c_COMBS(X27763,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27763),c_fconj),hAPP(c_fequal,X27764))),X27765)) = hAPP(hAPP(c_Set_Oinsert(X27763),X27764),c_Orderings_Obot__class_Obot(tc_fun(X27763,tc_HOL_Obool))) )
      & ( hBOOL(hAPP(X27765,X27764))
        | hAPP(c_Set_OCollect(X27763),hAPP(hAPP(c_COMBS(X27763,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27763),c_fconj),hAPP(c_fequal,X27764))),X27765)) = c_Orderings_Obot__class_Obot(tc_fun(X27763,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5493])]) ).

cnf(i_0_7026,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_5494]) ).

cnf(i_0_7027,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_5495]) ).

fof(i_0_7028,plain,
    ! [X29170,X29171,X29172,X29173] :
      ( ( hBOOL(hAPP(hAPP(c_member(X29173),X29172),hAPP(c_List_Oset(X29173),X29170)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29173,X29173)),hAPP(hAPP(c_Product__Type_OPair(X29173,X29173),X29172),X29171)),hAPP(c_List_Oset(tc_prod(X29173,X29173)),hAPP(hAPP(c_List_Ozip(X29173,X29173),X29170),X29170)))) )
      & ( X29172 = X29171
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29173,X29173)),hAPP(hAPP(c_Product__Type_OPair(X29173,X29173),X29172),X29171)),hAPP(c_List_Oset(tc_prod(X29173,X29173)),hAPP(hAPP(c_List_Ozip(X29173,X29173),X29170),X29170)))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X29173),X29172),hAPP(c_List_Oset(X29173),X29170)))
        | X29172 != X29171
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X29173,X29173)),hAPP(hAPP(c_Product__Type_OPair(X29173,X29173),X29172),X29171)),hAPP(c_List_Oset(tc_prod(X29173,X29173)),hAPP(hAPP(c_List_Ozip(X29173,X29173),X29170),X29170)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zip__same])])]) ).

fof(i_0_7029,plain,
    ! [X29152,X29153,X29154,X29155,X29156,X29157] :
      ( ( hBOOL(hAPP(hAPP(c_member(X29157),X29155),hAPP(c_List_Oset(X29157),X29153)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29157,X29156)),hAPP(hAPP(c_Product__Type_OPair(X29157,X29156),X29155),X29154)),hAPP(c_List_Oset(tc_prod(X29157,X29156)),hAPP(hAPP(c_List_Ozip(X29157,X29156),X29153),X29152)))) )
      & ( hBOOL(hAPP(hAPP(c_member(X29156),X29154),hAPP(c_List_Oset(X29156),X29152)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29157,X29156)),hAPP(hAPP(c_Product__Type_OPair(X29157,X29156),X29155),X29154)),hAPP(c_List_Oset(tc_prod(X29157,X29156)),hAPP(hAPP(c_List_Ozip(X29157,X29156),X29153),X29152)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5496])])]) ).

fof(i_0_7030,plain,
    ! [X29164,X29165,X29166,X29167,X29168,X29169] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29169,X29168)),hAPP(hAPP(c_Product__Type_OPair(X29169,X29168),X29167),X29166)),hAPP(c_List_Oset(tc_prod(X29169,X29168)),hAPP(hAPP(c_List_Ozip(X29169,X29168),X29165),X29164))))
      | hBOOL(hAPP(hAPP(c_member(X29169),X29167),hAPP(c_List_Oset(X29169),X29165))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__zip__leftD])]) ).

fof(i_0_7031,plain,
    ! [X29158,X29159,X29160,X29161,X29162,X29163] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29163,X29162)),hAPP(hAPP(c_Product__Type_OPair(X29163,X29162),X29161),X29160)),hAPP(c_List_Oset(tc_prod(X29163,X29162)),hAPP(hAPP(c_List_Ozip(X29163,X29162),X29159),X29158))))
      | hBOOL(hAPP(hAPP(c_member(X29162),X29160),hAPP(c_List_Oset(X29162),X29158))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__zip__rightD])]) ).

fof(i_0_7032,plain,
    ! [X24118,X24119,X24120,X24121,X24122,X24123] :
      ( ~ c_Finite__Set_Ofolding(X24123,X24122,X24121,X24120)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24123),X24119))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24123),X24118))
      | hAPP(c_Fun_Ocomp(X24122,X24122,X24122,hAPP(X24120,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24123,tc_HOL_Obool)),X24119),X24118))),hAPP(X24120,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24123,tc_HOL_Obool)),X24119),X24118))) = hAPP(c_Fun_Ocomp(X24122,X24122,X24122,hAPP(X24120,X24119)),hAPP(X24120,X24118)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Ounion__inter])]) ).

fof(i_0_7033,plain,
    ! [X20302,X20303,X20304] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X20304)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20304),hAPP(c_Groups_Oabs__class_Oabs(X20304),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20304),hAPP(c_Groups_Oabs__class_Oabs(X20304),X20303)),hAPP(c_Groups_Oabs__class_Oabs(X20304),X20302)))),hAPP(c_Groups_Oabs__class_Oabs(X20304),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20304),X20303),X20302)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq3])]) ).

cnf(i_0_7034,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_5497]) ).

fof(i_0_7035,plain,
    ! [X19014] :
      ( ( ~ 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)),X19014)),X19014)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19014),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19014),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)),X19014)),X19014)),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_7036,plain,
    ! [X32923,X32924,X32925,X32926] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X32926)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32925),X32924))
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X32925,X32926),X32924),X32923) = hAPP(hAPP(c_Finite__Set_Ofold(X32925,X32926,hAPP(hAPP(c_COMBB(X32926,tc_fun(X32926,X32926),X32925),c_Lattices_Osemilattice__inf__class_Oinf(X32926)),X32923)),c_Orderings_Otop__class_Otop(X32926)),X32924) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INFI__fold__inf])]) ).

fof(i_0_7037,plain,
    ! [X32919,X32920,X32921,X32922] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X32922)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32921),X32920))
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X32921,X32922),X32920),X32919) = hAPP(hAPP(c_Finite__Set_Ofold(X32921,X32922,hAPP(hAPP(c_COMBB(X32922,tc_fun(X32922,X32922),X32921),c_Lattices_Osemilattice__sup__class_Osup(X32922)),X32919)),c_Orderings_Obot__class_Obot(X32922)),X32920) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUPR__fold__sup])]) ).

fof(i_0_7038,plain,
    ! [X32255,X32256,X32257,X32258] :
      ( ( c_Wellfounded_Oacyclic(X32258,X32255)
        | ~ c_Wellfounded_Oacyclic(X32258,hAPP(hAPP(c_Set_Oinsert(tc_prod(X32258,X32258)),hAPP(hAPP(c_Product__Type_OPair(X32258,X32258),X32257),X32256)),X32255)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32258,X32258)),hAPP(hAPP(c_Product__Type_OPair(X32258,X32258),X32256),X32257)),c_Transitive__Closure_Ortrancl(X32258,X32255)))
        | ~ c_Wellfounded_Oacyclic(X32258,hAPP(hAPP(c_Set_Oinsert(tc_prod(X32258,X32258)),hAPP(hAPP(c_Product__Type_OPair(X32258,X32258),X32257),X32256)),X32255)) )
      & ( ~ c_Wellfounded_Oacyclic(X32258,X32255)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X32258,X32258)),hAPP(hAPP(c_Product__Type_OPair(X32258,X32258),X32256),X32257)),c_Transitive__Closure_Ortrancl(X32258,X32255)))
        | c_Wellfounded_Oacyclic(X32258,hAPP(hAPP(c_Set_Oinsert(tc_prod(X32258,X32258)),hAPP(hAPP(c_Product__Type_OPair(X32258,X32258),X32257),X32256)),X32255)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5498])])]) ).

fof(i_0_7039,plain,
    ! [X32242,X32243,X32244,X32245] :
      ( ( c_Wellfounded_Owf(X32245,X32242)
        | ~ c_Wellfounded_Owf(X32245,hAPP(hAPP(c_Set_Oinsert(tc_prod(X32245,X32245)),hAPP(hAPP(c_Product__Type_OPair(X32245,X32245),X32244),X32243)),X32242)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32245,X32245)),hAPP(hAPP(c_Product__Type_OPair(X32245,X32245),X32243),X32244)),c_Transitive__Closure_Ortrancl(X32245,X32242)))
        | ~ c_Wellfounded_Owf(X32245,hAPP(hAPP(c_Set_Oinsert(tc_prod(X32245,X32245)),hAPP(hAPP(c_Product__Type_OPair(X32245,X32245),X32244),X32243)),X32242)) )
      & ( ~ c_Wellfounded_Owf(X32245,X32242)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X32245,X32245)),hAPP(hAPP(c_Product__Type_OPair(X32245,X32245),X32243),X32244)),c_Transitive__Closure_Ortrancl(X32245,X32242)))
        | c_Wellfounded_Owf(X32245,hAPP(hAPP(c_Set_Oinsert(tc_prod(X32245,X32245)),hAPP(hAPP(c_Product__Type_OPair(X32245,X32245),X32244),X32243)),X32242)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5499])])]) ).

cnf(i_0_7040,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_5500]) ).

fof(i_0_7041,plain,
    ! [X32548,X32549,X32550,X32551,X32552,X32553] :
      ( ~ c_Relation_Osingle__valued(X32553,X32552,X32551)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32553,X32552)),hAPP(hAPP(c_Product__Type_OPair(X32553,X32552),X32550),X32549)),X32551))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32553,X32552)),hAPP(hAPP(c_Product__Type_OPair(X32553,X32552),X32550),X32548)),X32551))
      | X32549 = X32548 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_single__valuedD])]) ).

fof(i_0_7042,plain,
    ! [X27737,X27738,X27739] : hAPP(c_Set_OCollect(X27739),hAPP(hAPP(c_COMBS(X27739,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27739),c_fdisj),X27738)),X27737)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27739,tc_HOL_Obool)),hAPP(c_Set_OCollect(X27739),X27738)),hAPP(c_Set_OCollect(X27739),X27737)),
    inference(variable_rename,[status(thm)],[fact_Collect__disj__eq]) ).

fof(i_0_7043,plain,
    ! [X27740,X27741,X27742] : hAPP(c_Set_OCollect(X27742),hAPP(hAPP(c_COMBS(X27742,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27742),c_fconj),X27741)),X27740)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27742,tc_HOL_Obool)),hAPP(c_Set_OCollect(X27742),X27741)),hAPP(c_Set_OCollect(X27742),X27740)),
    inference(variable_rename,[status(thm)],[fact_Collect__conj__eq]) ).

fof(i_0_7044,plain,
    ! [X33052,X33053,X33054,X33055,X33057,X33058,X33059,X33062] :
      ( ( hBOOL(hAPP(hAPP(c_member(X33053),esk493_3(X33052,X33053,X33054)),X33054))
        | ~ hBOOL(hAPP(hAPP(c_member(X33053),X33055),X33054))
        | ~ c_Wellfounded_Owf(X33053,X33052) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X33053,X33053)),hAPP(hAPP(c_Product__Type_OPair(X33053,X33053),X33057),esk493_3(X33052,X33053,X33054))),X33052))
        | ~ hBOOL(hAPP(hAPP(c_member(X33053),X33057),X33054))
        | ~ hBOOL(hAPP(hAPP(c_member(X33053),X33055),X33054))
        | ~ c_Wellfounded_Owf(X33053,X33052) )
      & ( hBOOL(hAPP(hAPP(c_member(X33059),esk495_2(X33058,X33059)),esk494_2(X33058,X33059)))
        | c_Wellfounded_Owf(X33059,X33058) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X33059,X33059)),hAPP(hAPP(c_Product__Type_OPair(X33059,X33059),esk496_3(X33058,X33059,X33062)),X33062)),X33058))
        | ~ hBOOL(hAPP(hAPP(c_member(X33059),X33062),esk494_2(X33058,X33059)))
        | c_Wellfounded_Owf(X33059,X33058) )
      & ( hBOOL(hAPP(hAPP(c_member(X33059),esk496_3(X33058,X33059,X33062)),esk494_2(X33058,X33059)))
        | ~ hBOOL(hAPP(hAPP(c_member(X33059),X33062),esk494_2(X33058,X33059)))
        | c_Wellfounded_Owf(X33059,X33058) ) ),
    inference(distribute,[status(thm)],[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_5501])])])])])]) ).

cnf(i_0_7045,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_5502]) ).

cnf(i_0_7046,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_5503]) ).

cnf(i_0_7047,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_5504]) ).

cnf(i_0_7048,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_5505]) ).

cnf(i_0_7049,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_5506]) ).

cnf(i_0_7050,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_5507]) ).

cnf(i_0_7051,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_5508]) ).

fof(i_0_7052,plain,
    ! [X30650,X30651,X30652,X30653,X30654,X30655] :
      ( ~ c_List_Olist__all2(X30655,X30654,X30653,X30652,X30651)
      | c_List_Olist__all2(X30655,X30654,X30653,hAPP(hAPP(c_List_Odrop(X30655),X30650),X30652),hAPP(hAPP(c_List_Odrop(X30654),X30650),X30651)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__dropI])]) ).

fof(i_0_7053,plain,
    ! [X30637,X30638,X30639,X30640,X30641,X30642] :
      ( ~ c_List_Olist__all2(X30642,X30641,X30640,X30639,X30638)
      | c_List_Olist__all2(X30642,X30641,X30640,hAPP(hAPP(c_List_Otake(X30642),X30637),X30639),hAPP(hAPP(c_List_Otake(X30641),X30637),X30638)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__takeI])]) ).

fof(i_0_7054,plain,
    ! [X32494,X32495,X32496,X32497] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32497,X32497)),hAPP(hAPP(c_Product__Type_OPair(X32497,X32497),X32496),X32495)),c_Transitive__Closure_Ortrancl(X32497,hAPP(c_Relation_Oconverse(X32497,X32497),X32494))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X32497,X32497)),hAPP(hAPP(c_Product__Type_OPair(X32497,X32497),X32495),X32496)),c_Transitive__Closure_Ortrancl(X32497,X32494))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__converseD])]) ).

fof(i_0_7055,plain,
    ! [X33847,X33848,X33849,X33850] :
      ( ~ c_Relation_Oantisym(X33850,X33849)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X33850,X33850)),hAPP(hAPP(c_Product__Type_OPair(X33850,X33850),X33848),X33847)),X33849))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X33850,X33850)),hAPP(hAPP(c_Product__Type_OPair(X33850,X33850),X33847),X33848)),X33849))
      | X33848 = X33847 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_antisymD])]) ).

fof(i_0_7056,plain,
    ! [X33839,X33840,X33841,X33842,X33843,X33844] :
      ( ( ~ c_Relation_Oantisym(X33840,X33839)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X33840,X33840)),hAPP(hAPP(c_Product__Type_OPair(X33840,X33840),X33841),X33842)),X33839))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X33840,X33840)),hAPP(hAPP(c_Product__Type_OPair(X33840,X33840),X33842),X33841)),X33839))
        | X33841 = X33842 )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X33844,X33844)),hAPP(hAPP(c_Product__Type_OPair(X33844,X33844),esk546_2(X33843,X33844)),esk547_2(X33843,X33844))),X33843))
        | c_Relation_Oantisym(X33844,X33843) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X33844,X33844)),hAPP(hAPP(c_Product__Type_OPair(X33844,X33844),esk547_2(X33843,X33844)),esk546_2(X33843,X33844))),X33843))
        | c_Relation_Oantisym(X33844,X33843) )
      & ( esk546_2(X33843,X33844) != esk547_2(X33843,X33844)
        | c_Relation_Oantisym(X33844,X33843) ) ),
    inference(distribute,[status(thm)],[inference(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_7057,plain,
    ! [X28194,X28195,X28196,X28197] :
      ( ~ c_Wellfounded_Owf(X28197,X28196)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28197,X28197)),hAPP(hAPP(c_Product__Type_OPair(X28197,X28197),X28195),X28194)),X28196))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28197,X28197)),hAPP(hAPP(c_Product__Type_OPair(X28197,X28197),X28194),X28195)),X28196)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5509])]) ).

fof(i_0_7058,plain,
    ! [X28190,X28191,X28192,X28193] :
      ( ~ c_Wellfounded_Owf(X28193,X28192)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28193,X28193)),hAPP(hAPP(c_Product__Type_OPair(X28193,X28193),X28191),X28190)),X28192))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28193,X28193)),hAPP(hAPP(c_Product__Type_OPair(X28193,X28193),X28190),X28191)),X28192)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5510])]) ).

fof(i_0_7059,plain,
    ! [X29698,X29699,X29700,X29701,X29702] :
      ( ~ class_Rings_Osemiring__0(X29702)
      | hAPP(c_List_Omonoid__add__class_Olistsum(X29702),hAPP(hAPP(c_List_Omap(X29701,X29702),hAPP(hAPP(c_COMBB(X29702,X29702,X29701),hAPP(c_Groups_Otimes__class_Otimes(X29702),X29700)),X29699)),X29698)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X29702),X29700),hAPP(c_List_Omonoid__add__class_Olistsum(X29702),hAPP(hAPP(c_List_Omap(X29701,X29702),X29699),X29698))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__const__mult])]) ).

fof(i_0_7060,plain,
    ! [X23252,X23253,X23254,X23255,X23256,X23257] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X23257,X23256),tc_HOL_Obool)),X23255),X23254))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23257,tc_HOL_Obool)),X23253),X23252))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23256,tc_HOL_Obool)),hAPP(c_Relation_OImage(X23257,X23256,X23255),X23253)),hAPP(c_Relation_OImage(X23257,X23256,X23254),X23252))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Image__mono])]) ).

fof(i_0_7061,plain,
    ! [X22347,X22348,X22349] :
      ( ( X22349 = 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),X22347)),X22348)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22347))
        | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22349,X22348),X22347)) )
      & ( X22348 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X22347) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22349,X22348),X22347)) )
      & ( 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),X22347)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22348))
        | X22348 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22349,X22348),X22347)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22347)),X22348))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22348))
        | X22348 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22349,X22348),X22347)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22348),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22347)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22348))
        | X22348 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22349,X22348),X22347)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22347)),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)),X22348))
        | X22348 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22349,X22348),X22347)) )
      & ( X22348 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X22348 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X22349 != 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),X22347)),X22348)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22347))
        | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22349,X22348),X22347)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22348))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22348))
        | X22348 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X22349 != 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),X22347)),X22348)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22347))
        | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22349,X22348),X22347)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22348),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22347)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22347)),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)),X22348))
        | X22348 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X22349 != 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),X22347)),X22348)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22347))
        | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22349,X22348),X22347)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22348))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22347)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22347)),X22348))
        | X22348 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X22349 != 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),X22347)),X22348)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22347))
        | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22349,X22348),X22347)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22348),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22347)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22347)),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),X22347)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22347)),X22348))
        | X22348 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X22349 != 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),X22347)),X22348)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22347))
        | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22349,X22348),X22347)) )
      & ( X22348 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X22347) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X22349 != 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),X22347)),X22348)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22347))
        | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22349,X22348),X22347)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22348))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22348))
        | hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X22347) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X22349 != 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),X22347)),X22348)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22347))
        | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22349,X22348),X22347)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22348),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22347)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22347)),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)),X22348))
        | hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X22347) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X22349 != 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),X22347)),X22348)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22347))
        | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22349,X22348),X22347)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22348))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22347)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22347)),X22348))
        | hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X22347) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X22349 != 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),X22347)),X22348)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22347))
        | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22349,X22348),X22347)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22348),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22347)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22347)),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),X22347)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22347)),X22348))
        | hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X22347) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X22349 != 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),X22347)),X22348)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22347))
        | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22349,X22348),X22347)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5511])])]) ).

fof(i_0_7062,plain,
    ! [X22340,X22341,X22342,X22343,X22344] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(X22344,X22343)),hAPP(X22344,X22342)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X22341,X22341)),hAPP(hAPP(c_Product__Type_OPair(X22341,X22341),X22343),X22342)),X22340))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X22341,X22341)),hAPP(hAPP(c_Product__Type_OPair(X22341,X22341),X22343),X22342)),c_Wellfounded_Omlex__prod(X22341,X22344,X22340))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mlex__leq])]) ).

fof(i_0_7063,plain,
    ! [X21598,X21599,X21600,X21601] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21601),c_Groups_Ozero__class_Ozero(X21601)),hAPP(c_Int_Onumber__class_Onumber__of(X21601),X21599)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21601),X21600),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21601),X21598),hAPP(c_Int_Onumber__class_Onumber__of(X21601),X21599))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21601),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21601),X21600),hAPP(c_Int_Onumber__class_Onumber__of(X21601),X21599))),X21598))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21601)
        | ~ class_Int_Onumber(X21601) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21601),hAPP(c_Int_Onumber__class_Onumber__of(X21601),X21599)),c_Groups_Ozero__class_Ozero(X21601)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21601),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21601),X21598),hAPP(c_Int_Onumber__class_Onumber__of(X21601),X21599))),X21600))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21601),c_Groups_Ozero__class_Ozero(X21601)),hAPP(c_Int_Onumber__class_Onumber__of(X21601),X21599)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21601),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21601),X21600),hAPP(c_Int_Onumber__class_Onumber__of(X21601),X21599))),X21598))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21601)
        | ~ class_Int_Onumber(X21601) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21601),hAPP(c_Int_Onumber__class_Onumber__of(X21601),X21599)),c_Groups_Ozero__class_Ozero(X21601)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21601),c_Groups_Ozero__class_Ozero(X21601)),X21598))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21601),c_Groups_Ozero__class_Ozero(X21601)),hAPP(c_Int_Onumber__class_Onumber__of(X21601),X21599)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21601),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21601),X21600),hAPP(c_Int_Onumber__class_Onumber__of(X21601),X21599))),X21598))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21601)
        | ~ class_Int_Onumber(X21601) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21601),c_Groups_Ozero__class_Ozero(X21601)),hAPP(c_Int_Onumber__class_Onumber__of(X21601),X21599)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21601),c_Groups_Ozero__class_Ozero(X21601)),hAPP(c_Int_Onumber__class_Onumber__of(X21601),X21599)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21601),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21601),X21600),hAPP(c_Int_Onumber__class_Onumber__of(X21601),X21599))),X21598))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21601)
        | ~ class_Int_Onumber(X21601) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21601),hAPP(c_Int_Onumber__class_Onumber__of(X21601),X21599)),c_Groups_Ozero__class_Ozero(X21601)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21601),hAPP(c_Int_Onumber__class_Onumber__of(X21601),X21599)),c_Groups_Ozero__class_Ozero(X21601)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21601),c_Groups_Ozero__class_Ozero(X21601)),hAPP(c_Int_Onumber__class_Onumber__of(X21601),X21599)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21601),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21601),X21600),hAPP(c_Int_Onumber__class_Onumber__of(X21601),X21599))),X21598))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21601)
        | ~ class_Int_Onumber(X21601) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21601),c_Groups_Ozero__class_Ozero(X21601)),X21598))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21601),hAPP(c_Int_Onumber__class_Onumber__of(X21601),X21599)),c_Groups_Ozero__class_Ozero(X21601)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21601),c_Groups_Ozero__class_Ozero(X21601)),hAPP(c_Int_Onumber__class_Onumber__of(X21601),X21599)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21601),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21601),X21600),hAPP(c_Int_Onumber__class_Onumber__of(X21601),X21599))),X21598))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21601)
        | ~ class_Int_Onumber(X21601) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21601),hAPP(c_Int_Onumber__class_Onumber__of(X21601),X21599)),c_Groups_Ozero__class_Ozero(X21601)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21601),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21601),X21598),hAPP(c_Int_Onumber__class_Onumber__of(X21601),X21599))),X21600))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21601),c_Groups_Ozero__class_Ozero(X21601)),hAPP(c_Int_Onumber__class_Onumber__of(X21601),X21599)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21601),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21601),X21600),hAPP(c_Int_Onumber__class_Onumber__of(X21601),X21599))),X21598))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21601)
        | ~ class_Int_Onumber(X21601) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21601),c_Groups_Ozero__class_Ozero(X21601)),X21598))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21601),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21601),X21598),hAPP(c_Int_Onumber__class_Onumber__of(X21601),X21599))),X21600))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21601),c_Groups_Ozero__class_Ozero(X21601)),hAPP(c_Int_Onumber__class_Onumber__of(X21601),X21599)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21601),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21601),X21600),hAPP(c_Int_Onumber__class_Onumber__of(X21601),X21599))),X21598))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21601)
        | ~ class_Int_Onumber(X21601) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21601),c_Groups_Ozero__class_Ozero(X21601)),hAPP(c_Int_Onumber__class_Onumber__of(X21601),X21599)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21601),X21600),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21601),X21598),hAPP(c_Int_Onumber__class_Onumber__of(X21601),X21599))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21601),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21601),X21600),hAPP(c_Int_Onumber__class_Onumber__of(X21601),X21599))),X21598))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21601)
        | ~ class_Int_Onumber(X21601) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21601),hAPP(c_Int_Onumber__class_Onumber__of(X21601),X21599)),c_Groups_Ozero__class_Ozero(X21601)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21601),hAPP(c_Int_Onumber__class_Onumber__of(X21601),X21599)),c_Groups_Ozero__class_Ozero(X21601)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21601),X21600),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21601),X21598),hAPP(c_Int_Onumber__class_Onumber__of(X21601),X21599))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21601),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21601),X21600),hAPP(c_Int_Onumber__class_Onumber__of(X21601),X21599))),X21598))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21601)
        | ~ class_Int_Onumber(X21601) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21601),c_Groups_Ozero__class_Ozero(X21601)),X21598))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21601),hAPP(c_Int_Onumber__class_Onumber__of(X21601),X21599)),c_Groups_Ozero__class_Ozero(X21601)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21601),X21600),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21601),X21598),hAPP(c_Int_Onumber__class_Onumber__of(X21601),X21599))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21601),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21601),X21600),hAPP(c_Int_Onumber__class_Onumber__of(X21601),X21599))),X21598))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21601)
        | ~ class_Int_Onumber(X21601) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21601),hAPP(c_Int_Onumber__class_Onumber__of(X21601),X21599)),c_Groups_Ozero__class_Ozero(X21601)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21601),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21601),X21598),hAPP(c_Int_Onumber__class_Onumber__of(X21601),X21599))),X21600))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21601),X21600),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21601),X21598),hAPP(c_Int_Onumber__class_Onumber__of(X21601),X21599))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21601),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21601),X21600),hAPP(c_Int_Onumber__class_Onumber__of(X21601),X21599))),X21598))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21601)
        | ~ class_Int_Onumber(X21601) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21601),c_Groups_Ozero__class_Ozero(X21601)),X21598))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21601),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21601),X21598),hAPP(c_Int_Onumber__class_Onumber__of(X21601),X21599))),X21600))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21601),X21600),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21601),X21598),hAPP(c_Int_Onumber__class_Onumber__of(X21601),X21599))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21601),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21601),X21600),hAPP(c_Int_Onumber__class_Onumber__of(X21601),X21599))),X21598))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21601)
        | ~ class_Int_Onumber(X21601) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5512])])]) ).

fof(i_0_7064,plain,
    ! [X21588,X21589,X21590,X21591] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21591),c_Groups_Ozero__class_Ozero(X21591)),hAPP(c_Int_Onumber__class_Onumber__of(X21591),X21589)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21591),X21590),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21591),X21588),hAPP(c_Int_Onumber__class_Onumber__of(X21591),X21589))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21591),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21591),X21590),hAPP(c_Int_Onumber__class_Onumber__of(X21591),X21589))),X21588))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21591)
        | ~ class_Int_Onumber(X21591) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21591),hAPP(c_Int_Onumber__class_Onumber__of(X21591),X21589)),c_Groups_Ozero__class_Ozero(X21591)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21591),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21591),X21588),hAPP(c_Int_Onumber__class_Onumber__of(X21591),X21589))),X21590))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21591),c_Groups_Ozero__class_Ozero(X21591)),hAPP(c_Int_Onumber__class_Onumber__of(X21591),X21589)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21591),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21591),X21590),hAPP(c_Int_Onumber__class_Onumber__of(X21591),X21589))),X21588))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21591)
        | ~ class_Int_Onumber(X21591) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21591),hAPP(c_Int_Onumber__class_Onumber__of(X21591),X21589)),c_Groups_Ozero__class_Ozero(X21591)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21591),c_Groups_Ozero__class_Ozero(X21591)),X21588))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21591),c_Groups_Ozero__class_Ozero(X21591)),hAPP(c_Int_Onumber__class_Onumber__of(X21591),X21589)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21591),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21591),X21590),hAPP(c_Int_Onumber__class_Onumber__of(X21591),X21589))),X21588))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21591)
        | ~ class_Int_Onumber(X21591) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21591),c_Groups_Ozero__class_Ozero(X21591)),hAPP(c_Int_Onumber__class_Onumber__of(X21591),X21589)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21591),c_Groups_Ozero__class_Ozero(X21591)),hAPP(c_Int_Onumber__class_Onumber__of(X21591),X21589)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21591),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21591),X21590),hAPP(c_Int_Onumber__class_Onumber__of(X21591),X21589))),X21588))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21591)
        | ~ class_Int_Onumber(X21591) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21591),hAPP(c_Int_Onumber__class_Onumber__of(X21591),X21589)),c_Groups_Ozero__class_Ozero(X21591)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21591),hAPP(c_Int_Onumber__class_Onumber__of(X21591),X21589)),c_Groups_Ozero__class_Ozero(X21591)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21591),c_Groups_Ozero__class_Ozero(X21591)),hAPP(c_Int_Onumber__class_Onumber__of(X21591),X21589)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21591),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21591),X21590),hAPP(c_Int_Onumber__class_Onumber__of(X21591),X21589))),X21588))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21591)
        | ~ class_Int_Onumber(X21591) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21591),c_Groups_Ozero__class_Ozero(X21591)),X21588))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21591),hAPP(c_Int_Onumber__class_Onumber__of(X21591),X21589)),c_Groups_Ozero__class_Ozero(X21591)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21591),c_Groups_Ozero__class_Ozero(X21591)),hAPP(c_Int_Onumber__class_Onumber__of(X21591),X21589)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21591),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21591),X21590),hAPP(c_Int_Onumber__class_Onumber__of(X21591),X21589))),X21588))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21591)
        | ~ class_Int_Onumber(X21591) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21591),hAPP(c_Int_Onumber__class_Onumber__of(X21591),X21589)),c_Groups_Ozero__class_Ozero(X21591)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21591),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21591),X21588),hAPP(c_Int_Onumber__class_Onumber__of(X21591),X21589))),X21590))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21591),c_Groups_Ozero__class_Ozero(X21591)),hAPP(c_Int_Onumber__class_Onumber__of(X21591),X21589)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21591),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21591),X21590),hAPP(c_Int_Onumber__class_Onumber__of(X21591),X21589))),X21588))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21591)
        | ~ class_Int_Onumber(X21591) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21591),c_Groups_Ozero__class_Ozero(X21591)),X21588))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21591),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21591),X21588),hAPP(c_Int_Onumber__class_Onumber__of(X21591),X21589))),X21590))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21591),c_Groups_Ozero__class_Ozero(X21591)),hAPP(c_Int_Onumber__class_Onumber__of(X21591),X21589)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21591),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21591),X21590),hAPP(c_Int_Onumber__class_Onumber__of(X21591),X21589))),X21588))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21591)
        | ~ class_Int_Onumber(X21591) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21591),c_Groups_Ozero__class_Ozero(X21591)),hAPP(c_Int_Onumber__class_Onumber__of(X21591),X21589)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21591),X21590),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21591),X21588),hAPP(c_Int_Onumber__class_Onumber__of(X21591),X21589))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21591),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21591),X21590),hAPP(c_Int_Onumber__class_Onumber__of(X21591),X21589))),X21588))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21591)
        | ~ class_Int_Onumber(X21591) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21591),hAPP(c_Int_Onumber__class_Onumber__of(X21591),X21589)),c_Groups_Ozero__class_Ozero(X21591)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21591),hAPP(c_Int_Onumber__class_Onumber__of(X21591),X21589)),c_Groups_Ozero__class_Ozero(X21591)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21591),X21590),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21591),X21588),hAPP(c_Int_Onumber__class_Onumber__of(X21591),X21589))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21591),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21591),X21590),hAPP(c_Int_Onumber__class_Onumber__of(X21591),X21589))),X21588))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21591)
        | ~ class_Int_Onumber(X21591) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21591),c_Groups_Ozero__class_Ozero(X21591)),X21588))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21591),hAPP(c_Int_Onumber__class_Onumber__of(X21591),X21589)),c_Groups_Ozero__class_Ozero(X21591)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21591),X21590),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21591),X21588),hAPP(c_Int_Onumber__class_Onumber__of(X21591),X21589))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21591),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21591),X21590),hAPP(c_Int_Onumber__class_Onumber__of(X21591),X21589))),X21588))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21591)
        | ~ class_Int_Onumber(X21591) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21591),hAPP(c_Int_Onumber__class_Onumber__of(X21591),X21589)),c_Groups_Ozero__class_Ozero(X21591)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21591),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21591),X21588),hAPP(c_Int_Onumber__class_Onumber__of(X21591),X21589))),X21590))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21591),X21590),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21591),X21588),hAPP(c_Int_Onumber__class_Onumber__of(X21591),X21589))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21591),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21591),X21590),hAPP(c_Int_Onumber__class_Onumber__of(X21591),X21589))),X21588))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21591)
        | ~ class_Int_Onumber(X21591) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21591),c_Groups_Ozero__class_Ozero(X21591)),X21588))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21591),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21591),X21588),hAPP(c_Int_Onumber__class_Onumber__of(X21591),X21589))),X21590))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21591),X21590),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21591),X21588),hAPP(c_Int_Onumber__class_Onumber__of(X21591),X21589))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21591),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21591),X21590),hAPP(c_Int_Onumber__class_Onumber__of(X21591),X21589))),X21588))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21591)
        | ~ class_Int_Onumber(X21591) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5513])])]) ).

cnf(i_0_7065,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_5480]) ).

fof(i_0_7066,plain,
    ! [X27310,X27311,X27312,X27313] : hAPP(c_Set_Oimage(tc_prod(X27313,X27312),tc_prod(X27312,X27313),hAPP(c_Product__Type_Oprod_Oprod__case(X27313,X27312,tc_prod(X27312,X27313)),hAPP(c_COMBC(X27312,X27313,tc_prod(X27312,X27313)),c_Product__Type_OPair(X27312,X27313)))),hAPP(hAPP(c_Product__Type_OSigma(X27313,X27312),X27311),hAPP(c_COMBK(tc_fun(X27312,tc_HOL_Obool),X27313),X27310))) = hAPP(hAPP(c_Product__Type_OSigma(X27312,X27313),X27310),hAPP(c_COMBK(tc_fun(X27313,tc_HOL_Obool),X27312),X27311)),
    inference(variable_rename,[status(thm)],[fact_swap__product]) ).

cnf(i_0_7067,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_5514]) ).

fof(i_0_7068,plain,
    ! [X24142,X24143,X24144,X24145] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X24145),X24144),X24143))
      | hBOOL(hAPP(hAPP(c_member(tc_fun(X24145,tc_HOL_Obool)),hAPP(c_Relation_OImage(X24145,X24145,X24142),hAPP(hAPP(c_Set_Oinsert(X24145),X24144),c_Orderings_Obot__class_Obot(tc_fun(X24145,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(X24145),X24143),X24142))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_quotientI])]) ).

fof(i_0_7069,plain,
    ! [X23293,X23294,X23295,X23296,X23297] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X23297),X23296),hAPP(c_Relation_OImage(X23295,X23297,X23294),hAPP(hAPP(c_Set_Oinsert(X23295),X23293),c_Orderings_Obot__class_Obot(tc_fun(X23295,tc_HOL_Obool))))))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X23295,X23297)),hAPP(hAPP(c_Product__Type_OPair(X23295,X23297),X23293),X23296)),X23294)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X23295,X23297)),hAPP(hAPP(c_Product__Type_OPair(X23295,X23297),X23293),X23296)),X23294))
        | hBOOL(hAPP(hAPP(c_member(X23297),X23296),hAPP(c_Relation_OImage(X23295,X23297,X23294),hAPP(hAPP(c_Set_Oinsert(X23295),X23293),c_Orderings_Obot__class_Obot(tc_fun(X23295,tc_HOL_Obool)))))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Image__singleton__iff])]) ).

fof(i_0_7070,plain,
    ! [X31612,X31613,X31614,X31615,X31616] :
      ( ( ~ c_List_Olist__all2(X31616,X31615,X31614,hAPP(c_List_Orev(X31616),X31613),hAPP(c_List_Orev(X31615),X31612))
        | c_List_Olist__all2(X31616,X31615,X31614,X31613,X31612) )
      & ( ~ c_List_Olist__all2(X31616,X31615,X31614,X31613,X31612)
        | c_List_Olist__all2(X31616,X31615,X31614,hAPP(c_List_Orev(X31616),X31613),hAPP(c_List_Orev(X31615),X31612)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__rev])]) ).

cnf(i_0_7071,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),esk409_2(X2,X1))),hAPP(c_List_Oset(X1),esk410_2(X2,X1))) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),esk408_2(X2,X1)))
    | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5492]) ).

fof(i_0_7072,plain,
    ! [X22192,X22193,X22194] :
      ( ( 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),esk90_3(X22192,X22193,X22194)),esk91_3(X22192,X22193,X22194))))
        | hBOOL(hAPP(hAPP(X22192,X22194),X22193))
        | ~ 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),X22194),X22193))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk91_3(X22192,X22193,X22194)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(X22192,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),esk90_3(X22192,X22193,X22194))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),esk91_3(X22192,X22193,X22194))))
        | hBOOL(hAPP(hAPP(X22192,X22194),X22193))
        | ~ 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),X22194),X22193))) )
      & ( ~ hBOOL(hAPP(hAPP(X22192,esk90_3(X22192,X22193,X22194)),esk91_3(X22192,X22193,X22194)))
        | hBOOL(hAPP(hAPP(X22192,X22194),X22193))
        | ~ 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),X22194),X22193))) ) ),
    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_7073,plain,
    ! [X25609,X25610,X25611,X25612] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk199_4(X25609,X25610,X25611,X25612)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X25611)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25612),X25610))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25612),X25611)),X25610))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X25610),X25609))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25611)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk200_4(X25609,X25610,X25611,X25612)),X25609))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25612),X25610))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25612),X25611)),X25610))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X25610),X25609))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25611)) )
      & ( X25612 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk200_4(X25609,X25610,X25611,X25612)),esk199_4(X25609,X25610,X25611,X25612))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25612),X25610))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25612),X25611)),X25610))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X25610),X25609))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25611)) ) ),
    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_7074,plain,
    ! [X19743,X19744,X19745,X19746] :
      ( ~ class_Divides_Osemiring__div(X19746)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19746),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19746),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19746),X19745),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X19746),X19744),X19745))),c_Divides_Odiv__class_Omod(X19746,X19744,X19745))),X19743) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19746),X19744),X19743) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mod__equality2])]) ).

fof(i_0_7075,plain,
    ! [X31607,X31608,X31609,X31610,X31611] :
      ( ( ~ c_List_Olist__all2(X31611,X31610,X31609,hAPP(c_List_Orev(X31611),X31608),X31607)
        | c_List_Olist__all2(X31611,X31610,X31609,X31608,hAPP(c_List_Orev(X31610),X31607)) )
      & ( ~ c_List_Olist__all2(X31611,X31610,X31609,X31608,hAPP(c_List_Orev(X31610),X31607))
        | c_List_Olist__all2(X31611,X31610,X31609,hAPP(c_List_Orev(X31611),X31608),X31607) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__rev1])]) ).

fof(i_0_7076,plain,
    ! [X28681,X28682,X28683,X28686,X28687,X28688,X28689,X28690] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28683),tc_List_Olist(X28683))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28683),tc_List_Olist(X28683)),c_List_Olist_ONil(X28683)),X28682)),c_List_Olexord(X28683,X28681)))
        | X28682 = hAPP(hAPP(c_List_Olist_OCons(X28683),esk317_3(X28681,X28682,X28683)),esk318_3(X28681,X28682,X28683)) )
      & ( X28687 != hAPP(hAPP(c_List_Olist_OCons(X28688),X28689),X28690)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28688),tc_List_Olist(X28688))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28688),tc_List_Olist(X28688)),c_List_Olist_ONil(X28688)),X28687)),c_List_Olexord(X28688,X28686))) ) ),
    inference(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_7077,plain,
    ! [X27177,X27178,X27179,X27180] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27180,tc_HOL_Obool)),hAPP(c_Set_Oimage(X27179,X27180,X27178),hAPP(c_Set_Ovimage(X27179,X27180,X27178),X27177))),X27177)),
    inference(variable_rename,[status(thm)],[fact_image__vimage__subset]) ).

fof(i_0_7078,plain,
    ! [X31593,X31594,X31595,X31596,X31597] :
      ( ~ class_Orderings_Olinorder(X31597)
      | ~ c_Fun_Oinj__on(X31596,X31597,X31595,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X31596,tc_HOL_Obool)),hAPP(c_List_Oset(X31596),X31594)),hAPP(c_List_Oset(X31596),X31593)))
      | ~ c_List_Olinorder__class_Osorted(X31597,hAPP(hAPP(c_List_Omap(X31596,X31597),X31595),X31594))
      | ~ hBOOL(hAPP(c_List_Odistinct(X31597),hAPP(hAPP(c_List_Omap(X31596,X31597),X31595),X31594)))
      | ~ c_List_Olinorder__class_Osorted(X31597,hAPP(hAPP(c_List_Omap(X31596,X31597),X31595),X31593))
      | ~ hBOOL(hAPP(c_List_Odistinct(X31597),hAPP(hAPP(c_List_Omap(X31596,X31597),X31595),X31593)))
      | hAPP(c_List_Oset(X31596),X31594) != hAPP(c_List_Oset(X31596),X31593)
      | X31594 = X31593 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__sorted__distinct__set__unique])]) ).

fof(i_0_7079,plain,
    ! [X17921,X17922,X17923,X17924,X17925,X17927,X17928,X17929,X17930,X17931,X17932] :
      ( ( hBOOL(hAPP(X17925,X17923))
        | X17921 = X17923
        | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X17925,X17924),X17923,X17922,X17921) )
      & ( c_Natural_Oevaln(X17924,X17923,X17922,esk32_5(X17921,X17922,X17923,X17924,X17925))
        | X17921 = X17923
        | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X17925,X17924),X17923,X17922,X17921) )
      & ( c_Natural_Oevaln(c_Com_Ocom_OWhile(X17925,X17924),esk32_5(X17921,X17922,X17923,X17924,X17925),X17922,X17921)
        | X17921 = X17923
        | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X17925,X17924),X17923,X17922,X17921) )
      & ( hBOOL(hAPP(X17925,X17923))
        | ~ hBOOL(hAPP(X17925,X17923))
        | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X17925,X17924),X17923,X17922,X17921) )
      & ( c_Natural_Oevaln(X17924,X17923,X17922,esk32_5(X17921,X17922,X17923,X17924,X17925))
        | ~ hBOOL(hAPP(X17925,X17923))
        | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X17925,X17924),X17923,X17922,X17921) )
      & ( c_Natural_Oevaln(c_Com_Ocom_OWhile(X17925,X17924),esk32_5(X17921,X17922,X17923,X17924,X17925),X17922,X17921)
        | ~ hBOOL(hAPP(X17925,X17923))
        | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X17925,X17924),X17923,X17922,X17921) )
      & ( X17927 != X17929
        | hBOOL(hAPP(X17931,X17929))
        | c_Natural_Oevaln(c_Com_Ocom_OWhile(X17931,X17930),X17929,X17928,X17927) )
      & ( ~ hBOOL(hAPP(X17931,X17929))
        | ~ c_Natural_Oevaln(X17930,X17929,X17928,X17932)
        | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X17931,X17930),X17932,X17928,X17927)
        | c_Natural_Oevaln(c_Com_Ocom_OWhile(X17931,X17930),X17929,X17928,X17927) ) ),
    inference(distribute,[status(thm)],[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_5515])])])])])]) ).

fof(i_0_7080,plain,
    ! [X19500,X19501,X19502,X19503] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19503))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19502))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19502),X19501))
      | 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),X19501),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19500,X19503))),X19502))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult2__lemma__aux3])]) ).

fof(i_0_7081,plain,
    ! [X27439,X27440,X27441] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27441),X27440))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27441,X27441),tc_HOL_Obool)),X27439),hAPP(hAPP(c_Product__Type_OSigma(X27441,X27441),X27440),hAPP(c_COMBK(tc_fun(X27441,tc_HOL_Obool),X27441),X27440))))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X27441,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X27441),X27440),X27439))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__quotient])]) ).

fof(i_0_7082,plain,
    ! [X29435,X29436,X29437,X29438,X29439,X29440] : hAPP(c_List_Ofoldl(X29440,X29439,X29438,X29437),hAPP(hAPP(c_List_Oappend(X29439),X29436),X29435)) = hAPP(c_List_Ofoldl(X29440,X29439,X29438,hAPP(c_List_Ofoldl(X29440,X29439,X29438,X29437),X29436)),X29435),
    inference(variable_rename,[status(thm)],[fact_foldl__append]) ).

cnf(i_0_7083,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk410_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)),esk408_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_5492]) ).

cnf(i_0_7084,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk409_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)),esk408_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_5492]) ).

fof(i_0_7085,plain,
    ! [X32490,X32491,X32492,X32493] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32493,X32493)),hAPP(hAPP(c_Product__Type_OPair(X32493,X32493),X32492),X32491)),c_Transitive__Closure_Ortrancl(X32493,X32490)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X32493,X32493)),hAPP(hAPP(c_Product__Type_OPair(X32493,X32493),X32491),X32492)),c_Transitive__Closure_Ortrancl(X32493,hAPP(c_Relation_Oconverse(X32493,X32493),X32490)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__converseI])]) ).

fof(i_0_7086,plain,
    ! [X33540,X33541,X33542] :
      ( ( 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),esk518_3(X33540,X33541,X33542)),esk519_3(X33540,X33541,X33542))))
        | hBOOL(hAPP(hAPP(X33540,X33542),X33541))
        | ~ 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),X33542),X33541))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk518_3(X33540,X33541,X33542)),esk519_3(X33540,X33541,X33542)))
        | hBOOL(hAPP(hAPP(X33540,esk518_3(X33540,X33541,X33542)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk519_3(X33540,X33541,X33542)),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | hBOOL(hAPP(hAPP(X33540,X33542),X33541))
        | ~ 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),X33542),X33541))) )
      & ( ~ hBOOL(hAPP(hAPP(X33540,esk518_3(X33540,X33541,X33542)),esk519_3(X33540,X33541,X33542)))
        | hBOOL(hAPP(hAPP(X33540,X33542),X33541))
        | ~ 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),X33542),X33541))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5516])])])]) ).

fof(i_0_7087,plain,
    ! [X29184,X29185,X29186,X29187,X29188] : hAPP(hAPP(c_List_Ozip(X29188,X29187),hAPP(hAPP(c_List_Oappend(X29188),X29186),X29185)),X29184) = hAPP(hAPP(c_List_Oappend(tc_prod(X29188,X29187)),hAPP(hAPP(c_List_Ozip(X29188,X29187),X29186),hAPP(hAPP(c_List_Otake(X29187),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29188)),X29186)),X29184))),hAPP(hAPP(c_List_Ozip(X29188,X29187),X29185),hAPP(hAPP(c_List_Odrop(X29187),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29188)),X29186)),X29184))),
    inference(variable_rename,[status(thm)],[fact_zip__append1]) ).

fof(i_0_7088,plain,
    ! [X23061,X23062,X23063,X23064] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23064,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23064,tc_HOL_Obool)),X23063),X23062)),X23061))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23064,tc_HOL_Obool)),X23063),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23064,tc_HOL_Obool)),X23062),X23061))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23064,tc_HOL_Obool)),X23063),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23064,tc_HOL_Obool)),X23062),X23061)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23064,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23064,tc_HOL_Obool)),X23063),X23062)),X23061)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Diff__subset__conv])]) ).

fof(i_0_7089,plain,
    ! [X17218,X17219,X17220,X17221,X17222] :
      ( ( c_Natural_Oevaln(X17222,X17220,X17219,esk17_5(X17218,X17219,X17220,X17221,X17222))
        | ~ c_Natural_Oevaln(c_Com_Ocom_OSemi(X17222,X17221),X17220,X17219,X17218) )
      & ( c_Natural_Oevaln(X17221,esk17_5(X17218,X17219,X17220,X17221,X17222),X17219,X17218)
        | ~ c_Natural_Oevaln(c_Com_Ocom_OSemi(X17222,X17221),X17220,X17219,X17218) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5517])])])]) ).

fof(i_0_7090,plain,
    ! [X17195,X17196,X17197,X17198,X17199,X17201,X17202,X17203,X17204,X17205,X17206] :
      ( ( c_Natural_Oevaln(X17199,X17197,X17196,esk16_5(X17195,X17196,X17197,X17198,X17199))
        | ~ c_Natural_Oevaln(c_Com_Ocom_OSemi(X17199,X17198),X17197,X17196,X17195) )
      & ( c_Natural_Oevaln(X17198,esk16_5(X17195,X17196,X17197,X17198,X17199),X17196,X17195)
        | ~ c_Natural_Oevaln(c_Com_Ocom_OSemi(X17199,X17198),X17197,X17196,X17195) )
      & ( ~ c_Natural_Oevaln(X17205,X17203,X17202,X17206)
        | ~ c_Natural_Oevaln(X17204,X17206,X17202,X17201)
        | c_Natural_Oevaln(c_Com_Ocom_OSemi(X17205,X17204),X17203,X17202,X17201) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evaln_Oequations_I4_J])])])])])]) ).

cnf(i_0_7091,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_5518]) ).

fof(i_0_7092,plain,
    ! [X24188,X24189,X24190,X24191] :
      ( ( X24190 = hAPP(c_Relation_OImage(X24191,X24191,X24188),hAPP(hAPP(c_Set_Oinsert(X24191),esk123_4(X24188,X24189,X24190,X24191)),c_Orderings_Obot__class_Obot(tc_fun(X24191,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X24191,tc_HOL_Obool)),X24190),hAPP(hAPP(c_Equiv__Relations_Oquotient(X24191),X24189),X24188))) )
      & ( hBOOL(hAPP(hAPP(c_member(X24191),esk123_4(X24188,X24189,X24190,X24191)),X24189))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X24191,tc_HOL_Obool)),X24190),hAPP(hAPP(c_Equiv__Relations_Oquotient(X24191),X24189),X24188))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5519])])])]) ).

cnf(i_0_7093,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_5520]) ).

cnf(i_0_7094,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_5521]) ).

cnf(i_0_7095,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_5522]) ).

fof(i_0_7096,plain,
    ! [X34008,X34009,X34010,X34011] :
      ( hAPP(c_Set_Oimage(X34011,X34010,X34009),c_Orderings_Otop__class_Otop(tc_fun(X34011,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X34010,tc_HOL_Obool))
      | hAPP(c_Set_Oimage(X34011,X34010,X34009),hAPP(c_Set_Oimage(X34010,X34011,c_Hilbert__Choice_Oinv__into(X34011,X34010,c_Orderings_Otop__class_Otop(tc_fun(X34011,tc_HOL_Obool)),X34009)),X34008)) = X34008 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__surj__f__inv__f])]) ).

fof(i_0_7097,plain,
    ! [X25620,X25621,X25622,X25623] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk203_4(X25620,X25621,X25622,X25623)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X25622)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25623),X25620))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X25623),X25622)),X25620))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25622)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk204_4(X25620,X25621,X25622,X25623)),X25621))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25623),X25620))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X25623),X25622)),X25620))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25622)) )
      & ( X25623 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk204_4(X25620,X25621,X25622,X25623)),esk203_4(X25620,X25621,X25622,X25623))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25623),X25620))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X25623),X25622)),X25620))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25622)) ) ),
    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_7098,plain,
    ! [X25640,X25641,X25642,X25643] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk211_4(X25640,X25641,X25642,X25643)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X25642)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25643),X25640))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X25643),X25642)),X25640))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25642)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk212_4(X25640,X25641,X25642,X25643)),X25641))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25643),X25640))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X25643),X25642)),X25640))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25642)) )
      & ( X25643 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk212_4(X25640,X25641,X25642,X25643)),esk211_4(X25640,X25641,X25642,X25643))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25643),X25640))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X25643),X25642)),X25640))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25642)) ) ),
    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_7099,plain,
    ! [X28970,X28971,X28972,X28973,X28974] :
      ( ( X28973 = hAPP(hAPP(c_List_Otake(X28974),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28974)),X28973)),X28971)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28974)),X28973)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28974)),X28971)))
        | hAPP(hAPP(c_List_Oappend(X28974),X28973),X28972) != hAPP(hAPP(c_List_Oappend(X28974),X28971),X28970) )
      & ( X28972 = hAPP(hAPP(c_List_Oappend(X28974),hAPP(hAPP(c_List_Odrop(X28974),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28974)),X28973)),X28971)),X28970)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28974)),X28973)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28974)),X28971)))
        | hAPP(hAPP(c_List_Oappend(X28974),X28973),X28972) != hAPP(hAPP(c_List_Oappend(X28974),X28971),X28970) )
      & ( hAPP(hAPP(c_List_Otake(X28974),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28974)),X28971)),X28973) = X28971
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28974)),X28973)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28974)),X28971)))
        | hAPP(hAPP(c_List_Oappend(X28974),X28973),X28972) != hAPP(hAPP(c_List_Oappend(X28974),X28971),X28970) )
      & ( hAPP(hAPP(c_List_Oappend(X28974),hAPP(hAPP(c_List_Odrop(X28974),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28974)),X28971)),X28973)),X28972) = X28970
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28974)),X28973)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28974)),X28971)))
        | hAPP(hAPP(c_List_Oappend(X28974),X28973),X28972) != hAPP(hAPP(c_List_Oappend(X28974),X28971),X28970) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28974)),X28973)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28974)),X28971)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28974)),X28973)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28974)),X28971)))
        | hAPP(hAPP(c_List_Oappend(X28974),X28973),X28972) = hAPP(hAPP(c_List_Oappend(X28974),X28971),X28970) )
      & ( hAPP(hAPP(c_List_Otake(X28974),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28974)),X28971)),X28973) != X28971
        | hAPP(hAPP(c_List_Oappend(X28974),hAPP(hAPP(c_List_Odrop(X28974),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28974)),X28971)),X28973)),X28972) != X28970
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28974)),X28973)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28974)),X28971)))
        | hAPP(hAPP(c_List_Oappend(X28974),X28973),X28972) = hAPP(hAPP(c_List_Oappend(X28974),X28971),X28970) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28974)),X28973)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28974)),X28971)))
        | X28973 != hAPP(hAPP(c_List_Otake(X28974),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28974)),X28973)),X28971)
        | X28972 != hAPP(hAPP(c_List_Oappend(X28974),hAPP(hAPP(c_List_Odrop(X28974),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28974)),X28973)),X28971)),X28970)
        | hAPP(hAPP(c_List_Oappend(X28974),X28973),X28972) = hAPP(hAPP(c_List_Oappend(X28974),X28971),X28970) )
      & ( hAPP(hAPP(c_List_Otake(X28974),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28974)),X28971)),X28973) != X28971
        | hAPP(hAPP(c_List_Oappend(X28974),hAPP(hAPP(c_List_Odrop(X28974),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28974)),X28971)),X28973)),X28972) != X28970
        | X28973 != hAPP(hAPP(c_List_Otake(X28974),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28974)),X28973)),X28971)
        | X28972 != hAPP(hAPP(c_List_Oappend(X28974),hAPP(hAPP(c_List_Odrop(X28974),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28974)),X28973)),X28971)),X28970)
        | hAPP(hAPP(c_List_Oappend(X28974),X28973),X28972) = hAPP(hAPP(c_List_Oappend(X28974),X28971),X28970) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5523])])]) ).

fof(i_0_7100,plain,
    ! [X24750,X24751,X24752,X24753,X24754] :
      ( ~ class_Groups_Ocomm__monoid__mult(X24754)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24753),X24752))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24753),X24751))
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24754),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24753,X24754),X24750),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24753,tc_HOL_Obool)),X24752),X24751))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24753,X24754),X24750),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24753,tc_HOL_Obool)),X24752),X24751))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24754),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24753,X24754),X24750),X24752)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24753,X24754),X24750),X24751)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__Un__Int])]) ).

fof(i_0_7101,plain,
    ! [X24745,X24746,X24747,X24748,X24749] :
      ( ~ class_Groups_Ocomm__monoid__mult(X24749)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24748),X24747))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24748),X24746))
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24749),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24748,X24749),X24745),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24748,tc_HOL_Obool)),X24747),X24746))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24748,X24749),X24745),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24748,tc_HOL_Obool)),X24747),X24746))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24749),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24748,X24749),X24745),X24747)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24748,X24749),X24745),X24746)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod_Ounion__inter])]) ).

fof(i_0_7102,plain,
    ! [X26328,X26329,X26330,X26331,X26332] :
      ( ~ class_Groups_Ocomm__monoid__add(X26332)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26331),X26330))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26331),X26329))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26332),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26331,X26332),X26328),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26331,tc_HOL_Obool)),X26330),X26329))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26331,X26332),X26328),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26331,tc_HOL_Obool)),X26330),X26329))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26332),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26331,X26332),X26328),X26330)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26331,X26332),X26328),X26329)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__Un__Int])]) ).

cnf(i_0_7103,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_5524]) ).

cnf(i_0_7104,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_5525]) ).

cnf(i_0_7105,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_5526]) ).

cnf(i_0_7106,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_5527]) ).

cnf(i_0_7107,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_5528]) ).

fof(i_0_7108,plain,
    ! [X24216,X24217,X24218,X24219,X24220,X24221] :
      ( ~ hBOOL(hAPP(hAPP(X24221,X24220),X24219))
      | ~ hBOOL(hAPP(hAPP(X24218,X24220),X24219))
      | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24217,tc_fun(X24216,tc_HOL_Obool))),X24221),X24218),X24220),X24219)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf2I])]) ).

fof(i_0_7109,plain,
    ! [X27199,X27200,X27201,X27202,X27203] :
      ( hAPP(c_Set_Oimage(X27203,X27202,X27201),c_Orderings_Otop__class_Otop(tc_fun(X27203,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X27202,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27203,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X27203,X27202,X27201),X27200)),X27199))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27202,tc_HOL_Obool)),X27200),hAPP(c_Set_Oimage(X27203,X27202,X27201),X27199))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vimage__subsetD])]) ).

fof(i_0_7110,plain,
    ! [X25603,X25604,X25605,X25606] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk197_4(X25603,X25604,X25605,X25606)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X25605)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25604),X25606))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25604),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X25606),X25605)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X25604),X25603))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25605)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk198_4(X25603,X25604,X25605,X25606)),X25603))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25604),X25606))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25604),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X25606),X25605)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X25604),X25603))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25605)) )
      & ( X25606 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk198_4(X25603,X25604,X25605,X25606)),esk197_4(X25603,X25604,X25605,X25606))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25604),X25606))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25604),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X25606),X25605)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X25604),X25603))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25605)) ) ),
    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_7111,plain,
    ! [X19048,X19049,X19050,X19051,X19052,X19053] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19053),X19052)),X19051) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19050),X19049)),X19048)
      | ~ 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),X19050),X19049)),X19048)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19048),X19050))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19051))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19050))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19050),X19053))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19052),X19049)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono2__lemma])]) ).

fof(i_0_7112,plain,
    ! [X32417,X32418,X32419,X32420,X32421] : hAPP(c_Relation_Oconverse(X32421,X32420),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X32419,tc_fun(tc_prod(X32421,X32420),tc_HOL_Obool)),X32418),X32417)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X32419,tc_fun(tc_prod(X32420,X32421),tc_HOL_Obool)),X32418),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X32421,X32420),tc_HOL_Obool),tc_fun(tc_prod(X32420,X32421),tc_HOL_Obool),X32419),c_Relation_Oconverse(X32421,X32420)),X32417)),
    inference(variable_rename,[status(thm)],[fact_converse__INTER]) ).

fof(i_0_7113,plain,
    ! [X32485,X32486,X32487,X32488,X32489] : hAPP(c_Relation_Oconverse(X32489,X32488),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X32487,tc_fun(tc_prod(X32489,X32488),tc_HOL_Obool)),X32486),X32485)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X32487,tc_fun(tc_prod(X32488,X32489),tc_HOL_Obool)),X32486),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X32489,X32488),tc_HOL_Obool),tc_fun(tc_prod(X32488,X32489),tc_HOL_Obool),X32487),c_Relation_Oconverse(X32489,X32488)),X32485)),
    inference(variable_rename,[status(thm)],[fact_converse__UNION]) ).

fof(i_0_7114,plain,
    ! [X23345] : X23345 = 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),esk110_1(X23345)),esk111_1(X23345))),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_7115,plain,
    ! [X23210,X23211,X23212,X23213,X23214,X23216,X23217,X23218,X23219,X23220,X23221] :
      ( ( hBOOL(hAPP(hAPP(c_member(X23212),esk108_4(X23210,X23211,X23212,X23213)),X23210))
        | ~ hBOOL(hAPP(hAPP(c_member(X23214),X23213),hAPP(c_Set_Oimage(X23212,X23214,X23211),X23210))) )
      & ( X23213 = hAPP(X23211,esk108_4(X23210,X23211,X23212,X23213))
        | ~ hBOOL(hAPP(hAPP(c_member(X23214),X23213),hAPP(c_Set_Oimage(X23212,X23214,X23211),X23210))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X23218),X23220),X23216))
        | X23219 != hAPP(X23217,X23220)
        | hBOOL(hAPP(hAPP(c_member(X23221),X23219),hAPP(c_Set_Oimage(X23218,X23221,X23217),X23216))) ) ),
    inference(distribute,[status(thm)],[inference(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_7116,plain,
    ! [X23705,X23706,X23707,X23708,X23709] :
      ( ( hAPP(hAPP(c_Equiv__Relations_Oquotient(X23709),hAPP(hAPP(c_Set_Oinsert(X23709),X23706),c_Orderings_Obot__class_Obot(tc_fun(X23709,tc_HOL_Obool)))),X23707) != hAPP(hAPP(c_Equiv__Relations_Oquotient(X23709),hAPP(hAPP(c_Set_Oinsert(X23709),X23705),c_Orderings_Obot__class_Obot(tc_fun(X23709,tc_HOL_Obool)))),X23707)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X23709,X23709)),hAPP(hAPP(c_Product__Type_OPair(X23709,X23709),X23706),X23705)),X23707))
        | ~ hBOOL(hAPP(hAPP(c_member(X23709),X23705),X23708))
        | ~ hBOOL(hAPP(hAPP(c_member(X23709),X23706),X23708))
        | ~ c_Equiv__Relations_Oequiv(X23709,X23708,X23707) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X23709,X23709)),hAPP(hAPP(c_Product__Type_OPair(X23709,X23709),X23706),X23705)),X23707))
        | hAPP(hAPP(c_Equiv__Relations_Oquotient(X23709),hAPP(hAPP(c_Set_Oinsert(X23709),X23706),c_Orderings_Obot__class_Obot(tc_fun(X23709,tc_HOL_Obool)))),X23707) = hAPP(hAPP(c_Equiv__Relations_Oquotient(X23709),hAPP(hAPP(c_Set_Oinsert(X23709),X23705),c_Orderings_Obot__class_Obot(tc_fun(X23709,tc_HOL_Obool)))),X23707)
        | ~ hBOOL(hAPP(hAPP(c_member(X23709),X23705),X23708))
        | ~ hBOOL(hAPP(hAPP(c_member(X23709),X23706),X23708))
        | ~ c_Equiv__Relations_Oequiv(X23709,X23708,X23707) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__equiv__class__iff2])])]) ).

fof(i_0_7117,plain,
    ! [X33990,X33991,X33992,X33993,X33994,X33995] :
      ( hAPP(c_Set_Oimage(X33995,X33994,X33993),X33992) != X33991
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X33994,tc_HOL_Obool)),X33990),X33991))
      | hAPP(c_Set_Oimage(X33995,X33994,X33993),hAPP(c_Set_Oimage(X33994,X33995,c_Hilbert__Choice_Oinv__into(X33995,X33994,X33992,X33993)),X33990)) = X33990 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__inv__into__cancel])]) ).

fof(i_0_7118,plain,
    ! [X33955,X33956,X33957] :
      ( ( ~ c_Fun_Oinj__on(X33957,X33956,X33955,c_Orderings_Otop__class_Otop(tc_fun(X33957,tc_HOL_Obool)))
        | hAPP(c_Fun_Ocomp(X33956,X33957,X33957,c_Hilbert__Choice_Oinv__into(X33957,X33956,c_Orderings_Otop__class_Otop(tc_fun(X33957,tc_HOL_Obool)),X33955)),X33955) = c_Fun_Oid(X33957) )
      & ( hAPP(c_Fun_Ocomp(X33956,X33957,X33957,c_Hilbert__Choice_Oinv__into(X33957,X33956,c_Orderings_Otop__class_Otop(tc_fun(X33957,tc_HOL_Obool)),X33955)),X33955) != c_Fun_Oid(X33957)
        | c_Fun_Oinj__on(X33957,X33956,X33955,c_Orderings_Otop__class_Otop(tc_fun(X33957,tc_HOL_Obool))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__iff])]) ).

cnf(i_0_7119,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_5529]) ).

fof(i_0_7120,plain,
    ! [X22243,X22244,X22245,X22246,X22247,X22248,X22249] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X22249,X22248,X22247),hAPP(c_Fun_Ocomp(X22246,tc_fun(X22248,X22247),X22249,X22245),X22244)),X22243) = hAPP(hAPP(X22245,hAPP(X22244,hAPP(c_Product__Type_Ofst(X22249,X22248),X22243))),hAPP(c_Product__Type_Osnd(X22249,X22248),X22243)),
    inference(variable_rename,[status(thm)],[fact_split__comp]) ).

fof(i_0_7121,plain,
    ! [X34139,X34140,X34141] :
      ( ~ c_Fun_Obij__betw(X34141,X34140,X34139,c_Orderings_Otop__class_Otop(tc_fun(X34141,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X34140,tc_HOL_Obool)))
      | c_Hilbert__Choice_Oinv__into(X34140,X34141,c_Orderings_Otop__class_Otop(tc_fun(X34140,tc_HOL_Obool)),c_Hilbert__Choice_Oinv__into(X34141,X34140,c_Orderings_Otop__class_Otop(tc_fun(X34141,tc_HOL_Obool)),X34139)) = X34139 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__inv__eq])]) ).

cnf(i_0_7122,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_5530]) ).

cnf(i_0_7123,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_5531]) ).

fof(i_0_7124,plain,
    ! [X23327,X23328] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X23328),X23327))
        | 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)),X23328)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X23327))) )
      & ( ~ 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)),X23328)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X23327)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X23328),X23327)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__relations_I5_J])]) ).

fof(i_0_7125,plain,
    ! [X23332,X23333] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X23333),X23332))
        | 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)),X23333)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X23332))) )
      & ( ~ 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)),X23333)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X23332)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X23333),X23332)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__relations_I4_J])]) ).

fof(i_0_7126,plain,
    ! [X25373,X25374,X25375] :
      ( ~ class_Orderings_Olinorder(X25375)
      | hAPP(X25374,hAPP(hAPP(c_Orderings_Oord__class_Omin(X25375),esk169_3(X25373,X25374,X25375)),esk170_3(X25373,X25374,X25375))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(X25375),hAPP(X25374,esk169_3(X25373,X25374,X25375))),hAPP(X25374,esk170_3(X25373,X25374,X25375)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25375),X25373))
      | X25373 = c_Orderings_Obot__class_Obot(tc_fun(X25375,tc_HOL_Obool))
      | hAPP(X25374,c_Big__Operators_Olattice_OInf__fin(X25375,c_Orderings_Oord__class_Omin(X25375),X25373)) = c_Big__Operators_Olattice_OInf__fin(X25375,c_Orderings_Oord__class_Omin(X25375),hAPP(c_Set_Oimage(X25375,X25375,X25374),X25373)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Ohom__commute])])]) ).

fof(i_0_7127,plain,
    ! [X25368,X25369,X25370] :
      ( ~ class_Orderings_Olinorder(X25370)
      | hAPP(X25369,hAPP(hAPP(c_Orderings_Oord__class_Omax(X25370),esk167_3(X25368,X25369,X25370)),esk168_3(X25368,X25369,X25370))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(X25370),hAPP(X25369,esk167_3(X25368,X25369,X25370))),hAPP(X25369,esk168_3(X25368,X25369,X25370)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25370),X25368))
      | X25368 = c_Orderings_Obot__class_Obot(tc_fun(X25370,tc_HOL_Obool))
      | hAPP(X25369,c_Big__Operators_Olattice_OSup__fin(X25370,c_Orderings_Oord__class_Omax(X25370),X25368)) = c_Big__Operators_Olattice_OSup__fin(X25370,c_Orderings_Oord__class_Omax(X25370),hAPP(c_Set_Oimage(X25370,X25370,X25369),X25368)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Ohom__commute])])]) ).

fof(i_0_7128,plain,
    ! [X30694,X30695,X30696,X30697,X30698,X30699] :
      ( ~ c_List_Olist__all2(X30699,X30698,X30697,X30696,X30695)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30694),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30699)),X30696)))
      | hBOOL(hAPP(hAPP(X30697,hAPP(hAPP(c_List_Onth(X30699),X30696),X30694)),hAPP(hAPP(c_List_Onth(X30698),X30695),X30694))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__nthD])]) ).

fof(i_0_7129,plain,
    ! [X30688,X30689,X30690,X30691,X30692,X30693] :
      ( ~ c_List_Olist__all2(X30693,X30692,X30691,X30690,X30689)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30688),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30692)),X30689)))
      | hBOOL(hAPP(hAPP(X30691,hAPP(hAPP(c_List_Onth(X30693),X30690),X30688)),hAPP(hAPP(c_List_Onth(X30692),X30689),X30688))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__nthD2])]) ).

fof(i_0_7130,plain,
    ! [X27224,X27225,X27226,X27227,X27228] :
      ( ~ c_Fun_Oinj__on(X27228,X27227,X27226,c_Orderings_Otop__class_Otop(tc_fun(X27228,tc_HOL_Obool)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27227,tc_HOL_Obool)),X27225),hAPP(c_Set_Oimage(X27228,X27227,X27226),X27224)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27228,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X27228,X27227,X27226),X27225)),X27224)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vimage__subsetI])]) ).

cnf(i_0_7131,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_5468]) ).

cnf(i_0_7132,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_5469]) ).

cnf(i_0_7133,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_5470]) ).

cnf(i_0_7134,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_5471]) ).

fof(i_0_7135,plain,
    ! [X21610,X21611,X21612,X21613] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21613),c_Groups_Ozero__class_Ozero(X21613)),hAPP(c_Int_Onumber__class_Onumber__of(X21613),X21610)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21613),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21613),X21612),hAPP(c_Int_Onumber__class_Onumber__of(X21613),X21610))),X21611))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21613),X21612),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21613),X21611),hAPP(c_Int_Onumber__class_Onumber__of(X21613),X21610))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21613)
        | ~ class_Int_Onumber(X21613) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21613),hAPP(c_Int_Onumber__class_Onumber__of(X21613),X21610)),c_Groups_Ozero__class_Ozero(X21613)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21613),X21611),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21613),X21612),hAPP(c_Int_Onumber__class_Onumber__of(X21613),X21610))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21613),c_Groups_Ozero__class_Ozero(X21613)),hAPP(c_Int_Onumber__class_Onumber__of(X21613),X21610)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21613),X21612),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21613),X21611),hAPP(c_Int_Onumber__class_Onumber__of(X21613),X21610))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21613)
        | ~ class_Int_Onumber(X21613) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21613),hAPP(c_Int_Onumber__class_Onumber__of(X21613),X21610)),c_Groups_Ozero__class_Ozero(X21613)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21613),X21612),c_Groups_Ozero__class_Ozero(X21613)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21613),c_Groups_Ozero__class_Ozero(X21613)),hAPP(c_Int_Onumber__class_Onumber__of(X21613),X21610)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21613),X21612),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21613),X21611),hAPP(c_Int_Onumber__class_Onumber__of(X21613),X21610))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21613)
        | ~ class_Int_Onumber(X21613) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21613),c_Groups_Ozero__class_Ozero(X21613)),hAPP(c_Int_Onumber__class_Onumber__of(X21613),X21610)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21613),c_Groups_Ozero__class_Ozero(X21613)),hAPP(c_Int_Onumber__class_Onumber__of(X21613),X21610)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21613),X21612),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21613),X21611),hAPP(c_Int_Onumber__class_Onumber__of(X21613),X21610))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21613)
        | ~ class_Int_Onumber(X21613) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21613),hAPP(c_Int_Onumber__class_Onumber__of(X21613),X21610)),c_Groups_Ozero__class_Ozero(X21613)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21613),hAPP(c_Int_Onumber__class_Onumber__of(X21613),X21610)),c_Groups_Ozero__class_Ozero(X21613)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21613),c_Groups_Ozero__class_Ozero(X21613)),hAPP(c_Int_Onumber__class_Onumber__of(X21613),X21610)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21613),X21612),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21613),X21611),hAPP(c_Int_Onumber__class_Onumber__of(X21613),X21610))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21613)
        | ~ class_Int_Onumber(X21613) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21613),X21612),c_Groups_Ozero__class_Ozero(X21613)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21613),hAPP(c_Int_Onumber__class_Onumber__of(X21613),X21610)),c_Groups_Ozero__class_Ozero(X21613)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21613),c_Groups_Ozero__class_Ozero(X21613)),hAPP(c_Int_Onumber__class_Onumber__of(X21613),X21610)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21613),X21612),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21613),X21611),hAPP(c_Int_Onumber__class_Onumber__of(X21613),X21610))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21613)
        | ~ class_Int_Onumber(X21613) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21613),hAPP(c_Int_Onumber__class_Onumber__of(X21613),X21610)),c_Groups_Ozero__class_Ozero(X21613)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21613),X21611),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21613),X21612),hAPP(c_Int_Onumber__class_Onumber__of(X21613),X21610))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21613),c_Groups_Ozero__class_Ozero(X21613)),hAPP(c_Int_Onumber__class_Onumber__of(X21613),X21610)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21613),X21612),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21613),X21611),hAPP(c_Int_Onumber__class_Onumber__of(X21613),X21610))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21613)
        | ~ class_Int_Onumber(X21613) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21613),X21612),c_Groups_Ozero__class_Ozero(X21613)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21613),X21611),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21613),X21612),hAPP(c_Int_Onumber__class_Onumber__of(X21613),X21610))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21613),c_Groups_Ozero__class_Ozero(X21613)),hAPP(c_Int_Onumber__class_Onumber__of(X21613),X21610)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21613),X21612),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21613),X21611),hAPP(c_Int_Onumber__class_Onumber__of(X21613),X21610))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21613)
        | ~ class_Int_Onumber(X21613) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21613),c_Groups_Ozero__class_Ozero(X21613)),hAPP(c_Int_Onumber__class_Onumber__of(X21613),X21610)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21613),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21613),X21612),hAPP(c_Int_Onumber__class_Onumber__of(X21613),X21610))),X21611))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21613),X21612),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21613),X21611),hAPP(c_Int_Onumber__class_Onumber__of(X21613),X21610))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21613)
        | ~ class_Int_Onumber(X21613) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21613),hAPP(c_Int_Onumber__class_Onumber__of(X21613),X21610)),c_Groups_Ozero__class_Ozero(X21613)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21613),hAPP(c_Int_Onumber__class_Onumber__of(X21613),X21610)),c_Groups_Ozero__class_Ozero(X21613)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21613),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21613),X21612),hAPP(c_Int_Onumber__class_Onumber__of(X21613),X21610))),X21611))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21613),X21612),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21613),X21611),hAPP(c_Int_Onumber__class_Onumber__of(X21613),X21610))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21613)
        | ~ class_Int_Onumber(X21613) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21613),X21612),c_Groups_Ozero__class_Ozero(X21613)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21613),hAPP(c_Int_Onumber__class_Onumber__of(X21613),X21610)),c_Groups_Ozero__class_Ozero(X21613)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21613),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21613),X21612),hAPP(c_Int_Onumber__class_Onumber__of(X21613),X21610))),X21611))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21613),X21612),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21613),X21611),hAPP(c_Int_Onumber__class_Onumber__of(X21613),X21610))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21613)
        | ~ class_Int_Onumber(X21613) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21613),hAPP(c_Int_Onumber__class_Onumber__of(X21613),X21610)),c_Groups_Ozero__class_Ozero(X21613)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21613),X21611),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21613),X21612),hAPP(c_Int_Onumber__class_Onumber__of(X21613),X21610))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21613),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21613),X21612),hAPP(c_Int_Onumber__class_Onumber__of(X21613),X21610))),X21611))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21613),X21612),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21613),X21611),hAPP(c_Int_Onumber__class_Onumber__of(X21613),X21610))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21613)
        | ~ class_Int_Onumber(X21613) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21613),X21612),c_Groups_Ozero__class_Ozero(X21613)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21613),X21611),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21613),X21612),hAPP(c_Int_Onumber__class_Onumber__of(X21613),X21610))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21613),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21613),X21612),hAPP(c_Int_Onumber__class_Onumber__of(X21613),X21610))),X21611))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21613),X21612),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21613),X21611),hAPP(c_Int_Onumber__class_Onumber__of(X21613),X21610))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21613)
        | ~ class_Int_Onumber(X21613) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5532])])]) ).

fof(i_0_7136,plain,
    ! [X21576,X21577,X21578,X21579] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21579),c_Groups_Ozero__class_Ozero(X21579)),hAPP(c_Int_Onumber__class_Onumber__of(X21579),X21576)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21579),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21579),X21578),hAPP(c_Int_Onumber__class_Onumber__of(X21579),X21576))),X21577))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21579),X21578),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21579),X21577),hAPP(c_Int_Onumber__class_Onumber__of(X21579),X21576))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21579)
        | ~ class_Int_Onumber(X21579) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21579),hAPP(c_Int_Onumber__class_Onumber__of(X21579),X21576)),c_Groups_Ozero__class_Ozero(X21579)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21579),X21577),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21579),X21578),hAPP(c_Int_Onumber__class_Onumber__of(X21579),X21576))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21579),c_Groups_Ozero__class_Ozero(X21579)),hAPP(c_Int_Onumber__class_Onumber__of(X21579),X21576)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21579),X21578),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21579),X21577),hAPP(c_Int_Onumber__class_Onumber__of(X21579),X21576))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21579)
        | ~ class_Int_Onumber(X21579) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21579),hAPP(c_Int_Onumber__class_Onumber__of(X21579),X21576)),c_Groups_Ozero__class_Ozero(X21579)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21579),X21578),c_Groups_Ozero__class_Ozero(X21579)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21579),c_Groups_Ozero__class_Ozero(X21579)),hAPP(c_Int_Onumber__class_Onumber__of(X21579),X21576)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21579),X21578),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21579),X21577),hAPP(c_Int_Onumber__class_Onumber__of(X21579),X21576))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21579)
        | ~ class_Int_Onumber(X21579) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21579),c_Groups_Ozero__class_Ozero(X21579)),hAPP(c_Int_Onumber__class_Onumber__of(X21579),X21576)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21579),c_Groups_Ozero__class_Ozero(X21579)),hAPP(c_Int_Onumber__class_Onumber__of(X21579),X21576)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21579),X21578),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21579),X21577),hAPP(c_Int_Onumber__class_Onumber__of(X21579),X21576))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21579)
        | ~ class_Int_Onumber(X21579) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21579),hAPP(c_Int_Onumber__class_Onumber__of(X21579),X21576)),c_Groups_Ozero__class_Ozero(X21579)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21579),hAPP(c_Int_Onumber__class_Onumber__of(X21579),X21576)),c_Groups_Ozero__class_Ozero(X21579)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21579),c_Groups_Ozero__class_Ozero(X21579)),hAPP(c_Int_Onumber__class_Onumber__of(X21579),X21576)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21579),X21578),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21579),X21577),hAPP(c_Int_Onumber__class_Onumber__of(X21579),X21576))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21579)
        | ~ class_Int_Onumber(X21579) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21579),X21578),c_Groups_Ozero__class_Ozero(X21579)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21579),hAPP(c_Int_Onumber__class_Onumber__of(X21579),X21576)),c_Groups_Ozero__class_Ozero(X21579)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21579),c_Groups_Ozero__class_Ozero(X21579)),hAPP(c_Int_Onumber__class_Onumber__of(X21579),X21576)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21579),X21578),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21579),X21577),hAPP(c_Int_Onumber__class_Onumber__of(X21579),X21576))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21579)
        | ~ class_Int_Onumber(X21579) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21579),hAPP(c_Int_Onumber__class_Onumber__of(X21579),X21576)),c_Groups_Ozero__class_Ozero(X21579)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21579),X21577),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21579),X21578),hAPP(c_Int_Onumber__class_Onumber__of(X21579),X21576))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21579),c_Groups_Ozero__class_Ozero(X21579)),hAPP(c_Int_Onumber__class_Onumber__of(X21579),X21576)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21579),X21578),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21579),X21577),hAPP(c_Int_Onumber__class_Onumber__of(X21579),X21576))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21579)
        | ~ class_Int_Onumber(X21579) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21579),X21578),c_Groups_Ozero__class_Ozero(X21579)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21579),X21577),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21579),X21578),hAPP(c_Int_Onumber__class_Onumber__of(X21579),X21576))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21579),c_Groups_Ozero__class_Ozero(X21579)),hAPP(c_Int_Onumber__class_Onumber__of(X21579),X21576)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21579),X21578),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21579),X21577),hAPP(c_Int_Onumber__class_Onumber__of(X21579),X21576))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21579)
        | ~ class_Int_Onumber(X21579) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21579),c_Groups_Ozero__class_Ozero(X21579)),hAPP(c_Int_Onumber__class_Onumber__of(X21579),X21576)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21579),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21579),X21578),hAPP(c_Int_Onumber__class_Onumber__of(X21579),X21576))),X21577))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21579),X21578),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21579),X21577),hAPP(c_Int_Onumber__class_Onumber__of(X21579),X21576))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21579)
        | ~ class_Int_Onumber(X21579) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21579),hAPP(c_Int_Onumber__class_Onumber__of(X21579),X21576)),c_Groups_Ozero__class_Ozero(X21579)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21579),hAPP(c_Int_Onumber__class_Onumber__of(X21579),X21576)),c_Groups_Ozero__class_Ozero(X21579)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21579),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21579),X21578),hAPP(c_Int_Onumber__class_Onumber__of(X21579),X21576))),X21577))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21579),X21578),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21579),X21577),hAPP(c_Int_Onumber__class_Onumber__of(X21579),X21576))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21579)
        | ~ class_Int_Onumber(X21579) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21579),X21578),c_Groups_Ozero__class_Ozero(X21579)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21579),hAPP(c_Int_Onumber__class_Onumber__of(X21579),X21576)),c_Groups_Ozero__class_Ozero(X21579)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21579),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21579),X21578),hAPP(c_Int_Onumber__class_Onumber__of(X21579),X21576))),X21577))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21579),X21578),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21579),X21577),hAPP(c_Int_Onumber__class_Onumber__of(X21579),X21576))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21579)
        | ~ class_Int_Onumber(X21579) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21579),hAPP(c_Int_Onumber__class_Onumber__of(X21579),X21576)),c_Groups_Ozero__class_Ozero(X21579)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21579),X21577),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21579),X21578),hAPP(c_Int_Onumber__class_Onumber__of(X21579),X21576))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21579),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21579),X21578),hAPP(c_Int_Onumber__class_Onumber__of(X21579),X21576))),X21577))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21579),X21578),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21579),X21577),hAPP(c_Int_Onumber__class_Onumber__of(X21579),X21576))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21579)
        | ~ class_Int_Onumber(X21579) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21579),X21578),c_Groups_Ozero__class_Ozero(X21579)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21579),X21577),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21579),X21578),hAPP(c_Int_Onumber__class_Onumber__of(X21579),X21576))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21579),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21579),X21578),hAPP(c_Int_Onumber__class_Onumber__of(X21579),X21576))),X21577))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21579),X21578),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21579),X21577),hAPP(c_Int_Onumber__class_Onumber__of(X21579),X21576))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21579)
        | ~ class_Int_Onumber(X21579) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5533])])]) ).

fof(i_0_7137,plain,
    ! [X32432,X32433,X32434,X32435,X32436] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32436,X32435)),hAPP(hAPP(c_Product__Type_OPair(X32436,X32435),X32434),X32433)),hAPP(c_Relation_Oconverse(X32435,X32436),X32432)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X32435,X32436)),hAPP(hAPP(c_Product__Type_OPair(X32435,X32436),X32433),X32434)),X32432)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32435,X32436)),hAPP(hAPP(c_Product__Type_OPair(X32435,X32436),X32433),X32434)),X32432))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X32436,X32435)),hAPP(hAPP(c_Product__Type_OPair(X32436,X32435),X32434),X32433)),hAPP(c_Relation_Oconverse(X32435,X32436),X32432))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_converse__iff])]) ).

fof(i_0_7138,plain,
    ! [X32422,X32423,X32424,X32425,X32426] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32426,X32425)),hAPP(hAPP(c_Product__Type_OPair(X32426,X32425),X32424),X32423)),hAPP(c_Relation_Oconverse(X32425,X32426),X32422)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X32425,X32426)),hAPP(hAPP(c_Product__Type_OPair(X32425,X32426),X32423),X32424)),X32422)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_converseD])]) ).

fof(i_0_7139,plain,
    ! [X23146,X23147,X23148,X23149,X23150,X23151] :
      ( ~ hBOOL(hAPP(hAPP(X23151,X23150),X23149))
      | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23148,tc_fun(X23147,tc_HOL_Obool))),X23151),X23146),X23150),X23149)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup2I1])]) ).

fof(i_0_7140,plain,
    ! [X23131,X23132,X23133,X23134,X23135,X23136] :
      ( ( ~ hBOOL(hAPP(hAPP(X23136,X23135),X23134))
        | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23132,tc_fun(X23131,tc_HOL_Obool))),X23133),X23136),X23135),X23134)) )
      & ( ~ hBOOL(hAPP(hAPP(X23133,X23135),X23134))
        | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23132,tc_fun(X23131,tc_HOL_Obool))),X23133),X23136),X23135),X23134)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5534])])]) ).

fof(i_0_7141,plain,
    ! [X23152,X23153,X23154,X23155,X23156,X23157] :
      ( ~ hBOOL(hAPP(hAPP(X23157,X23156),X23155))
      | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23154,tc_fun(X23153,tc_HOL_Obool))),X23152),X23157),X23156),X23155)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup2I2])]) ).

fof(i_0_7142,plain,
    ! [X23798,X23799,X23800,X23801,X23802] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23802,tc_HOL_Obool)),X23801),X23800))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23802,tc_HOL_Obool)),X23799),X23798))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23802,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23802,tc_HOL_Obool)),X23801),X23799)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23802,tc_HOL_Obool)),X23800),X23798))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__mono])]) ).

fof(i_0_7143,plain,
    ! [X22902,X22903,X22904,X22905,X22906] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22906,tc_HOL_Obool)),X22905),X22904))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22906,tc_HOL_Obool)),X22903),X22902))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22906,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22906,tc_HOL_Obool)),X22905),X22903)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22906,tc_HOL_Obool)),X22904),X22902))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Un__mono])]) ).

fof(i_0_7144,plain,
    ! [X20258,X20259,X20260,X20261,X20262] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20262,tc_HOL_Obool)),X20261),X20260))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20262,tc_HOL_Obool)),X20259),X20258))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20262,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20262,tc_HOL_Obool)),X20261),X20258)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20262,tc_HOL_Obool)),X20260),X20259))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Diff__mono])]) ).

fof(i_0_7145,plain,
    ! [X27098,X27099,X27100] :
      ( ~ class_Lattices_Oab__semigroup__idem__mult(X27100)
      | hAPP(X27099,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27100),esk269_3(X27098,X27099,X27100)),esk270_3(X27098,X27099,X27100))) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27100),hAPP(X27099,esk269_3(X27098,X27099,X27100))),hAPP(X27099,esk270_3(X27098,X27099,X27100)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27100),X27098))
      | X27098 = c_Orderings_Obot__class_Obot(tc_fun(X27100,tc_HOL_Obool))
      | hAPP(X27099,hAPP(c_Finite__Set_Ofold1(X27100,c_Groups_Otimes__class_Otimes(X27100)),X27098)) = hAPP(c_Finite__Set_Ofold1(X27100,c_Groups_Otimes__class_Otimes(X27100)),hAPP(c_Set_Oimage(X27100,X27100,X27099),X27098)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hom__fold1__commute])])]) ).

fof(i_0_7146,plain,
    ! [X26338,X26339,X26340,X26341,X26342] :
      ( ~ class_Groups_Ocomm__monoid__add(X26342)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26341),X26340))
      | ~ c_Fun_Oinj__on(X26341,X26341,X26339,X26340)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26341,X26342),X26338),hAPP(c_Set_Oimage(X26341,X26341,X26339),X26340)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26341,X26342),hAPP(c_Fun_Ocomp(X26341,X26342,X26341,X26338),X26339)),X26340) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum_Oreindex])]) ).

fof(i_0_7147,plain,
    ! [X25902,X25903,X25904,X25905,X25906] :
      ( ~ class_Groups_Ocomm__monoid__mult(X25906)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25905),X25904))
      | ~ c_Fun_Oinj__on(X25905,X25905,X25903,X25904)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25905,X25906),X25902),hAPP(c_Set_Oimage(X25905,X25905,X25903),X25904)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25905,X25906),hAPP(c_Fun_Ocomp(X25905,X25906,X25905,X25902),X25903)),X25904) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod_Oreindex])]) ).

fof(i_0_7148,plain,
    ! [X32640,X32641,X32642] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X32642,X32642)),hAPP(hAPP(c_Product__Type_OPair(X32642,X32642),esk462_3(X32640,X32641,X32642)),X32641)),X32640))
        | hBOOL(hAPP(hAPP(c_member(X32642),X32641),c_Wellfounded_Oacc(X32642,X32640))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X32642),esk462_3(X32640,X32641,X32642)),c_Wellfounded_Oacc(X32642,X32640)))
        | hBOOL(hAPP(hAPP(c_member(X32642),X32641),c_Wellfounded_Oacc(X32642,X32640))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc_OaccI])])])]) ).

fof(i_0_7149,plain,
    ! [X32636,X32637,X32638] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X32638,X32638)),hAPP(hAPP(c_Product__Type_OPair(X32638,X32638),esk461_3(X32636,X32637,X32638)),X32637)),X32636))
        | hBOOL(hAPP(hAPP(c_member(X32638),X32637),c_Wellfounded_Oacc(X32638,X32636))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X32638),esk461_3(X32636,X32637,X32638)),c_Wellfounded_Oacc(X32638,X32636)))
        | hBOOL(hAPP(hAPP(c_member(X32638),X32637),c_Wellfounded_Oacc(X32638,X32636))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5535])])])]) ).

fof(i_0_7150,plain,
    ! [X23481,X23482,X23483,X23484,X23485,X23486,X23487] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X23483),X23482),c_Wellfounded_Oacc(X23483,X23481)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X23483,X23483)),hAPP(hAPP(c_Product__Type_OPair(X23483,X23483),X23484),X23482)),X23481))
        | hBOOL(hAPP(hAPP(c_member(X23483),X23484),c_Wellfounded_Oacc(X23483,X23481))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X23487,X23487)),hAPP(hAPP(c_Product__Type_OPair(X23487,X23487),esk114_3(X23485,X23486,X23487)),X23486)),X23485))
        | hBOOL(hAPP(hAPP(c_member(X23487),X23486),c_Wellfounded_Oacc(X23487,X23485))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X23487),esk114_3(X23485,X23486,X23487)),c_Wellfounded_Oacc(X23487,X23485)))
        | hBOOL(hAPP(hAPP(c_member(X23487),X23486),c_Wellfounded_Oacc(X23487,X23485))) ) ),
    inference(distribute,[status(thm)],[inference(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_7151,plain,
    ! [X32251,X32252,X32253,X32254] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32254),tc_List_Olist(X32254))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32254),tc_List_Olist(X32254)),X32253),X32252)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X32254),c_List_Olistrel1(X32254,X32251))))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32254)),X32253) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32254)),X32252) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__listrel1__eq__len])]) ).

cnf(i_0_7152,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk410_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),esk408_2(X2,X1)))
    | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5492]) ).

cnf(i_0_7153,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk409_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),esk408_2(X2,X1)))
    | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5492]) ).

fof(i_0_7154,plain,
    ! [X29147,X29148,X29149,X29150,X29151] : hAPP(hAPP(c_List_Olist__update(X29151,hAPP(hAPP(c_List_Olist_OCons(X29151),X29150),X29149)),X29148),X29147) = c_Nat_Onat_Onat__case(tc_List_Olist(X29151),hAPP(hAPP(c_List_Olist_OCons(X29151),X29147),X29149),hAPP(hAPP(c_COMBB(tc_List_Olist(X29151),tc_List_Olist(X29151),tc_Nat_Onat),hAPP(c_List_Olist_OCons(X29151),X29150)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,X29151,tc_List_Olist(X29151)),c_List_Olist__update(X29151,X29149)),X29147)),X29148),
    inference(variable_rename,[status(thm)],[fact_list__update_Osimps_I2_J]) ).

fof(i_0_7155,plain,
    ! [X21997,X21998,X21999,X22000] : hAPP(c_Product__Type_Oprod_Oprod__case(X22000,X21999,X21998),hAPP(hAPP(c_COMBB(tc_fun(X21999,tc_prod(X22000,X21999)),tc_fun(X21999,X21998),X22000),hAPP(c_COMBB(tc_prod(X22000,X21999),X21998,X21999),X21997)),c_Product__Type_OPair(X22000,X21999))) = X21997,
    inference(variable_rename,[status(thm)],[fact_split__eta]) ).

fof(i_0_7156,plain,
    ! [X25626,X25627,X25628,X25629] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk205_4(X25626,X25627,X25628,X25629)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X25628)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25626),X25629))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25626),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25629),X25628)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25628)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk206_4(X25626,X25627,X25628,X25629)),X25627))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25626),X25629))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25626),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25629),X25628)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25628)) )
      & ( X25629 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk206_4(X25626,X25627,X25628,X25629)),esk205_4(X25626,X25627,X25628,X25629))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25626),X25629))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X25626),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25629),X25628)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25628)) ) ),
    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_7157,plain,
    ! [X25646,X25647,X25648,X25649] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk213_4(X25646,X25647,X25648,X25649)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X25648)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25646),X25649))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25646),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25649),X25648)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25648)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk214_4(X25646,X25647,X25648,X25649)),X25647))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25646),X25649))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25646),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25649),X25648)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25648)) )
      & ( X25649 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk214_4(X25646,X25647,X25648,X25649)),esk213_4(X25646,X25647,X25648,X25649))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25646),X25649))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25646),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25649),X25648)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25648)) ) ),
    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_7158,plain,
    ! [X27087,X27088,X27089] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27089,tc_HOL_Obool)),X27088),hAPP(hAPP(c_Set_Oinsert(X27089),X27087),c_Orderings_Obot__class_Obot(tc_fun(X27089,tc_HOL_Obool)))))
        | c_Partial__Function_Oflat__lub(X27089,X27087,X27088) = X27087 )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27089,tc_HOL_Obool)),X27088),hAPP(hAPP(c_Set_Oinsert(X27089),X27087),c_Orderings_Obot__class_Obot(tc_fun(X27089,tc_HOL_Obool)))))
        | c_Partial__Function_Oflat__lub(X27089,X27087,X27088) = c_HOL_OThe(X27089,hAPP(hAPP(c_COMBC(X27089,tc_fun(X27089,tc_HOL_Obool),tc_HOL_Obool),c_member(X27089)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27089,tc_HOL_Obool)),X27088),hAPP(hAPP(c_Set_Oinsert(X27089),X27087),c_Orderings_Obot__class_Obot(tc_fun(X27089,tc_HOL_Obool)))))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5536])]) ).

fof(i_0_7159,plain,
    ! [X30422,X30423,X30424,X30425] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk362_4(X30422,X30423,X30424,X30425)),X30425))
        | hAPP(hAPP(c_List_Otake(X30424),X30425),X30423) = hAPP(hAPP(c_List_Otake(X30424),X30425),X30422)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X30425),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30424)),X30422)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X30425),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30424)),X30423))) )
      & ( hAPP(hAPP(c_List_Onth(X30424),X30423),esk362_4(X30422,X30423,X30424,X30425)) != hAPP(hAPP(c_List_Onth(X30424),X30422),esk362_4(X30422,X30423,X30424,X30425))
        | hAPP(hAPP(c_List_Otake(X30424),X30425),X30423) = hAPP(hAPP(c_List_Otake(X30424),X30425),X30422)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X30425),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30424)),X30422)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X30425),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30424)),X30423))) ) ),
    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_7160,plain,
    ! [X21931,X21932,X21933,X21934] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X21934,X21934)),hAPP(hAPP(c_Product__Type_OPair(X21934,X21934),X21933),X21932)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X21934,X21934),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X21931)))
      | X21933 = X21932 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__pow__0__E])]) ).

fof(i_0_7161,plain,
    ! [X22324,X22325,X22326,X22327,X22328] :
      ( ~ hBOOL(hAPP(hAPP(X22328,X22327),X22326))
      | hBOOL(hAPP(hAPP(X22328,hAPP(c_Product__Type_Osnd(X22325,X22324),hAPP(hAPP(c_Product__Type_OPair(X22325,X22324),X22326),X22327))),hAPP(c_Product__Type_Ofst(X22325,X22324),hAPP(hAPP(c_Product__Type_OPair(X22325,X22324),X22326),X22327)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_exI__realizer])]) ).

fof(i_0_7162,plain,
    ! [X25747,X25748,X25749,X25750,X25751,X25752] :
      ( ( ~ c_Fun_Oinj__on(X25751,X25748,X25747,hAPP(c_Set_Oimage(X25752,X25751,X25750),X25749))
        | c_Fun_Oinj__on(X25752,X25748,hAPP(c_Fun_Ocomp(X25751,X25748,X25752,X25747),X25750),X25749)
        | ~ c_Fun_Oinj__on(X25752,X25751,X25750,X25749) )
      & ( ~ c_Fun_Oinj__on(X25752,X25748,hAPP(c_Fun_Ocomp(X25751,X25748,X25752,X25747),X25750),X25749)
        | c_Fun_Oinj__on(X25751,X25748,X25747,hAPP(c_Set_Oimage(X25752,X25751,X25750),X25749))
        | ~ c_Fun_Oinj__on(X25752,X25751,X25750,X25749) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comp__inj__on__iff])])]) ).

fof(i_0_7163,plain,
    ! [X26724,X26725,X26726,X26727,X26728] :
      ( hAPP(c_Set_Oimage(X26728,X26727,X26726),c_Orderings_Otop__class_Otop(tc_fun(X26728,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X26727,tc_HOL_Obool))
      | hAPP(c_Set_Oimage(X26727,X26725,X26724),c_Orderings_Otop__class_Otop(tc_fun(X26727,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X26725,tc_HOL_Obool))
      | hAPP(c_Set_Oimage(X26728,X26725,hAPP(c_Fun_Ocomp(X26727,X26725,X26728,X26724),X26726)),c_Orderings_Otop__class_Otop(tc_fun(X26728,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X26725,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comp__surj])]) ).

fof(i_0_7164,plain,
    ! [X19717,X19718,X19719] : 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),X19719),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19718),X19719))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19718,X19719))),X19717) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19718),X19717),
    inference(variable_rename,[status(thm)],[fact_zdiv__zmod__equality]) ).

fof(i_0_7165,plain,
    ! [X26275,X26276,X26277,X26278,X26279,X26280] :
      ( ~ class_Groups_Ocomm__monoid__add(X26280)
      | ~ c_Fun_Oinj__on(X26279,X26278,X26277,X26276)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26278,X26280),X26275),hAPP(c_Set_Oimage(X26279,X26278,X26277),X26276)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26279,X26280),hAPP(c_Fun_Ocomp(X26278,X26280,X26279,X26275),X26277)),X26276) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__reindex])]) ).

fof(i_0_7166,plain,
    ! [X25865,X25866,X25867,X25868,X25869,X25870] :
      ( ~ class_Groups_Ocomm__monoid__mult(X25870)
      | ~ c_Fun_Oinj__on(X25869,X25868,X25867,X25866)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25868,X25870),X25865),hAPP(c_Set_Oimage(X25869,X25868,X25867),X25866)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25869,X25870),hAPP(c_Fun_Ocomp(X25868,X25870,X25869,X25865),X25867)),X25866) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__reindex])]) ).

fof(i_0_7167,plain,
    ! [X24449,X24450,X24451] :
      ( ~ class_Orderings_Olinorder(X24451)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24451),X24450))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24451),X24449))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24451,tc_HOL_Obool)),X24450),X24449) = c_Orderings_Obot__class_Obot(tc_fun(X24451,tc_HOL_Obool))
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X24451),c_Big__Operators_Olattice_OSup__fin(X24451,c_Orderings_Oord__class_Omax(X24451),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24451,tc_HOL_Obool)),X24450),X24449))),c_Big__Operators_Olattice_OSup__fin(X24451,c_Orderings_Oord__class_Omax(X24451),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24451,tc_HOL_Obool)),X24450),X24449))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X24451),c_Big__Operators_Olattice_OSup__fin(X24451,c_Orderings_Oord__class_Omax(X24451),X24450)),c_Big__Operators_Olattice_OSup__fin(X24451,c_Orderings_Oord__class_Omax(X24451),X24449)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Ounion__inter])]) ).

fof(i_0_7168,plain,
    ! [X24505,X24506,X24507] :
      ( ~ class_Orderings_Olinorder(X24507)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24507),X24506))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24507),X24505))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24507,tc_HOL_Obool)),X24506),X24505) = c_Orderings_Obot__class_Obot(tc_fun(X24507,tc_HOL_Obool))
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X24507),c_Big__Operators_Olattice_OInf__fin(X24507,c_Orderings_Oord__class_Omin(X24507),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24507,tc_HOL_Obool)),X24506),X24505))),c_Big__Operators_Olattice_OInf__fin(X24507,c_Orderings_Oord__class_Omin(X24507),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24507,tc_HOL_Obool)),X24506),X24505))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X24507),c_Big__Operators_Olattice_OInf__fin(X24507,c_Orderings_Oord__class_Omin(X24507),X24506)),c_Big__Operators_Olattice_OInf__fin(X24507,c_Orderings_Oord__class_Omin(X24507),X24505)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Ounion__inter])]) ).

fof(i_0_7169,plain,
    ! [X28338,X28339,X28340,X28341,X28342] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28342)),X28341) = X28338
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28342),tc_List_Olist(X28342))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28342),tc_List_Olist(X28342)),X28341),X28340)),hAPP(c_List_Olexn(X28342,X28339),X28338))) )
      & ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28342)),X28340) = X28338
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28342),tc_List_Olist(X28342))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28342),tc_List_Olist(X28342)),X28341),X28340)),hAPP(c_List_Olexn(X28342,X28339),X28338))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexn__length])])]) ).

fof(i_0_7170,plain,
    ! [X32427,X32428,X32429,X32430,X32431] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32431,X32430)),hAPP(hAPP(c_Product__Type_OPair(X32431,X32430),X32429),X32428)),X32427))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X32430,X32431)),hAPP(hAPP(c_Product__Type_OPair(X32430,X32431),X32428),X32429)),hAPP(c_Relation_Oconverse(X32431,X32430),X32427))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_converseI])]) ).

fof(i_0_7171,plain,
    ! [X17951,X17952,X17953,X17954,X17956,X17957,X17958,X17959,X17960] :
      ( ( hBOOL(hAPP(X17954,X17952))
        | X17951 = X17952
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X17954,X17953)),X17952),X17951)) )
      & ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17953),X17952),esk35_4(X17951,X17952,X17953,X17954)))
        | X17951 = X17952
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X17954,X17953)),X17952),X17951)) )
      & ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X17954,X17953)),esk35_4(X17951,X17952,X17953,X17954)),X17951))
        | X17951 = X17952
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X17954,X17953)),X17952),X17951)) )
      & ( hBOOL(hAPP(X17954,X17952))
        | ~ hBOOL(hAPP(X17954,X17952))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X17954,X17953)),X17952),X17951)) )
      & ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17953),X17952),esk35_4(X17951,X17952,X17953,X17954)))
        | ~ hBOOL(hAPP(X17954,X17952))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X17954,X17953)),X17952),X17951)) )
      & ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X17954,X17953)),esk35_4(X17951,X17952,X17953,X17954)),X17951))
        | ~ hBOOL(hAPP(X17954,X17952))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X17954,X17953)),X17952),X17951)) )
      & ( X17956 != X17957
        | hBOOL(hAPP(X17959,X17957))
        | hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X17959,X17958)),X17957),X17956)) )
      & ( ~ hBOOL(hAPP(X17959,X17957))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17958),X17957),X17960))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X17959,X17958)),X17960),X17956))
        | hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X17959,X17958)),X17957),X17956)) ) ),
    inference(distribute,[status(thm)],[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_5537])])])])])]) ).

fof(i_0_7172,plain,
    ! [X28043,X28044,X28045,X28046,X28047,X28048] : hAPP(hAPP(c_Relation_Orel__comp(X28048,X28047,X28046),X28045),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28047,X28046),tc_HOL_Obool)),X28044),X28043)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28048,X28046),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X28048,X28047,X28046),X28045),X28044)),hAPP(hAPP(c_Relation_Orel__comp(X28048,X28047,X28046),X28045),X28043)),
    inference(variable_rename,[status(thm)],[fact_rel__comp__distrib]) ).

cnf(i_0_7173,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_5538]) ).

fof(i_0_7174,plain,
    ! [X22198,X22199,X22200,X22201] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X22201,tc_fun(X22200,tc_HOL_Obool))),X22199),X22198))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X22201,X22200)),hAPP(hAPP(c_Product__Type_OPair(X22201,X22200),X22199),X22198)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X22201,X22200),tc_HOL_Obool)))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X22201,X22200)),hAPP(hAPP(c_Product__Type_OPair(X22201,X22200),X22199),X22198)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X22201,X22200),tc_HOL_Obool))))
        | hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X22201,tc_fun(X22200,tc_HOL_Obool))),X22199),X22198)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bot__empty__eq2])]) ).

fof(i_0_7175,plain,
    ! [X31713,X31714] :
      ( ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X31714),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X31714))),X31713)))
      | c_List_Otranspose(X31714,c_List_Otranspose(X31714,X31713)) = c_List_OtakeWhile(tc_List_Olist(X31714),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X31714)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X31714),tc_List_Olist(X31714),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X31714))),X31713) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transpose__transpose])]) ).

fof(i_0_7176,plain,
    ! [X25383,X25384,X25385] :
      ( ~ class_Orderings_Olinorder(X25385)
      | hAPP(X25384,hAPP(hAPP(c_Orderings_Oord__class_Omin(X25385),esk173_3(X25383,X25384,X25385)),esk174_3(X25383,X25384,X25385))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(X25385),hAPP(X25384,esk173_3(X25383,X25384,X25385))),hAPP(X25384,esk174_3(X25383,X25384,X25385)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25385),X25383))
      | X25383 = c_Orderings_Obot__class_Obot(tc_fun(X25385,tc_HOL_Obool))
      | hAPP(X25384,c_Big__Operators_Olinorder__class_OMin(X25385,X25383)) = c_Big__Operators_Olinorder__class_OMin(X25385,hAPP(c_Set_Oimage(X25385,X25385,X25384),X25383)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Ohom__commute])])]) ).

fof(i_0_7177,plain,
    ! [X25378,X25379,X25380] :
      ( ~ class_Orderings_Olinorder(X25380)
      | hAPP(X25379,hAPP(hAPP(c_Orderings_Oord__class_Omax(X25380),esk171_3(X25378,X25379,X25380)),esk172_3(X25378,X25379,X25380))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(X25380),hAPP(X25379,esk171_3(X25378,X25379,X25380))),hAPP(X25379,esk172_3(X25378,X25379,X25380)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25380),X25378))
      | X25378 = c_Orderings_Obot__class_Obot(tc_fun(X25380,tc_HOL_Obool))
      | hAPP(X25379,c_Big__Operators_Olinorder__class_OMax(X25380,X25378)) = c_Big__Operators_Olinorder__class_OMax(X25380,hAPP(c_Set_Oimage(X25380,X25380,X25379),X25378)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Ohom__commute])])]) ).

fof(i_0_7178,plain,
    ! [X25393,X25394,X25395] :
      ( ~ class_Lattices_Olattice(X25395)
      | hAPP(X25394,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X25395),esk177_3(X25393,X25394,X25395)),esk178_3(X25393,X25394,X25395))) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X25395),hAPP(X25394,esk177_3(X25393,X25394,X25395))),hAPP(X25394,esk178_3(X25393,X25394,X25395)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25395),X25393))
      | X25393 = c_Orderings_Obot__class_Obot(tc_fun(X25395,tc_HOL_Obool))
      | hAPP(X25394,c_Big__Operators_Olattice__class_OSup__fin(X25395,X25393)) = c_Big__Operators_Olattice__class_OSup__fin(X25395,hAPP(c_Set_Oimage(X25395,X25395,X25394),X25393)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Ohom__commute])])]) ).

fof(i_0_7179,plain,
    ! [X25388,X25389,X25390] :
      ( ~ class_Lattices_Olattice(X25390)
      | hAPP(X25389,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25390),esk175_3(X25388,X25389,X25390)),esk176_3(X25388,X25389,X25390))) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25390),hAPP(X25389,esk175_3(X25388,X25389,X25390))),hAPP(X25389,esk176_3(X25388,X25389,X25390)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25390),X25388))
      | X25388 = c_Orderings_Obot__class_Obot(tc_fun(X25390,tc_HOL_Obool))
      | hAPP(X25389,c_Big__Operators_Olattice__class_OInf__fin(X25390,X25388)) = c_Big__Operators_Olattice__class_OInf__fin(X25390,hAPP(c_Set_Oimage(X25390,X25390,X25389),X25388)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Ohom__commute])])]) ).

fof(i_0_7180,plain,
    ! [X25632,X25633,X25636,X25638] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk209_2(X25632,X25633)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X25633)))
        | ~ hBOOL(hAPP(X25632,X25636))
        | ~ hBOOL(hAPP(X25632,esk207_2(X25632,X25633)))
        | ~ hBOOL(hAPP(X25632,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk207_2(X25632,X25633)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk208_2(X25632,X25633)),X25633))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25633)) )
      & ( hBOOL(hAPP(X25632,esk209_2(X25632,X25633)))
        | ~ hBOOL(hAPP(X25632,X25636))
        | ~ hBOOL(hAPP(X25632,esk207_2(X25632,X25633)))
        | ~ hBOOL(hAPP(X25632,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk207_2(X25632,X25633)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk208_2(X25632,X25633)),X25633))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25633)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X25638),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X25633)))
        | ~ hBOOL(hAPP(X25632,X25638))
        | hBOOL(hAPP(X25632,esk210_2(X25632,X25633)))
        | ~ hBOOL(hAPP(X25632,esk207_2(X25632,X25633)))
        | ~ hBOOL(hAPP(X25632,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk207_2(X25632,X25633)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk208_2(X25632,X25633)),X25633))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25633)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk209_2(X25632,X25633)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X25633)))
        | ~ hBOOL(hAPP(X25632,X25636))
        | hBOOL(hAPP(X25632,esk207_2(X25632,X25633)))
        | hBOOL(hAPP(X25632,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk207_2(X25632,X25633)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk208_2(X25632,X25633)),X25633))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25633)) )
      & ( hBOOL(hAPP(X25632,esk209_2(X25632,X25633)))
        | ~ hBOOL(hAPP(X25632,X25636))
        | hBOOL(hAPP(X25632,esk207_2(X25632,X25633)))
        | hBOOL(hAPP(X25632,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk207_2(X25632,X25633)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk208_2(X25632,X25633)),X25633))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25633)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X25638),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X25633)))
        | ~ hBOOL(hAPP(X25632,X25638))
        | hBOOL(hAPP(X25632,esk210_2(X25632,X25633)))
        | hBOOL(hAPP(X25632,esk207_2(X25632,X25633)))
        | hBOOL(hAPP(X25632,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk207_2(X25632,X25633)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk208_2(X25632,X25633)),X25633))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25633)) ) ),
    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_7181,plain,
    ! [X28574,X28575,X28576] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28576),tc_List_Olist(X28576))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28576),tc_List_Olist(X28576)),c_List_Olist_ONil(X28576)),X28575)),c_List_Olistrel(X28576,X28574)))
      | X28575 = c_List_Olist_ONil(X28576) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__Nil1])]) ).

cnf(i_0_7182,plain,
    ( hBOOL(hAPP(c_List_Odistinct(X2),c_List_Oconcat(X2,X1)))
    | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2)),esk408_2(X1,X2)),hAPP(c_List_Oset(tc_List_Olist(X2)),X1)))
    | esk409_2(X1,X2) != esk410_2(X1,X2)
    | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X2)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_5492]) ).

fof(i_0_7183,plain,
    ! [X26992,X26993] : c_Set_Othe__elem(X26993,X26992) = c_HOL_OThe(X26993,hAPP(hAPP(c_COMBB(tc_fun(X26993,tc_HOL_Obool),tc_HOL_Obool,X26993),hAPP(c_fequal,X26992)),hAPP(hAPP(c_COMBC(X26993,tc_fun(X26993,tc_HOL_Obool),tc_fun(X26993,tc_HOL_Obool)),c_Set_Oinsert(X26993)),c_Orderings_Obot__class_Obot(tc_fun(X26993,tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[fact_the__elem__def]) ).

cnf(i_0_7184,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk444_2(X2,X1)),esk444_2(X2,X1))),c_Transitive__Closure_Otrancl(X1,X2)))
    | c_Wellfounded_Oacyclic(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5539]) ).

cnf(i_0_7185,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk442_2(X2,X1)),esk442_2(X2,X1))),c_Transitive__Closure_Otrancl(X1,X2)))
    | c_Wellfounded_Oacyclic(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5495]) ).

fof(i_0_7186,plain,
    ! [X28527,X28528,X28529] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28529),tc_List_Olist(X28529))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28529),tc_List_Olist(X28529)),c_List_Olist_ONil(X28529)),X28528)),c_List_Olistrel1(X28529,X28527))),
    inference(variable_rename,[status(thm)],[i_0_5540]) ).

fof(i_0_7187,plain,
    ! [X28487,X28488,X28489] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28489),tc_List_Olist(X28489))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28489),tc_List_Olist(X28489)),c_List_Olist_ONil(X28489)),X28488)),c_List_Olex(X28489,X28487))),
    inference(variable_rename,[status(thm)],[i_0_5541]) ).

fof(i_0_7188,plain,
    ! [X23436,X23437] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X23437),X23436))
        | 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),X23437)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X23436)))
        | ~ c_Nat__Transfer_Onat__set(X23436)
        | ~ c_Nat__Transfer_Onat__set(X23437) )
      & ( ~ 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),X23437)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X23436)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X23437),X23436))
        | ~ c_Nat__Transfer_Onat__set(X23436)
        | ~ c_Nat__Transfer_Onat__set(X23437) ) ),
    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_7189,plain,
    ! [X23434,X23435] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X23435),X23434))
        | 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),X23435)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X23434)))
        | ~ c_Nat__Transfer_Onat__set(X23434)
        | ~ c_Nat__Transfer_Onat__set(X23435) )
      & ( ~ 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),X23435)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X23434)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X23435),X23434))
        | ~ c_Nat__Transfer_Onat__set(X23434)
        | ~ c_Nat__Transfer_Onat__set(X23435) ) ),
    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_7190,plain,
    ! [X28066,X28067,X28068,X28069] :
      ( hAPP(hAPP(c_Relation_Orel__comp(X28069,X28069,X28069),X28068),X28067) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X28069,X28069),tc_HOL_Obool))
      | hAPP(hAPP(c_Relation_Orel__comp(X28069,X28069,X28069),X28066),X28067) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X28069,X28069),tc_HOL_Obool))
      | hAPP(hAPP(c_Relation_Orel__comp(X28069,X28069,X28069),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28069,X28069),tc_HOL_Obool)),X28068),X28066)),X28067) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X28069,X28069),tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_union__comp__emptyL])]) ).

fof(i_0_7191,plain,
    ! [X23338] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23338) = 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),X23338),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_7192,plain,
    ! [X24008,X24009,X24010,X24011] :
      ( ~ class_Lattices_Olattice(X24011)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24011),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24011),X24010),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24011),X24009),X24008))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24011),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24011),X24010),X24009)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24011),X24010),X24008)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distrib__sup__le])]) ).

fof(i_0_7193,plain,
    ! [X22700,X22701,X22702,X22703] :
      ( ~ class_Orderings_Olinorder(X22703)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22703),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22703),X22702),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22703),X22701),X22700))),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22703),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22703),X22702),X22701)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22703),X22702),X22700)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Odistrib__sup__le])]) ).

fof(i_0_7194,plain,
    ! [X32874,X32875,X32876,X32877] :
      ( ~ class_Lattices_Osemilattice__inf(X32877)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32877),X32876))
      | ~ hBOOL(hAPP(hAPP(c_member(X32877),X32875),X32876))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X32877),hAPP(hAPP(c_Finite__Set_Ofold(X32877,X32877,c_Lattices_Osemilattice__inf__class_Oinf(X32877)),X32874),X32876)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X32877),X32875),X32874))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__inf__le__inf])]) ).

fof(i_0_7195,plain,
    ! [X32878,X32879,X32880,X32881] :
      ( ~ class_Orderings_Olinorder(X32881)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32881),X32880))
      | ~ hBOOL(hAPP(hAPP(c_member(X32881),X32879),X32880))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X32881),hAPP(hAPP(c_Finite__Set_Ofold(X32881,X32881,c_Orderings_Oord__class_Omin(X32881)),X32878),X32880)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X32881),X32879),X32878))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ofold__inf__le__inf])]) ).

fof(i_0_7196,plain,
    ! [X29109,X29110,X29111,X29112,X29113] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29113,tc_HOL_Obool)),hAPP(c_List_Oset(X29113),X29112)),X29111))
      | ~ hBOOL(hAPP(hAPP(c_member(X29113),X29110),X29111))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29113,tc_HOL_Obool)),hAPP(c_List_Oset(X29113),hAPP(hAPP(c_List_Olist__update(X29113,X29112),X29109),X29110))),X29111)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__update__subsetI])]) ).

fof(i_0_7197,plain,
    ! [X26416,X26417,X26418,X26419,X26420] :
      ( ~ class_Groups_Ocomm__monoid__add(X26420)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X26419),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26418),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26420),X26417),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X26419,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26418),X26416))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26420),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26420),X26417),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X26419,X26418))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26420),X26417),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26418),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26418),X26416)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__ub__add__nat])]) ).

fof(i_0_7198,plain,
    ! [X33785,X33786] :
      ( ~ c_Relation_Otrans(X33786,X33785)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X33786,X33786),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X33786,X33786,X33786),X33785),X33785)),X33785)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__O__subset])]) ).

fof(i_0_7199,plain,
    ! [X27326,X27327,X27328,X27329,X27330] : hAPP(hAPP(c_Product__Type_OSigma(X27330,X27329),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27330,tc_HOL_Obool)),X27328),X27327)),hAPP(c_COMBK(tc_fun(X27329,tc_HOL_Obool),X27330),X27326)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X27330,X27329),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X27330,X27329),X27328),hAPP(c_COMBK(tc_fun(X27329,tc_HOL_Obool),X27330),X27326))),hAPP(hAPP(c_Product__Type_OSigma(X27330,X27329),X27327),hAPP(c_COMBK(tc_fun(X27329,tc_HOL_Obool),X27330),X27326))),
    inference(variable_rename,[status(thm)],[fact_Times__Int__distrib1]) ).

fof(i_0_7200,plain,
    ! [X27300,X27301,X27302,X27303,X27304] : hAPP(hAPP(c_Product__Type_OSigma(X27304,X27303),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27304,tc_HOL_Obool)),X27302),X27301)),hAPP(c_COMBK(tc_fun(X27303,tc_HOL_Obool),X27304),X27300)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X27304,X27303),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X27304,X27303),X27302),hAPP(c_COMBK(tc_fun(X27303,tc_HOL_Obool),X27304),X27300))),hAPP(hAPP(c_Product__Type_OSigma(X27304,X27303),X27301),hAPP(c_COMBK(tc_fun(X27303,tc_HOL_Obool),X27304),X27300))),
    inference(variable_rename,[status(thm)],[fact_Times__Un__distrib1]) ).

fof(i_0_7201,plain,
    ! [X27343,X27344,X27345,X27346,X27347] : hAPP(hAPP(c_Product__Type_OSigma(X27347,X27346),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27347,tc_HOL_Obool)),X27345),X27344)),hAPP(c_COMBK(tc_fun(X27346,tc_HOL_Obool),X27347),X27343)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X27347,X27346),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X27347,X27346),X27345),hAPP(c_COMBK(tc_fun(X27346,tc_HOL_Obool),X27347),X27343))),hAPP(hAPP(c_Product__Type_OSigma(X27347,X27346),X27344),hAPP(c_COMBK(tc_fun(X27346,tc_HOL_Obool),X27347),X27343))),
    inference(variable_rename,[status(thm)],[fact_Times__Diff__distrib1]) ).

fof(i_0_7202,plain,
    ! [X25949,X25950,X25951,X25952,X25953] :
      ( ~ c_Fun_Oinj__on(X25953,X25952,X25951,X25950)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25952,tc_HOL_Obool)),hAPP(c_Set_Oimage(X25953,X25952,X25951),X25950)),X25949))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25952),X25949))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X25953),X25950)),hAPP(c_Finite__Set_Ocard(X25952),X25949))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__inj__on__le])]) ).

fof(i_0_7203,plain,
    ! [X32644,X32645,X32646,X32647] :
      ( ( hBOOL(hAPP(hAPP(c_member(X32646),esk463_4(X32644,X32645,X32646,X32647)),X32645))
        | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X32647,X32646,c_Groups_Otimes__class_Otimes(X32647)),X32644),c_Groups_Oone__class_Oone(X32647)),X32645) = c_Groups_Oone__class_Oone(X32647)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32646),X32645))
        | ~ class_Groups_Ocomm__monoid__mult(X32647) )
      & ( hAPP(X32644,esk463_4(X32644,X32645,X32646,X32647)) != c_Groups_Oone__class_Oone(X32647)
        | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X32647,X32646,c_Groups_Otimes__class_Otimes(X32647)),X32644),c_Groups_Oone__class_Oone(X32647)),X32645) = c_Groups_Oone__class_Oone(X32647)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32646),X32645))
        | ~ class_Groups_Ocomm__monoid__mult(X32647) ) ),
    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_7204,plain,
    ! [X32679,X32680,X32681,X32682] :
      ( ( hBOOL(hAPP(hAPP(c_member(X32681),esk469_4(X32679,X32680,X32681,X32682)),hAPP(c_List_Oset(X32681),X32680)))
        | hBOOL(hAPP(X32679,hAPP(hAPP(c_List_Onth(X32681),X32680),X32682)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32682),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32681)),X32680))) )
      & ( ~ hBOOL(hAPP(X32679,esk469_4(X32679,X32680,X32681,X32682)))
        | hBOOL(hAPP(X32679,hAPP(hAPP(c_List_Onth(X32681),X32680),X32682)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32682),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32681)),X32680))) ) ),
    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_7205,plain,
    ! [X28571,X28572,X28573] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28573),tc_List_Olist(X28573))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28573),tc_List_Olist(X28573)),X28572),c_List_Olist_ONil(X28573))),c_List_Olistrel(X28573,X28571)))
      | X28572 = c_List_Olist_ONil(X28573) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__Nil2])]) ).

fof(i_0_7206,plain,
    ! [X29984,X29985,X29986,X29987,X29988,X29989] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X29989)
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29988,X29989),X29987),hAPP(hAPP(c_COMBB(tc_fun(X29986,X29989),X29989,X29988),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29986,X29989),X29985)),X29984)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29986,X29989),X29985),hAPP(hAPP(c_COMBB(tc_fun(X29988,X29989),X29989,X29986),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29988,X29989),X29987)),hAPP(c_COMBC(X29988,X29986,X29989),X29984))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF__commute])]) ).

fof(i_0_7207,plain,
    ! [X24971,X24972,X24973,X24974,X24975,X24976] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X24976)
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24975,X24976),X24974),hAPP(hAPP(c_COMBB(tc_fun(X24973,X24976),X24976,X24975),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24973,X24976),X24972)),X24971)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24973,X24976),X24972),hAPP(hAPP(c_COMBB(tc_fun(X24975,X24976),X24976,X24973),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24975,X24976),X24974)),hAPP(c_COMBC(X24975,X24973,X24976),X24971))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUP__commute])]) ).

fof(i_0_7208,plain,
    ! [X28530,X28531,X28532] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28532),tc_List_Olist(X28532))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28532),tc_List_Olist(X28532)),X28531),c_List_Olist_ONil(X28532))),c_List_Olistrel1(X28532,X28530))),
    inference(variable_rename,[status(thm)],[i_0_5542]) ).

fof(i_0_7209,plain,
    ! [X28484,X28485,X28486] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28486),tc_List_Olist(X28486))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28486),tc_List_Olist(X28486)),X28485),c_List_Olist_ONil(X28486))),c_List_Olexord(X28486,X28484))),
    inference(variable_rename,[status(thm)],[i_0_5543]) ).

fof(i_0_7210,plain,
    ! [X28490,X28491,X28492] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28492),tc_List_Olist(X28492))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28492),tc_List_Olist(X28492)),X28491),c_List_Olist_ONil(X28492))),c_List_Olex(X28492,X28490))),
    inference(variable_rename,[status(thm)],[i_0_5544]) ).

fof(i_0_7211,plain,
    ! [X23509,X23510,X23511,X23512,X23513] :
      ( ( hAPP(c_Relation_OImage(X23513,X23513,X23511),hAPP(hAPP(c_Set_Oinsert(X23513),X23510),c_Orderings_Obot__class_Obot(tc_fun(X23513,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(X23513,X23513,X23511),hAPP(hAPP(c_Set_Oinsert(X23513),X23509),c_Orderings_Obot__class_Obot(tc_fun(X23513,tc_HOL_Obool))))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X23513,X23513)),hAPP(hAPP(c_Product__Type_OPair(X23513,X23513),X23510),X23509)),X23511))
        | ~ hBOOL(hAPP(hAPP(c_member(X23513),X23509),X23512))
        | ~ hBOOL(hAPP(hAPP(c_member(X23513),X23510),X23512))
        | ~ c_Equiv__Relations_Oequiv(X23513,X23512,X23511) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X23513,X23513)),hAPP(hAPP(c_Product__Type_OPair(X23513,X23513),X23510),X23509)),X23511))
        | hAPP(c_Relation_OImage(X23513,X23513,X23511),hAPP(hAPP(c_Set_Oinsert(X23513),X23510),c_Orderings_Obot__class_Obot(tc_fun(X23513,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(X23513,X23513,X23511),hAPP(hAPP(c_Set_Oinsert(X23513),X23509),c_Orderings_Obot__class_Obot(tc_fun(X23513,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_member(X23513),X23509),X23512))
        | ~ hBOOL(hAPP(hAPP(c_member(X23513),X23510),X23512))
        | ~ c_Equiv__Relations_Oequiv(X23513,X23512,X23511) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__equiv__class__iff])])]) ).

fof(i_0_7212,plain,
    ! [X26522,X26523,X26524] :
      ( ( hBOOL(hAPP(hAPP(c_member(X26524),esk235_3(X26522,X26523,X26524)),X26523))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26524,tc_Int_Oint),X26522),X26523) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26524,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X26524),c_Int_Onat),X26522)),X26523)) )
      & ( ~ c_Nat__Transfer_Ois__nat(hAPP(X26522,esk235_3(X26522,X26523,X26524)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26524,tc_Int_Oint),X26522),X26523) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26524,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X26524),c_Int_Onat),X26522)),X26523)) ) ),
    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_7213,plain,
    ! [X24806,X24807,X24808] :
      ( ( hBOOL(hAPP(hAPP(c_member(X24808),esk147_3(X24806,X24807,X24808)),X24807))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24808,tc_Int_Oint),X24806),X24807) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24808,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X24808),c_Int_Onat),X24806)),X24807)) )
      & ( ~ c_Nat__Transfer_Ois__nat(hAPP(X24806,esk147_3(X24806,X24807,X24808)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24808,tc_Int_Oint),X24806),X24807) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24808,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X24808),c_Int_Onat),X24806)),X24807)) ) ),
    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_7214,plain,
    ! [X28580,X28581,X28582,X28583] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28583),tc_List_Olist(X28583))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28583),tc_List_Olist(X28583)),X28582),X28581)),c_List_Olistrel(X28583,X28580)))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28583)),X28582) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28583)),X28581) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__eq__len])]) ).

fof(i_0_7215,plain,
    ! [X28523,X28524,X28525,X28526] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28526),tc_List_Olist(X28526))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28526),tc_List_Olist(X28526)),X28525),X28524)),c_List_Olistrel1(X28526,X28523)))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28526)),X28525) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28526)),X28524) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel1__eq__len])]) ).

fof(i_0_7216,plain,
    ! [X33878,X33879,X33880,X33881] :
      ( ~ c_Relation_Osym(X33881,X33880)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X33881,X33881)),hAPP(hAPP(c_Product__Type_OPair(X33881,X33881),X33879),X33878)),X33880))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X33881,X33881)),hAPP(hAPP(c_Product__Type_OPair(X33881,X33881),X33878),X33879)),X33880)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_symD])]) ).

fof(i_0_7217,plain,
    ! [X33870,X33871,X33872,X33873,X33874,X33875] :
      ( ( ~ c_Relation_Osym(X33871,X33870)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X33871,X33871)),hAPP(hAPP(c_Product__Type_OPair(X33871,X33871),X33872),X33873)),X33870))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X33871,X33871)),hAPP(hAPP(c_Product__Type_OPair(X33871,X33871),X33873),X33872)),X33870)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X33875,X33875)),hAPP(hAPP(c_Product__Type_OPair(X33875,X33875),esk548_2(X33874,X33875)),esk549_2(X33874,X33875))),X33874))
        | c_Relation_Osym(X33875,X33874) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X33875,X33875)),hAPP(hAPP(c_Product__Type_OPair(X33875,X33875),esk549_2(X33874,X33875)),esk548_2(X33874,X33875))),X33874))
        | c_Relation_Osym(X33875,X33874) ) ),
    inference(distribute,[status(thm)],[inference(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_7218,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_5545]) ).

cnf(i_0_7219,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_5546]) ).

fof(i_0_7220,plain,
    ! [X33235,X33236,X33237] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X33237),esk515_3(X33235,X33236,X33237)))
        | hBOOL(hAPP(X33235,X33236))
        | ~ hBOOL(hAPP(X33235,c_Orderings_Obot__class_Obot(tc_fun(X33237,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33237),X33236)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X33237),esk514_3(X33235,X33236,X33237)),esk515_3(X33235,X33236,X33237)))
        | hBOOL(hAPP(X33235,X33236))
        | ~ hBOOL(hAPP(X33235,c_Orderings_Obot__class_Obot(tc_fun(X33237,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33237),X33236)) )
      & ( hBOOL(hAPP(X33235,esk515_3(X33235,X33236,X33237)))
        | hBOOL(hAPP(X33235,X33236))
        | ~ hBOOL(hAPP(X33235,c_Orderings_Obot__class_Obot(tc_fun(X33237,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33237),X33236)) )
      & ( ~ hBOOL(hAPP(X33235,hAPP(hAPP(c_Set_Oinsert(X33237),esk514_3(X33235,X33236,X33237)),esk515_3(X33235,X33236,X33237))))
        | hBOOL(hAPP(X33235,X33236))
        | ~ hBOOL(hAPP(X33235,c_Orderings_Obot__class_Obot(tc_fun(X33237,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33237),X33236)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5547])])])]) ).

fof(i_0_7221,plain,
    ! [X31780,X31781,X31782,X31783,X31784] :
      ( ~ class_Orderings_Olinorder(X31784)
      | ~ c_List_Olinorder__class_Osorted(X31784,hAPP(c_List_Orev(X31784),hAPP(hAPP(c_List_Omap(X31783,X31784),X31782),X31781)))
      | hAPP(c_List_Ofilter(X31783,hAPP(hAPP(c_COMBB(X31784,tc_HOL_Obool,X31783),hAPP(c_Orderings_Oord__class_Oless(X31784),X31780)),X31782)),X31781) = c_List_OtakeWhile(X31783,hAPP(hAPP(c_COMBB(X31784,tc_HOL_Obool,X31783),hAPP(c_Orderings_Oord__class_Oless(X31784),X31780)),X31782),X31781) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_filter__equals__takeWhile__sorted__rev])]) ).

fof(i_0_7222,plain,
    ! [X30807,X30808,X30809,X30810] : hAPP(hAPP(c_Product__Type_OSigma(X30810,X30809),c_Complete__Lattice_OSup__class_OSup(tc_fun(X30810,tc_HOL_Obool),X30808)),X30807) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X30810,tc_HOL_Obool),tc_fun(tc_prod(X30810,X30809),tc_HOL_Obool)),X30808),hAPP(hAPP(c_COMBC(tc_fun(X30810,tc_HOL_Obool),tc_fun(X30810,tc_fun(X30809,tc_HOL_Obool)),tc_fun(tc_prod(X30810,X30809),tc_HOL_Obool)),c_Product__Type_OSigma(X30810,X30809)),X30807)),
    inference(variable_rename,[status(thm)],[fact_Sigma__Union]) ).

fof(i_0_7223,plain,
    ! [X25597,X25598,X25599,X25600] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk195_4(X25597,X25598,X25599,X25600)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X25599)))
        | X25600 = X25598
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X25600),X25599) != X25598
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X25598),X25597))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25599)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk196_4(X25597,X25598,X25599,X25600)),X25597))
        | X25600 = X25598
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X25600),X25599) != X25598
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X25598),X25597))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25599)) )
      & ( X25600 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk196_4(X25597,X25598,X25599,X25600)),esk195_4(X25597,X25598,X25599,X25600))
        | X25600 = X25598
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X25600),X25599) != X25598
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X25598),X25597))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25599)) ) ),
    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_7224,plain,
    ! [X25567,X25568,X25569,X25570] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk187_4(X25567,X25568,X25569,X25570)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X25569)))
        | X25570 = X25568
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25570),X25569) != X25568
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X25568),X25567))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25569)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk188_4(X25567,X25568,X25569,X25570)),X25567))
        | X25570 = X25568
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25570),X25569) != X25568
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X25568),X25567))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25569)) )
      & ( X25570 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk188_4(X25567,X25568,X25569,X25570)),esk187_4(X25567,X25568,X25569,X25570))
        | X25570 = X25568
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25570),X25569) != X25568
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X25568),X25567))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25569)) ) ),
    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_7225,plain,
    ! [X32800,X32801,X32802,X32803,X32804] : hAPP(hAPP(c_Finite__Set_Ofold(X32804,X32803,X32802),X32801),X32800) = c_HOL_OThe(X32803,c_Finite__Set_Ofold__graph(X32804,X32803,X32802,X32801,X32800)),
    inference(variable_rename,[status(thm)],[fact_fold__def]) ).

fof(i_0_7226,plain,
    ! [X21947,X21948,X21949,X21951,X21952,X21953,X21954,X21955,X21958] :
      ( ( ~ hBOOL(hAPP(X21949,esk81_3(X21947,X21948,X21949)))
        | hBOOL(hAPP(X21949,hAPP(hAPP(c_Product__Type_OPair(X21948,X21947),X21951),X21952))) )
      & ( ~ hBOOL(hAPP(X21955,hAPP(hAPP(c_Product__Type_OPair(X21954,X21953),esk82_3(X21953,X21954,X21955)),esk83_3(X21953,X21954,X21955))))
        | hBOOL(hAPP(X21955,X21958)) ) ),
    inference(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_7227,plain,
    ! [X34116,X34117,X34118,X34119,X34120] :
      ( ~ hBOOL(hAPP(X34120,hAPP(hAPP(c_Product__Type_OPair(X34119,X34118),X34117),X34116)))
      | hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(X34119,X34118,tc_HOL_Obool,X34120),X34117),X34116)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_curryI])]) ).

fof(i_0_7228,plain,
    ! [X24569,X24570,X24571] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24571),X24570))
      | 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(X24571),X24569)),hAPP(c_Finite__Set_Ocard(X24571),X24570))),hAPP(c_Finite__Set_Ocard(X24571),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24571,tc_HOL_Obool)),X24569),X24570)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__card__le__card__Diff])]) ).

fof(i_0_7229,plain,
    ! [X31956,X31957,X31958,X31959] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_fun(X31958,tc_HOL_Obool)),esk411_4(X31956,X31957,X31958,X31959)),X31959))
        | c_Fun_Oinj__on(X31958,X31957,X31956,c_Complete__Lattice_OInf__class_OInf(tc_fun(X31958,tc_HOL_Obool),X31959))
        | X31959 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X31958,tc_HOL_Obool),tc_HOL_Obool)) )
      & ( ~ c_Fun_Oinj__on(X31958,X31957,X31956,esk411_4(X31956,X31957,X31958,X31959))
        | c_Fun_Oinj__on(X31958,X31957,X31956,c_Complete__Lattice_OInf__class_OInf(tc_fun(X31958,tc_HOL_Obool),X31959))
        | X31959 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X31958,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_7230,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_5548]) ).

fof(i_0_7231,plain,
    ! [X33444,X33445,X33446,X33447,X33448,X33449,X33450,X33451,X33452] :
      ( ( hBOOL(hAPP(X33444,X33445))
        | ~ hBOOL(hAPP(hAPP(c_member(X33447),X33448),hAPP(c_List_Oset(X33447),c_List_Oreplicate(X33447,X33446,X33445))))
        | ~ hBOOL(hAPP(X33444,X33448)) )
      & ( X33446 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(X33447),X33448),hAPP(c_List_Oset(X33447),c_List_Oreplicate(X33447,X33446,X33445))))
        | ~ hBOOL(hAPP(X33444,X33448)) )
      & ( hBOOL(hAPP(hAPP(c_member(X33452),esk517_4(X33449,X33450,X33451,X33452)),hAPP(c_List_Oset(X33452),c_List_Oreplicate(X33452,X33451,X33450))))
        | ~ hBOOL(hAPP(X33449,X33450))
        | X33451 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hBOOL(hAPP(X33449,esk517_4(X33449,X33450,X33451,X33452)))
        | ~ hBOOL(hAPP(X33449,X33450))
        | X33451 = 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_7232,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_7233,plain,
    ! [X21829,X21830,X21831,X21832,X21833] :
      ( ( ~ c_Nitpick_Orefl_H(X21830,X21829)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X21830,X21830)),hAPP(hAPP(c_Product__Type_OPair(X21830,X21830),X21831),X21831)),X21829)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X21833,X21833)),hAPP(hAPP(c_Product__Type_OPair(X21833,X21833),esk80_2(X21832,X21833)),esk80_2(X21832,X21833))),X21832))
        | c_Nitpick_Orefl_H(X21833,X21832) ) ),
    inference(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_7234,plain,
    ! [X20176,X20177,X20178,X20180] :
      ( ( hBOOL(hAPP(X20177,esk66_3(X20176,X20177,X20178)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20176))
        | ~ hBOOL(hAPP(X20177,X20180))
        | hBOOL(hAPP(X20177,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20180),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20176),X20178))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20178)) )
      & ( ~ hBOOL(hAPP(X20177,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk66_3(X20176,X20177,X20178)),X20178)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20176))
        | ~ hBOOL(hAPP(X20177,X20180))
        | hBOOL(hAPP(X20177,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20180),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20176),X20178))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20178)) ) ),
    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_7235,plain,
    ! [X19802,X19803,X19804,X19806] :
      ( ( hBOOL(hAPP(X19803,esk62_3(X19802,X19803,X19804)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19802))
        | ~ hBOOL(hAPP(X19803,X19806))
        | hBOOL(hAPP(X19803,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19806),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19802),X19804))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19804)) )
      & ( ~ hBOOL(hAPP(X19803,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk62_3(X19802,X19803,X19804)),X19804)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19802))
        | ~ hBOOL(hAPP(X19803,X19806))
        | hBOOL(hAPP(X19803,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19806),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19802),X19804))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19804)) ) ),
    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_7236,plain,
    ! [X31951,X31952,X31953,X31954,X31955] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X31955,X31954)),hAPP(X31955,X31953)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X31952,X31952)),hAPP(hAPP(c_Product__Type_OPair(X31952,X31952),X31954),X31953)),c_List_Omeasures(X31952,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X31952,tc_Nat_Onat)),X31955),X31951)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_measures__less])]) ).

cnf(i_0_7237,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_7238,plain,
    ! [X24414,X24415,X24416,X24417,X24418,X24419,X24420] :
      ( ~ c_Finite__Set_Ofolding__idem(X24420,X24419,X24418,X24417)
      | hAPP(c_Fun_Ocomp(X24419,X24419,X24416,hAPP(X24418,X24415)),hAPP(c_Fun_Ocomp(X24419,X24419,X24416,hAPP(X24418,X24415)),X24414)) = hAPP(c_Fun_Ocomp(X24419,X24419,X24416,hAPP(X24418,X24415)),X24414) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__idem_Oidem__left__comp])]) ).

fof(i_0_7239,plain,
    ! [X22033,X22034,X22035,X22036,X22037,X22038,X22039] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X22039),X22038),hAPP(hAPP(X22037,X22036),X22035)))
      | hBOOL(hAPP(hAPP(c_member(X22039),X22038),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X22034,X22033,tc_fun(X22039,tc_HOL_Obool)),X22037),hAPP(hAPP(c_Product__Type_OPair(X22034,X22033),X22036),X22035)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__splitI])]) ).

fof(i_0_7240,plain,
    ! [X33434,X33435,X33436,X33437,X33439,X33440,X33441,X33442,X33443] :
      ( ( hBOOL(hAPP(hAPP(c_member(X33437),esk516_4(X33434,X33435,X33436,X33437)),hAPP(c_List_Oset(X33437),c_List_Oreplicate(X33437,X33436,X33435))))
        | hBOOL(hAPP(X33434,X33435))
        | X33436 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(X33434,esk516_4(X33434,X33435,X33436,X33437)))
        | hBOOL(hAPP(X33434,X33435))
        | X33436 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(X33439,X33440))
        | ~ hBOOL(hAPP(hAPP(c_member(X33442),X33443),hAPP(c_List_Oset(X33442),c_List_Oreplicate(X33442,X33441,X33440))))
        | hBOOL(hAPP(X33439,X33443)) )
      & ( X33441 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(X33442),X33443),hAPP(c_List_Oset(X33442),c_List_Oreplicate(X33442,X33441,X33440))))
        | hBOOL(hAPP(X33439,X33443)) ) ),
    inference(distribute,[status(thm)],[inference(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_7241,plain,
    ! [X28559,X28560,X28561,X28562] : hAPP(c_Relation_OImage(tc_List_Olist(X28562),tc_List_Olist(X28562),c_List_Olistrel(X28562,X28561)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X28562)),hAPP(hAPP(c_List_Olist_OCons(X28562),X28560),X28559)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X28562),tc_HOL_Obool)))) = c_List_Oset__Cons(X28562,hAPP(c_Relation_OImage(X28562,X28562,X28561),hAPP(hAPP(c_Set_Oinsert(X28562),X28560),c_Orderings_Obot__class_Obot(tc_fun(X28562,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(X28562),tc_List_Olist(X28562),c_List_Olistrel(X28562,X28561)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X28562)),X28559),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X28562),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[fact_listrel__Cons]) ).

fof(i_0_7242,plain,
    ! [X25887,X25888,X25889,X25890] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X25890,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X25889)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X25890,tc_HOL_Obool),tc_Nat_Onat),X25888),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X25887))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X25890,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X25887,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25889),X25887))),X25888),
    inference(variable_rename,[status(thm)],[fact_UN__le__add__shift]) ).

cnf(i_0_7243,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_7244,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]) ).

cnf(i_0_7245,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_5549]) ).

cnf(i_0_7246,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_5550]) ).

fof(i_0_7247,plain,
    ! [X28675,X28676,X28677,X28678,X28679,X28680] :
      ( X28678 != hAPP(hAPP(c_List_Olist_OCons(X28677),X28679),X28680)
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28677),tc_List_Olist(X28677))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28677),tc_List_Olist(X28677)),X28676),hAPP(hAPP(c_List_Oappend(X28677),X28676),X28678))),c_List_Olexord(X28677,X28675))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__append__rightI])])]) ).

fof(i_0_7248,plain,
    ! [X29241,X29242,X29243,X29244,X29245,X29246,X29247] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29241)),X29243) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29241)),X29242)
        | X29243 != X29242 )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29241,X29241)),X29244),hAPP(c_List_Oset(tc_prod(X29241,X29241)),hAPP(hAPP(c_List_Ozip(X29241,X29241),X29243),X29242))))
        | hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X29241,X29241,tc_HOL_Obool),c_fequal),X29244))
        | X29243 != X29242 )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29245,X29245)),esk332_3(X29245,X29246,X29247)),hAPP(c_List_Oset(tc_prod(X29245,X29245)),hAPP(hAPP(c_List_Ozip(X29245,X29245),X29247),X29246))))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29245)),X29247) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29245)),X29246)
        | X29247 = X29246 )
      & ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X29245,X29245,tc_HOL_Obool),c_fequal),esk332_3(X29245,X29246,X29247)))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29245)),X29247) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29245)),X29246)
        | X29247 = X29246 ) ),
    inference(distribute,[status(thm)],[inference(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_7249,plain,
    ! [X22335,X22336,X22337] :
      ( ( 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),esk92_3(X22335,X22336,X22337)),esk93_3(X22335,X22336,X22337))))
        | hBOOL(hAPP(hAPP(X22335,X22337),X22336))
        | ~ 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),X22337),X22336))) )
      & ( esk93_3(X22335,X22336,X22337) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(X22335,esk93_3(X22335,X22336,X22337)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,esk92_3(X22335,X22336,X22337),esk93_3(X22335,X22336,X22337))))
        | hBOOL(hAPP(hAPP(X22335,X22337),X22336))
        | ~ 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),X22337),X22336))) )
      & ( ~ hBOOL(hAPP(hAPP(X22335,esk92_3(X22335,X22336,X22337)),esk93_3(X22335,X22336,X22337)))
        | hBOOL(hAPP(hAPP(X22335,X22337),X22336))
        | ~ 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),X22337),X22336))) ) ),
    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_7250,plain,
    ! [X25785,X25786,X25787,X25788,X25789] :
      ( ~ c_Fun_Oinj__on(X25789,X25788,X25787,X25786)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X25789,tc_HOL_Obool)),X25785),X25786))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X25788,tc_HOL_Obool)),hAPP(c_Set_Oimage(X25789,X25788,X25787),X25785)),hAPP(c_Set_Oimage(X25789,X25788,X25787),X25786))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__strict__subset])]) ).

fof(i_0_7251,plain,
    ! [X17119,X17120,X17121,X17122] :
      ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17122),X17120),esk7_4(X17119,X17120,X17121,X17122)))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(X17122,X17121)),X17120),X17119)) )
      & ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17121),esk7_4(X17119,X17120,X17121,X17122)),X17119))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(X17122,X17121)),X17120),X17119)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5551])])])]) ).

fof(i_0_7252,plain,
    ! [X17093,X17094,X17095,X17096,X17098,X17099,X17100,X17101,X17102] :
      ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17096),X17094),esk6_4(X17093,X17094,X17095,X17096)))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(X17096,X17095)),X17094),X17093)) )
      & ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17095),esk6_4(X17093,X17094,X17095,X17096)),X17093))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(X17096,X17095)),X17094),X17093)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17101),X17099),X17102))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17100),X17102),X17098))
        | hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(X17101,X17100)),X17099),X17098)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evalc_Oequations_I4_J])])])])])]) ).

fof(i_0_7253,plain,
    ! [X25835,X25836,X25837,X25838,X25839,X25840] :
      ( ~ c_Fun_Oinj__on(X25840,X25839,X25838,X25837)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25840,tc_HOL_Obool)),X25836),X25837))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25840,tc_HOL_Obool)),X25835),X25837))
      | hAPP(c_Set_Oimage(X25840,X25839,X25838),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25840,tc_HOL_Obool)),X25836),X25835)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25839,tc_HOL_Obool)),hAPP(c_Set_Oimage(X25840,X25839,X25838),X25836)),hAPP(c_Set_Oimage(X25840,X25839,X25838),X25835)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__image__Int])]) ).

fof(i_0_7254,plain,
    ! [X25849,X25850,X25851,X25852,X25853,X25854] :
      ( ~ c_Fun_Oinj__on(X25854,X25853,X25852,X25851)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25854,tc_HOL_Obool)),X25850),X25851))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25854,tc_HOL_Obool)),X25849),X25851))
      | hAPP(c_Set_Oimage(X25854,X25853,X25852),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25854,tc_HOL_Obool)),X25850),X25849)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25853,tc_HOL_Obool)),hAPP(c_Set_Oimage(X25854,X25853,X25852),X25850)),hAPP(c_Set_Oimage(X25854,X25853,X25852),X25849)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__image__set__diff])]) ).

fof(i_0_7255,plain,
    ! [X31281,X31282,X31283] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X31283),X31282))
      | hAPP(c_List_Ofilter(X31283,hAPP(hAPP(c_COMBC(X31283,tc_fun(X31283,tc_HOL_Obool),tc_HOL_Obool),c_member(X31283)),hAPP(c_List_Oset(X31283),c_List_Osublist(X31283,X31282,X31281)))),X31282) = c_List_Osublist(X31283,X31282,X31281) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_filter__in__sublist])]) ).

cnf(i_0_7256,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_5552]) ).

cnf(i_0_7257,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk443_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_5480]) ).

cnf(i_0_7258,plain,
    ( hBOOL(hAPP(c_List_Odistinct(X2),c_List_Oconcat(X2,X1)))
    | esk409_2(X1,X2) != esk410_2(X1,X2)
    | ~ hBOOL(hAPP(c_List_Odistinct(X2),esk408_2(X1,X2)))
    | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X2)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_5492]) ).

fof(i_0_7259,plain,
    ! [X33996,X33997,X33998,X33999,X34000,X34001,X34002] :
      ( ( hAPP(c_Set_Oimage(X33998,X33997,X33996),c_Orderings_Otop__class_Otop(tc_fun(X33998,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X33997,tc_HOL_Obool))
        | hAPP(X33996,hAPP(c_Hilbert__Choice_Oinv__into(X33998,X33997,c_Orderings_Otop__class_Otop(tc_fun(X33998,tc_HOL_Obool)),X33996),X33999)) = X33999 )
      & ( hAPP(X34000,hAPP(c_Hilbert__Choice_Oinv__into(X34002,X34001,c_Orderings_Otop__class_Otop(tc_fun(X34002,tc_HOL_Obool)),X34000),esk556_3(X34000,X34001,X34002))) != esk556_3(X34000,X34001,X34002)
        | hAPP(c_Set_Oimage(X34002,X34001,X34000),c_Orderings_Otop__class_Otop(tc_fun(X34002,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X34001,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_7260,plain,
    ! [X33581,X33582,X33583,X33585,X33586,X33587,X33588,X33589] :
      ( ( hBOOL(hAPP(hAPP(c_member(X33583),esk521_3(X33581,X33582,X33583)),hAPP(c_List_Oset(X33583),X33581)))
        | ~ c_List_Olist__ex1(X33583,X33582,X33581) )
      & ( hBOOL(hAPP(X33582,esk521_3(X33581,X33582,X33583)))
        | ~ c_List_Olist__ex1(X33583,X33582,X33581) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X33583),X33585),hAPP(c_List_Oset(X33583),X33581)))
        | ~ hBOOL(hAPP(X33582,X33585))
        | X33585 = esk521_3(X33581,X33582,X33583)
        | ~ c_List_Olist__ex1(X33583,X33582,X33581) )
      & ( hBOOL(hAPP(hAPP(c_member(X33588),esk522_4(X33586,X33587,X33588,X33589)),hAPP(c_List_Oset(X33588),X33586)))
        | ~ hBOOL(hAPP(hAPP(c_member(X33588),X33589),hAPP(c_List_Oset(X33588),X33586)))
        | ~ hBOOL(hAPP(X33587,X33589))
        | c_List_Olist__ex1(X33588,X33587,X33586) )
      & ( hBOOL(hAPP(X33587,esk522_4(X33586,X33587,X33588,X33589)))
        | ~ hBOOL(hAPP(hAPP(c_member(X33588),X33589),hAPP(c_List_Oset(X33588),X33586)))
        | ~ hBOOL(hAPP(X33587,X33589))
        | c_List_Olist__ex1(X33588,X33587,X33586) )
      & ( esk522_4(X33586,X33587,X33588,X33589) != X33589
        | ~ hBOOL(hAPP(hAPP(c_member(X33588),X33589),hAPP(c_List_Oset(X33588),X33586)))
        | ~ hBOOL(hAPP(X33587,X33589))
        | c_List_Olist__ex1(X33588,X33587,X33586) ) ),
    inference(distribute,[status(thm)],[inference(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_7261,plain,
    ! [X33217,X33218,X33219,X33221,X33222,X33223,X33224,X33225] :
      ( ( hBOOL(hAPP(hAPP(c_member(X33219),esk510_3(X33217,X33218,X33219)),hAPP(c_List_Oset(X33219),X33217)))
        | ~ c_List_Olist__ex1(X33219,X33218,X33217) )
      & ( hBOOL(hAPP(X33218,esk510_3(X33217,X33218,X33219)))
        | ~ c_List_Olist__ex1(X33219,X33218,X33217) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X33219),X33221),hAPP(c_List_Oset(X33219),X33217)))
        | ~ hBOOL(hAPP(X33218,X33221))
        | X33221 = esk510_3(X33217,X33218,X33219)
        | ~ c_List_Olist__ex1(X33219,X33218,X33217) )
      & ( hBOOL(hAPP(hAPP(c_member(X33224),esk511_4(X33222,X33223,X33224,X33225)),hAPP(c_List_Oset(X33224),X33222)))
        | ~ hBOOL(hAPP(hAPP(c_member(X33224),X33225),hAPP(c_List_Oset(X33224),X33222)))
        | ~ hBOOL(hAPP(X33223,X33225))
        | c_List_Olist__ex1(X33224,X33223,X33222) )
      & ( hBOOL(hAPP(X33223,esk511_4(X33222,X33223,X33224,X33225)))
        | ~ hBOOL(hAPP(hAPP(c_member(X33224),X33225),hAPP(c_List_Oset(X33224),X33222)))
        | ~ hBOOL(hAPP(X33223,X33225))
        | c_List_Olist__ex1(X33224,X33223,X33222) )
      & ( esk511_4(X33222,X33223,X33224,X33225) != X33225
        | ~ hBOOL(hAPP(hAPP(c_member(X33224),X33225),hAPP(c_List_Oset(X33224),X33222)))
        | ~ hBOOL(hAPP(X33223,X33225))
        | c_List_Olist__ex1(X33224,X33223,X33222) ) ),
    inference(distribute,[status(thm)],[inference(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_7262,plain,
    ! [X25825,X25826,X25827] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25827),X25826))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25827,tc_HOL_Obool)),hAPP(c_Set_Oimage(X25827,X25827,X25825),X25826)),X25826))
      | ~ c_Fun_Oinj__on(X25827,X25827,X25825,X25826)
      | hAPP(c_Set_Oimage(X25827,X25827,X25825),X25826) = X25826 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_endo__inj__surj])]) ).

fof(i_0_7263,plain,
    ! [X30600,X30601,X30602,X30603,X30604] :
      ( ~ class_Orderings_Olinorder(X30604)
      | ~ hBOOL(hAPP(hAPP(c_member(X30604),hAPP(X30603,X30602)),hAPP(c_Set_Oimage(X30601,X30604,X30603),hAPP(c_List_Oset(X30601),X30600))))
      | c_List_Olinorder__class_Oinsort__insert__key(X30601,X30604,X30603,X30602,X30600) = X30600 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insort__insert__key__triv])]) ).

fof(i_0_7264,plain,
    ! [X30597,X30598,X30599] :
      ( ~ class_Orderings_Olinorder(X30599)
      | hAPP(c_List_Oset(X30599),c_List_Olinorder__class_Oinsort__insert__key(X30599,X30599,c_COMBI(X30599),X30598,X30597)) = hAPP(hAPP(c_Set_Oinsert(X30599),X30598),hAPP(c_List_Oset(X30599),X30597)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__insort__insert])]) ).

fof(i_0_7265,plain,
    ! [X28588,X28589,X28590] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28590,X28590),tc_HOL_Obool)),X28589),X28588))
      | ~ c_Relation_Orefl__on(X28590,c_Orderings_Otop__class_Otop(tc_fun(X28590,tc_HOL_Obool)),X28588)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X28590),tc_List_Olist(X28590)),tc_HOL_Obool)),c_List_Olistrel1(X28590,X28589)),c_List_Olistrel(X28590,X28588))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel1__subset__listrel])]) ).

cnf(i_0_7266,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_5553]) ).

cnf(i_0_7267,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_5538]) ).

fof(i_0_7268,plain,
    ! [X25271,X25272,X25273,X25274,X25275,X25276,X25277] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25276),X25272))
        | hAPP(hAPP(X25273,X25271),X25272) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X25277,X25276,X25275),X25271),X25274),X25272)
        | ~ c_Big__Operators_Ocomm__monoid__big(X25277,X25276,X25275,X25274,X25273) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X25276),X25272))
        | hAPP(hAPP(X25273,X25271),X25272) = X25274
        | ~ c_Big__Operators_Ocomm__monoid__big(X25277,X25276,X25275,X25274,X25273) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5554])])]) ).

fof(i_0_7269,plain,
    ! [X26067,X26068,X26069,X26070,X26071,X26072,X26073] :
      ( ~ c_Finite__Set_Ofolding__image(X26073,X26072,X26071,X26070,X26069)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26072),X26068))
      | hAPP(hAPP(X26069,X26067),X26068) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X26073,X26072,X26071),X26067),X26070),X26068) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image_Oeq__fold])]) ).

fof(i_0_7270,plain,
    ! [X32945,X32946,X32947,X32948,X32949,X32950] :
      ( ~ c_Finite__Set_Ofun__left__comm(X32950,X32949,X32948)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32950),X32947))
      | ~ hBOOL(hAPP(hAPP(c_member(X32950),X32946),X32947))
      | hAPP(hAPP(c_Finite__Set_Ofold(X32950,X32949,X32948),X32945),X32947) = hAPP(hAPP(X32948,X32946),hAPP(hAPP(c_Finite__Set_Ofold(X32950,X32949,X32948),X32945),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X32950,tc_HOL_Obool)),X32947),hAPP(hAPP(c_Set_Oinsert(X32950),X32946),c_Orderings_Obot__class_Obot(tc_fun(X32950,tc_HOL_Obool)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__rec])]) ).

fof(i_0_7271,plain,
    ! [X29284,X29285,X29286,X29287,X29289,X29290,X29291,X29292,X29294] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X29286)),esk336_4(X29284,X29285,X29286,X29287)),X29285))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X29286)),X29289),X29284))
        | c_Hoare__Mirabelle_Otriple__valid(X29286,X29287,X29289)
        | ~ c_Hoare__Mirabelle_Ohoare__valids(X29286,X29285,X29284) )
      & ( ~ c_Hoare__Mirabelle_Otriple__valid(X29286,X29287,esk336_4(X29284,X29285,X29286,X29287))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X29286)),X29289),X29284))
        | c_Hoare__Mirabelle_Otriple__valid(X29286,X29287,X29289)
        | ~ c_Hoare__Mirabelle_Ohoare__valids(X29286,X29285,X29284) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X29292)),X29294),X29291))
        | c_Hoare__Mirabelle_Otriple__valid(X29292,esk337_3(X29290,X29291,X29292),X29294)
        | c_Hoare__Mirabelle_Ohoare__valids(X29292,X29291,X29290) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X29292)),esk338_3(X29290,X29291,X29292)),X29290))
        | c_Hoare__Mirabelle_Ohoare__valids(X29292,X29291,X29290) )
      & ( ~ c_Hoare__Mirabelle_Otriple__valid(X29292,esk337_3(X29290,X29291,X29292),esk338_3(X29290,X29291,X29292))
        | c_Hoare__Mirabelle_Ohoare__valids(X29292,X29291,X29290) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hoare__valids__def])])])])])]) ).

fof(i_0_7272,plain,
    ! [X27128,X27129,X27130,X27131,X27132,X27133] : hAPP(c_Set_Ovimage(X27133,X27132,hAPP(c_Fun_Ocomp(X27131,X27132,X27133,X27130),X27129)),X27128) = hAPP(c_Set_Ovimage(X27133,X27131,X27129),hAPP(c_Set_Ovimage(X27131,X27132,X27130),X27128)),
    inference(variable_rename,[status(thm)],[fact_vimage__compose]) ).

fof(i_0_7273,plain,
    ! [X23193,X23194,X23195,X23196,X23197,X23198] : hAPP(c_Set_Oimage(X23198,X23197,hAPP(c_Fun_Ocomp(X23196,X23197,X23198,X23195),X23194)),X23193) = hAPP(c_Set_Oimage(X23196,X23197,X23195),hAPP(c_Set_Oimage(X23198,X23196,X23194),X23193)),
    inference(variable_rename,[status(thm)],[fact_image__compose]) ).

fof(i_0_7274,plain,
    ! [X32199,X32200,X32201,X32203,X32204,X32205,X32206] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32201,X32201)),X32200),c_Transitive__Closure_Ortrancl(X32201,X32199)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X32201,X32201)),X32200),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X32201,X32201),tc_HOL_Obool),esk440_3(X32199,X32200,X32201)),X32199))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32205,X32205)),X32204),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X32205,X32205),tc_HOL_Obool),X32206),X32203)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X32205,X32205)),X32204),c_Transitive__Closure_Ortrancl(X32205,X32203))) ) ),
    inference(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_7275,plain,
    ! [X30359,X30360,X30361,X30362,X30363,X30364,X30365] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(X30365,X30364,X30363,X30362),X30361),X30360),X30359) = hAPP(hAPP(X30360,hAPP(c_Product__Type_Ofst(X30364,X30363),hAPP(X30361,X30359))),hAPP(c_Product__Type_Osnd(X30364,X30363),hAPP(X30361,X30359))),
    inference(variable_rename,[status(thm)],[fact_scomp__unfold]) ).

fof(i_0_7276,plain,
    ! [X23504,X23505,X23506,X23507,X23508] :
      ( ( hAPP(c_Relation_OImage(X23508,X23508,X23506),hAPP(hAPP(c_Set_Oinsert(X23508),X23505),c_Orderings_Obot__class_Obot(tc_fun(X23508,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(X23508,X23508,X23506),hAPP(hAPP(c_Set_Oinsert(X23508),X23504),c_Orderings_Obot__class_Obot(tc_fun(X23508,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X23508,X23508)),hAPP(hAPP(c_Product__Type_OPair(X23508,X23508),X23505),X23504)),X23506))
        | ~ c_Equiv__Relations_Oequiv(X23508,X23507,X23506) )
      & ( hBOOL(hAPP(hAPP(c_member(X23508),X23505),X23507))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X23508,X23508)),hAPP(hAPP(c_Product__Type_OPair(X23508,X23508),X23505),X23504)),X23506))
        | ~ c_Equiv__Relations_Oequiv(X23508,X23507,X23506) )
      & ( hBOOL(hAPP(hAPP(c_member(X23508),X23504),X23507))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X23508,X23508)),hAPP(hAPP(c_Product__Type_OPair(X23508,X23508),X23505),X23504)),X23506))
        | ~ c_Equiv__Relations_Oequiv(X23508,X23507,X23506) )
      & ( hAPP(c_Relation_OImage(X23508,X23508,X23506),hAPP(hAPP(c_Set_Oinsert(X23508),X23505),c_Orderings_Obot__class_Obot(tc_fun(X23508,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(X23508,X23508,X23506),hAPP(hAPP(c_Set_Oinsert(X23508),X23504),c_Orderings_Obot__class_Obot(tc_fun(X23508,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_member(X23508),X23505),X23507))
        | ~ hBOOL(hAPP(hAPP(c_member(X23508),X23504),X23507))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X23508,X23508)),hAPP(hAPP(c_Product__Type_OPair(X23508,X23508),X23505),X23504)),X23506))
        | ~ c_Equiv__Relations_Oequiv(X23508,X23507,X23506) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__class__eq__iff])])]) ).

fof(i_0_7277,plain,
    ! [X18426,X18427,X18428] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18428),c_Groups_Ozero__class_Ozero(X18428)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18428),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18428),X18427),X18427)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18428),X18426),X18426))))
        | X18427 != c_Groups_Ozero__class_Ozero(X18428)
        | X18426 != c_Groups_Ozero__class_Ozero(X18428)
        | ~ class_Rings_Olinordered__ring__strict(X18428) )
      & ( X18427 = c_Groups_Ozero__class_Ozero(X18428)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18428),c_Groups_Ozero__class_Ozero(X18428)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18428),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18428),X18427),X18427)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18428),X18426),X18426))))
        | ~ class_Rings_Olinordered__ring__strict(X18428) )
      & ( X18426 = c_Groups_Ozero__class_Ozero(X18428)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18428),c_Groups_Ozero__class_Ozero(X18428)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18428),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18428),X18427),X18427)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18428),X18426),X18426))))
        | ~ class_Rings_Olinordered__ring__strict(X18428) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__squares__gt__zero__iff])])]) ).

fof(i_0_7278,plain,
    ! [X32267,X32268] : c_Transitive__Closure_Ortrancl(X32268,X32267) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(X32268,X32268),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(X32268,X32268),tc_HOL_Obool),tc_fun(tc_prod(X32268,X32268),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(X32268,X32268),tc_HOL_Obool)),X32267)),
    inference(variable_rename,[status(thm)],[fact_rtrancl__is__UN__rel__pow]) ).

fof(i_0_7279,plain,
    ! [X32101,X32102,X32103,X32104] :
      ( ( hBOOL(hAPP(hAPP(c_member(X32104),esk434_4(X32101,X32102,X32103,X32104)),hAPP(c_List_Oset(X32104),X32103)))
        | c_List_OtakeWhile(X32104,X32102,hAPP(hAPP(c_List_Oappend(X32104),X32103),X32101)) = hAPP(hAPP(c_List_Oappend(X32104),X32103),c_List_OtakeWhile(X32104,X32102,X32101)) )
      & ( ~ hBOOL(hAPP(X32102,esk434_4(X32101,X32102,X32103,X32104)))
        | c_List_OtakeWhile(X32104,X32102,hAPP(hAPP(c_List_Oappend(X32104),X32103),X32101)) = hAPP(hAPP(c_List_Oappend(X32104),X32103),c_List_OtakeWhile(X32104,X32102,X32101)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_takeWhile__append2])])])]) ).

fof(i_0_7280,plain,
    ! [X25759,X25760,X25761,X25762,X25763,X25764] :
      ( ~ c_Fun_Oinj__on(X25764,X25763,hAPP(c_Fun_Ocomp(X25762,X25763,X25764,X25761),X25760),X25759)
      | c_Fun_Oinj__on(X25762,X25763,X25761,hAPP(c_Set_Oimage(X25764,X25762,X25760),X25759)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__imageI])]) ).

fof(i_0_7281,plain,
    ! [X26482,X26483,X26484,X26486,X26487] :
      ( ( hBOOL(hAPP(hAPP(c_member(X26484),esk231_3(X26482,X26483,X26484)),X26483))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26484,tc_Nat_Onat),X26482),X26483) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26484),X26483)) )
      & ( hAPP(X26482,esk231_3(X26482,X26483,X26484)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26484,tc_Nat_Onat),X26482),X26483) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26484),X26483)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X26484),X26486),X26483))
        | esk231_3(X26482,X26483,X26484) = X26486
        | hAPP(X26482,X26486) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26484,tc_Nat_Onat),X26482),X26483) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26484),X26483)) )
      & ( hBOOL(hAPP(hAPP(c_member(X26484),esk232_4(X26482,X26483,X26484,X26487)),X26483))
        | ~ hBOOL(hAPP(hAPP(c_member(X26484),X26487),X26483))
        | hAPP(X26482,X26487) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26484,tc_Nat_Onat),X26482),X26483) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26484),X26483)) )
      & ( X26487 != esk232_4(X26482,X26483,X26484,X26487)
        | ~ hBOOL(hAPP(hAPP(c_member(X26484),X26487),X26483))
        | hAPP(X26482,X26487) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26484,tc_Nat_Onat),X26482),X26483) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26484),X26483)) )
      & ( hAPP(X26482,esk232_4(X26482,X26483,X26484,X26487)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(X26484),X26487),X26483))
        | hAPP(X26482,X26487) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26484,tc_Nat_Onat),X26482),X26483) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26484),X26483)) ) ),
    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_7282,plain,
    ! [X31528,X31529,X31530] :
      ( ~ class_Orderings_Olinorder(X31530)
      | ~ c_List_Olinorder__class_Osorted(X31530,X31529)
      | c_List_Olinorder__class_Osorted(X31530,c_List_Olinorder__class_Oinsort__insert__key(X31530,X31530,c_COMBI(X31530),X31528,X31529)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__insort__insert])]) ).

fof(i_0_7283,plain,
    ! [X20297,X20298,X20299,X20300,X20301] :
      ( ~ class_Rings_Olinordered__idom(X20301)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20301),hAPP(c_Groups_Oabs__class_Oabs(X20301),X20300)),X20299))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20301),hAPP(c_Groups_Oabs__class_Oabs(X20301),X20298)),X20297))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20301),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20301),hAPP(c_Groups_Oabs__class_Oabs(X20301),X20300)),hAPP(c_Groups_Oabs__class_Oabs(X20301),X20298))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20301),X20299),X20297))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__mult__less])]) ).

fof(i_0_7284,plain,
    ! [X32951,X32952,X32953,X32954,X32955,X32956] :
      ( ~ c_Finite__Set_Ofun__left__comm(X32956,X32955,X32954)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32956),X32953))
      | hAPP(hAPP(c_Finite__Set_Ofold(X32956,X32955,X32954),X32952),hAPP(hAPP(c_Set_Oinsert(X32956),X32951),X32953)) = hAPP(hAPP(X32954,X32951),hAPP(hAPP(c_Finite__Set_Ofold(X32956,X32955,X32954),X32952),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X32956,tc_HOL_Obool)),X32953),hAPP(hAPP(c_Set_Oinsert(X32956),X32951),c_Orderings_Obot__class_Obot(tc_fun(X32956,tc_HOL_Obool)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__insert__remove])]) ).

fof(i_0_7285,plain,
    ! [X31718,X31719,X31720,X31721,X31722] : c_List_OtakeWhile(X31722,X31721,hAPP(hAPP(c_List_Omap(X31720,X31722),X31719),X31718)) = hAPP(hAPP(c_List_Omap(X31720,X31722),X31719),c_List_OtakeWhile(X31720,hAPP(c_Fun_Ocomp(X31722,tc_HOL_Obool,X31720,X31721),X31719),X31718)),
    inference(variable_rename,[status(thm)],[fact_takeWhile__map]) ).

fof(i_0_7286,plain,
    ! [X23410,X23411,X23412,X23413,X23414,X23415] :
      ( ( X23415 != X23414
        | hAPP(c_Fun_Ofun__upd(X23413,X23412,X23411,X23414,X23410),X23415) = X23410 )
      & ( X23415 = X23414
        | hAPP(c_Fun_Ofun__upd(X23413,X23412,X23411,X23414,X23410),X23415) = hAPP(X23411,X23415) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__upd__def])]) ).

fof(i_0_7287,plain,
    ! [X23399,X23400,X23401,X23402,X23403,X23404] :
      ( X23404 = X23403
      | hAPP(c_Fun_Ofun__upd(X23402,X23401,X23400,X23403,X23399),X23404) = hAPP(X23400,X23404) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__upd__other])]) ).

fof(i_0_7288,plain,
    ! [X23386,X23387,X23388,X23389,X23390,X23391] :
      ( ( X23391 != X23390
        | hAPP(c_Fun_Ofun__upd(X23389,X23388,X23387,X23390,X23386),X23391) = X23386 )
      & ( X23391 = X23390
        | hAPP(c_Fun_Ofun__upd(X23389,X23388,X23387,X23390,X23386),X23391) = hAPP(X23387,X23391) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__upd__apply])]) ).

fof(i_0_7289,plain,
    ! [X26489,X26490,X26491,X26493,X26494] :
      ( ( hBOOL(hAPP(hAPP(c_member(X26491),esk233_3(X26489,X26490,X26491)),X26490))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26491,tc_Nat_Onat),X26489),X26490) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26491),X26490)) )
      & ( hAPP(X26489,esk233_3(X26489,X26490,X26491)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26491,tc_Nat_Onat),X26489),X26490) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26491),X26490)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X26491),X26493),X26490))
        | esk233_3(X26489,X26490,X26491) = X26493
        | hAPP(X26489,X26493) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26491,tc_Nat_Onat),X26489),X26490) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26491),X26490)) )
      & ( hBOOL(hAPP(hAPP(c_member(X26491),esk234_4(X26489,X26490,X26491,X26494)),X26490))
        | ~ hBOOL(hAPP(hAPP(c_member(X26491),X26494),X26490))
        | hAPP(X26489,X26494) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26491,tc_Nat_Onat),X26489),X26490) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26491),X26490)) )
      & ( X26494 != esk234_4(X26489,X26490,X26491,X26494)
        | ~ hBOOL(hAPP(hAPP(c_member(X26491),X26494),X26490))
        | hAPP(X26489,X26494) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26491,tc_Nat_Onat),X26489),X26490) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26491),X26490)) )
      & ( hAPP(X26489,esk234_4(X26489,X26490,X26491,X26494)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(X26491),X26494),X26490))
        | hAPP(X26489,X26494) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26491,tc_Nat_Onat),X26489),X26490) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26491),X26490)) ) ),
    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_7290,plain,
    ! [X32511,X32512,X32513] :
      ( ~ c_Relation_Orefl__on(X32513,X32512,X32511)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X32513,X32513),tc_HOL_Obool)),X32511),hAPP(hAPP(c_Relation_Orel__comp(X32513,X32513,X32513),hAPP(c_Relation_Oconverse(X32513,X32513),X32511)),X32511))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__on__comp__subset])]) ).

fof(i_0_7291,plain,
    ! [X23381,X23382,X23383,X23384,X23385] : hAPP(c_Fun_Ofun__upd(X23385,X23384,X23383,X23382,X23381),X23382) = X23381,
    inference(variable_rename,[status(thm)],[fact_fun__upd__same]) ).

fof(i_0_7292,plain,
    ! [X25753,X25754,X25755,X25756,X25757,X25758] :
      ( ~ c_Fun_Oinj__on(X25758,X25757,X25756,X25755)
      | ~ c_Fun_Oinj__on(X25757,X25754,X25753,hAPP(c_Set_Oimage(X25758,X25757,X25756),X25755))
      | c_Fun_Oinj__on(X25758,X25754,hAPP(c_Fun_Ocomp(X25757,X25754,X25758,X25753),X25756),X25755) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comp__inj__on])]) ).

fof(i_0_7293,plain,
    ! [X30605,X30606,X30607,X30608,X30609] : c_Enum_Oproduct(X30609,X30608,hAPP(hAPP(c_List_Olist_OCons(X30609),X30607),X30606),X30605) = hAPP(hAPP(c_List_Oappend(tc_prod(X30609,X30608)),hAPP(hAPP(c_List_Omap(X30608,tc_prod(X30609,X30608)),hAPP(c_Product__Type_OPair(X30609,X30608),X30607)),X30605)),c_Enum_Oproduct(X30609,X30608,X30606,X30605)),
    inference(variable_rename,[status(thm)],[fact_product_Osimps_I2_J]) ).

cnf(i_0_7294,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_5555]) ).

cnf(i_0_7295,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_5556]) ).

fof(i_0_7296,plain,
    ! [X29464,X29465] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X29465),hAPP(c_List_Oset(tc_Nat_Onat),X29464)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X29465),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)),X29464))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_elem__le__sum])]) ).

fof(i_0_7297,plain,
    ! [X23275,X23276,X23277,X23278,X23279,X23280] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X23280),X23279),X23278))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X23280,X23277)),hAPP(hAPP(c_Product__Type_OPair(X23280,X23277),X23279),X23276)),X23275))
      | hBOOL(hAPP(hAPP(c_member(X23277),X23276),hAPP(c_Relation_OImage(X23280,X23277,X23275),X23278))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__ImageI])]) ).

fof(i_0_7298,plain,
    ! [X29748,X29749,X29750,X29751,X29752,X29753] : hAPP(hAPP(c_List_Omap(X29753,X29752),X29751),hAPP(hAPP(c_List_Omap(X29750,X29753),X29749),X29748)) = hAPP(hAPP(c_List_Omap(X29750,X29752),hAPP(c_Fun_Ocomp(X29753,X29752,X29750,X29751),X29749)),X29748),
    inference(variable_rename,[status(thm)],[fact_map__map]) ).

fof(i_0_7299,plain,
    ! [X29742,X29743,X29744,X29745,X29746,X29747] : hAPP(hAPP(c_List_Omap(X29747,X29746),X29745),hAPP(hAPP(c_List_Omap(X29744,X29747),X29743),X29742)) = hAPP(hAPP(c_List_Omap(X29744,X29746),hAPP(c_Fun_Ocomp(X29747,X29746,X29744,X29745),X29743)),X29742),
    inference(variable_rename,[status(thm)],[fact_List_Omap_Ocompositionality]) ).

fof(i_0_7300,plain,
    ! [X28783,X28784,X28785,X28786] : hAPP(hAPP(c_List_Otake(X28786),X28785),hAPP(hAPP(c_List_Olist_OCons(X28786),X28784),X28783)) = c_Nat_Onat_Onat__case(tc_List_Olist(X28786),c_List_Olist_ONil(X28786),hAPP(hAPP(c_COMBB(tc_List_Olist(X28786),tc_List_Olist(X28786),tc_Nat_Onat),hAPP(c_List_Olist_OCons(X28786),X28784)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(X28786),tc_List_Olist(X28786)),c_List_Otake(X28786)),X28783)),X28785),
    inference(variable_rename,[status(thm)],[fact_take__Cons]) ).

fof(i_0_7301,plain,
    ! [X23258,X23259,X23260,X23261,X23262] : hAPP(c_Relation_OImage(X23262,X23261,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X23262,X23261),tc_HOL_Obool)),X23260),X23259)),X23258) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23261,tc_HOL_Obool)),hAPP(c_Relation_OImage(X23262,X23261,X23260),X23258)),hAPP(c_Relation_OImage(X23262,X23261,X23259),X23258)),
    inference(variable_rename,[status(thm)],[fact_Un__Image]) ).

fof(i_0_7302,plain,
    ! [X30369,X30370,X30371,X30372,X30373] :
      ( ( X30373 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
        | hAPP(c_Random_Oiterate(X30372,X30371,X30373,X30370),X30369) = hAPP(c_Product__Type_OPair(X30372,X30371),X30369) )
      & ( X30373 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
        | hAPP(c_Random_Oiterate(X30372,X30371,X30373,X30370),X30369) = hAPP(hAPP(c_Product__Type_Oscomp(X30371,X30372,X30371,tc_prod(X30372,X30371)),hAPP(X30370,X30369)),c_Random_Oiterate(X30372,X30371,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X30373),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X30370)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_iterate_Osimps])]) ).

fof(i_0_7303,plain,
    ! [X23489,X23490,X23491,X23492,X23493] :
      ( ~ c_Equiv__Relations_Oequiv(X23493,X23492,X23491)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X23493,X23493)),hAPP(hAPP(c_Product__Type_OPair(X23493,X23493),X23490),X23489)),X23491))
      | hAPP(c_Relation_OImage(X23493,X23493,X23491),hAPP(hAPP(c_Set_Oinsert(X23493),X23490),c_Orderings_Obot__class_Obot(tc_fun(X23493,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(X23493,X23493,X23491),hAPP(hAPP(c_Set_Oinsert(X23493),X23489),c_Orderings_Obot__class_Obot(tc_fun(X23493,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__class__eq])]) ).

fof(i_0_7304,plain,
    ! [X27373,X27374,X27375,X27376,X27377,X27378] :
      ( ( hBOOL(hAPP(hAPP(c_member(X27378),X27376),X27374))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27378,X27377)),hAPP(hAPP(c_Product__Type_OPair(X27378,X27377),X27376),X27375)),hAPP(hAPP(c_Product__Type_OSigma(X27378,X27377),X27374),X27373))) )
      & ( hBOOL(hAPP(hAPP(c_member(X27377),X27375),hAPP(X27373,X27376)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27378,X27377)),hAPP(hAPP(c_Product__Type_OPair(X27378,X27377),X27376),X27375)),hAPP(hAPP(c_Product__Type_OSigma(X27378,X27377),X27374),X27373))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5557])])]) ).

fof(i_0_7305,plain,
    ! [X27355,X27356,X27357,X27358,X27359,X27360] :
      ( ( hBOOL(hAPP(hAPP(c_member(X27360),X27358),X27356))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27360,X27359)),hAPP(hAPP(c_Product__Type_OPair(X27360,X27359),X27358),X27357)),hAPP(hAPP(c_Product__Type_OSigma(X27360,X27359),X27356),X27355))) )
      & ( hBOOL(hAPP(hAPP(c_member(X27359),X27357),hAPP(X27355,X27358)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27360,X27359)),hAPP(hAPP(c_Product__Type_OPair(X27360,X27359),X27358),X27357)),hAPP(hAPP(c_Product__Type_OSigma(X27360,X27359),X27356),X27355))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X27360),X27358),X27356))
        | ~ hBOOL(hAPP(hAPP(c_member(X27359),X27357),hAPP(X27355,X27358)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X27360,X27359)),hAPP(hAPP(c_Product__Type_OPair(X27360,X27359),X27358),X27357)),hAPP(hAPP(c_Product__Type_OSigma(X27360,X27359),X27356),X27355))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__Sigma__iff])])]) ).

fof(i_0_7306,plain,
    ! [X27367,X27368,X27369,X27370,X27371,X27372] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27372,X27371)),hAPP(hAPP(c_Product__Type_OPair(X27372,X27371),X27370),X27369)),hAPP(hAPP(c_Product__Type_OSigma(X27372,X27371),X27368),X27367)))
      | hBOOL(hAPP(hAPP(c_member(X27371),X27369),hAPP(X27367,X27370))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SigmaD2])]) ).

fof(i_0_7307,plain,
    ! [X28577,X28578,X28579] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28579,X28579),tc_HOL_Obool)),X28578),X28577))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X28579),tc_List_Olist(X28579)),tc_HOL_Obool)),c_List_Olistrel(X28579,X28578)),c_List_Olistrel(X28579,X28577))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__mono])]) ).

fof(i_0_7308,plain,
    ! [X28515,X28516,X28517] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28517,X28517),tc_HOL_Obool)),X28516),X28515))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X28517),tc_List_Olist(X28517)),tc_HOL_Obool)),c_List_Olistrel1(X28517,X28516)),c_List_Olistrel1(X28517,X28515))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel1__mono])]) ).

fof(i_0_7309,plain,
    ! [X34172,X34173,X34174] :
      ( ~ c_Fun_Obij__betw(X34174,X34173,X34172,c_Orderings_Otop__class_Otop(tc_fun(X34174,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X34173,tc_HOL_Obool)))
      | c_Fun_Oinj__on(X34174,X34173,X34172,c_Orderings_Otop__class_Otop(tc_fun(X34174,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__is__inj])]) ).

cnf(i_0_7310,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_5558]) ).

fof(i_0_7311,plain,
    ! [X30345,X30346,X30347,X30348,X30349,X30350,X30351] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(X30351,X30350,X30349,X30348),X30347),X30346),X30345) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X30350,X30349,X30348),X30346),hAPP(X30347,X30345)),
    inference(variable_rename,[status(thm)],[fact_scomp__def]) ).

fof(i_0_7312,plain,
    ! [X30329,X30330,X30331,X30332,X30333,X30334,X30335] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(X30335,X30334,X30333,X30332),X30331),X30330),X30329) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X30334,X30333,X30332),X30330),hAPP(X30331,X30329)),
    inference(variable_rename,[status(thm)],[fact_scomp__apply]) ).

fof(i_0_7313,plain,
    ! [X22907,X22908,X22909,X22910] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22910,tc_HOL_Obool)),X22909),X22908))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22910,tc_HOL_Obool)),X22907),X22908))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22910,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22910,tc_HOL_Obool)),X22909),X22907)),X22908)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Un__least])]) ).

fof(i_0_7314,plain,
    ! [X24137,X24138,X24139,X24140,X24141] :
      ( ~ c_Finite__Set_Ofolding__one(X24141,X24140,X24139)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24141),X24138))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24141),X24137))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24141,tc_HOL_Obool)),X24138),X24137) = c_Orderings_Obot__class_Obot(tc_fun(X24141,tc_HOL_Obool))
      | hAPP(hAPP(X24140,hAPP(X24139,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24141,tc_HOL_Obool)),X24138),X24137))),hAPP(X24139,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24141,tc_HOL_Obool)),X24138),X24137))) = hAPP(hAPP(X24140,hAPP(X24139,X24138)),hAPP(X24139,X24137)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one_Ounion__inter])]) ).

fof(i_0_7315,plain,
    ! [X26074,X26075,X26076,X26077,X26078] :
      ( ~ c_Fun_Oinj__on(X26078,X26077,X26076,X26075)
      | ~ hBOOL(hAPP(hAPP(c_member(X26077),X26074),hAPP(c_Set_Oimage(X26078,X26077,X26076),X26075)))
      | hAPP(X26076,hAPP(c_Fun_Othe__inv__into(X26078,X26077,X26075,X26076),X26074)) = X26074 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_f__the__inv__into__f])]) ).

cnf(i_0_7316,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_5559]) ).

cnf(i_0_7317,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_5560]) ).

fof(i_0_7318,plain,
    ! [X30857,X30858,X30859,X30860] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X30860,tc_HOL_Obool),tc_fun(X30859,tc_HOL_Obool)),X30858),hAPP(hAPP(c_COMBC(tc_fun(X30860,tc_HOL_Obool),tc_fun(X30860,tc_fun(X30859,tc_HOL_Obool)),tc_fun(X30859,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30860,tc_fun(X30859,tc_HOL_Obool))),X30857)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30860,tc_fun(X30859,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X30860,tc_HOL_Obool),X30858)),X30857),
    inference(variable_rename,[status(thm)],[fact_INT__extend__simps_I8_J]) ).

fof(i_0_7319,plain,
    ! [X30813,X30814,X30815,X30816] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X30816,tc_HOL_Obool),tc_fun(X30815,tc_HOL_Obool)),X30814),hAPP(hAPP(c_COMBC(tc_fun(X30816,tc_HOL_Obool),tc_fun(X30816,tc_fun(X30815,tc_HOL_Obool)),tc_fun(X30815,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X30816,tc_fun(X30815,tc_HOL_Obool))),X30813)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X30816,tc_fun(X30815,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X30816,tc_HOL_Obool),X30814)),X30813),
    inference(variable_rename,[status(thm)],[fact_UN__extend__simps_I8_J]) ).

fof(i_0_7320,plain,
    ! [X30853,X30854,X30855,X30856] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30856,tc_fun(X30855,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X30856,tc_HOL_Obool),X30854)),X30853) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X30856,tc_HOL_Obool),tc_fun(X30855,tc_HOL_Obool)),X30854),hAPP(hAPP(c_COMBC(tc_fun(X30856,tc_HOL_Obool),tc_fun(X30856,tc_fun(X30855,tc_HOL_Obool)),tc_fun(X30855,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30856,tc_fun(X30855,tc_HOL_Obool))),X30853)),
    inference(variable_rename,[status(thm)],[fact_INT__simps_I8_J]) ).

fof(i_0_7321,plain,
    ! [X30817,X30818,X30819,X30820] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X30820,tc_fun(X30819,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X30820,tc_HOL_Obool),X30818)),X30817) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X30820,tc_HOL_Obool),tc_fun(X30819,tc_HOL_Obool)),X30818),hAPP(hAPP(c_COMBC(tc_fun(X30820,tc_HOL_Obool),tc_fun(X30820,tc_fun(X30819,tc_HOL_Obool)),tc_fun(X30819,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X30820,tc_fun(X30819,tc_HOL_Obool))),X30817)),
    inference(variable_rename,[status(thm)],[fact_UN__simps_I8_J]) ).

fof(i_0_7322,plain,
    ! [X25703,X25704,X25705,X25706,X25707,X25708,X25709,X25710,X25711,X25712] :
      ( ( ~ c_Fun_Oinj__on(X25706,X25705,X25704,X25703)
        | ~ hBOOL(hAPP(hAPP(c_member(X25706),X25707),X25703))
        | ~ hBOOL(hAPP(hAPP(c_member(X25706),X25708),X25703))
        | hAPP(X25704,X25707) != hAPP(X25704,X25708)
        | X25707 = X25708 )
      & ( hBOOL(hAPP(hAPP(c_member(X25712),esk215_4(X25709,X25710,X25711,X25712)),X25709))
        | c_Fun_Oinj__on(X25712,X25711,X25710,X25709) )
      & ( hBOOL(hAPP(hAPP(c_member(X25712),esk216_4(X25709,X25710,X25711,X25712)),X25709))
        | c_Fun_Oinj__on(X25712,X25711,X25710,X25709) )
      & ( hAPP(X25710,esk215_4(X25709,X25710,X25711,X25712)) = hAPP(X25710,esk216_4(X25709,X25710,X25711,X25712))
        | c_Fun_Oinj__on(X25712,X25711,X25710,X25709) )
      & ( esk215_4(X25709,X25710,X25711,X25712) != esk216_4(X25709,X25710,X25711,X25712)
        | c_Fun_Oinj__on(X25712,X25711,X25710,X25709) ) ),
    inference(distribute,[status(thm)],[inference(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_7323,plain,
    ! [X32187,X32188,X32189] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X32189,X32189),tc_HOL_Obool)),X32188),X32187))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X32189,X32189),tc_HOL_Obool)),X32187),c_Transitive__Closure_Ortrancl(X32189,X32188)))
      | c_Transitive__Closure_Ortrancl(X32189,X32187) = c_Transitive__Closure_Ortrancl(X32189,X32188) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__subset])]) ).

fof(i_0_7324,plain,
    ! [X23514,X23515,X23516,X23517,X23518] :
      ( hAPP(c_Relation_OImage(X23518,X23518,X23517),hAPP(hAPP(c_Set_Oinsert(X23518),X23516),c_Orderings_Obot__class_Obot(tc_fun(X23518,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(X23518,X23518,X23517),hAPP(hAPP(c_Set_Oinsert(X23518),X23515),c_Orderings_Obot__class_Obot(tc_fun(X23518,tc_HOL_Obool))))
      | ~ c_Equiv__Relations_Oequiv(X23518,X23514,X23517)
      | ~ hBOOL(hAPP(hAPP(c_member(X23518),X23515),X23514))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X23518,X23518)),hAPP(hAPP(c_Product__Type_OPair(X23518,X23518),X23516),X23515)),X23517)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__equiv__class])]) ).

fof(i_0_7325,plain,
    ! [X27361,X27362,X27363,X27364,X27365,X27366] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27366,X27365)),hAPP(hAPP(c_Product__Type_OPair(X27366,X27365),X27364),X27363)),hAPP(hAPP(c_Product__Type_OSigma(X27366,X27365),X27362),X27361)))
      | hBOOL(hAPP(hAPP(c_member(X27366),X27364),X27362)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SigmaD1])]) ).

fof(i_0_7326,plain,
    ! [X24662,X24663,X24664,X24665,X24667] :
      ( ( hBOOL(hAPP(hAPP(c_member(X24664),esk141_4(X24662,X24663,X24664,X24665)),X24663))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24664,X24665),X24662),X24663) != c_Groups_Ozero__class_Ozero(X24665)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24664),X24663))
        | ~ class_Rings_Ocomm__semiring__1(X24665)
        | ~ class_Rings_Ono__zero__divisors(X24665) )
      & ( hAPP(X24662,esk141_4(X24662,X24663,X24664,X24665)) = c_Groups_Ozero__class_Ozero(X24665)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24664,X24665),X24662),X24663) != c_Groups_Ozero__class_Ozero(X24665)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24664),X24663))
        | ~ class_Rings_Ocomm__semiring__1(X24665)
        | ~ class_Rings_Ono__zero__divisors(X24665) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X24664),X24667),X24663))
        | hAPP(X24662,X24667) != c_Groups_Ozero__class_Ozero(X24665)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24664,X24665),X24662),X24663) = c_Groups_Ozero__class_Ozero(X24665)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24664),X24663))
        | ~ class_Rings_Ocomm__semiring__1(X24665)
        | ~ class_Rings_Ono__zero__divisors(X24665) ) ),
    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_7327,plain,
    ! [X24542,X24543,X24544,X24545] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24545),X24544))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X24543),hAPP(c_Set_Oimage(X24545,X24543,X24542),X24544))),hAPP(c_Finite__Set_Ocard(X24545),X24544))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__image__le])]) ).

fof(i_0_7328,plain,
    ! [X30581,X30582,X30583,X30584,X30585] :
      ( ~ class_Orderings_Olinorder(X30585)
      | hBOOL(hAPP(hAPP(c_member(X30585),hAPP(X30584,X30583)),hAPP(c_Set_Oimage(X30582,X30585,X30584),hAPP(c_List_Oset(X30582),X30581))))
      | c_List_Olinorder__class_Oinsort__insert__key(X30582,X30585,X30584,X30583,X30581) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30582,X30585,X30584),X30583),X30581) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5561])]) ).

cnf(i_0_7329,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_5562]) ).

fof(i_0_7330,plain,
    ! [X29846,X29847,X29848,X29849,X29850,X29851,X29852,X29853,X29854] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29849,tc_fun(X29848,tc_HOL_Obool)),X29847),X29846) != c_Orderings_Otop__class_Otop(tc_fun(X29848,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(X29849),X29850),X29847))
        | hAPP(X29846,X29850) = c_Orderings_Otop__class_Otop(tc_fun(X29848,tc_HOL_Obool)) )
      & ( hBOOL(hAPP(hAPP(c_member(X29854),esk353_4(X29851,X29852,X29853,X29854)),X29852))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29854,tc_fun(X29853,tc_HOL_Obool)),X29852),X29851) = c_Orderings_Otop__class_Otop(tc_fun(X29853,tc_HOL_Obool)) )
      & ( hAPP(X29851,esk353_4(X29851,X29852,X29853,X29854)) != c_Orderings_Otop__class_Otop(tc_fun(X29853,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29854,tc_fun(X29853,tc_HOL_Obool)),X29852),X29851) = c_Orderings_Otop__class_Otop(tc_fun(X29853,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_7331,plain,
    ! [X25050,X25051,X25052,X25053,X25054,X25055,X25056,X25057,X25058] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25053,tc_fun(X25052,tc_HOL_Obool)),X25051),X25050) != c_Orderings_Obot__class_Obot(tc_fun(X25052,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(X25053),X25054),X25051))
        | hAPP(X25050,X25054) = c_Orderings_Obot__class_Obot(tc_fun(X25052,tc_HOL_Obool)) )
      & ( hBOOL(hAPP(hAPP(c_member(X25058),esk156_4(X25055,X25056,X25057,X25058)),X25056))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25058,tc_fun(X25057,tc_HOL_Obool)),X25056),X25055) = c_Orderings_Obot__class_Obot(tc_fun(X25057,tc_HOL_Obool)) )
      & ( hAPP(X25055,esk156_4(X25055,X25056,X25057,X25058)) != c_Orderings_Obot__class_Obot(tc_fun(X25057,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25058,tc_fun(X25057,tc_HOL_Obool)),X25056),X25055) = c_Orderings_Obot__class_Obot(tc_fun(X25057,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_7332,plain,
    ! [X29856,X29857,X29858,X29859,X29860,X29861,X29862,X29863,X29864] :
      ( ( c_Orderings_Otop__class_Otop(tc_fun(X29859,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29858,tc_fun(X29859,tc_HOL_Obool)),X29857),X29856)
        | ~ hBOOL(hAPP(hAPP(c_member(X29858),X29860),X29857))
        | hAPP(X29856,X29860) = c_Orderings_Otop__class_Otop(tc_fun(X29859,tc_HOL_Obool)) )
      & ( hBOOL(hAPP(hAPP(c_member(X29863),esk354_4(X29861,X29862,X29863,X29864)),X29862))
        | c_Orderings_Otop__class_Otop(tc_fun(X29864,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29863,tc_fun(X29864,tc_HOL_Obool)),X29862),X29861) )
      & ( hAPP(X29861,esk354_4(X29861,X29862,X29863,X29864)) != c_Orderings_Otop__class_Otop(tc_fun(X29864,tc_HOL_Obool))
        | c_Orderings_Otop__class_Otop(tc_fun(X29864,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29863,tc_fun(X29864,tc_HOL_Obool)),X29862),X29861) ) ),
    inference(distribute,[status(thm)],[inference(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_7333,plain,
    ! [X25067,X25068,X25069,X25070,X25071,X25072,X25073,X25074,X25075] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(X25070,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25069,tc_fun(X25070,tc_HOL_Obool)),X25068),X25067)
        | ~ hBOOL(hAPP(hAPP(c_member(X25069),X25071),X25068))
        | hAPP(X25067,X25071) = c_Orderings_Obot__class_Obot(tc_fun(X25070,tc_HOL_Obool)) )
      & ( hBOOL(hAPP(hAPP(c_member(X25074),esk157_4(X25072,X25073,X25074,X25075)),X25073))
        | c_Orderings_Obot__class_Obot(tc_fun(X25075,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25074,tc_fun(X25075,tc_HOL_Obool)),X25073),X25072) )
      & ( hAPP(X25072,esk157_4(X25072,X25073,X25074,X25075)) != c_Orderings_Obot__class_Obot(tc_fun(X25075,tc_HOL_Obool))
        | c_Orderings_Obot__class_Obot(tc_fun(X25075,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25074,tc_fun(X25075,tc_HOL_Obool)),X25073),X25072) ) ),
    inference(distribute,[status(thm)],[inference(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_7334,plain,
    ! [X32096,X32097,X32098,X32099] :
      ( ( hBOOL(hAPP(hAPP(c_member(X32099),esk433_4(X32096,X32097,X32098,X32099)),X32097))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X32099,tc_Nat_Onat),X32098),X32097) != hAPP(c_Nat_OSuc,X32096) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X32098,esk433_4(X32096,X32097,X32098,X32099))))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X32099,tc_Nat_Onat),X32098),X32097) != hAPP(c_Nat_OSuc,X32096) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__SucD])])])]) ).

fof(i_0_7335,plain,
    ! [X24330,X24331,X24332] :
      ( ~ class_Lattices_Olattice(X24332)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24332),X24331))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24332),X24330))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24332,tc_HOL_Obool)),X24331),X24330) = c_Orderings_Obot__class_Obot(tc_fun(X24332,tc_HOL_Obool))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24332),c_Big__Operators_Olattice__class_OInf__fin(X24332,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24332,tc_HOL_Obool)),X24331),X24330))),c_Big__Operators_Olattice__class_OInf__fin(X24332,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24332,tc_HOL_Obool)),X24331),X24330))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24332),c_Big__Operators_Olattice__class_OInf__fin(X24332,X24331)),c_Big__Operators_Olattice__class_OInf__fin(X24332,X24330)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Ounion__inter])]) ).

fof(i_0_7336,plain,
    ! [X24324,X24325,X24326] :
      ( ~ class_Lattices_Olattice(X24326)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24326),X24325))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24326),X24324))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24326,tc_HOL_Obool)),X24325),X24324) = c_Orderings_Obot__class_Obot(tc_fun(X24326,tc_HOL_Obool))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24326),c_Big__Operators_Olattice__class_OSup__fin(X24326,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24326,tc_HOL_Obool)),X24325),X24324))),c_Big__Operators_Olattice__class_OSup__fin(X24326,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24326,tc_HOL_Obool)),X24325),X24324))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24326),c_Big__Operators_Olattice__class_OSup__fin(X24326,X24325)),c_Big__Operators_Olattice__class_OSup__fin(X24326,X24324)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Ounion__inter])]) ).

fof(i_0_7337,plain,
    ! [X24336,X24337,X24338] :
      ( ~ class_Orderings_Olinorder(X24338)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24338),X24337))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24338),X24336))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24338,tc_HOL_Obool)),X24337),X24336) = c_Orderings_Obot__class_Obot(tc_fun(X24338,tc_HOL_Obool))
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X24338),c_Big__Operators_Olinorder__class_OMax(X24338,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24338,tc_HOL_Obool)),X24337),X24336))),c_Big__Operators_Olinorder__class_OMax(X24338,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24338,tc_HOL_Obool)),X24337),X24336))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X24338),c_Big__Operators_Olinorder__class_OMax(X24338,X24337)),c_Big__Operators_Olinorder__class_OMax(X24338,X24336)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Ounion__inter])]) ).

fof(i_0_7338,plain,
    ! [X24385,X24386,X24387] :
      ( ~ class_Orderings_Olinorder(X24387)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24387),X24386))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24387),X24385))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24387,tc_HOL_Obool)),X24386),X24385) = c_Orderings_Obot__class_Obot(tc_fun(X24387,tc_HOL_Obool))
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X24387),c_Big__Operators_Olinorder__class_OMin(X24387,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24387,tc_HOL_Obool)),X24386),X24385))),c_Big__Operators_Olinorder__class_OMin(X24387,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24387,tc_HOL_Obool)),X24386),X24385))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X24387),c_Big__Operators_Olinorder__class_OMin(X24387,X24386)),c_Big__Operators_Olinorder__class_OMin(X24387,X24385)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Ounion__inter])]) ).

fof(i_0_7339,plain,
    ! [X31905,X31906,X31909,X31910,X31911] :
      ( ( X31905 = hAPP(hAPP(c_List_Olist_OCons(X31906),esk406_2(X31905,X31906)),esk405_2(X31905,X31906))
        | X31905 = c_List_Olist_ONil(X31906)
        | ~ c_List_Olinorder__class_Osorted(X31906,X31905)
        | ~ class_Orderings_Olinorder(X31906) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X31906),X31909),hAPP(c_List_Oset(X31906),esk405_2(X31905,X31906))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31906),esk406_2(X31905,X31906)),X31909))
        | X31905 = c_List_Olist_ONil(X31906)
        | ~ c_List_Olinorder__class_Osorted(X31906,X31905)
        | ~ class_Orderings_Olinorder(X31906) )
      & ( c_List_Olinorder__class_Osorted(X31906,esk405_2(X31905,X31906))
        | X31905 = c_List_Olist_ONil(X31906)
        | ~ c_List_Olinorder__class_Osorted(X31906,X31905)
        | ~ class_Orderings_Olinorder(X31906) )
      & ( X31905 != c_List_Olist_ONil(X31906)
        | c_List_Olinorder__class_Osorted(X31906,X31905)
        | ~ class_Orderings_Olinorder(X31906) )
      & ( hBOOL(hAPP(hAPP(c_member(X31906),esk407_4(X31905,X31906,X31910,X31911)),hAPP(c_List_Oset(X31906),X31910)))
        | X31905 != hAPP(hAPP(c_List_Olist_OCons(X31906),X31911),X31910)
        | ~ c_List_Olinorder__class_Osorted(X31906,X31910)
        | c_List_Olinorder__class_Osorted(X31906,X31905)
        | ~ class_Orderings_Olinorder(X31906) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31906),X31911),esk407_4(X31905,X31906,X31910,X31911)))
        | X31905 != hAPP(hAPP(c_List_Olist_OCons(X31906),X31911),X31910)
        | ~ c_List_Olinorder__class_Osorted(X31906,X31910)
        | c_List_Olinorder__class_Osorted(X31906,X31905)
        | ~ class_Orderings_Olinorder(X31906) ) ),
    inference(distribute,[status(thm)],[inference(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_7340,plain,
    ! [X26951,X26952,X26953,X26954,X26955,X26956,X26957] :
      ( ( hAPP(X26954,X26952) != hAPP(X26954,X26951)
        | X26952 = X26951
        | ~ hBOOL(hAPP(hAPP(c_member(X26956),X26951),X26953))
        | ~ hBOOL(hAPP(hAPP(c_member(X26956),X26952),X26953))
        | ~ c_Typedef_Otype__definition(X26957,X26956,X26955,X26954,X26953) )
      & ( X26952 != X26951
        | hAPP(X26954,X26952) = hAPP(X26954,X26951)
        | ~ hBOOL(hAPP(hAPP(c_member(X26956),X26951),X26953))
        | ~ hBOOL(hAPP(hAPP(c_member(X26956),X26952),X26953))
        | ~ c_Typedef_Otype__definition(X26957,X26956,X26955,X26954,X26953) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_type__definition_OAbs__inject])])]) ).

fof(i_0_7341,plain,
    ! [X33333,X33334] :
      ( ( ~ c_Wellfounded_Oacyclic(X33334,hAPP(c_Set_OCollect(tc_prod(X33334,X33334)),hAPP(c_Product__Type_Oprod_Oprod__case(X33334,X33334,tc_HOL_Obool),c_Predicate_Oconversep(X33334,X33334,X33333))))
        | c_Wellfounded_Oacyclic(X33334,hAPP(c_Set_OCollect(tc_prod(X33334,X33334)),hAPP(c_Product__Type_Oprod_Oprod__case(X33334,X33334,tc_HOL_Obool),X33333))) )
      & ( ~ c_Wellfounded_Oacyclic(X33334,hAPP(c_Set_OCollect(tc_prod(X33334,X33334)),hAPP(c_Product__Type_Oprod_Oprod__case(X33334,X33334,tc_HOL_Obool),X33333)))
        | c_Wellfounded_Oacyclic(X33334,hAPP(c_Set_OCollect(tc_prod(X33334,X33334)),hAPP(c_Product__Type_Oprod_Oprod__case(X33334,X33334,tc_HOL_Obool),c_Predicate_Oconversep(X33334,X33334,X33333)))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acyclicP__converse])]) ).

cnf(i_0_7342,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_5497]) ).

fof(i_0_7343,plain,
    ! [X23119,X23120,X23121,X23122] : hAPP(c_Relation_OField(X23122),hAPP(hAPP(c_Set_Oinsert(tc_prod(X23122,X23122)),hAPP(hAPP(c_Product__Type_OPair(X23122,X23122),X23121),X23120)),X23119)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23122,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X23122),X23121),hAPP(hAPP(c_Set_Oinsert(X23122),X23120),c_Orderings_Obot__class_Obot(tc_fun(X23122,tc_HOL_Obool))))),hAPP(c_Relation_OField(X23122),X23119)),
    inference(variable_rename,[status(thm)],[fact_Field__insert]) ).

fof(i_0_7344,plain,
    ! [X29422,X29423,X29424] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X29424),X29423))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X29424),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X29423),X29422))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_start__le__sum])]) ).

cnf(i_0_7345,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_5563]) ).

fof(i_0_7346,plain,
    ! [X21687,X21688,X21689,X21690,X21691,X21692] : c_Nitpick_Opair__box_Opair__box__size(X21692,X21691,X21690,X21689,c_Nitpick_Opair__box_OPairBox(X21692,X21691,X21688,X21687)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X21690,X21688)),hAPP(X21689,X21687))),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_7347,plain,
    ! [X31072,X31073,X31074] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_fun(X31074,tc_HOL_Obool)),esk379_3(X31072,X31073,X31074)),X31073))
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X31072),hAPP(c_Finite__Set_Ocard(tc_fun(X31074,tc_HOL_Obool)),X31073)) = hAPP(c_Finite__Set_Ocard(X31074),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31074,tc_HOL_Obool),X31073))
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X31074,tc_HOL_Obool)),esk378_3(X31072,X31073,X31074)),X31073))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31074),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31074,tc_HOL_Obool),X31073)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X31074,tc_HOL_Obool)),X31073)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_fun(X31074,tc_HOL_Obool)),esk380_3(X31072,X31073,X31074)),X31073))
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X31072),hAPP(c_Finite__Set_Ocard(tc_fun(X31074,tc_HOL_Obool)),X31073)) = hAPP(c_Finite__Set_Ocard(X31074),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31074,tc_HOL_Obool),X31073))
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X31074,tc_HOL_Obool)),esk378_3(X31072,X31073,X31074)),X31073))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31074),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31074,tc_HOL_Obool),X31073)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X31074,tc_HOL_Obool)),X31073)) )
      & ( esk379_3(X31072,X31073,X31074) != esk380_3(X31072,X31073,X31074)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X31072),hAPP(c_Finite__Set_Ocard(tc_fun(X31074,tc_HOL_Obool)),X31073)) = hAPP(c_Finite__Set_Ocard(X31074),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31074,tc_HOL_Obool),X31073))
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X31074,tc_HOL_Obool)),esk378_3(X31072,X31073,X31074)),X31073))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31074),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31074,tc_HOL_Obool),X31073)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X31074,tc_HOL_Obool)),X31073)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31074,tc_HOL_Obool)),esk379_3(X31072,X31073,X31074)),esk380_3(X31072,X31073,X31074)) != c_Orderings_Obot__class_Obot(tc_fun(X31074,tc_HOL_Obool))
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X31072),hAPP(c_Finite__Set_Ocard(tc_fun(X31074,tc_HOL_Obool)),X31073)) = hAPP(c_Finite__Set_Ocard(X31074),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31074,tc_HOL_Obool),X31073))
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X31074,tc_HOL_Obool)),esk378_3(X31072,X31073,X31074)),X31073))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31074),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31074,tc_HOL_Obool),X31073)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X31074,tc_HOL_Obool)),X31073)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_fun(X31074,tc_HOL_Obool)),esk379_3(X31072,X31073,X31074)),X31073))
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X31072),hAPP(c_Finite__Set_Ocard(tc_fun(X31074,tc_HOL_Obool)),X31073)) = hAPP(c_Finite__Set_Ocard(X31074),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31074,tc_HOL_Obool),X31073))
        | hAPP(c_Finite__Set_Ocard(X31074),esk378_3(X31072,X31073,X31074)) != X31072
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31074),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31074,tc_HOL_Obool),X31073)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X31074,tc_HOL_Obool)),X31073)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_fun(X31074,tc_HOL_Obool)),esk380_3(X31072,X31073,X31074)),X31073))
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X31072),hAPP(c_Finite__Set_Ocard(tc_fun(X31074,tc_HOL_Obool)),X31073)) = hAPP(c_Finite__Set_Ocard(X31074),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31074,tc_HOL_Obool),X31073))
        | hAPP(c_Finite__Set_Ocard(X31074),esk378_3(X31072,X31073,X31074)) != X31072
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31074),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31074,tc_HOL_Obool),X31073)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X31074,tc_HOL_Obool)),X31073)) )
      & ( esk379_3(X31072,X31073,X31074) != esk380_3(X31072,X31073,X31074)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X31072),hAPP(c_Finite__Set_Ocard(tc_fun(X31074,tc_HOL_Obool)),X31073)) = hAPP(c_Finite__Set_Ocard(X31074),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31074,tc_HOL_Obool),X31073))
        | hAPP(c_Finite__Set_Ocard(X31074),esk378_3(X31072,X31073,X31074)) != X31072
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31074),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31074,tc_HOL_Obool),X31073)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X31074,tc_HOL_Obool)),X31073)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31074,tc_HOL_Obool)),esk379_3(X31072,X31073,X31074)),esk380_3(X31072,X31073,X31074)) != c_Orderings_Obot__class_Obot(tc_fun(X31074,tc_HOL_Obool))
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X31072),hAPP(c_Finite__Set_Ocard(tc_fun(X31074,tc_HOL_Obool)),X31073)) = hAPP(c_Finite__Set_Ocard(X31074),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31074,tc_HOL_Obool),X31073))
        | hAPP(c_Finite__Set_Ocard(X31074),esk378_3(X31072,X31073,X31074)) != X31072
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31074),c_Complete__Lattice_OSup__class_OSup(tc_fun(X31074,tc_HOL_Obool),X31073)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X31074,tc_HOL_Obool)),X31073)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__partition])])])]) ).

fof(i_0_7348,plain,
    ! [X31515,X31516,X31517] :
      ( ~ class_Orderings_Olinorder(X31517)
      | c_List_Olinorder__class_Osorted(X31517,hAPP(c_List_Ofilter(X31517,hAPP(hAPP(c_COMBC(X31517,X31517,tc_HOL_Obool),c_fequal),hAPP(X31516,X31515))),X31515)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__same])]) ).

fof(i_0_7349,plain,
    ! [X26736,X26737,X26738,X26739,X26740] :
      ( ~ c_Fun_Oinj__on(X26740,X26739,X26738,c_Orderings_Otop__class_Otop(tc_fun(X26740,tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(X26737,X26740,X26736,c_Orderings_Otop__class_Otop(tc_fun(X26737,tc_HOL_Obool)))
      | c_Fun_Oinj__on(X26737,X26739,hAPP(c_Fun_Ocomp(X26740,X26739,X26737,X26738),X26736),c_Orderings_Otop__class_Otop(tc_fun(X26737,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__comp])]) ).

fof(i_0_7350,plain,
    ! [X29114,X29115,X29116,X29117] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29117,tc_HOL_Obool)),hAPP(c_List_Oset(X29117),hAPP(hAPP(c_List_Olist__update(X29117,X29116),X29115),X29114))),hAPP(hAPP(c_Set_Oinsert(X29117),X29114),hAPP(c_List_Oset(X29117),X29116)))),
    inference(variable_rename,[status(thm)],[fact_set__update__subset__insert]) ).

cnf(i_0_7351,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_5564]) ).

fof(i_0_7352,plain,
    ! [X24473,X24474,X24475] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24475,tc_HOL_Obool)),X24474),hAPP(hAPP(c_Set_Oinsert(X24475),X24473),c_Orderings_Obot__class_Obot(tc_fun(X24475,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X24475,tc_HOL_Obool))
        | c_Big__Operators_Olattice_OInf__fin(X24475,c_Orderings_Oord__class_Omin(X24475),X24474) = X24473
        | ~ hBOOL(hAPP(hAPP(c_member(X24475),X24473),X24474))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24475),X24474))
        | ~ class_Orderings_Olinorder(X24475) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24475,tc_HOL_Obool)),X24474),hAPP(hAPP(c_Set_Oinsert(X24475),X24473),c_Orderings_Obot__class_Obot(tc_fun(X24475,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X24475,tc_HOL_Obool))
        | c_Big__Operators_Olattice_OInf__fin(X24475,c_Orderings_Oord__class_Omin(X24475),X24474) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X24475),X24473),c_Big__Operators_Olattice_OInf__fin(X24475,c_Orderings_Oord__class_Omin(X24475),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24475,tc_HOL_Obool)),X24474),hAPP(hAPP(c_Set_Oinsert(X24475),X24473),c_Orderings_Obot__class_Obot(tc_fun(X24475,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(hAPP(c_member(X24475),X24473),X24474))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24475),X24474))
        | ~ class_Orderings_Olinorder(X24475) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oremove])])]) ).

fof(i_0_7353,plain,
    ! [X24411,X24412,X24413] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24413,tc_HOL_Obool)),X24412),hAPP(hAPP(c_Set_Oinsert(X24413),X24411),c_Orderings_Obot__class_Obot(tc_fun(X24413,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X24413,tc_HOL_Obool))
        | c_Big__Operators_Olattice_OSup__fin(X24413,c_Orderings_Oord__class_Omax(X24413),X24412) = X24411
        | ~ hBOOL(hAPP(hAPP(c_member(X24413),X24411),X24412))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24413),X24412))
        | ~ class_Orderings_Olinorder(X24413) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24413,tc_HOL_Obool)),X24412),hAPP(hAPP(c_Set_Oinsert(X24413),X24411),c_Orderings_Obot__class_Obot(tc_fun(X24413,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X24413,tc_HOL_Obool))
        | c_Big__Operators_Olattice_OSup__fin(X24413,c_Orderings_Oord__class_Omax(X24413),X24412) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X24413),X24411),c_Big__Operators_Olattice_OSup__fin(X24413,c_Orderings_Oord__class_Omax(X24413),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24413,tc_HOL_Obool)),X24412),hAPP(hAPP(c_Set_Oinsert(X24413),X24411),c_Orderings_Obot__class_Obot(tc_fun(X24413,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(hAPP(c_member(X24413),X24411),X24412))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24413),X24412))
        | ~ class_Orderings_Olinorder(X24413) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oremove])])]) ).

fof(i_0_7354,plain,
    ! [X26498,X26499,X26500] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26500,tc_Nat_Onat),X26499),X26498) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26500,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X26500),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X26499)),X26498)),
    inference(variable_rename,[status(thm)],[fact_transfer__nat__int__sum__prod2_I1_J]) ).

fof(i_0_7355,plain,
    ! [X24646,X24647,X24648] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24648,tc_Nat_Onat),X24647),X24646) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24648,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X24648),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X24647)),X24646)),
    inference(variable_rename,[status(thm)],[fact_transfer__nat__int__sum__prod2_I2_J]) ).

fof(i_0_7356,plain,
    ! [X27185,X27186,X27187,X27188,X27189] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X27189),X27188),hAPP(c_Set_Ovimage(X27189,X27187,X27186),hAPP(hAPP(c_Set_Oinsert(X27187),X27185),c_Orderings_Obot__class_Obot(tc_fun(X27187,tc_HOL_Obool))))))
        | hAPP(X27186,X27188) = X27185 )
      & ( hAPP(X27186,X27188) != X27185
        | hBOOL(hAPP(hAPP(c_member(X27189),X27188),hAPP(c_Set_Ovimage(X27189,X27187,X27186),hAPP(hAPP(c_Set_Oinsert(X27187),X27185),c_Orderings_Obot__class_Obot(tc_fun(X27187,tc_HOL_Obool)))))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vimage__singleton__eq])]) ).

cnf(i_0_7357,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_5565]) ).

fof(i_0_7358,plain,
    ! [X25677,X25678,X25679,X25680,X25681,X25682] :
      ( ~ c_Fun_Oinj__on(X25682,X25681,hAPP(c_Fun_Ocomp(X25680,X25681,X25682,X25679),X25678),X25677)
      | c_Fun_Oinj__on(X25682,X25680,X25678,X25677) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__imageI2])]) ).

cnf(i_0_7359,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_5566]) ).

fof(i_0_7360,plain,
    ! [X23566,X23567,X23568,X23569] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23569),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23569,tc_HOL_Obool)),X23568),hAPP(hAPP(c_Set_Oinsert(X23569),X23567),X23566))))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X23569),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23569,tc_HOL_Obool)),X23568),X23566))) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23569),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23569,tc_HOL_Obool)),X23568),X23566)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X23569),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23569,tc_HOL_Obool)),X23568),hAPP(hAPP(c_Set_Oinsert(X23569),X23567),X23566)))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Diff__insert])]) ).

fof(i_0_7361,plain,
    ! [X27774,X27775,X27776] : hAPP(hAPP(c_Set_Oinsert(X27776),X27775),X27774) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27776,tc_HOL_Obool)),hAPP(c_Set_OCollect(X27776),hAPP(hAPP(c_COMBC(X27776,X27776,tc_HOL_Obool),c_fequal),X27775))),X27774),
    inference(variable_rename,[status(thm)],[fact_insert__def]) ).

cnf(i_0_7362,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_5567]) ).

cnf(i_0_7363,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_5568]) ).

cnf(i_0_7364,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_7365,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_7366,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_5502]) ).

cnf(i_0_7367,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_5503]) ).

cnf(i_0_7368,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_5504]) ).

cnf(i_0_7369,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_5505]) ).

fof(i_0_7370,plain,
    ! [X19968,X19969,X19970,X19971,X19972,X19973] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19973),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19973),X19972),X19971)),X19970) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19973),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19973),X19969),X19971)),X19968)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19973),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19973),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19973),X19972),X19969)),X19971)),X19970) = X19968
        | ~ class_Rings_Oring(X19973) )
      & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19973),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19973),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19973),X19972),X19969)),X19971)),X19970) != X19968
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19973),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19973),X19972),X19971)),X19970) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19973),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19973),X19969),X19971)),X19968)
        | ~ class_Rings_Oring(X19973) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__add__iff1])])]) ).

fof(i_0_7371,plain,
    ! [X19962,X19963,X19964,X19965,X19966,X19967] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19967),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19967),X19966),X19965)),X19964) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19967),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19967),X19963),X19965)),X19962)
        | X19964 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19967),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19967),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19967),X19963),X19966)),X19965)),X19962)
        | ~ class_Rings_Oring(X19967) )
      & ( X19964 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19967),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19967),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19967),X19963),X19966)),X19965)),X19962)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19967),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19967),X19966),X19965)),X19964) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19967),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19967),X19963),X19965)),X19962)
        | ~ class_Rings_Oring(X19967) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__add__iff2])])]) ).

fof(i_0_7372,plain,
    ! [X32522,X32523,X32524,X32525,X32526,X32527] :
      ( ~ c_Relation_Osingle__valued(X32527,X32526,hAPP(c_Relation_Oconverse(X32526,X32527),X32525))
      | X32524 = c_Orderings_Obot__class_Obot(tc_fun(X32523,tc_HOL_Obool))
      | hAPP(c_Relation_OImage(X32526,X32527,X32525),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X32523,tc_fun(X32526,tc_HOL_Obool)),X32524),X32522)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X32523,tc_fun(X32527,tc_HOL_Obool)),X32524),hAPP(hAPP(c_COMBB(tc_fun(X32526,tc_HOL_Obool),tc_fun(X32527,tc_HOL_Obool),X32523),c_Relation_OImage(X32526,X32527,X32525)),X32522)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Image__INT__eq])]) ).

fof(i_0_7373,plain,
    ! [X31225,X31226,X31227] : hAPP(c_Product__Type_Osnd(tc_List_Olist(X31227),tc_List_Olist(X31227)),c_List_Opartition(X31227,X31226,X31225)) = hAPP(c_List_Ofilter(X31227,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,X31227,c_fNot),X31226)),X31225),
    inference(variable_rename,[status(thm)],[fact_partition__filter2]) ).

cnf(i_0_7374,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_5571]) ).

fof(i_0_7375,plain,
    ! [X33971,X33972,X33973,X33974,X33975] :
      ( ~ c_Fun_Oinj__on(X33975,X33974,X33973,X33972)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X33975,tc_HOL_Obool)),X33971),X33972))
      | hAPP(c_Set_Oimage(X33974,X33975,c_Hilbert__Choice_Oinv__into(X33975,X33974,X33972,X33973)),hAPP(c_Set_Oimage(X33975,X33974,X33973),X33971)) = X33971 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__image__cancel])]) ).

fof(i_0_7376,plain,
    ! [X27123,X27124,X27125,X27126,X27127] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27127,tc_HOL_Obool)),X27126),X27125))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27124,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X27124,X27127,X27123),X27126)),hAPP(c_Set_Ovimage(X27124,X27127,X27123),X27125))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vimage__mono])]) ).

fof(i_0_7377,plain,
    ! [X23168,X23169,X23170,X23171,X23172] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23172,tc_HOL_Obool)),X23171),X23170))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23169,tc_HOL_Obool)),hAPP(c_Set_Oimage(X23172,X23169,X23168),X23171)),hAPP(c_Set_Oimage(X23172,X23169,X23168),X23170))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__mono])]) ).

fof(i_0_7378,plain,
    ! [X24927,X24928,X24929,X24930,X24931,X24932] :
      ( ~ c_Equiv__Relations_Oequiv(X24932,X24931,X24930)
      | ~ c_Equiv__Relations_Ocongruent(X24932,tc_fun(X24929,tc_HOL_Obool),X24930,X24928)
      | ~ hBOOL(hAPP(hAPP(c_member(X24932),X24927),X24931))
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24932,tc_fun(X24929,tc_HOL_Obool)),hAPP(c_Relation_OImage(X24932,X24932,X24930),hAPP(hAPP(c_Set_Oinsert(X24932),X24927),c_Orderings_Obot__class_Obot(tc_fun(X24932,tc_HOL_Obool))))),X24928) = hAPP(X24928,X24927) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__equiv__class])]) ).

fof(i_0_7379,plain,
    ! [X24502,X24503,X24504] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24504,tc_HOL_Obool)),X24503),hAPP(hAPP(c_Set_Oinsert(X24504),X24502),c_Orderings_Obot__class_Obot(tc_fun(X24504,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X24504,tc_HOL_Obool))
        | c_Big__Operators_Olattice_OInf__fin(X24504,c_Orderings_Oord__class_Omin(X24504),hAPP(hAPP(c_Set_Oinsert(X24504),X24502),X24503)) = X24502
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24504),X24503))
        | ~ class_Orderings_Olinorder(X24504) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24504,tc_HOL_Obool)),X24503),hAPP(hAPP(c_Set_Oinsert(X24504),X24502),c_Orderings_Obot__class_Obot(tc_fun(X24504,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X24504,tc_HOL_Obool))
        | c_Big__Operators_Olattice_OInf__fin(X24504,c_Orderings_Oord__class_Omin(X24504),hAPP(hAPP(c_Set_Oinsert(X24504),X24502),X24503)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X24504),X24502),c_Big__Operators_Olattice_OInf__fin(X24504,c_Orderings_Oord__class_Omin(X24504),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24504,tc_HOL_Obool)),X24503),hAPP(hAPP(c_Set_Oinsert(X24504),X24502),c_Orderings_Obot__class_Obot(tc_fun(X24504,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24504),X24503))
        | ~ class_Orderings_Olinorder(X24504) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oinsert__remove])])]) ).

fof(i_0_7380,plain,
    ! [X24446,X24447,X24448] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24448,tc_HOL_Obool)),X24447),hAPP(hAPP(c_Set_Oinsert(X24448),X24446),c_Orderings_Obot__class_Obot(tc_fun(X24448,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X24448,tc_HOL_Obool))
        | c_Big__Operators_Olattice_OSup__fin(X24448,c_Orderings_Oord__class_Omax(X24448),hAPP(hAPP(c_Set_Oinsert(X24448),X24446),X24447)) = X24446
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24448),X24447))
        | ~ class_Orderings_Olinorder(X24448) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24448,tc_HOL_Obool)),X24447),hAPP(hAPP(c_Set_Oinsert(X24448),X24446),c_Orderings_Obot__class_Obot(tc_fun(X24448,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X24448,tc_HOL_Obool))
        | c_Big__Operators_Olattice_OSup__fin(X24448,c_Orderings_Oord__class_Omax(X24448),hAPP(hAPP(c_Set_Oinsert(X24448),X24446),X24447)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X24448),X24446),c_Big__Operators_Olattice_OSup__fin(X24448,c_Orderings_Oord__class_Omax(X24448),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24448,tc_HOL_Obool)),X24447),hAPP(hAPP(c_Set_Oinsert(X24448),X24446),c_Orderings_Obot__class_Obot(tc_fun(X24448,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24448),X24447))
        | ~ class_Orderings_Olinorder(X24448) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oinsert__remove])])]) ).

fof(i_0_7381,plain,
    ! [X17888,X17889,X17890,X17891,X17892,X17893,X17894,X17895,X17896,X17897,X17898] :
      ( hAPP(X17898,hAPP(X17897,X17896)) != hAPP(X17895,hAPP(X17894,X17893))
      | hAPP(hAPP(c_Fun_Ocomp(X17892,X17891,X17890,X17898),X17897),X17896) = hAPP(hAPP(c_Fun_Ocomp(X17889,X17891,X17888,X17895),X17894),X17893) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comp__cong])]) ).

cnf(i_0_7382,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_5572]) ).

fof(i_0_7383,plain,
    ! [X33958,X33959,X33960] :
      ( ~ c_Fun_Oinj__on(X33960,X33959,X33958,c_Orderings_Otop__class_Otop(tc_fun(X33960,tc_HOL_Obool)))
      | hAPP(c_Fun_Ocomp(X33959,X33960,X33960,c_Hilbert__Choice_Oinv__into(X33960,X33959,c_Orderings_Otop__class_Otop(tc_fun(X33960,tc_HOL_Obool)),X33958)),X33958) = c_Fun_Oid(X33960) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__o__cancel])]) ).

fof(i_0_7384,plain,
    ! [X23579,X23580,X23581,X23582,X23583] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23583,tc_HOL_Obool)),X23580),hAPP(hAPP(c_Set_Oinsert(X23583),X23579),c_Orderings_Obot__class_Obot(tc_fun(X23583,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X23583,tc_HOL_Obool))
        | hAPP(X23581,X23580) = X23579
        | ~ hBOOL(hAPP(hAPP(c_member(X23583),X23579),X23580))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23583),X23580))
        | ~ c_Finite__Set_Ofolding__one(X23583,X23582,X23581) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23583,tc_HOL_Obool)),X23580),hAPP(hAPP(c_Set_Oinsert(X23583),X23579),c_Orderings_Obot__class_Obot(tc_fun(X23583,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X23583,tc_HOL_Obool))
        | hAPP(X23581,X23580) = hAPP(hAPP(X23582,X23579),hAPP(X23581,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23583,tc_HOL_Obool)),X23580),hAPP(hAPP(c_Set_Oinsert(X23583),X23579),c_Orderings_Obot__class_Obot(tc_fun(X23583,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(hAPP(c_member(X23583),X23579),X23580))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23583),X23580))
        | ~ c_Finite__Set_Ofolding__one(X23583,X23582,X23581) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one_Oremove])])]) ).

fof(i_0_7385,plain,
    ! [X24557,X24558,X24559] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24559),X24558))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24559),X24557))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X24559),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24559,tc_HOL_Obool)),X24558),X24557))),hAPP(c_Finite__Set_Ocard(X24559),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24559,tc_HOL_Obool)),X24558),X24557))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X24559),X24558)),hAPP(c_Finite__Set_Ocard(X24559),X24557)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card_Ounion__inter])]) ).

fof(i_0_7386,plain,
    ! [X24560,X24561,X24562] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24562),X24561))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24562),X24560))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X24562),X24561)),hAPP(c_Finite__Set_Ocard(X24562),X24560)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X24562),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24562,tc_HOL_Obool)),X24561),X24560))),hAPP(c_Finite__Set_Ocard(X24562),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24562,tc_HOL_Obool)),X24561),X24560))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Un__Int])]) ).

fof(i_0_7387,plain,
    ! [X31078,X31079,X31080,X31081] :
      ( ( hBOOL(hAPP(X31081,esk381_4(X31078,X31079,X31080,X31081)))
        | c_Wellfounded_Owf(tc_prod(X31078,X31080),c_Recdef_Osame__fst(X31078,X31080,X31081,X31079)) )
      & ( ~ c_Wellfounded_Owf(X31080,hAPP(X31079,esk381_4(X31078,X31079,X31080,X31081)))
        | c_Wellfounded_Owf(tc_prod(X31078,X31080),c_Recdef_Osame__fst(X31078,X31080,X31081,X31079)) ) ),
    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_7388,plain,
    ! [X21813,X21814,X21815,X21816,X21817] :
      ( ( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X21817,X21816,X21815),X21814),X21813))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X21817,X21816)),hAPP(hAPP(c_Product__Type_OPair(X21817,X21816),X21814),X21813)),X21815)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X21817,X21816)),hAPP(hAPP(c_Product__Type_OPair(X21817,X21816),X21814),X21813)),X21815))
        | hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X21817,X21816,X21815),X21814),X21813)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__rel__def])]) ).

fof(i_0_7389,plain,
    ! [X34167,X34168,X34169,X34170,X34171] :
      ( ~ c_Fun_Obij__betw(X34171,X34170,X34169,X34168,X34167)
      | c_Fun_Oinj__on(X34171,X34170,X34169,X34168) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__betw__imp__inj__on])]) ).

cnf(i_0_7390,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_5573]) ).

fof(i_0_7391,plain,
    ! [X32181,X32182,X32183] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X32183,tc_HOL_Obool)),hAPP(c_Relation_OImage(X32183,X32183,X32182),X32181)),X32181))
      | hAPP(c_Relation_OImage(X32183,X32183,c_Transitive__Closure_Ortrancl(X32183,X32182)),X32181) = X32181 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Image__closed__trancl])]) ).

cnf(i_0_7392,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_5574]) ).

fof(i_0_7393,plain,
    ! [X32234,X32235,X32236,X32237] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32237,X32237)),hAPP(hAPP(c_Product__Type_OPair(X32237,X32237),X32236),X32235)),c_Transitive__Closure_Ortrancl(X32237,X32234)))
      | ~ hBOOL(hAPP(hAPP(c_member(X32237),X32235),c_Wellfounded_Oacc(X32237,X32234)))
      | hBOOL(hAPP(hAPP(c_member(X32237),X32236),c_Wellfounded_Oacc(X32237,X32234))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc__downwards__aux])]) ).

fof(i_0_7394,plain,
    ! [X32238,X32239,X32240,X32241] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X32241),X32240),c_Wellfounded_Oacc(X32241,X32239)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32241,X32241)),hAPP(hAPP(c_Product__Type_OPair(X32241,X32241),X32238),X32240)),c_Transitive__Closure_Ortrancl(X32241,X32239)))
      | hBOOL(hAPP(hAPP(c_member(X32241),X32238),c_Wellfounded_Oacc(X32241,X32239))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc__downwards])]) ).

fof(i_0_7395,plain,
    ! [X24597,X24598,X24599,X24600] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24600),X24599))
      | ~ hBOOL(hAPP(hAPP(c_member(X24600),X24598),X24599))
      | hBOOL(hAPP(hAPP(c_member(X24600),X24598),X24597))
      | hAPP(c_Finite__Set_Ocard(X24600),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24600,tc_HOL_Obool)),X24599),hAPP(hAPP(c_Set_Oinsert(X24600),X24598),X24597))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X24600),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24600,tc_HOL_Obool)),X24599),X24597))),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5575])]) ).

cnf(i_0_7396,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_5576]) ).

fof(i_0_7397,plain,
    ! [X30161,X30162,X30163,X30164,X30165] :
      ( ( X30165 != c_Orderings_Obot__class_Obot(tc_fun(X30164,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30164,tc_fun(X30163,tc_HOL_Obool)),X30165),hAPP(hAPP(c_COMBB(tc_fun(X30163,tc_HOL_Obool),tc_fun(X30163,tc_HOL_Obool),X30164),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X30163,tc_HOL_Obool)),X30162)),X30161)) = c_Orderings_Otop__class_Otop(tc_fun(X30163,tc_HOL_Obool)) )
      & ( X30165 = c_Orderings_Obot__class_Obot(tc_fun(X30164,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30164,tc_fun(X30163,tc_HOL_Obool)),X30165),hAPP(hAPP(c_COMBB(tc_fun(X30163,tc_HOL_Obool),tc_fun(X30163,tc_HOL_Obool),X30164),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X30163,tc_HOL_Obool)),X30162)),X30161)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X30163,tc_HOL_Obool)),X30162),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30164,tc_fun(X30163,tc_HOL_Obool)),X30165),X30161)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__simps_I2_J])]) ).

fof(i_0_7398,plain,
    ! [X30201,X30202,X30203,X30204,X30205] :
      ( ( X30205 != c_Orderings_Obot__class_Obot(tc_fun(X30204,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30204,tc_fun(X30203,tc_HOL_Obool)),X30205),hAPP(hAPP(c_COMBB(tc_fun(X30203,tc_HOL_Obool),tc_fun(X30203,tc_HOL_Obool),X30204),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X30203,tc_HOL_Obool)),X30202)),X30201)) = c_Orderings_Otop__class_Otop(tc_fun(X30203,tc_HOL_Obool)) )
      & ( X30205 = c_Orderings_Obot__class_Obot(tc_fun(X30204,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30204,tc_fun(X30203,tc_HOL_Obool)),X30205),hAPP(hAPP(c_COMBB(tc_fun(X30203,tc_HOL_Obool),tc_fun(X30203,tc_HOL_Obool),X30204),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X30203,tc_HOL_Obool)),X30202)),X30201)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X30203,tc_HOL_Obool)),X30202),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X30204,tc_fun(X30203,tc_HOL_Obool)),X30205),X30201)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__simps_I4_J])]) ).

fof(i_0_7399,plain,
    ! [X25218,X25219,X25220,X25221,X25222] :
      ( ( X25222 != c_Orderings_Obot__class_Obot(tc_fun(X25221,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25221,tc_fun(X25220,tc_HOL_Obool)),X25222),hAPP(hAPP(c_COMBB(tc_fun(X25220,tc_HOL_Obool),tc_fun(X25220,tc_HOL_Obool),X25221),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25220,tc_HOL_Obool)),X25219)),X25218)) = c_Orderings_Obot__class_Obot(tc_fun(X25220,tc_HOL_Obool)) )
      & ( X25222 = c_Orderings_Obot__class_Obot(tc_fun(X25221,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25221,tc_fun(X25220,tc_HOL_Obool)),X25222),hAPP(hAPP(c_COMBB(tc_fun(X25220,tc_HOL_Obool),tc_fun(X25220,tc_HOL_Obool),X25221),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25220,tc_HOL_Obool)),X25219)),X25218)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25220,tc_HOL_Obool)),X25219),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25221,tc_fun(X25220,tc_HOL_Obool)),X25222),X25218)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__simps_I3_J])]) ).

fof(i_0_7400,plain,
    ! [X29920,X29921,X29922,X29923,X29924] :
      ( ( X29924 != c_Orderings_Obot__class_Obot(tc_fun(X29923,tc_HOL_Obool))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29922,tc_HOL_Obool)),X29921),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29923,tc_fun(X29922,tc_HOL_Obool)),X29924),X29920)) = X29921 )
      & ( X29924 = c_Orderings_Obot__class_Obot(tc_fun(X29923,tc_HOL_Obool))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29922,tc_HOL_Obool)),X29921),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29923,tc_fun(X29922,tc_HOL_Obool)),X29924),X29920)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29923,tc_fun(X29922,tc_HOL_Obool)),X29924),hAPP(hAPP(c_COMBB(tc_fun(X29922,tc_HOL_Obool),tc_fun(X29922,tc_HOL_Obool),X29923),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29922,tc_HOL_Obool)),X29921)),X29920)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I2_J])]) ).

fof(i_0_7401,plain,
    ! [X25208,X25209,X25210,X25211,X25212] :
      ( ( X25212 != c_Orderings_Obot__class_Obot(tc_fun(X25211,tc_HOL_Obool))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25210,tc_HOL_Obool)),X25209),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25211,tc_fun(X25210,tc_HOL_Obool)),X25212),X25208)) = X25209 )
      & ( X25212 = c_Orderings_Obot__class_Obot(tc_fun(X25211,tc_HOL_Obool))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25210,tc_HOL_Obool)),X25209),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25211,tc_fun(X25210,tc_HOL_Obool)),X25212),X25208)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25211,tc_fun(X25210,tc_HOL_Obool)),X25212),hAPP(hAPP(c_COMBB(tc_fun(X25210,tc_HOL_Obool),tc_fun(X25210,tc_HOL_Obool),X25211),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25210,tc_HOL_Obool)),X25209)),X25208)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I3_J])]) ).

fof(i_0_7402,plain,
    ! [X30182,X30183,X30184,X30185,X30186] :
      ( ( X30186 != c_Orderings_Obot__class_Obot(tc_fun(X30185,tc_HOL_Obool))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X30184,tc_HOL_Obool)),X30183),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X30185,tc_fun(X30184,tc_HOL_Obool)),X30186),X30182)) = X30183 )
      & ( X30186 = c_Orderings_Obot__class_Obot(tc_fun(X30185,tc_HOL_Obool))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X30184,tc_HOL_Obool)),X30183),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X30185,tc_fun(X30184,tc_HOL_Obool)),X30186),X30182)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30185,tc_fun(X30184,tc_HOL_Obool)),X30186),hAPP(hAPP(c_COMBB(tc_fun(X30184,tc_HOL_Obool),tc_fun(X30184,tc_HOL_Obool),X30185),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X30184,tc_HOL_Obool)),X30183)),X30182)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I4_J])]) ).

fof(i_0_7403,plain,
    ! [X23674,X23675,X23676,X23677,X23678] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23678,tc_HOL_Obool)),X23675),hAPP(hAPP(c_Set_Oinsert(X23678),X23674),c_Orderings_Obot__class_Obot(tc_fun(X23678,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X23678,tc_HOL_Obool))
        | hAPP(X23676,hAPP(hAPP(c_Set_Oinsert(X23678),X23674),X23675)) = X23674
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23678),X23675))
        | ~ c_Finite__Set_Ofolding__one(X23678,X23677,X23676) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23678,tc_HOL_Obool)),X23675),hAPP(hAPP(c_Set_Oinsert(X23678),X23674),c_Orderings_Obot__class_Obot(tc_fun(X23678,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X23678,tc_HOL_Obool))
        | hAPP(X23676,hAPP(hAPP(c_Set_Oinsert(X23678),X23674),X23675)) = hAPP(hAPP(X23677,X23674),hAPP(X23676,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23678,tc_HOL_Obool)),X23675),hAPP(hAPP(c_Set_Oinsert(X23678),X23674),c_Orderings_Obot__class_Obot(tc_fun(X23678,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23678),X23675))
        | ~ c_Finite__Set_Ofolding__one(X23678,X23677,X23676) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one_Oinsert__remove])])]) ).

fof(i_0_7404,plain,
    ! [X24354,X24355,X24356] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24356,tc_HOL_Obool)),X24355),hAPP(hAPP(c_Set_Oinsert(X24356),X24354),c_Orderings_Obot__class_Obot(tc_fun(X24356,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X24356,tc_HOL_Obool))
        | c_Big__Operators_Olinorder__class_OMin(X24356,X24355) = X24354
        | ~ hBOOL(hAPP(hAPP(c_member(X24356),X24354),X24355))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24356),X24355))
        | ~ class_Orderings_Olinorder(X24356) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24356,tc_HOL_Obool)),X24355),hAPP(hAPP(c_Set_Oinsert(X24356),X24354),c_Orderings_Obot__class_Obot(tc_fun(X24356,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X24356,tc_HOL_Obool))
        | c_Big__Operators_Olinorder__class_OMin(X24356,X24355) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X24356),X24354),c_Big__Operators_Olinorder__class_OMin(X24356,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24356,tc_HOL_Obool)),X24355),hAPP(hAPP(c_Set_Oinsert(X24356),X24354),c_Orderings_Obot__class_Obot(tc_fun(X24356,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(hAPP(c_member(X24356),X24354),X24355))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24356),X24355))
        | ~ class_Orderings_Olinorder(X24356) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Oremove])])]) ).

fof(i_0_7405,plain,
    ! [X24245,X24246,X24247] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24247,tc_HOL_Obool)),X24246),hAPP(hAPP(c_Set_Oinsert(X24247),X24245),c_Orderings_Obot__class_Obot(tc_fun(X24247,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X24247,tc_HOL_Obool))
        | c_Big__Operators_Olinorder__class_OMax(X24247,X24246) = X24245
        | ~ hBOOL(hAPP(hAPP(c_member(X24247),X24245),X24246))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24247),X24246))
        | ~ class_Orderings_Olinorder(X24247) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24247,tc_HOL_Obool)),X24246),hAPP(hAPP(c_Set_Oinsert(X24247),X24245),c_Orderings_Obot__class_Obot(tc_fun(X24247,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X24247,tc_HOL_Obool))
        | c_Big__Operators_Olinorder__class_OMax(X24247,X24246) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X24247),X24245),c_Big__Operators_Olinorder__class_OMax(X24247,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24247,tc_HOL_Obool)),X24246),hAPP(hAPP(c_Set_Oinsert(X24247),X24245),c_Orderings_Obot__class_Obot(tc_fun(X24247,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(hAPP(c_member(X24247),X24245),X24246))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24247),X24246))
        | ~ class_Orderings_Olinorder(X24247) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Oremove])])]) ).

fof(i_0_7406,plain,
    ! [X24242,X24243,X24244] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24244,tc_HOL_Obool)),X24243),hAPP(hAPP(c_Set_Oinsert(X24244),X24242),c_Orderings_Obot__class_Obot(tc_fun(X24244,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X24244,tc_HOL_Obool))
        | c_Big__Operators_Olattice__class_OSup__fin(X24244,X24243) = X24242
        | ~ hBOOL(hAPP(hAPP(c_member(X24244),X24242),X24243))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24244),X24243))
        | ~ class_Lattices_Olattice(X24244) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24244,tc_HOL_Obool)),X24243),hAPP(hAPP(c_Set_Oinsert(X24244),X24242),c_Orderings_Obot__class_Obot(tc_fun(X24244,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X24244,tc_HOL_Obool))
        | c_Big__Operators_Olattice__class_OSup__fin(X24244,X24243) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24244),X24242),c_Big__Operators_Olattice__class_OSup__fin(X24244,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24244,tc_HOL_Obool)),X24243),hAPP(hAPP(c_Set_Oinsert(X24244),X24242),c_Orderings_Obot__class_Obot(tc_fun(X24244,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(hAPP(c_member(X24244),X24242),X24243))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24244),X24243))
        | ~ class_Lattices_Olattice(X24244) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oremove])])]) ).

fof(i_0_7407,plain,
    ! [X24239,X24240,X24241] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24241,tc_HOL_Obool)),X24240),hAPP(hAPP(c_Set_Oinsert(X24241),X24239),c_Orderings_Obot__class_Obot(tc_fun(X24241,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X24241,tc_HOL_Obool))
        | c_Big__Operators_Olattice__class_OInf__fin(X24241,X24240) = X24239
        | ~ hBOOL(hAPP(hAPP(c_member(X24241),X24239),X24240))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24241),X24240))
        | ~ class_Lattices_Olattice(X24241) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24241,tc_HOL_Obool)),X24240),hAPP(hAPP(c_Set_Oinsert(X24241),X24239),c_Orderings_Obot__class_Obot(tc_fun(X24241,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X24241,tc_HOL_Obool))
        | c_Big__Operators_Olattice__class_OInf__fin(X24241,X24240) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24241),X24239),c_Big__Operators_Olattice__class_OInf__fin(X24241,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24241,tc_HOL_Obool)),X24240),hAPP(hAPP(c_Set_Oinsert(X24241),X24239),c_Orderings_Obot__class_Obot(tc_fun(X24241,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(hAPP(c_member(X24241),X24239),X24240))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24241),X24240))
        | ~ class_Lattices_Olattice(X24241) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oremove])])]) ).

fof(i_0_7408,plain,
    ! [X26932,X26933,X26934,X26935,X26936,X26937] :
      ( ~ c_Typedef_Otype__definition(X26937,X26936,X26935,X26934,X26933)
      | hBOOL(hAPP(hAPP(c_member(X26936),hAPP(X26935,X26932)),X26933)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_type__definition_ORep])]) ).

fof(i_0_7409,plain,
    ! [X26958,X26959,X26960,X26961,X26962,X26963] :
      ( ~ c_Typedef_Otype__definition(X26963,X26962,X26961,X26960,X26959)
      | ~ hBOOL(hAPP(hAPP(c_member(X26962),X26958),X26959))
      | hAPP(X26961,hAPP(X26960,X26958)) = X26958 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_type__definition_OAbs__inverse])]) ).

fof(i_0_7410,plain,
    ! [X31505,X31506,X31507,X31508,X31509] :
      ( ( ~ c_List_Olinorder__class_Osorted(X31509,hAPP(hAPP(c_List_Omap(X31508,X31509),X31507),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X31508,X31509,X31507),X31506),X31505)))
        | c_List_Olinorder__class_Osorted(X31509,hAPP(hAPP(c_List_Omap(X31508,X31509),X31507),X31505))
        | ~ class_Orderings_Olinorder(X31509) )
      & ( ~ c_List_Olinorder__class_Osorted(X31509,hAPP(hAPP(c_List_Omap(X31508,X31509),X31507),X31505))
        | c_List_Olinorder__class_Osorted(X31509,hAPP(hAPP(c_List_Omap(X31508,X31509),X31507),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X31508,X31509,X31507),X31506),X31505)))
        | ~ class_Orderings_Olinorder(X31509) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__insort__key])])]) ).

fof(i_0_7411,plain,
    ! [X20191,X20192,X20193] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk68_3(X20191,X20192,X20193)),X20193))
        | ~ hBOOL(hAPP(X20192,X20191))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20191),X20193))
        | hBOOL(hAPP(X20192,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
      & ( hBOOL(hAPP(X20192,esk68_3(X20191,X20192,X20193)))
        | ~ hBOOL(hAPP(X20192,X20191))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20191),X20193))
        | hBOOL(hAPP(X20192,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
      & ( ~ hBOOL(hAPP(X20192,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,esk68_3(X20191,X20192,X20193)),X20193)))
        | ~ hBOOL(hAPP(X20192,X20191))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20191),X20193))
        | hBOOL(hAPP(X20192,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_7412,plain,
    ! [X19720,X19721,X19722] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19722),X19721)),X19720) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19722),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19721),X19720))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19722),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19721,X19720))),X19720)),
    inference(variable_rename,[status(thm)],[fact_zdiv__zmult1__eq]) ).

fof(i_0_7413,plain,
    ! [X19562,X19563,X19564] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19564),X19563)),X19562) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19564),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19563),X19562))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19564),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19563,X19562))),X19562)),
    inference(variable_rename,[status(thm)],[fact_div__mult1__eq]) ).

fof(i_0_7414,plain,
    ! [X20124,X20125,X20126,X20127,X20128] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20127),X20126)),X20125) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20128),X20126)),X20124)
        | 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),X20127),X20128)),X20126)),X20125) = X20124
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20128),X20127)) )
      & ( 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),X20127),X20128)),X20126)),X20125) != X20124
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20127),X20126)),X20125) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20128),X20126)),X20124)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20128),X20127)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__eq__add__iff1])])]) ).

fof(i_0_7415,plain,
    ! [X20139,X20140,X20141,X20142,X20143] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20143),X20141)),X20140) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20142),X20141)),X20139)
        | X20140 = 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),X20142),X20143)),X20141)),X20139)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20143),X20142)) )
      & ( X20140 != 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),X20142),X20143)),X20141)),X20139)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20143),X20141)),X20140) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20142),X20141)),X20139)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20143),X20142)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__eq__add__iff2])])]) ).

fof(i_0_7416,plain,
    ! [X24885,X24886,X24887,X24888,X24889,X24890] :
      ( ~ class_Groups_Oab__semigroup__mult(X24890)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24889),X24888))
      | hBOOL(hAPP(hAPP(c_member(X24889),X24887),X24888))
      | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X24890,X24889,c_Groups_Otimes__class_Otimes(X24890)),X24886),X24885),hAPP(hAPP(c_Set_Oinsert(X24889),X24887),X24888)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24890),hAPP(X24886,X24887)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X24890,X24889,c_Groups_Otimes__class_Otimes(X24890)),X24886),X24885),X24888)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5577])]) ).

cnf(i_0_7417,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_5578]) ).

fof(i_0_7418,plain,
    ! [X24064,X24065,X24066,X24067] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24067,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24067,tc_HOL_Obool)),X24066),X24065)),X24064) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24067,tc_HOL_Obool)),X24066),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24067,tc_HOL_Obool)),X24065),X24064))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24067,tc_HOL_Obool)),X24064),X24066)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24067,tc_HOL_Obool)),X24064),X24066))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24067,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24067,tc_HOL_Obool)),X24066),X24065)),X24064) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24067,tc_HOL_Obool)),X24066),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24067,tc_HOL_Obool)),X24065),X24064)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Un__Int__assoc__eq])]) ).

fof(i_0_7419,plain,
    ! [X29967,X29968,X29969,X29970,X29971] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29971,tc_fun(X29970,tc_HOL_Obool)),X29969),hAPP(hAPP(c_COMBB(tc_fun(X29970,tc_HOL_Obool),tc_fun(X29970,tc_HOL_Obool),X29971),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X29970,tc_HOL_Obool)),X29968)),X29967)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X29970,tc_HOL_Obool)),X29968),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29971,tc_fun(X29970,tc_HOL_Obool)),X29969),X29967)),
    inference(variable_rename,[status(thm)],[fact_INT__simps_I7_J]) ).

fof(i_0_7420,plain,
    ! [X25117,X25118,X25119,X25120,X25121] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25121,tc_fun(X25120,tc_HOL_Obool)),X25119),hAPP(hAPP(c_COMBB(tc_fun(X25120,tc_HOL_Obool),tc_fun(X25120,tc_HOL_Obool),X25121),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25120,tc_HOL_Obool)),X25118)),X25117)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25120,tc_HOL_Obool)),X25118),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25121,tc_fun(X25120,tc_HOL_Obool)),X25119),X25117)),
    inference(variable_rename,[status(thm)],[fact_UN__simps_I5_J]) ).

fof(i_0_7421,plain,
    ! [X30032,X30033,X30034,X30035,X30036] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X30036,tc_fun(X30035,tc_HOL_Obool)),X30034),hAPP(hAPP(c_COMBB(tc_fun(X30035,tc_HOL_Obool),tc_fun(X30035,tc_HOL_Obool),X30036),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X30035,tc_HOL_Obool)),X30033)),X30032)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X30035,tc_HOL_Obool)),X30033),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30036,tc_fun(X30035,tc_HOL_Obool)),X30034),X30032)),
    inference(variable_rename,[status(thm)],[fact_UN__simps_I7_J]) ).

fof(i_0_7422,plain,
    ! [X25132,X25133,X25134,X25135,X25136] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25136,tc_HOL_Obool)),X25135),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25134,tc_fun(X25136,tc_HOL_Obool)),X25133),X25132)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25134,tc_fun(X25136,tc_HOL_Obool)),X25133),hAPP(hAPP(c_COMBB(tc_fun(X25136,tc_HOL_Obool),tc_fun(X25136,tc_HOL_Obool),X25134),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25136,tc_HOL_Obool)),X25135)),X25132)),
    inference(variable_rename,[status(thm)],[fact_Int__UN__distrib]) ).

fof(i_0_7423,plain,
    ! [X25127,X25128,X25129,X25130,X25131] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25131,tc_HOL_Obool)),X25130),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25129,tc_fun(X25131,tc_HOL_Obool)),X25128),X25127)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25129,tc_fun(X25131,tc_HOL_Obool)),X25128),hAPP(hAPP(c_COMBB(tc_fun(X25131,tc_HOL_Obool),tc_fun(X25131,tc_HOL_Obool),X25129),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25131,tc_HOL_Obool)),X25130)),X25127)),
    inference(variable_rename,[status(thm)],[fact_UN__extend__simps_I5_J]) ).

fof(i_0_7424,plain,
    ! [X29957,X29958,X29959,X29960,X29961] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X29961,tc_HOL_Obool)),X29960),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29959,tc_fun(X29961,tc_HOL_Obool)),X29958),X29957)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29959,tc_fun(X29961,tc_HOL_Obool)),X29958),hAPP(hAPP(c_COMBB(tc_fun(X29961,tc_HOL_Obool),tc_fun(X29961,tc_HOL_Obool),X29959),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X29961,tc_HOL_Obool)),X29960)),X29957)),
    inference(variable_rename,[status(thm)],[fact_INT__extend__simps_I7_J]) ).

fof(i_0_7425,plain,
    ! [X29952,X29953,X29954,X29955,X29956] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X29956,tc_HOL_Obool)),X29955),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29954,tc_fun(X29956,tc_HOL_Obool)),X29953),X29952)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29954,tc_fun(X29956,tc_HOL_Obool)),X29953),hAPP(hAPP(c_COMBB(tc_fun(X29956,tc_HOL_Obool),tc_fun(X29956,tc_HOL_Obool),X29954),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X29956,tc_HOL_Obool)),X29955)),X29952)),
    inference(variable_rename,[status(thm)],[fact_Un__INT__distrib]) ).

fof(i_0_7426,plain,
    ! [X30037,X30038,X30039,X30040,X30041] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X30041,tc_HOL_Obool)),X30040),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30039,tc_fun(X30041,tc_HOL_Obool)),X30038),X30037)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X30039,tc_fun(X30041,tc_HOL_Obool)),X30038),hAPP(hAPP(c_COMBB(tc_fun(X30041,tc_HOL_Obool),tc_fun(X30041,tc_HOL_Obool),X30039),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X30041,tc_HOL_Obool)),X30040)),X30037)),
    inference(variable_rename,[status(thm)],[fact_UN__extend__simps_I7_J]) ).

fof(i_0_7427,plain,
    ! [X28062,X28063,X28064,X28065] :
      ( hAPP(hAPP(c_Relation_Orel__comp(X28065,X28065,X28065),X28064),X28063) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X28065,X28065),tc_HOL_Obool))
      | hAPP(hAPP(c_Relation_Orel__comp(X28065,X28065,X28065),X28064),X28062) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X28065,X28065),tc_HOL_Obool))
      | hAPP(hAPP(c_Relation_Orel__comp(X28065,X28065,X28065),X28064),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28065,X28065),tc_HOL_Obool)),X28063),X28062)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X28065,X28065),tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_union__comp__emptyR])]) ).

cnf(i_0_7428,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_5530]) ).

cnf(i_0_7429,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_5531]) ).

fof(i_0_7430,plain,
    ! [X34197,X34198,X34199,X34200,X34201] :
      ( ( ~ c_Fun_Obij__betw(X34200,X34198,X34201,X34199,X34197)
        | hAPP(c_Finite__Set_Ocard(X34200),X34199) = hAPP(c_Finite__Set_Ocard(X34198),X34197)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X34198),X34197))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X34200),X34199)) )
      & ( hAPP(c_Finite__Set_Ocard(X34200),X34199) != hAPP(c_Finite__Set_Ocard(X34198),X34197)
        | c_Fun_Obij__betw(X34200,X34198,esk565_4(X34197,X34198,X34199,X34200),X34199,X34197)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X34198),X34197))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X34200),X34199)) ) ),
    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_7431,plain,
    ! [X26922,X26923,X26924,X26925,X26926] :
      ( ~ c_Typedef_Otype__definition(X26926,X26925,X26924,X26923,X26922)
      | hAPP(c_Set_Oimage(X26926,X26925,X26924),c_Orderings_Otop__class_Otop(tc_fun(X26926,tc_HOL_Obool))) = X26922 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_type__definition_ORep__range])]) ).

fof(i_0_7432,plain,
    ! [X24115,X24116,X24117] : hAPP(hAPP(c_Equiv__Relations_Oquotient(X24117),hAPP(hAPP(c_Set_Oinsert(X24117),X24116),c_Orderings_Obot__class_Obot(tc_fun(X24117,tc_HOL_Obool)))),X24115) = hAPP(hAPP(c_Set_Oinsert(tc_fun(X24117,tc_HOL_Obool)),hAPP(c_Relation_OImage(X24117,X24117,X24115),hAPP(hAPP(c_Set_Oinsert(X24117),X24116),c_Orderings_Obot__class_Obot(tc_fun(X24117,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X24117,tc_HOL_Obool),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_singleton__quotient]) ).

fof(i_0_7433,plain,
    ! [X25005,X25006,X25007,X25008,X25009,X25010] :
      ( ~ c_Equiv__Relations_Ocongruent(X25010,X25009,X25008,X25007)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X25010,X25010)),hAPP(hAPP(c_Product__Type_OPair(X25010,X25010),X25006),X25005)),X25008))
      | hAPP(X25007,X25006) = hAPP(X25007,X25005) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_congruentD])]) ).

fof(i_0_7434,plain,
    ! [X32190,X32191,X32192] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X32192,X32192),tc_HOL_Obool)),X32191),c_Transitive__Closure_Ortrancl(X32192,X32190)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X32192,X32192),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X32192,X32191)),c_Transitive__Closure_Ortrancl(X32192,X32190))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__subset__rtrancl])]) ).

cnf(i_0_7435,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_5522]) ).

cnf(i_0_7436,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_5518]) ).

fof(i_0_7437,plain,
    ! [X32207,X32208,X32209,X32210] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32210,X32210)),X32209),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X32210,X32210),tc_HOL_Obool),X32208),X32207)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X32210,X32210)),X32209),c_Transitive__Closure_Ortrancl(X32210,X32207))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__pow__imp__rtrancl])]) ).

fof(i_0_7438,plain,
    ! [X23477,X23478,X23479,X23480] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X23480),X23479),c_Wellfounded_Oacc(X23480,X23478)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X23480,X23480)),hAPP(hAPP(c_Product__Type_OPair(X23480,X23480),X23477),X23479)),X23478))
      | hBOOL(hAPP(hAPP(c_member(X23480),X23477),c_Wellfounded_Oacc(X23480,X23478))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc__downward])]) ).

fof(i_0_7439,plain,
    ! [X31941,X31942,X31943] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X31943,X31943)),hAPP(hAPP(c_Product__Type_OPair(X31943,X31943),X31942),X31941)),c_List_Omeasures(X31943,c_List_Olist_ONil(tc_fun(X31943,tc_Nat_Onat))))),
    inference(variable_rename,[status(thm)],[i_0_5579]) ).

fof(i_0_7440,plain,
    ! [X24382,X24383,X24384] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24384,tc_HOL_Obool)),X24383),hAPP(hAPP(c_Set_Oinsert(X24384),X24382),c_Orderings_Obot__class_Obot(tc_fun(X24384,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X24384,tc_HOL_Obool))
        | c_Big__Operators_Olinorder__class_OMin(X24384,hAPP(hAPP(c_Set_Oinsert(X24384),X24382),X24383)) = X24382
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24384),X24383))
        | ~ class_Orderings_Olinorder(X24384) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24384,tc_HOL_Obool)),X24383),hAPP(hAPP(c_Set_Oinsert(X24384),X24382),c_Orderings_Obot__class_Obot(tc_fun(X24384,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X24384,tc_HOL_Obool))
        | c_Big__Operators_Olinorder__class_OMin(X24384,hAPP(hAPP(c_Set_Oinsert(X24384),X24382),X24383)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X24384),X24382),c_Big__Operators_Olinorder__class_OMin(X24384,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24384,tc_HOL_Obool)),X24383),hAPP(hAPP(c_Set_Oinsert(X24384),X24382),c_Orderings_Obot__class_Obot(tc_fun(X24384,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24384),X24383))
        | ~ class_Orderings_Olinorder(X24384) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Oinsert__remove])])]) ).

fof(i_0_7441,plain,
    ! [X24327,X24328,X24329] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24329,tc_HOL_Obool)),X24328),hAPP(hAPP(c_Set_Oinsert(X24329),X24327),c_Orderings_Obot__class_Obot(tc_fun(X24329,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X24329,tc_HOL_Obool))
        | c_Big__Operators_Olinorder__class_OMax(X24329,hAPP(hAPP(c_Set_Oinsert(X24329),X24327),X24328)) = X24327
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24329),X24328))
        | ~ class_Orderings_Olinorder(X24329) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24329,tc_HOL_Obool)),X24328),hAPP(hAPP(c_Set_Oinsert(X24329),X24327),c_Orderings_Obot__class_Obot(tc_fun(X24329,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X24329,tc_HOL_Obool))
        | c_Big__Operators_Olinorder__class_OMax(X24329,hAPP(hAPP(c_Set_Oinsert(X24329),X24327),X24328)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X24329),X24327),c_Big__Operators_Olinorder__class_OMax(X24329,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24329,tc_HOL_Obool)),X24328),hAPP(hAPP(c_Set_Oinsert(X24329),X24327),c_Orderings_Obot__class_Obot(tc_fun(X24329,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24329),X24328))
        | ~ class_Orderings_Olinorder(X24329) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Oinsert__remove])])]) ).

fof(i_0_7442,plain,
    ! [X24315,X24316,X24317] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24317,tc_HOL_Obool)),X24316),hAPP(hAPP(c_Set_Oinsert(X24317),X24315),c_Orderings_Obot__class_Obot(tc_fun(X24317,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X24317,tc_HOL_Obool))
        | c_Big__Operators_Olattice__class_OSup__fin(X24317,hAPP(hAPP(c_Set_Oinsert(X24317),X24315),X24316)) = X24315
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24317),X24316))
        | ~ class_Lattices_Olattice(X24317) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24317,tc_HOL_Obool)),X24316),hAPP(hAPP(c_Set_Oinsert(X24317),X24315),c_Orderings_Obot__class_Obot(tc_fun(X24317,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X24317,tc_HOL_Obool))
        | c_Big__Operators_Olattice__class_OSup__fin(X24317,hAPP(hAPP(c_Set_Oinsert(X24317),X24315),X24316)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24317),X24315),c_Big__Operators_Olattice__class_OSup__fin(X24317,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24317,tc_HOL_Obool)),X24316),hAPP(hAPP(c_Set_Oinsert(X24317),X24315),c_Orderings_Obot__class_Obot(tc_fun(X24317,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24317),X24316))
        | ~ class_Lattices_Olattice(X24317) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oinsert__remove])])]) ).

fof(i_0_7443,plain,
    ! [X24318,X24319,X24320] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24320,tc_HOL_Obool)),X24319),hAPP(hAPP(c_Set_Oinsert(X24320),X24318),c_Orderings_Obot__class_Obot(tc_fun(X24320,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X24320,tc_HOL_Obool))
        | c_Big__Operators_Olattice__class_OInf__fin(X24320,hAPP(hAPP(c_Set_Oinsert(X24320),X24318),X24319)) = X24318
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24320),X24319))
        | ~ class_Lattices_Olattice(X24320) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24320,tc_HOL_Obool)),X24319),hAPP(hAPP(c_Set_Oinsert(X24320),X24318),c_Orderings_Obot__class_Obot(tc_fun(X24320,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X24320,tc_HOL_Obool))
        | c_Big__Operators_Olattice__class_OInf__fin(X24320,hAPP(hAPP(c_Set_Oinsert(X24320),X24318),X24319)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24320),X24318),c_Big__Operators_Olattice__class_OInf__fin(X24320,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24320,tc_HOL_Obool)),X24319),hAPP(hAPP(c_Set_Oinsert(X24320),X24318),c_Orderings_Obot__class_Obot(tc_fun(X24320,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24320),X24319))
        | ~ class_Lattices_Olattice(X24320) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oinsert__remove])])]) ).

fof(i_0_7444,plain,
    ! [X26927,X26928,X26929,X26930,X26931] :
      ( ~ c_Typedef_Otype__definition(X26931,X26930,X26929,X26928,X26927)
      | hAPP(c_Set_Oimage(X26930,X26931,X26928),X26927) = c_Orderings_Otop__class_Otop(tc_fun(X26931,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_type__definition_OAbs__image])]) ).

fof(i_0_7445,plain,
    ! [X30771,X30772,X30773,X30774] :
      ( ~ c_Fun_Oinj__on(X30774,X30773,X30772,c_Complete__Lattice_OSup__class_OSup(tc_fun(X30774,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_List_Olist(X30774),tc_fun(X30774,tc_HOL_Obool),c_List_Oset(X30774)),X30771)))
      | c_Fun_Oinj__on(tc_List_Olist(X30774),tc_List_Olist(X30773),hAPP(c_List_Omap(X30774,X30773),X30772),X30771) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__mapI])]) ).

fof(i_0_7446,plain,
    ! [X21568,X21569,X21570,X21571] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21571),c_Groups_Ozero__class_Ozero(X21571)),X21569))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21571),X21570),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21571),X21568),X21569)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21571),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21571),X21570),X21569)),X21568))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21571) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21571),X21569),c_Groups_Ozero__class_Ozero(X21571)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21571),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21571),X21568),X21569)),X21570))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21571),c_Groups_Ozero__class_Ozero(X21571)),X21569))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21571),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21571),X21570),X21569)),X21568))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21571) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21571),X21569),c_Groups_Ozero__class_Ozero(X21571)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21571),c_Groups_Ozero__class_Ozero(X21571)),X21568))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21571),c_Groups_Ozero__class_Ozero(X21571)),X21569))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21571),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21571),X21570),X21569)),X21568))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21571) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21571),c_Groups_Ozero__class_Ozero(X21571)),X21569))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21571),c_Groups_Ozero__class_Ozero(X21571)),X21569))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21571),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21571),X21570),X21569)),X21568))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21571) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21571),X21569),c_Groups_Ozero__class_Ozero(X21571)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21571),X21569),c_Groups_Ozero__class_Ozero(X21571)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21571),c_Groups_Ozero__class_Ozero(X21571)),X21569))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21571),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21571),X21570),X21569)),X21568))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21571) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21571),c_Groups_Ozero__class_Ozero(X21571)),X21568))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21571),X21569),c_Groups_Ozero__class_Ozero(X21571)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21571),c_Groups_Ozero__class_Ozero(X21571)),X21569))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21571),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21571),X21570),X21569)),X21568))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21571) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21571),X21569),c_Groups_Ozero__class_Ozero(X21571)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21571),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21571),X21568),X21569)),X21570))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21571),c_Groups_Ozero__class_Ozero(X21571)),X21569))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21571),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21571),X21570),X21569)),X21568))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21571) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21571),c_Groups_Ozero__class_Ozero(X21571)),X21568))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21571),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21571),X21568),X21569)),X21570))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21571),c_Groups_Ozero__class_Ozero(X21571)),X21569))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21571),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21571),X21570),X21569)),X21568))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21571) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21571),c_Groups_Ozero__class_Ozero(X21571)),X21569))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21571),X21570),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21571),X21568),X21569)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21571),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21571),X21570),X21569)),X21568))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21571) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21571),X21569),c_Groups_Ozero__class_Ozero(X21571)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21571),X21569),c_Groups_Ozero__class_Ozero(X21571)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21571),X21570),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21571),X21568),X21569)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21571),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21571),X21570),X21569)),X21568))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21571) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21571),c_Groups_Ozero__class_Ozero(X21571)),X21568))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21571),X21569),c_Groups_Ozero__class_Ozero(X21571)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21571),X21570),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21571),X21568),X21569)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21571),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21571),X21570),X21569)),X21568))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21571) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21571),X21569),c_Groups_Ozero__class_Ozero(X21571)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21571),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21571),X21568),X21569)),X21570))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21571),X21570),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21571),X21568),X21569)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21571),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21571),X21570),X21569)),X21568))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21571) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21571),c_Groups_Ozero__class_Ozero(X21571)),X21568))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21571),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21571),X21568),X21569)),X21570))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21571),X21570),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21571),X21568),X21569)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21571),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21571),X21570),X21569)),X21568))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21571) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5580])])]) ).

fof(i_0_7447,plain,
    ! [X21460,X21461,X21462,X21463] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21463),c_Groups_Ozero__class_Ozero(X21463)),X21461))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21463),X21462),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21463),X21460),X21461)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21463),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21463),X21462),X21461)),X21460))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21463) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21463),X21461),c_Groups_Ozero__class_Ozero(X21463)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21463),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21463),X21460),X21461)),X21462))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21463),c_Groups_Ozero__class_Ozero(X21463)),X21461))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21463),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21463),X21462),X21461)),X21460))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21463) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21463),X21461),c_Groups_Ozero__class_Ozero(X21463)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21463),c_Groups_Ozero__class_Ozero(X21463)),X21460))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21463),c_Groups_Ozero__class_Ozero(X21463)),X21461))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21463),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21463),X21462),X21461)),X21460))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21463) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21463),c_Groups_Ozero__class_Ozero(X21463)),X21461))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21463),c_Groups_Ozero__class_Ozero(X21463)),X21461))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21463),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21463),X21462),X21461)),X21460))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21463) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21463),X21461),c_Groups_Ozero__class_Ozero(X21463)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21463),X21461),c_Groups_Ozero__class_Ozero(X21463)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21463),c_Groups_Ozero__class_Ozero(X21463)),X21461))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21463),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21463),X21462),X21461)),X21460))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21463) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21463),c_Groups_Ozero__class_Ozero(X21463)),X21460))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21463),X21461),c_Groups_Ozero__class_Ozero(X21463)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21463),c_Groups_Ozero__class_Ozero(X21463)),X21461))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21463),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21463),X21462),X21461)),X21460))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21463) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21463),X21461),c_Groups_Ozero__class_Ozero(X21463)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21463),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21463),X21460),X21461)),X21462))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21463),c_Groups_Ozero__class_Ozero(X21463)),X21461))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21463),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21463),X21462),X21461)),X21460))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21463) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21463),c_Groups_Ozero__class_Ozero(X21463)),X21460))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21463),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21463),X21460),X21461)),X21462))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21463),c_Groups_Ozero__class_Ozero(X21463)),X21461))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21463),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21463),X21462),X21461)),X21460))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21463) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21463),c_Groups_Ozero__class_Ozero(X21463)),X21461))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21463),X21462),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21463),X21460),X21461)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21463),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21463),X21462),X21461)),X21460))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21463) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21463),X21461),c_Groups_Ozero__class_Ozero(X21463)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21463),X21461),c_Groups_Ozero__class_Ozero(X21463)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21463),X21462),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21463),X21460),X21461)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21463),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21463),X21462),X21461)),X21460))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21463) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21463),c_Groups_Ozero__class_Ozero(X21463)),X21460))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21463),X21461),c_Groups_Ozero__class_Ozero(X21463)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21463),X21462),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21463),X21460),X21461)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21463),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21463),X21462),X21461)),X21460))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21463) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21463),X21461),c_Groups_Ozero__class_Ozero(X21463)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21463),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21463),X21460),X21461)),X21462))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21463),X21462),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21463),X21460),X21461)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21463),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21463),X21462),X21461)),X21460))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21463) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21463),c_Groups_Ozero__class_Ozero(X21463)),X21460))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21463),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21463),X21460),X21461)),X21462))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21463),X21462),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21463),X21460),X21461)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21463),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21463),X21462),X21461)),X21460))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21463) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5581])])]) ).

fof(i_0_7448,plain,
    ! [X33983,X33984,X33985,X33986] :
      ( ~ c_Fun_Oinj__on(X33986,X33985,X33984,c_Orderings_Otop__class_Otop(tc_fun(X33986,tc_HOL_Obool)))
      | hAPP(c_Set_Oimage(X33985,X33986,c_Hilbert__Choice_Oinv__into(X33986,X33985,c_Orderings_Otop__class_Otop(tc_fun(X33986,tc_HOL_Obool)),X33984)),hAPP(c_Set_Oimage(X33986,X33985,X33984),X33983)) = X33983 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__image__comp])]) ).

fof(i_0_7449,plain,
    ! [X33979,X33980,X33981,X33982] :
      ( ~ c_Fun_Oinj__on(X33982,X33981,X33980,c_Orderings_Otop__class_Otop(tc_fun(X33982,tc_HOL_Obool)))
      | hAPP(c_Set_Oimage(X33981,X33982,c_Hilbert__Choice_Oinv__into(X33982,X33981,c_Orderings_Otop__class_Otop(tc_fun(X33982,tc_HOL_Obool)),X33980)),hAPP(c_Set_Oimage(X33982,X33981,X33980),X33979)) = X33979 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__inv__f__f])]) ).

fof(i_0_7450,plain,
    ! [X29024,X29025,X29026,X29027,X29028,X29029] : hAPP(hAPP(c_List_Olist__update(tc_prod(X29029,X29028),hAPP(hAPP(c_List_Ozip(X29029,X29028),X29027),X29026)),X29025),X29024) = hAPP(hAPP(c_List_Ozip(X29029,X29028),hAPP(hAPP(c_List_Olist__update(X29029,X29027),X29025),hAPP(c_Product__Type_Ofst(X29029,X29028),X29024))),hAPP(hAPP(c_List_Olist__update(X29028,X29026),X29025),hAPP(c_Product__Type_Osnd(X29029,X29028),X29024))),
    inference(variable_rename,[status(thm)],[fact_update__zip]) ).

cnf(i_0_7451,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_5525]) ).

cnf(i_0_7452,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_5524]) ).

cnf(i_0_7453,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_5526]) ).

cnf(i_0_7454,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_5527]) ).

cnf(i_0_7455,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_5528]) ).

cnf(i_0_7456,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_5582]) ).

fof(i_0_7457,plain,
    ! [X27689] : 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)),X27689)))),
    inference(variable_rename,[status(thm)],[fact_finite__Collect__le__nat]) ).

fof(i_0_7458,plain,
    ! [X27688] : 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)),X27688)))),
    inference(variable_rename,[status(thm)],[fact_finite__Collect__less__nat]) ).

fof(i_0_7459,plain,
    ! [X28021,X28022,X28023,X28024,X28025,X28026,X28027] : hAPP(hAPP(c_Relation_Orel__comp(X28027,X28026,X28025),hAPP(hAPP(c_Relation_Orel__comp(X28027,X28024,X28026),X28023),X28022)),X28021) = hAPP(hAPP(c_Relation_Orel__comp(X28027,X28024,X28025),X28023),hAPP(hAPP(c_Relation_Orel__comp(X28024,X28026,X28025),X28022),X28021)),
    inference(variable_rename,[status(thm)],[fact_O__assoc]) ).

fof(i_0_7460,plain,
    ! [X26426,X26427,X26428,X26429,X26430] :
      ( ~ class_Groups_Ocomm__monoid__add(X26430)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26429),X26428))
      | ~ hBOOL(hAPP(hAPP(c_member(X26429),X26427),X26428))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26429,X26430),X26426),X26428) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26430),hAPP(X26426,X26427)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26429,X26430),X26426),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26429,tc_HOL_Obool)),X26428),hAPP(hAPP(c_Set_Oinsert(X26429),X26427),c_Orderings_Obot__class_Obot(tc_fun(X26429,tc_HOL_Obool)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum_Oremove])]) ).

fof(i_0_7461,plain,
    ! [X26421,X26422,X26423,X26424,X26425] :
      ( ~ class_Groups_Ocomm__monoid__add(X26425)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26424),X26423))
      | ~ hBOOL(hAPP(hAPP(c_member(X26424),X26422),X26423))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26424,X26425),X26421),X26423) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26425),hAPP(X26421,X26422)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26424,X26425),X26421),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26424,tc_HOL_Obool)),X26423),hAPP(hAPP(c_Set_Oinsert(X26424),X26422),c_Orderings_Obot__class_Obot(tc_fun(X26424,tc_HOL_Obool)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__diff1_H])]) ).

fof(i_0_7462,plain,
    ! [X24774,X24775,X24776,X24777,X24778] :
      ( ~ class_Groups_Ocomm__monoid__mult(X24778)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24777),X24776))
      | ~ hBOOL(hAPP(hAPP(c_member(X24777),X24775),X24776))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24777,X24778),X24774),X24776) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24778),hAPP(X24774,X24775)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24777,X24778),X24774),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24777,tc_HOL_Obool)),X24776),hAPP(hAPP(c_Set_Oinsert(X24777),X24775),c_Orderings_Obot__class_Obot(tc_fun(X24777,tc_HOL_Obool)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod_Oremove])]) ).

fof(i_0_7463,plain,
    ! [X29980,X29981,X29982,X29983] : hAPP(c_Set_OPow(X29983),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29982,tc_fun(X29983,tc_HOL_Obool)),X29981),X29980)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29982,tc_fun(tc_fun(X29983,tc_HOL_Obool),tc_HOL_Obool)),X29981),hAPP(hAPP(c_COMBB(tc_fun(X29983,tc_HOL_Obool),tc_fun(tc_fun(X29983,tc_HOL_Obool),tc_HOL_Obool),X29982),c_Set_OPow(X29983)),X29980)),
    inference(variable_rename,[status(thm)],[fact_Pow__INT__eq]) ).

fof(i_0_7464,plain,
    ! [X19037,X19038,X19039] :
      ( ~ 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),X19039),X19038)),X19037)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19037),X19039))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19039))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19038)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_q__pos__lemma])]) ).

fof(i_0_7465,plain,
    ! [X34179,X34180,X34181,X34182] :
      ( ~ c_Fun_Obij__betw(X34182,X34181,X34180,c_Orderings_Obot__class_Obot(tc_fun(X34182,tc_HOL_Obool)),X34179)
      | X34179 = c_Orderings_Obot__class_Obot(tc_fun(X34181,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__betw__empty1])]) ).

fof(i_0_7466,plain,
    ! [X34183,X34184,X34185,X34186] :
      ( ~ c_Fun_Obij__betw(X34186,X34185,X34184,X34183,c_Orderings_Obot__class_Obot(tc_fun(X34185,tc_HOL_Obool)))
      | X34183 = c_Orderings_Obot__class_Obot(tc_fun(X34186,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__betw__empty2])]) ).

fof(i_0_7467,plain,
    ! [X25986,X25987,X25988] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X25988,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X25987)),X25986) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25988,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X25988,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X25987)),X25986)),hAPP(X25986,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[fact_UN__le__eq__Un0]) ).

fof(i_0_7468,plain,
    ! [X24566,X24567,X24568] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24568),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24568,tc_HOL_Obool)),X24567),X24566)))
      | hAPP(c_Finite__Set_Ocard(X24568),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24568,tc_HOL_Obool)),X24567),X24566)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X24568),X24567)),hAPP(c_Finite__Set_Ocard(X24568),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24568,tc_HOL_Obool)),X24567),X24566))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Diff__subset__Int])]) ).

cnf(i_0_7469,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_7470,plain,
    ! [X29883,X29884,X29885,X29886,X29887] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29887,tc_fun(X29886,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X29887,tc_HOL_Obool)),X29885),X29884)),X29883) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29886,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29887,tc_fun(X29886,tc_HOL_Obool)),X29885),X29883)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29887,tc_fun(X29886,tc_HOL_Obool)),X29884),X29883)),
    inference(variable_rename,[status(thm)],[fact_INT__Un]) ).

fof(i_0_7471,plain,
    ! [X25112,X25113,X25114,X25115,X25116] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25116,tc_fun(X25115,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25116,tc_HOL_Obool)),X25114),X25113)),X25112) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25115,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25116,tc_fun(X25115,tc_HOL_Obool)),X25114),X25112)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25116,tc_fun(X25115,tc_HOL_Obool)),X25113),X25112)),
    inference(variable_rename,[status(thm)],[fact_UN__Un]) ).

fof(i_0_7472,plain,
    ! [X32230,X32231,X32232,X32233] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32233,X32233)),hAPP(hAPP(c_Product__Type_OPair(X32233,X32233),X32232),X32230)),c_Transitive__Closure_Ortrancl(X32233,X32231)))
        | X32232 = X32230
        | hBOOL(hAPP(hAPP(c_member(X32233),X32232),hAPP(c_Relation_ODomain(X32233,X32233),X32231))) )
      & ( X32232 != X32230
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X32233,X32233)),hAPP(hAPP(c_Product__Type_OPair(X32233,X32233),X32232),X32230)),c_Transitive__Closure_Ortrancl(X32233,X32231)))
        | hBOOL(hAPP(hAPP(c_member(X32233),X32232),hAPP(c_Relation_ODomain(X32233,X32233),X32231))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5583])])]) ).

cnf(i_0_7473,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_5584]) ).

fof(i_0_7474,plain,
    ! [X25353,X25354,X25355,X25356,X25357,X25358,X25359] :
      ( ~ c_Big__Operators_Ocomm__monoid__big(X25359,X25358,X25357,X25356,X25355)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X25358),X25354))
      | hAPP(hAPP(X25355,X25353),X25354) = X25356 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5585])]) ).

fof(i_0_7475,plain,
    ! [X19299,X19300,X19301] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19301,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X19301,tc_HOL_Obool)),X19300)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X19301,tc_HOL_Obool)),X19299)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19301,tc_HOL_Obool)),X19299),X19300)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19301,tc_HOL_Obool)),X19299),X19300))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19301,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X19301,tc_HOL_Obool)),X19300)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X19301,tc_HOL_Obool)),X19299))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Compl__subset__Compl__iff])]) ).

fof(i_0_7476,plain,
    ! [X29837,X29838,X29839,X29840,X29841] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X29841),X29840),X29839))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29838,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29841,tc_fun(X29838,tc_HOL_Obool)),X29839),X29837)),hAPP(X29837,X29840))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__lower])]) ).

fof(i_0_7477,plain,
    ! [X32184,X32185,X32186] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X32186,X32186),tc_HOL_Obool)),X32185),X32184))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X32186,X32186),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X32186,X32185)),c_Transitive__Closure_Ortrancl(X32186,X32184))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__mono])]) ).

fof(i_0_7478,plain,
    ! [X29972,X29973,X29974,X29975,X29976,X29977] : hAPP(c_Set_Ovimage(X29977,X29976,X29975),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29974,tc_fun(X29976,tc_HOL_Obool)),X29973),X29972)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29974,tc_fun(X29977,tc_HOL_Obool)),X29973),hAPP(hAPP(c_COMBB(tc_fun(X29976,tc_HOL_Obool),tc_fun(X29977,tc_HOL_Obool),X29974),c_Set_Ovimage(X29977,X29976,X29975)),X29972)),
    inference(variable_rename,[status(thm)],[fact_vimage__INT]) ).

fof(i_0_7479,plain,
    ! [X27153,X27154,X27155,X27156,X27157,X27158] : hAPP(c_Set_Ovimage(X27158,X27157,X27156),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27155,tc_fun(X27157,tc_HOL_Obool)),X27154),X27153)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27155,tc_fun(X27158,tc_HOL_Obool)),X27154),hAPP(hAPP(c_COMBB(tc_fun(X27157,tc_HOL_Obool),tc_fun(X27158,tc_HOL_Obool),X27155),c_Set_Ovimage(X27158,X27157,X27156)),X27153)),
    inference(variable_rename,[status(thm)],[fact_vimage__UN]) ).

fof(i_0_7480,plain,
    ! [X24839,X24840,X24841,X24842,X24843,X24844] : hAPP(c_Relation_OImage(X24844,X24843,X24842),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24841,tc_fun(X24844,tc_HOL_Obool)),X24840),X24839)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24841,tc_fun(X24843,tc_HOL_Obool)),X24840),hAPP(hAPP(c_COMBB(tc_fun(X24844,tc_HOL_Obool),tc_fun(X24843,tc_HOL_Obool),X24841),c_Relation_OImage(X24844,X24843,X24842)),X24839)),
    inference(variable_rename,[status(thm)],[fact_Image__UN]) ).

fof(i_0_7481,plain,
    ! [X25095,X25096,X25097,X25098,X25099,X25100] : hAPP(c_Set_Oimage(X25100,X25099,X25098),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25097,tc_fun(X25100,tc_HOL_Obool)),X25096),X25095)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25097,tc_fun(X25099,tc_HOL_Obool)),X25096),hAPP(hAPP(c_COMBB(tc_fun(X25100,tc_HOL_Obool),tc_fun(X25099,tc_HOL_Obool),X25097),c_Set_Oimage(X25100,X25099,X25098)),X25095)),
    inference(variable_rename,[status(thm)],[fact_image__UN]) ).

fof(i_0_7482,plain,
    ! [X21490,X21491,X21492,X21493,X21494] :
      ( ~ class_Fields_Ofield(X21494)
      | X21493 = c_Groups_Ozero__class_Ozero(X21494)
      | X21492 = c_Groups_Ozero__class_Ozero(X21494)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21494),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21494),X21491),X21493)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21494),X21490),X21492)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21494),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21494),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21494),X21491),X21492)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21494),X21490),X21493))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21494),X21493),X21492)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__frac__eq])]) ).

fof(i_0_7483,plain,
    ! [X21469,X21470,X21471,X21472,X21473] :
      ( ~ class_Fields_Ofield(X21473)
      | X21472 = c_Groups_Ozero__class_Ozero(X21473)
      | X21471 = c_Groups_Ozero__class_Ozero(X21473)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21473),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21473),X21470),X21472)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21473),X21469),X21471)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21473),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21473),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21473),X21470),X21471)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21473),X21469),X21472))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21473),X21472),X21471)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__frac__eq])]) ).

fof(i_0_7484,plain,
    ! [X27777,X27778] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X27778,tc_HOL_Obool)),X27777) = hAPP(c_Set_OCollect(X27778),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X27778),c_fNot),hAPP(hAPP(c_COMBC(X27778,tc_fun(X27778,tc_HOL_Obool),tc_HOL_Obool),c_member(X27778)),X27777))),
    inference(variable_rename,[status(thm)],[fact_Compl__eq]) ).

cnf(i_0_7485,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_5586]) ).

fof(i_0_7486,plain,
    ! [X30622,X30623,X30624,X30625,X30626] :
      ( ~ c_List_Olist__all2(X30626,X30625,X30624,X30623,X30622)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30626)),X30623) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30625)),X30622) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__lengthD])]) ).

fof(i_0_7487,plain,
    ! [X19246,X19247,X19248] :
      ( ( ~ 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,X19248)),X19247)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19248)),X19246)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19247),X19246)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19247),X19246))
        | 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,X19248)),X19247)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19248)),X19246))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mult__le__cancel1])]) ).

fof(i_0_7488,plain,
    ! [X18864,X18865,X18866] :
      ( ( ~ 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,X18866)),X18865)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X18866)),X18864)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18865),X18864)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18865),X18864))
        | 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,X18866)),X18865)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X18866)),X18864))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mult__less__cancel1])]) ).

fof(i_0_7489,plain,
    ! [X19518,X19519,X19520,X19521,X19522] :
      ( ( ~ hBOOL(hAPP(hAPP(X19519,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19518),X19520)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19518,X19520)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19522))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19522),X19520))
        | X19518 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19520),X19521)),X19522)
        | hBOOL(hAPP(hAPP(X19519,X19521),X19522))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19520)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk53_3(X19518,X19519,X19520)))
        | hBOOL(hAPP(hAPP(X19519,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19518),X19520)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19518,X19520)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19520)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk53_3(X19518,X19519,X19520)),X19520))
        | hBOOL(hAPP(hAPP(X19519,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19518),X19520)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19518,X19520)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19520)) )
      & ( X19518 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19520),esk52_3(X19518,X19519,X19520))),esk53_3(X19518,X19519,X19520))
        | hBOOL(hAPP(hAPP(X19519,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19518),X19520)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19518,X19520)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19520)) )
      & ( ~ hBOOL(hAPP(hAPP(X19519,esk52_3(X19518,X19519,X19520)),esk53_3(X19518,X19519,X19520)))
        | hBOOL(hAPP(hAPP(X19519,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19518),X19520)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19518,X19520)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19520)) ) ),
    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_7490,plain,
    ! [X30567,X30568,X30569,X30570,X30571] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X30570),X30568),hAPP(c_List_Oset(X30570),X30567)))
        | ~ hBOOL(hAPP(c_List_Odistinct(X30570),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30570,X30571,X30569),X30568),X30567)))
        | ~ class_Orderings_Olinorder(X30571) )
      & ( hBOOL(hAPP(c_List_Odistinct(X30570),X30567))
        | ~ hBOOL(hAPP(c_List_Odistinct(X30570),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30570,X30571,X30569),X30568),X30567)))
        | ~ class_Orderings_Olinorder(X30571) )
      & ( hBOOL(hAPP(hAPP(c_member(X30570),X30568),hAPP(c_List_Oset(X30570),X30567)))
        | ~ hBOOL(hAPP(c_List_Odistinct(X30570),X30567))
        | hBOOL(hAPP(c_List_Odistinct(X30570),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30570,X30571,X30569),X30568),X30567)))
        | ~ class_Orderings_Olinorder(X30571) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5587])])]) ).

fof(i_0_7491,plain,
    ! [X33966,X33967,X33968,X33969,X33970] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X33970,tc_HOL_Obool)),X33969),hAPP(c_Set_Oimage(X33968,X33970,X33967),X33966)))
      | c_Fun_Oinj__on(X33970,X33968,c_Hilbert__Choice_Oinv__into(X33968,X33970,X33966,X33967),X33969) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__inv__into])]) ).

fof(i_0_7492,plain,
    ! [X24845,X24846,X24847,X24848,X24849,X24850] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24850,tc_fun(X24849,tc_HOL_Obool)),X24848),hAPP(c_Fun_Ocomp(X24847,tc_fun(X24849,tc_HOL_Obool),X24850,X24846),X24845)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24847,tc_fun(X24849,tc_HOL_Obool)),hAPP(c_Set_Oimage(X24850,X24847,X24845),X24848)),X24846),
    inference(variable_rename,[status(thm)],[fact_UN__o]) ).

fof(i_0_7493,plain,
    ! [X26367,X26368,X26369,X26370,X26371] :
      ( ~ class_Groups_Ocomm__monoid__add(X26371)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26370),X26369))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26370,X26371),X26368),hAPP(hAPP(c_Set_Oinsert(X26370),X26367),X26369)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26371),hAPP(X26368,X26367)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26370,X26371),X26368),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26370,tc_HOL_Obool)),X26369),hAPP(hAPP(c_Set_Oinsert(X26370),X26367),c_Orderings_Obot__class_Obot(tc_fun(X26370,tc_HOL_Obool)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum_Oinsert__remove])]) ).

fof(i_0_7494,plain,
    ! [X24755,X24756,X24757,X24758,X24759] :
      ( ~ class_Groups_Ocomm__monoid__mult(X24759)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24758),X24757))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24758,X24759),X24756),hAPP(hAPP(c_Set_Oinsert(X24758),X24755),X24757)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24759),hAPP(X24756,X24755)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24758,X24759),X24756),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24758,tc_HOL_Obool)),X24757),hAPP(hAPP(c_Set_Oinsert(X24758),X24755),c_Orderings_Obot__class_Obot(tc_fun(X24758,tc_HOL_Obool)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod_Oinsert__remove])]) ).

fof(i_0_7495,plain,
    ! [X34012,X34013,X34014,X34015,X34016] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X34016),X34015),hAPP(c_Set_Oimage(X34014,X34016,X34013),X34012)))
      | hAPP(X34013,hAPP(c_Hilbert__Choice_Oinv__into(X34014,X34016,X34012,X34013),X34015)) = X34015 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_f__inv__into__f])]) ).

fof(i_0_7496,plain,
    ! [X19525,X19526,X19527,X19528,X19529] :
      ( ( ~ hBOOL(hAPP(hAPP(X19526,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19525),X19527)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19525,X19527)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19527),X19529))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19529),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | X19525 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19527),X19528)),X19529)
        | hBOOL(hAPP(hAPP(X19526,X19528),X19529))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19527),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19527),esk55_3(X19525,X19526,X19527)))
        | hBOOL(hAPP(hAPP(X19526,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19525),X19527)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19525,X19527)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19527),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk55_3(X19525,X19526,X19527)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(X19526,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19525),X19527)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19525,X19527)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19527),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( X19525 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19527),esk54_3(X19525,X19526,X19527))),esk55_3(X19525,X19526,X19527))
        | hBOOL(hAPP(hAPP(X19526,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19525),X19527)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19525,X19527)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19527),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( ~ hBOOL(hAPP(hAPP(X19526,esk54_3(X19525,X19526,X19527)),esk55_3(X19525,X19526,X19527)))
        | hBOOL(hAPP(hAPP(X19526,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19525),X19527)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19525,X19527)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19527),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_7497,plain,
    ! [X29774,X29775] : hAPP(hAPP(c_List_Ozip(X29775,X29775),X29774),X29774) = hAPP(hAPP(c_List_Omap(X29775,tc_prod(X29775,X29775)),hAPP(hAPP(c_COMBS(X29775,X29775,tc_prod(X29775,X29775)),c_Product__Type_OPair(X29775,X29775)),c_COMBI(X29775))),X29774),
    inference(variable_rename,[status(thm)],[fact_zip__same__conv__map]) ).

fof(i_0_7498,plain,
    ! [X24079,X24080] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X24080),X24079) = 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)),X24080)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X24079))),
    inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J]) ).

fof(i_0_7499,plain,
    ! [X23325,X23326] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X23326),X23325) = 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)),X23326)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X23325))),
    inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J]) ).

fof(i_0_7500,plain,
    ! [X34065,X34066,X34067] :
      ( ( hAPP(c_Set_Oimage(X34067,X34066,X34065),c_Orderings_Otop__class_Otop(tc_fun(X34067,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X34066,tc_HOL_Obool))
        | hAPP(c_Fun_Ocomp(X34067,X34066,X34066,X34065),c_Hilbert__Choice_Oinv__into(X34067,X34066,c_Orderings_Otop__class_Otop(tc_fun(X34067,tc_HOL_Obool)),X34065)) = c_Fun_Oid(X34066) )
      & ( hAPP(c_Fun_Ocomp(X34067,X34066,X34066,X34065),c_Hilbert__Choice_Oinv__into(X34067,X34066,c_Orderings_Otop__class_Otop(tc_fun(X34067,tc_HOL_Obool)),X34065)) != c_Fun_Oid(X34066)
        | hAPP(c_Set_Oimage(X34067,X34066,X34065),c_Orderings_Otop__class_Otop(tc_fun(X34067,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X34066,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_surj__iff])]) ).

fof(i_0_7501,plain,
    ! [X20629,X20630,X20631] :
      ( ~ class_Rings_Olinordered__semidom(X20631)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20631),c_Groups_Ozero__class_Ozero(X20631)),X20630))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20631),X20630),c_Groups_Oone__class_Oone(X20631)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20631),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20631),X20630),hAPP(hAPP(c_Power_Opower__class_Opower(X20631),X20630),X20629))),hAPP(hAPP(c_Power_Opower__class_Opower(X20631),X20630),X20629))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__Suc__less])]) ).

fof(i_0_7502,plain,
    ! [X26938,X26939,X26940,X26941,X26942,X26943,X26944] :
      ( ( hAPP(X26942,X26939) != hAPP(X26942,X26938)
        | X26939 = X26938
        | ~ c_Typedef_Otype__definition(X26944,X26943,X26942,X26941,X26940) )
      & ( X26939 != X26938
        | hAPP(X26942,X26939) = hAPP(X26942,X26938)
        | ~ c_Typedef_Otype__definition(X26944,X26943,X26942,X26941,X26940) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_type__definition_ORep__inject])])]) ).

fof(i_0_7503,plain,
    ! [X27399,X27400,X27401,X27402] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X27402,X27401)),hAPP(hAPP(c_Product__Type_OSigma(X27402,X27401),X27400),hAPP(c_COMBK(tc_fun(X27401,tc_HOL_Obool),X27402),X27399))))
      | X27400 = c_Orderings_Obot__class_Obot(tc_fun(X27402,tc_HOL_Obool))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X27401),X27399)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__cartesian__productD2])]) ).

fof(i_0_7504,plain,
    ! [X27395,X27396,X27397,X27398] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X27398,X27397)),hAPP(hAPP(c_Product__Type_OSigma(X27398,X27397),X27396),hAPP(c_COMBK(tc_fun(X27397,tc_HOL_Obool),X27398),X27395))))
      | X27395 = c_Orderings_Obot__class_Obot(tc_fun(X27397,tc_HOL_Obool))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X27398),X27396)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__cartesian__productD1])]) ).

fof(i_0_7505,plain,
    ! [X26945,X26946,X26947,X26948,X26949,X26950] :
      ( ~ c_Typedef_Otype__definition(X26950,X26949,X26948,X26947,X26946)
      | hAPP(X26947,hAPP(X26948,X26945)) = X26945 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_type__definition_ORep__inverse])]) ).

fof(i_0_7506,plain,
    ! [X34187,X34188,X34189,X34190,X34191] :
      ( ~ c_Fun_Obij__betw(X34191,X34190,X34189,X34188,X34187)
      | hAPP(c_Finite__Set_Ocard(X34191),X34188) = hAPP(c_Finite__Set_Ocard(X34190),X34187) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__betw__same__card])]) ).

cnf(i_0_7507,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_5588]) ).

fof(i_0_7508,plain,
    ! [X20305,X20306,X20307] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X20307)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20307),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20307),hAPP(c_Groups_Oabs__class_Oabs(X20307),X20306)),hAPP(c_Groups_Oabs__class_Oabs(X20307),X20305))),hAPP(c_Groups_Oabs__class_Oabs(X20307),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20307),X20306),X20305)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq2])]) ).

fof(i_0_7509,plain,
    ! [X20308,X20309,X20310] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X20310)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20310),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20310),hAPP(c_Groups_Oabs__class_Oabs(X20310),X20309)),hAPP(c_Groups_Oabs__class_Oabs(X20310),X20308))),hAPP(c_Groups_Oabs__class_Oabs(X20310),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20310),X20308),X20309)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq2__sym])]) ).

cnf(i_0_7510,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_5589]) ).

fof(i_0_7511,plain,
    ! [X27190,X27191,X27192,X27193,X27194] : hAPP(c_Set_Ovimage(X27194,X27193,X27192),hAPP(hAPP(c_Set_Oinsert(X27193),X27191),X27190)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27194,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X27194,X27193,X27192),hAPP(hAPP(c_Set_Oinsert(X27193),X27191),c_Orderings_Obot__class_Obot(tc_fun(X27193,tc_HOL_Obool))))),hAPP(c_Set_Ovimage(X27194,X27193,X27192),X27190)),
    inference(variable_rename,[status(thm)],[fact_vimage__insert]) ).

fof(i_0_7512,plain,
    ! [X23370,X23371,X23372,X23373,X23374] :
      ( ( c_Fun_Ofun__upd(X23374,X23373,X23372,X23371,X23370) != X23372
        | hAPP(X23372,X23371) = X23370 )
      & ( hAPP(X23372,X23371) != X23370
        | c_Fun_Ofun__upd(X23374,X23373,X23372,X23371,X23370) = X23372 ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__upd__idem__iff])]) ).

fof(i_0_7513,plain,
    ! [X30663,X30664,X30665,X30666] :
      ( ( ~ c_List_Olist__all2(X30666,X30665,X30664,c_List_Olist_ONil(X30666),X30663)
        | X30663 = c_List_Olist_ONil(X30665) )
      & ( X30663 != c_List_Olist_ONil(X30665)
        | c_List_Olist__all2(X30666,X30665,X30664,c_List_Olist_ONil(X30666),X30663) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__Nil])]) ).

fof(i_0_7514,plain,
    ! [X30667,X30668,X30669,X30670] :
      ( ( ~ c_List_Olist__all2(X30670,X30669,X30668,X30667,c_List_Olist_ONil(X30669))
        | X30667 = c_List_Olist_ONil(X30670) )
      & ( X30667 != c_List_Olist_ONil(X30670)
        | c_List_Olist__all2(X30670,X30669,X30668,X30667,c_List_Olist_ONil(X30669)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__Nil2])]) ).

fof(i_0_7515,plain,
    ! [X34175,X34176,X34177] :
      ( ( ~ c_Fun_Obij__betw(X34177,X34177,c_Fun_Oid(X34177),X34176,X34175)
        | X34176 = X34175 )
      & ( X34176 != X34175
        | c_Fun_Obij__betw(X34177,X34177,c_Fun_Oid(X34177),X34176,X34175) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__betw__id__iff])]) ).

fof(i_0_7516,plain,
    ! [X30782,X30783,X30784,X30785,X30786] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30786,X30785)),hAPP(hAPP(c_Product__Type_OPair(X30786,X30785),X30784),X30783)),X30782))
      | hBOOL(hAPP(hAPP(c_member(X30786),X30784),hAPP(c_Relation_ODomain(X30786,X30785),X30782))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DomainI])]) ).

fof(i_0_7517,plain,
    ! [X28255,X28256,X28257,X28258,X28259] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28259,X28258)),hAPP(hAPP(c_Product__Type_OPair(X28259,X28258),X28257),X28256)),X28255))
      | hBOOL(hAPP(hAPP(c_member(X28258),X28256),hAPP(c_Relation_ORange(X28259,X28258),X28255))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_RangeI])]) ).

fof(i_0_7518,plain,
    ! [X28873,X28874,X28875,X28876] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X28876),X28875))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28874,tc_HOL_Obool)),hAPP(c_List_Oset(X28874),hAPP(hAPP(c_List_Odrop(X28874),X28875),X28873))),hAPP(c_List_Oset(X28874),hAPP(hAPP(c_List_Odrop(X28874),X28876),X28873)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__drop__subset__set__drop])]) ).

fof(i_0_7519,plain,
    ! [X28910,X28911,X28912,X28913] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X28913),X28912))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28911,tc_HOL_Obool)),hAPP(c_List_Oset(X28911),hAPP(hAPP(c_List_Otake(X28911),X28913),X28910))),hAPP(c_List_Oset(X28911),hAPP(hAPP(c_List_Otake(X28911),X28912),X28910)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__take__subset__set__take])]) ).

fof(i_0_7520,plain,
    ! [X30634,X30635,X30636] :
      ( ( X30636 != X30635
        | c_List_Olist__all2(X30634,X30634,c_fequal,X30636,X30635) )
      & ( ~ c_List_Olist__all2(X30634,X30634,c_fequal,X30636,X30635)
        | X30636 = X30635 ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__eq])]) ).

fof(i_0_7521,plain,
    ! [X30491,X30492,X30493] :
      ( ~ class_Orderings_Olinorder(X30493)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30493),X30492))
      | c_List_Olinorder__class_Osorted__list__of__set(X30493,hAPP(hAPP(c_Set_Oinsert(X30493),X30491),X30492)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30493,X30493,c_COMBI(X30493)),X30491),c_List_Olinorder__class_Osorted__list__of__set(X30493,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X30493,tc_HOL_Obool)),X30492),hAPP(hAPP(c_Set_Oinsert(X30493),X30491),c_Orderings_Obot__class_Obot(tc_fun(X30493,tc_HOL_Obool)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__list__of__set__insert])]) ).

fof(i_0_7522,plain,
    ! [X20588,X20589,X20590,X20591] :
      ( ~ class_Rings_Olinordered__semidom(X20591)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20591),hAPP(hAPP(c_Power_Opower__class_Opower(X20591),X20590),hAPP(c_Nat_OSuc,X20589))),hAPP(hAPP(c_Power_Opower__class_Opower(X20591),X20588),hAPP(c_Nat_OSuc,X20589))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20591),c_Groups_Ozero__class_Ozero(X20591)),X20588))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20591),X20590),X20588)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__le__imp__le__base])]) ).

cnf(i_0_7523,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_5590]) ).

fof(i_0_7524,plain,
    ! [X32870,X32871,X32872,X32873] :
      ( ~ class_Lattices_Osemilattice__sup(X32873)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32873),X32872))
      | ~ hBOOL(hAPP(hAPP(c_member(X32873),X32871),X32872))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X32873),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X32873),X32871),X32870)),hAPP(hAPP(c_Finite__Set_Ofold(X32873,X32873,c_Lattices_Osemilattice__sup__class_Osup(X32873)),X32870),X32872))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__le__fold__sup])]) ).

fof(i_0_7525,plain,
    ! [X32882,X32883,X32884,X32885] :
      ( ~ class_Orderings_Olinorder(X32885)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32885),X32884))
      | ~ hBOOL(hAPP(hAPP(c_member(X32885),X32883),X32884))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X32885),hAPP(hAPP(c_Orderings_Oord__class_Omax(X32885),X32883),X32882)),hAPP(hAPP(c_Finite__Set_Ofold(X32885,X32885,c_Orderings_Oord__class_Omax(X32885)),X32882),X32884))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__le__fold__sup])]) ).

fof(i_0_7526,plain,
    ! [X30794,X30795,X30796,X30797] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X30797,X30796),tc_HOL_Obool)),X30795),X30794))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X30797,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X30797,X30796),X30795)),hAPP(c_Relation_ODomain(X30797,X30796),X30794))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Domain__mono])]) ).

fof(i_0_7527,plain,
    ! [X33976,X33977,X33978] :
      ( ~ c_Fun_Oinj__on(X33978,X33977,X33976,c_Orderings_Otop__class_Otop(tc_fun(X33978,tc_HOL_Obool)))
      | hAPP(c_Set_Oimage(X33977,X33978,c_Hilbert__Choice_Oinv__into(X33978,X33977,c_Orderings_Otop__class_Otop(tc_fun(X33978,tc_HOL_Obool)),X33976)),c_Orderings_Otop__class_Otop(tc_fun(X33977,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X33978,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__imp__surj__inv])]) ).

cnf(i_0_7528,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_5591]) ).

fof(i_0_7529,plain,
    ! [X21522,X21523,X21524] :
      ( ~ class_Fields_Olinordered__field(X21524)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21524),X21523),X21522))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21524),X21523),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21524),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21524),X21523),X21522)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21524),c_Groups_Oone__class_Oone(X21524)),c_Groups_Oone__class_Oone(X21524))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__half__sum])]) ).

fof(i_0_7530,plain,
    ! [X24102,X24103] :
      ( ~ c_Nat__Transfer_Onat__set(X24103)
      | ~ c_Nat__Transfer_Onat__set(X24102)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X24103),X24102) = 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),X24103)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X24102))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J])]) ).

fof(i_0_7531,plain,
    ! [X23432,X23433] :
      ( ~ c_Nat__Transfer_Onat__set(X23433)
      | ~ c_Nat__Transfer_Onat__set(X23432)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X23433),X23432) = 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),X23433)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X23432))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J])]) ).

fof(i_0_7532,plain,
    ! [X25519,X25520,X25521,X25522,X25523] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25523),X25520),X25522))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25523),X25522),X25521))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X25523,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X25523,X25522,X25521)),c_SetInterval_Oord__class_OatLeastAtMost(X25523,X25520,X25519)))
        | ~ class_Orderings_Oorder(X25523) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25523),X25521),X25519))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25523),X25522),X25521))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X25523,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X25523,X25522,X25521)),c_SetInterval_Oord__class_OatLeastAtMost(X25523,X25520,X25519)))
        | ~ class_Orderings_Oorder(X25523) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25523),X25520),X25522))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25523),X25521),X25519))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25523),X25522),X25521))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X25523,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X25523,X25522,X25521)),c_SetInterval_Oord__class_OatLeastAtMost(X25523,X25520,X25519)))
        | ~ class_Orderings_Oorder(X25523) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25523),X25520),X25519))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X25523,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X25523,X25522,X25521)),c_SetInterval_Oord__class_OatLeastAtMost(X25523,X25520,X25519)))
        | ~ class_Orderings_Oorder(X25523) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25523),X25522),X25521))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25523),X25520),X25519))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X25523,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X25523,X25522,X25521)),c_SetInterval_Oord__class_OatLeastAtMost(X25523,X25520,X25519)))
        | ~ class_Orderings_Oorder(X25523) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25523),X25520),X25522))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25523),X25520),X25522))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25523),X25521),X25519))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25523),X25520),X25519))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X25523,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X25523,X25522,X25521)),c_SetInterval_Oord__class_OatLeastAtMost(X25523,X25520,X25519)))
        | ~ class_Orderings_Oorder(X25523) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25523),X25521),X25519))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25523),X25520),X25522))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25523),X25521),X25519))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25523),X25520),X25519))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X25523,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X25523,X25522,X25521)),c_SetInterval_Oord__class_OatLeastAtMost(X25523,X25520,X25519)))
        | ~ class_Orderings_Oorder(X25523) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5592])])]) ).

fof(i_0_7533,plain,
    ! [X18289,X18290,X18291,X18292,X18293] :
      ( ~ class_Rings_Osemiring(X18293)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18293),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18293),X18292),X18291)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18293),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18293),X18290),X18291)),X18289)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18293),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18293),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18293),X18292),X18290)),X18291)),X18289) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_combine__common__factor])]) ).

fof(i_0_7534,plain,
    ! [X27336,X27337] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27337,X27337),tc_HOL_Obool)),c_Relation_OId__on(X27337,X27336)),hAPP(hAPP(c_Product__Type_OSigma(X27337,X27337),X27336),hAPP(c_COMBK(tc_fun(X27337,tc_HOL_Obool),X27337),X27336)))),
    inference(variable_rename,[status(thm)],[fact_Id__on__subset__Times]) ).

fof(i_0_7535,plain,
    ! [X31856,X31857] :
      ( ~ class_Orderings_Olinorder(X31857)
      | c_List_Olinorder__class_Osort__key(X31857,X31857,c_COMBI(X31857),X31856) = hAPP(c_List_Ofoldl(tc_List_Olist(X31857),X31857,hAPP(c_COMBC(X31857,tc_List_Olist(X31857),tc_List_Olist(X31857)),c_List_Olinorder__class_Oinsort__key(X31857,X31857,c_COMBI(X31857))),c_List_Olist_ONil(X31857)),X31856) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sort__foldl__insort])]) ).

fof(i_0_7536,plain,
    ! [X28252,X28253,X28254] : hAPP(c_Relation_ORange(X28254,X28253),hAPP(c_Set_OCollect(tc_prod(X28254,X28253)),hAPP(c_Product__Type_Oprod_Oprod__case(X28254,X28253,tc_HOL_Obool),X28252))) = hAPP(c_Set_OCollect(X28253),hAPP(hAPP(c_COMBB(tc_fun(X28254,tc_HOL_Obool),tc_HOL_Obool,X28253),c_HOL_OEx(X28254)),hAPP(c_COMBC(X28254,X28253,tc_HOL_Obool),X28252))),
    inference(variable_rename,[status(thm)],[fact_Range__Collect__split]) ).

fof(i_0_7537,plain,
    ! [X27318,X27319,X27320] :
      ( ~ c_Equiv__Relations_Oequiv(X27320,X27319,X27318)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27320,X27320),tc_HOL_Obool)),X27318),hAPP(hAPP(c_Product__Type_OSigma(X27320,X27320),X27319),hAPP(c_COMBK(tc_fun(X27320,tc_HOL_Obool),X27320),X27319)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__type])]) ).

fof(i_0_7538,plain,
    ! [X30110,X30111,X30112,X30113,X30114] : hAPP(c_Fun_Ocomp(tc_List_Olist(X30114),tc_List_Olist(X30113),tc_List_Olist(X30112),hAPP(c_List_Omap(X30114,X30113),X30111)),hAPP(c_List_Omap(X30112,X30114),X30110)) = hAPP(c_List_Omap(X30112,X30113),hAPP(c_Fun_Ocomp(X30114,X30113,X30112,X30111),X30110)),
    inference(variable_rename,[status(thm)],[fact_List_Omap_Ocomp]) ).

fof(i_0_7539,plain,
    ! [X30105,X30106,X30107,X30108,X30109] : hAPP(c_Fun_Ocomp(tc_List_Olist(X30109),tc_List_Olist(X30108),tc_List_Olist(X30107),hAPP(c_List_Omap(X30109,X30108),X30106)),hAPP(c_List_Omap(X30107,X30109),X30105)) = hAPP(c_List_Omap(X30107,X30108),hAPP(c_Fun_Ocomp(X30109,X30108,X30107,X30106),X30105)),
    inference(variable_rename,[status(thm)],[fact_map__comp__map]) ).

fof(i_0_7540,plain,
    ! [X27630,X27631,X27632,X27633,X27634] :
      ( ~ c_Relation_Orefl__on(X27634,X27633,X27632)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27634,X27634)),hAPP(hAPP(c_Product__Type_OPair(X27634,X27634),X27631),X27630)),X27632))
      | hBOOL(hAPP(hAPP(c_member(X27634),X27631),X27633)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__onD1])]) ).

fof(i_0_7541,plain,
    ! [X27635,X27636,X27637,X27638,X27639] :
      ( ~ c_Relation_Orefl__on(X27639,X27638,X27637)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27639,X27639)),hAPP(hAPP(c_Product__Type_OPair(X27639,X27639),X27636),X27635)),X27637))
      | hBOOL(hAPP(hAPP(c_member(X27639),X27635),X27638)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__onD2])]) ).

cnf(i_0_7542,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_5593]) ).

fof(i_0_7543,plain,
    ! [X28584,X28585] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X28585),tc_List_Olist(X28585))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X28585),tc_List_Olist(X28585)),c_List_Olist_ONil(X28585)),c_List_Olist_ONil(X28585))),c_List_Olistrel(X28585,X28584))),
    inference(variable_rename,[status(thm)],[fact_listrel_ONil]) ).

fof(i_0_7544,plain,
    ! [X30877,X30878,X30879] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X30879,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X30879,tc_HOL_Obool),X30878)),X30877) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X30879,tc_HOL_Obool),tc_fun(X30879,tc_HOL_Obool)),X30878),hAPP(hAPP(c_COMBC(tc_fun(X30879,tc_HOL_Obool),tc_fun(X30879,tc_HOL_Obool),tc_fun(X30879,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X30879,tc_HOL_Obool))),X30877)),
    inference(variable_rename,[status(thm)],[fact_Int__Union2]) ).

fof(i_0_7545,plain,
    ! [X25347,X25348,X25349,X25350] :
      ( ( X25349 = X25348
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X25350,X25350)),hAPP(hAPP(c_Product__Type_OPair(X25350,X25350),X25349),X25348)),c_Relation_OId__on(X25350,X25347))) )
      & ( hBOOL(hAPP(hAPP(c_member(X25350),X25349),X25347))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X25350,X25350)),hAPP(hAPP(c_Product__Type_OPair(X25350,X25350),X25349),X25348)),c_Relation_OId__on(X25350,X25347))) )
      & ( X25349 != X25348
        | ~ hBOOL(hAPP(hAPP(c_member(X25350),X25349),X25347))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X25350,X25350)),hAPP(hAPP(c_Product__Type_OPair(X25350,X25350),X25349),X25348)),c_Relation_OId__on(X25350,X25347))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Id__on__iff])])]) ).

fof(i_0_7546,plain,
    ! [X24699,X24700,X24701,X24702] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X24702),X24700))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X24702,X24701)),c_Sum__Type_OPlus(X24702,X24701,X24700,X24699))) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X24701),X24699))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X24702,X24701)),c_Sum__Type_OPlus(X24702,X24701,X24700,X24699))) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24702),X24700))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24701),X24699))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X24702,X24701)),c_Sum__Type_OPlus(X24702,X24701,X24700,X24699))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Plus__iff])])]) ).

fof(i_0_7547,plain,
    ! [X24691,X24692,X24693,X24694] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X24694,X24693)),c_Sum__Type_OPlus(X24694,X24693,X24692,X24691)))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X24694),X24692)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__PlusD_I1_J])]) ).

fof(i_0_7548,plain,
    ! [X24687,X24688,X24689,X24690] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X24690,X24689)),c_Sum__Type_OPlus(X24690,X24689,X24688,X24687)))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X24689),X24687)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__PlusD_I2_J])]) ).

fof(i_0_7549,plain,
    ! [X27251,X27252,X27253,X27254,X27255,X27256] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X27256),X27255),X27254))
      | ~ hBOOL(hAPP(hAPP(c_member(X27253),X27252),hAPP(X27251,X27255)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X27256,X27253)),hAPP(hAPP(c_Product__Type_OPair(X27256,X27253),X27255),X27252)),hAPP(hAPP(c_Product__Type_OSigma(X27256,X27253),X27254),X27251))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SigmaI])]) ).

fof(i_0_7550,plain,
    ! [X30980,X30981,X30982] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_fun(X30982,tc_HOL_Obool)),esk373_3(X30980,X30981,X30982)),hAPP(hAPP(c_Set_Oinsert(tc_fun(X30982,tc_HOL_Obool)),X30981),X30980)))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X30982,tc_HOL_Obool)),X30981),c_Complete__Lattice_OSup__class_OSup(tc_fun(X30982,tc_HOL_Obool),X30980)) = c_Orderings_Obot__class_Obot(tc_fun(X30982,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X30982,tc_HOL_Obool)),X30981),X30980)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_fun(X30982,tc_HOL_Obool)),esk374_3(X30980,X30981,X30982)),hAPP(hAPP(c_Set_Oinsert(tc_fun(X30982,tc_HOL_Obool)),X30981),X30980)))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X30982,tc_HOL_Obool)),X30981),c_Complete__Lattice_OSup__class_OSup(tc_fun(X30982,tc_HOL_Obool),X30980)) = c_Orderings_Obot__class_Obot(tc_fun(X30982,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X30982,tc_HOL_Obool)),X30981),X30980)) )
      & ( esk373_3(X30980,X30981,X30982) != esk374_3(X30980,X30981,X30982)
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X30982,tc_HOL_Obool)),X30981),c_Complete__Lattice_OSup__class_OSup(tc_fun(X30982,tc_HOL_Obool),X30980)) = c_Orderings_Obot__class_Obot(tc_fun(X30982,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X30982,tc_HOL_Obool)),X30981),X30980)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X30982,tc_HOL_Obool)),esk373_3(X30980,X30981,X30982)),esk374_3(X30980,X30981,X30982)) != c_Orderings_Obot__class_Obot(tc_fun(X30982,tc_HOL_Obool))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X30982,tc_HOL_Obool)),X30981),c_Complete__Lattice_OSup__class_OSup(tc_fun(X30982,tc_HOL_Obool),X30980)) = c_Orderings_Obot__class_Obot(tc_fun(X30982,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X30982,tc_HOL_Obool)),X30981),X30980)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5594])])])]) ).

fof(i_0_7551,plain,
    ! [X29414,X29415,X29416,X29417] :
      ( ~ class_Groups_Osemigroup__add(X29417)
      | hAPP(c_List_Ofoldl(X29417,X29417,c_Groups_Oplus__class_Oplus(X29417),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X29417),X29416),X29415)),X29414) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X29417),X29416),hAPP(c_List_Ofoldl(X29417,X29417,c_Groups_Oplus__class_Oplus(X29417),X29415),X29414)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_foldl__assoc])]) ).

fof(i_0_7552,plain,
    ! [X22009,X22010,X22011] : hBOOL(hAPP(hAPP(c_member(tc_prod(X22011,X22011)),hAPP(hAPP(c_Product__Type_OPair(X22011,X22011),X22010),X22010)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X22011,X22011),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22009))),
    inference(variable_rename,[status(thm)],[fact_rel__pow__0__I]) ).

cnf(i_0_7553,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_5595]) ).

fof(i_0_7554,plain,
    ! [X29193,X29194,X29195,X29196,X29197] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29197),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29196)),X29195)))
        | hAPP(hAPP(c_List_Olist__update(X29196,hAPP(hAPP(c_List_Oappend(X29196),X29195),X29194)),X29197),X29193) = hAPP(hAPP(c_List_Oappend(X29196),hAPP(hAPP(c_List_Olist__update(X29196,X29195),X29197),X29193)),X29194) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29197),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29196)),X29195)))
        | hAPP(hAPP(c_List_Olist__update(X29196,hAPP(hAPP(c_List_Oappend(X29196),X29195),X29194)),X29197),X29193) = hAPP(hAPP(c_List_Oappend(X29196),X29195),hAPP(hAPP(c_List_Olist__update(X29196,X29194),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X29197),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29196)),X29195))),X29193)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5596])]) ).

fof(i_0_7555,plain,
    ! [X23735,X23736,X23737,X23738,X23739] :
      ( ~ c_Equiv__Relations_Oequiv(X23739,X23738,X23737)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X23739,tc_HOL_Obool)),X23736),hAPP(hAPP(c_Equiv__Relations_Oquotient(X23739),X23738),X23737)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X23739,tc_HOL_Obool)),X23735),hAPP(hAPP(c_Equiv__Relations_Oquotient(X23739),X23738),X23737)))
      | X23736 = X23735
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23739,tc_HOL_Obool)),X23736),X23735) = c_Orderings_Obot__class_Obot(tc_fun(X23739,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_quotient__disj])]) ).

fof(i_0_7556,plain,
    ! [X30210,X30211,X30212] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30212),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30211)),X30210)))
      | hAPP(c_Random_Opick(X30211,hAPP(hAPP(c_List_Omap(X30211,tc_prod(tc_Code__Numeral_Ocode__numeral,X30211)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X30211),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),X30210)),hAPP(c_Code__Numeral_Oof__nat,X30212)) = hAPP(hAPP(c_List_Onth(X30211),X30210),X30212) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pick__same])]) ).

fof(i_0_7557,plain,
    ! [X21572,X21573,X21574,X21575] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21575),c_Groups_Ozero__class_Ozero(X21575)),X21572))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21575),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21575),X21574),X21572)),X21573))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21575),X21574),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21575),X21573),X21572)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21575) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21575),X21572),c_Groups_Ozero__class_Ozero(X21575)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21575),X21573),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21575),X21574),X21572)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21575),c_Groups_Ozero__class_Ozero(X21575)),X21572))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21575),X21574),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21575),X21573),X21572)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21575) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21575),X21572),c_Groups_Ozero__class_Ozero(X21575)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21575),X21574),c_Groups_Ozero__class_Ozero(X21575)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21575),c_Groups_Ozero__class_Ozero(X21575)),X21572))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21575),X21574),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21575),X21573),X21572)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21575) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21575),c_Groups_Ozero__class_Ozero(X21575)),X21572))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21575),c_Groups_Ozero__class_Ozero(X21575)),X21572))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21575),X21574),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21575),X21573),X21572)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21575) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21575),X21572),c_Groups_Ozero__class_Ozero(X21575)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21575),X21572),c_Groups_Ozero__class_Ozero(X21575)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21575),c_Groups_Ozero__class_Ozero(X21575)),X21572))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21575),X21574),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21575),X21573),X21572)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21575) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21575),X21574),c_Groups_Ozero__class_Ozero(X21575)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21575),X21572),c_Groups_Ozero__class_Ozero(X21575)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21575),c_Groups_Ozero__class_Ozero(X21575)),X21572))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21575),X21574),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21575),X21573),X21572)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21575) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21575),X21572),c_Groups_Ozero__class_Ozero(X21575)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21575),X21573),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21575),X21574),X21572)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21575),c_Groups_Ozero__class_Ozero(X21575)),X21572))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21575),X21574),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21575),X21573),X21572)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21575) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21575),X21574),c_Groups_Ozero__class_Ozero(X21575)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21575),X21573),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21575),X21574),X21572)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21575),c_Groups_Ozero__class_Ozero(X21575)),X21572))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21575),X21574),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21575),X21573),X21572)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21575) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21575),c_Groups_Ozero__class_Ozero(X21575)),X21572))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21575),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21575),X21574),X21572)),X21573))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21575),X21574),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21575),X21573),X21572)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21575) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21575),X21572),c_Groups_Ozero__class_Ozero(X21575)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21575),X21572),c_Groups_Ozero__class_Ozero(X21575)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21575),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21575),X21574),X21572)),X21573))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21575),X21574),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21575),X21573),X21572)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21575) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21575),X21574),c_Groups_Ozero__class_Ozero(X21575)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21575),X21572),c_Groups_Ozero__class_Ozero(X21575)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21575),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21575),X21574),X21572)),X21573))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21575),X21574),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21575),X21573),X21572)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21575) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21575),X21572),c_Groups_Ozero__class_Ozero(X21575)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21575),X21573),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21575),X21574),X21572)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21575),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21575),X21574),X21572)),X21573))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21575),X21574),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21575),X21573),X21572)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21575) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21575),X21574),c_Groups_Ozero__class_Ozero(X21575)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21575),X21573),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21575),X21574),X21572)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21575),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21575),X21574),X21572)),X21573))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21575),X21574),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21575),X21573),X21572)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21575) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5597])])]) ).

fof(i_0_7558,plain,
    ! [X21464,X21465,X21466,X21467] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21467),c_Groups_Ozero__class_Ozero(X21467)),X21464))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21467),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21467),X21466),X21464)),X21465))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21467),X21466),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21467),X21465),X21464)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21467) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21467),X21464),c_Groups_Ozero__class_Ozero(X21467)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21467),X21465),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21467),X21466),X21464)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21467),c_Groups_Ozero__class_Ozero(X21467)),X21464))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21467),X21466),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21467),X21465),X21464)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21467) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21467),X21464),c_Groups_Ozero__class_Ozero(X21467)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21467),X21466),c_Groups_Ozero__class_Ozero(X21467)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21467),c_Groups_Ozero__class_Ozero(X21467)),X21464))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21467),X21466),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21467),X21465),X21464)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21467) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21467),c_Groups_Ozero__class_Ozero(X21467)),X21464))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21467),c_Groups_Ozero__class_Ozero(X21467)),X21464))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21467),X21466),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21467),X21465),X21464)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21467) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21467),X21464),c_Groups_Ozero__class_Ozero(X21467)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21467),X21464),c_Groups_Ozero__class_Ozero(X21467)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21467),c_Groups_Ozero__class_Ozero(X21467)),X21464))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21467),X21466),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21467),X21465),X21464)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21467) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21467),X21466),c_Groups_Ozero__class_Ozero(X21467)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21467),X21464),c_Groups_Ozero__class_Ozero(X21467)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21467),c_Groups_Ozero__class_Ozero(X21467)),X21464))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21467),X21466),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21467),X21465),X21464)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21467) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21467),X21464),c_Groups_Ozero__class_Ozero(X21467)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21467),X21465),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21467),X21466),X21464)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21467),c_Groups_Ozero__class_Ozero(X21467)),X21464))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21467),X21466),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21467),X21465),X21464)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21467) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21467),X21466),c_Groups_Ozero__class_Ozero(X21467)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21467),X21465),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21467),X21466),X21464)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21467),c_Groups_Ozero__class_Ozero(X21467)),X21464))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21467),X21466),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21467),X21465),X21464)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21467) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21467),c_Groups_Ozero__class_Ozero(X21467)),X21464))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21467),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21467),X21466),X21464)),X21465))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21467),X21466),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21467),X21465),X21464)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21467) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21467),X21464),c_Groups_Ozero__class_Ozero(X21467)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21467),X21464),c_Groups_Ozero__class_Ozero(X21467)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21467),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21467),X21466),X21464)),X21465))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21467),X21466),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21467),X21465),X21464)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21467) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21467),X21466),c_Groups_Ozero__class_Ozero(X21467)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21467),X21464),c_Groups_Ozero__class_Ozero(X21467)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21467),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21467),X21466),X21464)),X21465))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21467),X21466),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21467),X21465),X21464)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21467) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21467),X21464),c_Groups_Ozero__class_Ozero(X21467)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21467),X21465),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21467),X21466),X21464)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21467),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21467),X21466),X21464)),X21465))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21467),X21466),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21467),X21465),X21464)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21467) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21467),X21466),c_Groups_Ozero__class_Ozero(X21467)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21467),X21465),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21467),X21466),X21464)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21467),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21467),X21466),X21464)),X21465))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21467),X21466),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21467),X21465),X21464)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21467) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5598])])]) ).

fof(i_0_7559,plain,
    ! [X25919,X25920] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X25920),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X25919),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25919),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X25920)))))
      | X25920 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X25919),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25919),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X25920))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__card__intvl__is__intvl])]) ).

fof(i_0_7560,plain,
    ! [X24234,X24235,X24236,X24237,X24238] :
      ( ( hBOOL(hAPP(hAPP(X24236,X24235),X24237))
        | ~ hBOOL(hAPP(hAPP(c_member(X24238),X24237),c_SetInterval_Oord_OatLeastAtMost(X24238,X24236,X24235,X24234))) )
      & ( hBOOL(hAPP(hAPP(X24236,X24237),X24234))
        | ~ hBOOL(hAPP(hAPP(c_member(X24238),X24237),c_SetInterval_Oord_OatLeastAtMost(X24238,X24236,X24235,X24234))) )
      & ( ~ hBOOL(hAPP(hAPP(X24236,X24235),X24237))
        | ~ hBOOL(hAPP(hAPP(X24236,X24237),X24234))
        | hBOOL(hAPP(hAPP(c_member(X24238),X24237),c_SetInterval_Oord_OatLeastAtMost(X24238,X24236,X24235,X24234))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OatLeastAtMost__iff])])]) ).

fof(i_0_7561,plain,
    ! [X24205,X24206,X24207,X24208,X24209] :
      ( ( hBOOL(hAPP(hAPP(X24207,X24206),X24208))
        | ~ hBOOL(hAPP(hAPP(c_member(X24209),X24208),c_SetInterval_Oord_OgreaterThanLessThan(X24209,X24207,X24206,X24205))) )
      & ( hBOOL(hAPP(hAPP(X24207,X24208),X24205))
        | ~ hBOOL(hAPP(hAPP(c_member(X24209),X24208),c_SetInterval_Oord_OgreaterThanLessThan(X24209,X24207,X24206,X24205))) )
      & ( ~ hBOOL(hAPP(hAPP(X24207,X24206),X24208))
        | ~ hBOOL(hAPP(hAPP(X24207,X24208),X24205))
        | hBOOL(hAPP(hAPP(c_member(X24209),X24208),c_SetInterval_Oord_OgreaterThanLessThan(X24209,X24207,X24206,X24205))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OgreaterThanLessThan__iff])])]) ).

cnf(i_0_7562,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_5599]) ).

cnf(i_0_7563,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_5600]) ).

fof(i_0_7564,plain,
    ! [X28419,X28420] : c_List_Oset__Cons(X28420,X28419,hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X28420)),c_List_Olist_ONil(X28420)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X28420),tc_HOL_Obool)))) = hAPP(c_Set_Oimage(X28420,tc_List_Olist(X28420),hAPP(hAPP(c_COMBC(X28420,tc_List_Olist(X28420),tc_List_Olist(X28420)),c_List_Olist_OCons(X28420)),c_List_Olist_ONil(X28420))),X28419),
    inference(variable_rename,[status(thm)],[fact_set__Cons__sing__Nil]) ).

fof(i_0_7565,plain,
    ! [X29888,X29889,X29890,X29891,X29892,X29893] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X29893),X29892),X29891))
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29893,tc_fun(X29890,tc_HOL_Obool)),X29891),hAPP(hAPP(c_COMBB(tc_fun(X29890,tc_HOL_Obool),tc_fun(X29890,tc_HOL_Obool),X29893),hAPP(c_Set_Oinsert(X29890),X29889)),X29888)) = hAPP(hAPP(c_Set_Oinsert(X29890),X29889),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29893,tc_fun(X29890,tc_HOL_Obool)),X29891),X29888)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__insert__distrib])]) ).

fof(i_0_7566,plain,
    ! [X25175,X25176,X25177,X25178,X25179,X25180] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X25180),X25179),X25178))
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25180,tc_fun(X25177,tc_HOL_Obool)),X25178),hAPP(hAPP(c_COMBB(tc_fun(X25177,tc_HOL_Obool),tc_fun(X25177,tc_HOL_Obool),X25180),hAPP(c_Set_Oinsert(X25177),X25176)),X25175)) = hAPP(hAPP(c_Set_Oinsert(X25177),X25176),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25180,tc_fun(X25177,tc_HOL_Obool)),X25178),X25175)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__insert__distrib])]) ).

fof(i_0_7567,plain,
    ! [X27977,X27978,X27981,X27982,X27983,X27984] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27978),X27977))
        | X27977 = hAPP(c_Set_Oimage(tc_Nat_Onat,X27978,esk295_2(X27977,X27978)),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)),esk294_2(X27977,X27978)))) )
      & ( X27981 != hAPP(c_Set_Oimage(tc_Nat_Onat,X27982,X27984),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)),X27983)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X27982),X27981)) ) ),
    inference(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_7568,plain,
    ! [X27801,X27802,X27803,X27804] :
      ( X27804 != hAPP(c_Set_Oimage(tc_Nat_Onat,X27803,X27802),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)),X27801)))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X27803),X27804)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__seg__image__imp__finite])]) ).

fof(i_0_7569,plain,
    ! [X28997,X28998,X28999] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X28999),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28998)),X28997)))
      | hAPP(hAPP(c_List_Oappend(X28998),hAPP(hAPP(c_List_Otake(X28998),X28999),X28997)),hAPP(hAPP(c_List_Olist_OCons(X28998),hAPP(c_List_Ohd(X28998),hAPP(hAPP(c_List_Odrop(X28998),X28999),X28997))),c_List_Olist_ONil(X28998))) = hAPP(hAPP(c_List_Otake(X28998),hAPP(c_Nat_OSuc,X28999)),X28997) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__hd__drop])]) ).

fof(i_0_7570,plain,
    ! [X20380,X20381,X20382,X20383] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20383,tc_HOL_Obool)),X20382),hAPP(hAPP(c_Set_Oinsert(X20383),X20381),X20380)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20383,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20383,tc_HOL_Obool)),X20382),hAPP(hAPP(c_Set_Oinsert(X20383),X20381),c_Orderings_Obot__class_Obot(tc_fun(X20383,tc_HOL_Obool))))),X20380),
    inference(variable_rename,[status(thm)],[fact_Diff__insert2]) ).

fof(i_0_7571,plain,
    ! [X32140,X32141,X32142] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32142),tc_List_Olist(X32142))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32142),tc_List_Olist(X32142)),X32141),X32141)),c_List_Olistrel(X32142,c_Transitive__Closure_Ortrancl(X32142,X32140)))),
    inference(variable_rename,[status(thm)],[fact_listrel__rtrancl__refl]) ).

cnf(i_0_7572,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_5601]) ).

fof(i_0_7573,plain,
    ! [X31961,X31962,X31963] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_fun(X31963,tc_HOL_Obool)),esk412_3(X31961,X31962,X31963)),X31962))
        | X31962 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X31963,tc_HOL_Obool),tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X31963,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X31963,tc_HOL_Obool),X31962)),X31961)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X31963,tc_HOL_Obool)),esk412_3(X31961,X31962,X31963)),X31961))
        | X31962 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X31963,tc_HOL_Obool),tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X31963,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X31963,tc_HOL_Obool),X31962)),X31961)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inter__subset])])])]) ).

fof(i_0_7574,plain,
    ! [X19532,X19533,X19534] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19534))
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,X19533,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19532),X19534)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19532),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19533),X19532),X19534))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19533,X19532)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__zmult2__eq])]) ).

fof(i_0_7575,plain,
    ! [X23803,X23804,X23805,X23806] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23806,tc_HOL_Obool)),X23805),X23804))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23806,tc_HOL_Obool)),X23805),X23803))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23806,tc_HOL_Obool)),X23805),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23806,tc_HOL_Obool)),X23804),X23803))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__greatest])]) ).

fof(i_0_7576,plain,
    ! [X33647,X33648,X33649] :
      ( ( ~ c_List_Olist__ex(tc_Int_Oint,X33649,c_List_Oupto(X33648,X33647))
        | ~ c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint,c_fNot),X33649),X33648,X33647) )
      & ( c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint,c_fNot),X33649),X33648,X33647)
        | c_List_Olist__ex(tc_Int_Oint,X33649,c_List_Oupto(X33648,X33647)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5602])]) ).

fof(i_0_7577,plain,
    ! [X22719,X22720] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X22720),hAPP(c_Nat_OSuc,X22719)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,X22719),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)),X22719)),X22720),
    inference(variable_rename,[status(thm)],[fact_max__Suc2]) ).

cnf(i_0_7578,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_5555]) ).

fof(i_0_7579,plain,
    ! [X28058,X28059,X28060,X28061] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28061,X28061),tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X28060),X28059)),X28058) = hAPP(hAPP(c_Relation_Orel__comp(X28061,X28061,X28061),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28061,X28061),tc_HOL_Obool),X28060),X28058)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28061,X28061),tc_HOL_Obool),X28059),X28058)),
    inference(variable_rename,[status(thm)],[fact_rel__pow__add]) ).

fof(i_0_7580,plain,
    ! [X31010,X31011,X31012] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X31012,tc_HOL_Obool),tc_HOL_Obool)),X31011),X31010))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X31012,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X31012,tc_HOL_Obool),X31010)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X31012,tc_HOL_Obool),X31011))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inter__anti__mono])]) ).

fof(i_0_7581,plain,
    ! [X30804,X30805,X30806] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X30806,tc_HOL_Obool),tc_HOL_Obool)),X30805),X30804))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X30806,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X30806,tc_HOL_Obool),X30805)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X30806,tc_HOL_Obool),X30804))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Union__mono])]) ).

fof(i_0_7582,plain,
    ! [X20420,X20421,X20422] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X20422)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20422),hAPP(c_Groups_Oabs__class_Oabs(X20422),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20422),X20421),X20420))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20422),hAPP(c_Groups_Oabs__class_Oabs(X20422),X20421)),hAPP(c_Groups_Oabs__class_Oabs(X20422),X20420)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq4])]) ).

fof(i_0_7583,plain,
    ! [X20294,X20295,X20296] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X20296)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20296),hAPP(c_Groups_Oabs__class_Oabs(X20296),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20296),X20295),X20294))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20296),hAPP(c_Groups_Oabs__class_Oabs(X20296),X20295)),hAPP(c_Groups_Oabs__class_Oabs(X20296),X20294)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq])]) ).

cnf(i_0_7584,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_5603]) ).

fof(i_0_7585,plain,
    ! [X25474,X25475,X25476,X25477,X25478] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25478),X25475),X25477))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25478),X25477),X25476))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25478,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X25478,X25477,X25476)),c_SetInterval_Oord__class_OatLeastAtMost(X25478,X25475,X25474)))
        | ~ class_Orderings_Oorder(X25478) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25478),X25476),X25474))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25478),X25477),X25476))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25478,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X25478,X25477,X25476)),c_SetInterval_Oord__class_OatLeastAtMost(X25478,X25475,X25474)))
        | ~ class_Orderings_Oorder(X25478) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25478),X25477),X25476))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25478,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X25478,X25477,X25476)),c_SetInterval_Oord__class_OatLeastAtMost(X25478,X25475,X25474)))
        | ~ class_Orderings_Oorder(X25478) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25478),X25475),X25477))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25478),X25476),X25474))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25478,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X25478,X25477,X25476)),c_SetInterval_Oord__class_OatLeastAtMost(X25478,X25475,X25474)))
        | ~ class_Orderings_Oorder(X25478) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5604])])]) ).

fof(i_0_7586,plain,
    ! [X22509,X22510] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X22510),hAPP(c_Nat_OSuc,X22509)) = 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)),X22509)),X22510),
    inference(variable_rename,[status(thm)],[fact_min__Suc2]) ).

fof(i_0_7587,plain,
    ! [X24521,X24522,X24523] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24523),X24522))
      | ~ hBOOL(hAPP(hAPP(c_member(X24523),X24521),X24522))
      | hAPP(c_Finite__Set_Ocard(X24523),X24522) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X24523),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24523,tc_HOL_Obool)),X24522),hAPP(hAPP(c_Set_Oinsert(X24523),X24521),c_Orderings_Obot__class_Obot(tc_fun(X24523,tc_HOL_Obool)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card_Oremove])]) ).

fof(i_0_7588,plain,
    ! [X29048,X29049,X29050,X29051,X29052,X29053,X29054] : hAPP(hAPP(c_List_Ozip(X29054,X29053),hAPP(hAPP(c_List_Olist__update(X29054,X29052),X29051),X29050)),hAPP(hAPP(c_List_Olist__update(X29053,X29049),X29051),X29048)) = hAPP(hAPP(c_List_Olist__update(tc_prod(X29054,X29053),hAPP(hAPP(c_List_Ozip(X29054,X29053),X29052),X29049)),X29051),hAPP(hAPP(c_Product__Type_OPair(X29054,X29053),X29050),X29048)),
    inference(variable_rename,[status(thm)],[fact_zip__update]) ).

fof(i_0_7589,plain,
    ! [X26806,X26807,X26808,X26809,X26810] :
      ( ~ c_Fun_Oinj__on(X26810,X26809,X26808,c_Orderings_Otop__class_Otop(tc_fun(X26810,tc_HOL_Obool)))
      | hAPP(c_Set_Oimage(X26810,X26809,X26808),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26810,tc_HOL_Obool)),X26807),X26806)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26809,tc_HOL_Obool)),hAPP(c_Set_Oimage(X26810,X26809,X26808),X26807)),hAPP(c_Set_Oimage(X26810,X26809,X26808),X26806)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__Int])]) ).

fof(i_0_7590,plain,
    ! [X26811,X26812,X26813,X26814,X26815] :
      ( ~ c_Fun_Oinj__on(X26815,X26814,X26813,c_Orderings_Otop__class_Otop(tc_fun(X26815,tc_HOL_Obool)))
      | hAPP(c_Set_Oimage(X26815,X26814,X26813),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26815,tc_HOL_Obool)),X26812),X26811)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26814,tc_HOL_Obool)),hAPP(c_Set_Oimage(X26815,X26814,X26813),X26812)),hAPP(c_Set_Oimage(X26815,X26814,X26813),X26811)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__set__diff])]) ).

fof(i_0_7591,plain,
    ! [X26054,X26055,X26056,X26057] :
      ( ~ c_Fun_Oinj__on(X26057,X26056,X26055,X26054)
      | hAPP(c_Set_Oimage(X26056,X26057,c_Fun_Othe__inv__into(X26057,X26056,X26054,X26055)),hAPP(c_Set_Oimage(X26057,X26056,X26055),X26054)) = X26054 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_the__inv__into__onto])]) ).

fof(i_0_7592,plain,
    ! [X22018,X22019,X22020,X22021,X22022,X22023] : c_Nitpick_Opair__box_Opair__box__case(X22023,X22022,X22021,X22020,c_Nitpick_Opair__box_OPairBox(X22023,X22022,X22019,X22018)) = hAPP(hAPP(X22020,X22019),X22018),
    inference(variable_rename,[status(thm)],[fact_pair__box_Osimps_I2_J]) ).

fof(i_0_7593,plain,
    ! [X22012,X22013,X22014,X22015,X22016,X22017] : c_Nitpick_Opair__box_Opair__box__rec(X22017,X22016,X22015,X22014,c_Nitpick_Opair__box_OPairBox(X22017,X22016,X22013,X22012)) = hAPP(hAPP(X22014,X22013),X22012),
    inference(variable_rename,[status(thm)],[fact_pair__box_Orecs]) ).

fof(i_0_7594,plain,
    ! [X31757,X31758,X31759,X31760,X31761] : hAPP(hAPP(c_List_Ozip(X31761,X31760),c_List_OtakeWhile(X31761,X31759,X31758)),X31757) = c_List_OtakeWhile(tc_prod(X31761,X31760),hAPP(c_Fun_Ocomp(X31761,tc_HOL_Obool,tc_prod(X31761,X31760),X31759),c_Product__Type_Ofst(X31761,X31760)),hAPP(hAPP(c_List_Ozip(X31761,X31760),X31758),X31757)),
    inference(variable_rename,[status(thm)],[fact_zip__takeWhile__fst]) ).

cnf(i_0_7595,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_5605]) ).

cnf(i_0_7596,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_5606]) ).

cnf(i_0_7597,plain,
    ( X2 = hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk479_2(X2,X1)),esk479_2(X2,X1))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Relation_OId(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_5607]) ).

fof(i_0_7598,plain,
    ! [X17714,X17715,X17716,X17717,X17718] :
      ( ( ~ hBOOL(hAPP(X17718,X17715))
        | hBOOL(hAPP(X17718,X17715))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X17718,X17717,X17716)),X17715),X17714)) )
      & ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17716),X17715),X17714))
        | hBOOL(hAPP(X17718,X17715))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X17718,X17717,X17716)),X17715),X17714)) )
      & ( ~ hBOOL(hAPP(X17718,X17715))
        | hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17717),X17715),X17714))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X17718,X17717,X17716)),X17715),X17714)) )
      & ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17716),X17715),X17714))
        | hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17717),X17715),X17714))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X17718,X17717,X17716)),X17715),X17714)) )
      & ( ~ hBOOL(hAPP(X17718,X17715))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17717),X17715),X17714))
        | hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X17718,X17717,X17716)),X17715),X17714)) )
      & ( hBOOL(hAPP(X17718,X17715))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17716),X17715),X17714))
        | hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X17718,X17717,X17716)),X17715),X17714)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5608])])]) ).

fof(i_0_7599,plain,
    ! [X17709,X17710,X17711,X17712,X17713] :
      ( ( ~ hBOOL(hAPP(X17713,X17710))
        | hBOOL(hAPP(X17713,X17710))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X17713,X17712,X17711)),X17710),X17709)) )
      & ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17711),X17710),X17709))
        | hBOOL(hAPP(X17713,X17710))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X17713,X17712,X17711)),X17710),X17709)) )
      & ( ~ hBOOL(hAPP(X17713,X17710))
        | hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17712),X17710),X17709))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X17713,X17712,X17711)),X17710),X17709)) )
      & ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17711),X17710),X17709))
        | hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17712),X17710),X17709))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X17713,X17712,X17711)),X17710),X17709)) )
      & ( ~ hBOOL(hAPP(X17713,X17710))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17712),X17710),X17709))
        | hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X17713,X17712,X17711)),X17710),X17709)) )
      & ( hBOOL(hAPP(X17713,X17710))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17711),X17710),X17709))
        | hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X17713,X17712,X17711)),X17710),X17709)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5609])])]) ).

fof(i_0_7600,plain,
    ! [X17648,X17649,X17650,X17651,X17652] :
      ( ( ~ hBOOL(hAPP(X17652,X17649))
        | hBOOL(hAPP(X17652,X17649))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X17652,X17651,X17650)),X17649),X17648)) )
      & ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17650),X17649),X17648))
        | hBOOL(hAPP(X17652,X17649))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X17652,X17651,X17650)),X17649),X17648)) )
      & ( ~ hBOOL(hAPP(X17652,X17649))
        | hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17651),X17649),X17648))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X17652,X17651,X17650)),X17649),X17648)) )
      & ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17650),X17649),X17648))
        | hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17651),X17649),X17648))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X17652,X17651,X17650)),X17649),X17648)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5610])])]) ).

cnf(i_0_7601,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_7602,plain,
    ! [X18106,X18107,X18108] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18108),X18107))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18106))
      | 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),X18106)),X18108)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18106)),X18107))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult__zless__mono2__lemma])]) ).

cnf(i_0_7603,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_5546]) ).

cnf(i_0_7604,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_7605,plain,
    ! [X23938,X23939,X23940,X23941] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23941,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23941,tc_HOL_Obool)),X23940),X23939)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23941,tc_HOL_Obool)),X23938),X23939)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23941,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23941,tc_HOL_Obool)),X23940),X23939)),X23938),
    inference(variable_rename,[status(thm)],[fact_Diff__Int2]) ).

fof(i_0_7606,plain,
    ! [X23962,X23963,X23964,X23965] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23965,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23965,tc_HOL_Obool)),X23964),X23963)),X23962) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23965,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23965,tc_HOL_Obool)),X23964),X23962)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23965,tc_HOL_Obool)),X23963),X23962)),
    inference(variable_rename,[status(thm)],[fact_Int__Un__distrib2]) ).

fof(i_0_7607,plain,
    ! [X23942,X23943,X23944,X23945] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23945,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23945,tc_HOL_Obool)),X23944),X23943)),X23942) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23945,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23945,tc_HOL_Obool)),X23944),X23942)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23945,tc_HOL_Obool)),X23943),X23942)),
    inference(variable_rename,[status(thm)],[fact_Diff__Int__distrib2]) ).

fof(i_0_7608,plain,
    ! [X23966,X23967,X23968,X23969] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23969,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23969,tc_HOL_Obool)),X23968),X23967)),X23966) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23969,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23969,tc_HOL_Obool)),X23968),X23966)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23969,tc_HOL_Obool)),X23967),X23966)),
    inference(variable_rename,[status(thm)],[fact_Un__Int__distrib2]) ).

fof(i_0_7609,plain,
    ! [X22834,X22835,X22836,X22837] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X22837,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22837,tc_HOL_Obool)),X22836),X22835)),X22834) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22837,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X22837,tc_HOL_Obool)),X22836),X22834)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X22837,tc_HOL_Obool)),X22835),X22834)),
    inference(variable_rename,[status(thm)],[fact_Un__Diff]) ).

fof(i_0_7610,plain,
    ! [X25592,X25593,X25594] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk193_3(X25592,X25593,X25594)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X25594)))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X25593),X25594) = X25593
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X25593),c_Groups_Oone__class_Oone(tc_Int_Oint))),X25592))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25594)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk194_3(X25592,X25593,X25594)),X25592))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X25593),X25594) = X25593
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X25593),c_Groups_Oone__class_Oone(tc_Int_Oint))),X25592))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25594)) )
      & ( X25593 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk194_3(X25592,X25593,X25594)),esk193_3(X25592,X25593,X25594))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X25593),X25594) = X25593
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X25593),c_Groups_Oone__class_Oone(tc_Int_Oint))),X25592))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25594)) ) ),
    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_7611,plain,
    ! [X25615,X25616,X25617] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk201_3(X25615,X25616,X25617)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X25617)))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25616),X25617) = X25616
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25616),c_Groups_Oone__class_Oone(tc_Int_Oint))),X25615))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25617)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk202_3(X25615,X25616,X25617)),X25615))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25616),X25617) = X25616
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25616),c_Groups_Oone__class_Oone(tc_Int_Oint))),X25615))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25617)) )
      & ( X25616 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk202_3(X25615,X25616,X25617)),esk201_3(X25615,X25616,X25617))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25616),X25617) = X25616
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25616),c_Groups_Oone__class_Oone(tc_Int_Oint))),X25615))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25617)) ) ),
    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_7612,plain,
    ! [X28984,X28985,X28986,X28987] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X28987),X28986)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28985)),X28984)))
      | hAPP(hAPP(c_List_Otake(X28985),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X28987),X28986)),X28984) = hAPP(hAPP(c_List_Oappend(X28985),hAPP(hAPP(c_List_Otake(X28985),X28987),X28984)),hAPP(hAPP(c_List_Otake(X28985),X28986),hAPP(hAPP(c_List_Odrop(X28985),X28987),X28984))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__add])]) ).

fof(i_0_7613,plain,
    ! [X24604,X24605,X24606] :
      ( ( hBOOL(hAPP(hAPP(c_member(X24606),esk138_3(X24604,X24605,X24606)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24606,tc_HOL_Obool)),X24605),X24604)))
        | hAPP(c_Finite__Set_Ocard(X24606),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24606,tc_HOL_Obool)),X24605),X24604)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X24606),X24605)),hAPP(c_Finite__Set_Ocard(X24606),X24604))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24606),X24604))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24606),X24605)) )
      & ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Finite__Set_Ocard(X24606),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24606,tc_HOL_Obool)),X24605),X24604)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X24606),X24605)),hAPP(c_Finite__Set_Ocard(X24606),X24604))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24606),X24604))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24606),X24605)) ) ),
    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_7614,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_7615,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_7616,plain,
    ! [X24587,X24588,X24589] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24589),X24588))
      | ~ hBOOL(hAPP(hAPP(c_member(X24589),X24587),X24588))
      | hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X24589),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24589,tc_HOL_Obool)),X24588),hAPP(hAPP(c_Set_Oinsert(X24589),X24587),c_Orderings_Obot__class_Obot(tc_fun(X24589,tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(X24589),X24588) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Suc__Diff1])]) ).

fof(i_0_7617,plain,
    ! [X23631,X23632,X23633,X23634,X23635,X23636] :
      ( ~ c_Finite__Set_Ofolding(X23636,X23635,X23634,X23633)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23636),X23632))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23636),X23631))
      | hAPP(c_Fun_Ocomp(X23635,X23635,X23635,hAPP(X23633,X23631)),hAPP(X23633,X23632)) = hAPP(c_Fun_Ocomp(X23635,X23635,X23635,hAPP(X23633,X23632)),hAPP(X23633,X23631)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__comp_H_H])]) ).

fof(i_0_7618,plain,
    ! [X31778,X31779] :
      ( X31779 = c_List_Olist_ONil(X31778)
      | ~ hBOOL(hAPP(c_List_Odistinct(X31778),X31779))
      | c_List_OtakeWhile(X31778,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X31778),c_fNot),hAPP(hAPP(c_COMBC(X31778,X31778,tc_HOL_Obool),c_fequal),c_List_Olast(X31778,X31779))),X31779) = c_List_Obutlast(X31778,X31779) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_takeWhile__not__last])]) ).

fof(i_0_7619,plain,
    ! [X30048,X30049,X30050,X30051] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X30051,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30050,tc_fun(X30051,tc_HOL_Obool)),X30049),X30048)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X30050,tc_fun(X30051,tc_HOL_Obool)),X30049),hAPP(hAPP(c_COMBB(tc_fun(X30051,tc_HOL_Obool),tc_fun(X30051,tc_HOL_Obool),X30050),c_Groups_Ouminus__class_Ouminus(tc_fun(X30051,tc_HOL_Obool))),X30048)),
    inference(variable_rename,[status(thm)],[fact_Compl__INT]) ).

fof(i_0_7620,plain,
    ! [X30052,X30053,X30054,X30055] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X30055,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X30054,tc_fun(X30055,tc_HOL_Obool)),X30053),X30052)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30054,tc_fun(X30055,tc_HOL_Obool)),X30053),hAPP(hAPP(c_COMBB(tc_fun(X30055,tc_HOL_Obool),tc_fun(X30055,tc_HOL_Obool),X30054),c_Groups_Ouminus__class_Ouminus(tc_fun(X30055,tc_HOL_Obool))),X30052)),
    inference(variable_rename,[status(thm)],[fact_Compl__UN]) ).

fof(i_0_7621,plain,
    ! [X26870,X26871,X26872,X26873] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X26873,X26872,hAPP(hAPP(c_Set_Oinsert(X26873),X26871),c_Orderings_Obot__class_Obot(tc_fun(X26873,tc_HOL_Obool)))),X26870))
        | X26871 = X26870 )
      & ( X26871 != X26870
        | hBOOL(hAPP(c_Finite__Set_Ofold1Set(X26873,X26872,hAPP(hAPP(c_Set_Oinsert(X26873),X26871),c_Orderings_Obot__class_Obot(tc_fun(X26873,tc_HOL_Obool)))),X26870)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1Set__sing])]) ).

fof(i_0_7622,plain,
    ! [X30586,X30587,X30588] :
      ( ~ class_Orderings_Olinorder(X30588)
      | hBOOL(hAPP(hAPP(c_member(X30588),X30587),hAPP(c_List_Oset(X30588),X30586)))
      | c_List_Olinorder__class_Oinsort__insert__key(X30588,X30588,c_COMBI(X30588),X30587,X30586) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30588,X30588,c_COMBI(X30588)),X30587),X30586) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5615])]) ).

fof(i_0_7623,plain,
    ! [X23107,X23108,X23109,X23110,X23111] :
      ( ( ~ c_Relation_Oirrefl(X23108,X23107)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X23108,X23108)),hAPP(hAPP(c_Product__Type_OPair(X23108,X23108),X23109),X23109)),X23107)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X23111,X23111)),hAPP(hAPP(c_Product__Type_OPair(X23111,X23111),esk106_2(X23110,X23111)),esk106_2(X23110,X23111))),X23110))
        | c_Relation_Oirrefl(X23111,X23110) ) ),
    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_7624,plain,
    ! [X24160,X24161,X24162,X24163,X24164,X24165] :
      ( ~ c_Finite__Set_Ofolding(X24165,X24164,X24163,X24162)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24165),X24161))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24165),X24160))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24165,tc_HOL_Obool)),X24161),X24160) != c_Orderings_Obot__class_Obot(tc_fun(X24165,tc_HOL_Obool))
      | hAPP(X24162,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24165,tc_HOL_Obool)),X24161),X24160)) = hAPP(c_Fun_Ocomp(X24164,X24164,X24164,hAPP(X24162,X24161)),hAPP(X24162,X24160)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Ounion])]) ).

fof(i_0_7625,plain,
    ! [X19544,X19545,X19546,X19548,X19549,X19550,X19551] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19544),esk56_3(X19544,X19545,X19546))),X19545))
        | X19544 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(X19546,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19545),X19544))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19545),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19544),hAPP(c_Nat_OSuc,esk56_3(X19544,X19545,X19546)))))
        | X19544 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(X19546,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19545),X19544))) )
      & ( hBOOL(hAPP(X19546,esk56_3(X19544,X19545,X19546)))
        | X19544 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(X19546,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19545),X19544))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19544),esk56_3(X19544,X19545,X19546))),X19545))
        | hBOOL(hAPP(X19546,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(X19546,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19545),X19544))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19545),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19544),hAPP(c_Nat_OSuc,esk56_3(X19544,X19545,X19546)))))
        | hBOOL(hAPP(X19546,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(X19546,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19545),X19544))) )
      & ( hBOOL(hAPP(X19546,esk56_3(X19544,X19545,X19546)))
        | hBOOL(hAPP(X19546,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(X19546,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19545),X19544))) )
      & ( X19548 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(X19550,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | hBOOL(hAPP(X19550,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19549),X19548))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19548),X19551)),X19549))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19549),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19548),hAPP(c_Nat_OSuc,X19551))))
        | ~ hBOOL(hAPP(X19550,X19551))
        | hBOOL(hAPP(X19550,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19549),X19548))) ) ),
    inference(distribute,[status(thm)],[inference(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_7626,plain,
    ! [X24601,X24602,X24603] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24603),X24602))
      | hAPP(c_Finite__Set_Ocard(X24603),hAPP(hAPP(c_Set_Oinsert(X24603),X24601),X24602)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X24603),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24603,tc_HOL_Obool)),X24602),hAPP(hAPP(c_Set_Oinsert(X24603),X24601),c_Orderings_Obot__class_Obot(tc_fun(X24603,tc_HOL_Obool)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card_Oinsert__remove])]) ).

fof(i_0_7627,plain,
    ! [X18067,X18068,X18069,X18070,X18071,X18072,X18073,X18074,X18075] :
      ( hAPP(c_Fun_Ocomp(X18074,X18073,X18072,X18071),X18070) != hAPP(c_Fun_Ocomp(X18069,X18073,X18072,X18068),X18067)
      | hAPP(X18071,hAPP(X18070,X18075)) = hAPP(X18068,hAPP(X18067,X18075)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_o__eq__elim])])]) ).

fof(i_0_7628,plain,
    ! [X18058,X18059,X18060,X18061,X18062,X18063,X18064,X18065,X18066] :
      ( hAPP(c_Fun_Ocomp(X18066,X18065,X18064,X18063),X18062) != hAPP(c_Fun_Ocomp(X18061,X18065,X18064,X18060),X18059)
      | hAPP(X18063,hAPP(X18062,X18058)) = hAPP(X18060,hAPP(X18059,X18058)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_o__eq__dest])]) ).

fof(i_0_7629,plain,
    ! [X30539,X30540,X30541,X30542] :
      ( ~ class_Orderings_Olinorder(X30542)
      | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30542,X30542,c_COMBI(X30542)),X30541),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30542,X30542,c_COMBI(X30542)),X30540),X30539)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30542,X30542,c_COMBI(X30542)),X30540),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30542,X30542,c_COMBI(X30542)),X30541),X30539)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insort__left__comm])]) ).

fof(i_0_7630,plain,
    ! [X27916,X27917,X27918,X27919,X27920,X27921,X27922] :
      ( hAPP(c_Fun_Ocomp(X27922,X27921,X27920,X27919),X27918) != hAPP(c_Fun_Ocomp(X27921,X27921,X27920,c_Fun_Oid(X27921)),X27917)
      | hAPP(X27919,hAPP(X27918,X27916)) = hAPP(X27917,X27916) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_o__eq__id__dest])]) ).

fof(i_0_7631,plain,
    ! [X31867,X31868,X31869,X31870] :
      ( ( ~ hBOOL(hAPP(c_List_Odistinct(X31869),c_List_Olinorder__class_Osort__key(X31869,X31870,X31868,X31867)))
        | hBOOL(hAPP(c_List_Odistinct(X31869),X31867))
        | ~ class_Orderings_Olinorder(X31870) )
      & ( ~ hBOOL(hAPP(c_List_Odistinct(X31869),X31867))
        | hBOOL(hAPP(c_List_Odistinct(X31869),c_List_Olinorder__class_Osort__key(X31869,X31870,X31868,X31867)))
        | ~ class_Orderings_Olinorder(X31870) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__sort])])]) ).

fof(i_0_7632,plain,
    ! [X23473,X23474,X23475,X23476] :
      ( ~ c_Equiv__Relations_Oequiv(X23476,X23475,X23474)
      | ~ hBOOL(hAPP(hAPP(c_member(X23476),X23473),X23475))
      | hBOOL(hAPP(hAPP(c_member(X23476),X23473),hAPP(c_Relation_OImage(X23476,X23476,X23474),hAPP(hAPP(c_Set_Oinsert(X23476),X23473),c_Orderings_Obot__class_Obot(tc_fun(X23476,tc_HOL_Obool)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__class__self])]) ).

fof(i_0_7633,plain,
    ! [X26792,X26793,X26794,X26795,X26796] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X26795),hAPP(X26794,X26793)),hAPP(c_Set_Oimage(X26796,X26795,X26794),X26792)))
        | hBOOL(hAPP(hAPP(c_member(X26796),X26793),X26792))
        | ~ c_Fun_Oinj__on(X26796,X26795,X26794,c_Orderings_Otop__class_Otop(tc_fun(X26796,tc_HOL_Obool))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X26796),X26793),X26792))
        | hBOOL(hAPP(hAPP(c_member(X26795),hAPP(X26794,X26793)),hAPP(c_Set_Oimage(X26796,X26795,X26794),X26792)))
        | ~ c_Fun_Oinj__on(X26796,X26795,X26794,c_Orderings_Otop__class_Otop(tc_fun(X26796,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_7634,plain,
    ! [X30147,X30148,X30149,X30150,X30151] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X30151)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X30150,tc_HOL_Obool)),X30149),X30148))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X30151),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30150,X30151),X30148),X30147)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30150,X30151),X30149),X30147))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF__subset])]) ).

fof(i_0_7635,plain,
    ! [X25165,X25166,X25167,X25168,X25169] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X25169)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25168,tc_HOL_Obool)),X25167),X25166))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25169),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25168,X25169),X25167),X25165)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25168,X25169),X25166),X25165))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUP__subset])]) ).

fof(i_0_7636,plain,
    ! [X28198,X28199,X28200] :
      ( ~ c_Wellfounded_Owf(X28200,X28199)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28200,X28200)),hAPP(hAPP(c_Product__Type_OPair(X28200,X28200),X28198),X28198)),X28199)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5617])]) ).

fof(i_0_7637,plain,
    ! [X28187,X28188,X28189] :
      ( ~ c_Wellfounded_Owf(X28189,X28188)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28189,X28189)),hAPP(hAPP(c_Product__Type_OPair(X28189,X28189),X28187),X28187)),X28188)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5618])]) ).

fof(i_0_7638,plain,
    ! [X25198,X25199,X25200,X25201,X25202] :
      ( ( X25202 != c_Orderings_Obot__class_Obot(tc_fun(X25201,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25201,tc_fun(X25200,tc_HOL_Obool)),X25202),hAPP(hAPP(c_COMBB(tc_fun(X25200,tc_HOL_Obool),tc_fun(X25200,tc_HOL_Obool),X25201),hAPP(c_Set_Oinsert(X25200),X25199)),X25198)) = c_Orderings_Obot__class_Obot(tc_fun(X25200,tc_HOL_Obool)) )
      & ( X25202 = c_Orderings_Obot__class_Obot(tc_fun(X25201,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25201,tc_fun(X25200,tc_HOL_Obool)),X25202),hAPP(hAPP(c_COMBB(tc_fun(X25200,tc_HOL_Obool),tc_fun(X25200,tc_HOL_Obool),X25201),hAPP(c_Set_Oinsert(X25200),X25199)),X25198)) = hAPP(hAPP(c_Set_Oinsert(X25200),X25199),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25201,tc_fun(X25200,tc_HOL_Obool)),X25202),X25198)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__simps_I1_J])]) ).

fof(i_0_7639,plain,
    ! [X25191,X25192,X25193,X25194,X25195] :
      ( ( X25195 != c_Orderings_Obot__class_Obot(tc_fun(X25194,tc_HOL_Obool))
        | hAPP(hAPP(c_Set_Oinsert(X25193),X25192),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25194,tc_fun(X25193,tc_HOL_Obool)),X25195),X25191)) = hAPP(hAPP(c_Set_Oinsert(X25193),X25192),c_Orderings_Obot__class_Obot(tc_fun(X25193,tc_HOL_Obool))) )
      & ( X25195 = c_Orderings_Obot__class_Obot(tc_fun(X25194,tc_HOL_Obool))
        | hAPP(hAPP(c_Set_Oinsert(X25193),X25192),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25194,tc_fun(X25193,tc_HOL_Obool)),X25195),X25191)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25194,tc_fun(X25193,tc_HOL_Obool)),X25195),hAPP(hAPP(c_COMBB(tc_fun(X25193,tc_HOL_Obool),tc_fun(X25193,tc_HOL_Obool),X25194),hAPP(c_Set_Oinsert(X25193),X25192)),X25191)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I1_J])]) ).

cnf(i_0_7640,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_7641,plain,
    ! [X26199,X26200,X26201,X26202,X26203] :
      ( ~ class_Rings_Osemiring__0(X26203)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26203),X26202),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26201,X26203),X26200),X26199)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26201,X26203),hAPP(hAPP(c_COMBB(X26203,X26203,X26201),hAPP(c_Groups_Otimes__class_Otimes(X26203),X26202)),X26200)),X26199) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__right__distrib])]) ).

fof(i_0_7642,plain,
    ! [X22350,X22351,X22352,X22353,X22354] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X22354,X22353)),hAPP(X22354,X22352)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X22351,X22351)),hAPP(hAPP(c_Product__Type_OPair(X22351,X22351),X22353),X22352)),c_Wellfounded_Omlex__prod(X22351,X22354,X22350))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mlex__less])]) ).

fof(i_0_7643,plain,
    ! [X26649,X26650,X26651,X26652,X26653] : hAPP(c_Set_Oimage(X26653,X26652,hAPP(hAPP(c_COMBB(X26651,X26652,X26653),X26650),X26649)),c_Orderings_Otop__class_Otop(tc_fun(X26653,tc_HOL_Obool))) = hAPP(c_Set_Oimage(X26651,X26652,X26650),hAPP(c_Set_Oimage(X26653,X26651,X26649),c_Orderings_Otop__class_Otop(tc_fun(X26653,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_range__composition]) ).

fof(i_0_7644,plain,
    ! [X31852,X31853] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk400_2(X31852,X31853)),esk401_2(X31852,X31853)))
        | c_List_Olinorder__class_Osorted(X31853,X31852)
        | ~ class_Orderings_Olinorder(X31853) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk401_2(X31852,X31853)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31853)),X31852)))
        | c_List_Olinorder__class_Osorted(X31853,X31852)
        | ~ class_Orderings_Olinorder(X31853) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31853),hAPP(hAPP(c_List_Onth(X31853),X31852),esk400_2(X31852,X31853))),hAPP(hAPP(c_List_Onth(X31853),X31852),esk401_2(X31852,X31853))))
        | c_List_Olinorder__class_Osorted(X31853,X31852)
        | ~ class_Orderings_Olinorder(X31853) ) ),
    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_7645,plain,
    ! [X31583,X31584,X31585,X31586] :
      ( ( ~ c_List_Olinorder__class_Osorted(X31584,X31583)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31585),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31584)),X31583)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31586),X31585))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31584),hAPP(hAPP(c_List_Onth(X31584),X31583),X31586)),hAPP(hAPP(c_List_Onth(X31584),X31583),X31585)))
        | ~ class_Orderings_Olinorder(X31584) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk395_2(X31583,X31584)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31584)),X31583)))
        | c_List_Olinorder__class_Osorted(X31584,X31583)
        | ~ class_Orderings_Olinorder(X31584) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk396_2(X31583,X31584)),esk395_2(X31583,X31584)))
        | c_List_Olinorder__class_Osorted(X31584,X31583)
        | ~ class_Orderings_Olinorder(X31584) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31584),hAPP(hAPP(c_List_Onth(X31584),X31583),esk396_2(X31583,X31584))),hAPP(hAPP(c_List_Onth(X31584),X31583),esk395_2(X31583,X31584))))
        | c_List_Olinorder__class_Osorted(X31584,X31583)
        | ~ class_Orderings_Olinorder(X31584) ) ),
    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_7646,plain,
    ! [X29648,X29649,X29650,X29651,X29652,X29653] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X29653),X29652),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29651,tc_fun(X29653,tc_HOL_Obool)),X29650),X29649)))
      | ~ hBOOL(hAPP(hAPP(c_member(X29651),X29648),X29650))
      | hBOOL(hAPP(hAPP(c_member(X29653),X29652),hAPP(X29649,X29648))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__D])]) ).

fof(i_0_7647,plain,
    ! [X29642,X29643,X29644,X29645,X29646,X29647] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X29647),X29646),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29645,tc_fun(X29647,tc_HOL_Obool)),X29644),X29643)))
      | hBOOL(hAPP(hAPP(c_member(X29647),X29646),hAPP(X29643,X29642)))
      | ~ hBOOL(hAPP(hAPP(c_member(X29645),X29642),X29644)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5620])]) ).

fof(i_0_7648,plain,
    ! [X29407,X29408,X29409] :
      ( ~ class_Groups_Omonoid__add(X29409)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X29409),X29408),hAPP(c_List_Ofoldl(X29409,X29409,c_Groups_Oplus__class_Oplus(X29409),c_Groups_Ozero__class_Ozero(X29409)),X29407)) = hAPP(c_List_Ofoldl(X29409,X29409,c_Groups_Oplus__class_Oplus(X29409),X29408),X29407) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_foldl__absorb0])]) ).

fof(i_0_7649,plain,
    ! [X29071,X29072,X29073,X29074,X29075,X29076] :
      ( X29076 = X29075
      | hAPP(hAPP(c_List_Olist__update(X29074,hAPP(hAPP(c_List_Olist__update(X29074,X29073),X29076),X29072)),X29075),X29071) = hAPP(hAPP(c_List_Olist__update(X29074,hAPP(hAPP(c_List_Olist__update(X29074,X29073),X29075),X29071)),X29076),X29072) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__update__swap])]) ).

fof(i_0_7650,plain,
    ! [X28012,X28013,X28014] : hAPP(hAPP(c_Relation_Orel__comp(X28014,X28014,X28014),X28013),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28014,X28014),tc_HOL_Obool),X28012),X28013)) = hAPP(hAPP(c_Relation_Orel__comp(X28014,X28014,X28014),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28014,X28014),tc_HOL_Obool),X28012),X28013)),X28013),
    inference(variable_rename,[status(thm)],[fact_rel__pow__commute]) ).

fof(i_0_7651,plain,
    ! [X34324,X34325,X34326,X34327,X34328,X34329,X34330,X34331,X34332,X34333] :
      ( ( X34324 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hBOOL(hAPP(X34326,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ epred2_3(X34326,X34325,X34324) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34324))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34328))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34328),X34324))
        | X34325 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34324),X34327)),X34328)
        | hBOOL(hAPP(X34326,X34327))
        | ~ epred2_3(X34326,X34325,X34324) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34324),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34324),X34330))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X34330),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | X34325 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34324),X34329)),X34330)
        | hBOOL(hAPP(X34326,X34329))
        | ~ epred2_3(X34326,X34325,X34324) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34331),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)),X34331))
        | X34331 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34333,X34332,X34331) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34331),esk573_3(X34331,X34332,X34333)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34331))
        | X34331 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34333,X34332,X34331) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk573_3(X34331,X34332,X34333)),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)),X34331))
        | X34331 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34333,X34332,X34331) )
      & ( X34332 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34331),esk572_3(X34331,X34332,X34333))),esk573_3(X34331,X34332,X34333))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34331))
        | X34331 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34333,X34332,X34331) )
      & ( ~ hBOOL(hAPP(X34333,esk572_3(X34331,X34332,X34333)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34331))
        | X34331 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34333,X34332,X34331) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34331),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)),esk571_3(X34331,X34332,X34333)))
        | X34331 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34333,X34332,X34331) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34331),esk573_3(X34331,X34332,X34333)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk571_3(X34331,X34332,X34333)))
        | X34331 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34333,X34332,X34331) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk573_3(X34331,X34332,X34333)),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)),esk571_3(X34331,X34332,X34333)))
        | X34331 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34333,X34332,X34331) )
      & ( X34332 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34331),esk572_3(X34331,X34332,X34333))),esk573_3(X34331,X34332,X34333))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk571_3(X34331,X34332,X34333)))
        | X34331 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34333,X34332,X34331) )
      & ( ~ hBOOL(hAPP(X34333,esk572_3(X34331,X34332,X34333)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk571_3(X34331,X34332,X34333)))
        | X34331 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34333,X34332,X34331) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34331),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk571_3(X34331,X34332,X34333)),X34331))
        | X34331 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34333,X34332,X34331) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34331),esk573_3(X34331,X34332,X34333)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk571_3(X34331,X34332,X34333)),X34331))
        | X34331 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34333,X34332,X34331) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk573_3(X34331,X34332,X34333)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk571_3(X34331,X34332,X34333)),X34331))
        | X34331 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34333,X34332,X34331) )
      & ( X34332 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34331),esk572_3(X34331,X34332,X34333))),esk573_3(X34331,X34332,X34333))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk571_3(X34331,X34332,X34333)),X34331))
        | X34331 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34333,X34332,X34331) )
      & ( ~ hBOOL(hAPP(X34333,esk572_3(X34331,X34332,X34333)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk571_3(X34331,X34332,X34333)),X34331))
        | X34331 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34333,X34332,X34331) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34331),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | X34332 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34331),esk570_3(X34331,X34332,X34333))),esk571_3(X34331,X34332,X34333))
        | X34331 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34333,X34332,X34331) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34331),esk573_3(X34331,X34332,X34333)))
        | X34332 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34331),esk570_3(X34331,X34332,X34333))),esk571_3(X34331,X34332,X34333))
        | X34331 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34333,X34332,X34331) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk573_3(X34331,X34332,X34333)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | X34332 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34331),esk570_3(X34331,X34332,X34333))),esk571_3(X34331,X34332,X34333))
        | X34331 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34333,X34332,X34331) )
      & ( X34332 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34331),esk572_3(X34331,X34332,X34333))),esk573_3(X34331,X34332,X34333))
        | X34332 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34331),esk570_3(X34331,X34332,X34333))),esk571_3(X34331,X34332,X34333))
        | X34331 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34333,X34332,X34331) )
      & ( ~ hBOOL(hAPP(X34333,esk572_3(X34331,X34332,X34333)))
        | X34332 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34331),esk570_3(X34331,X34332,X34333))),esk571_3(X34331,X34332,X34333))
        | X34331 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34333,X34332,X34331) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34331),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(X34333,esk570_3(X34331,X34332,X34333)))
        | X34331 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34333,X34332,X34331) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34331),esk573_3(X34331,X34332,X34333)))
        | ~ hBOOL(hAPP(X34333,esk570_3(X34331,X34332,X34333)))
        | X34331 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34333,X34332,X34331) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk573_3(X34331,X34332,X34333)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(X34333,esk570_3(X34331,X34332,X34333)))
        | X34331 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34333,X34332,X34331) )
      & ( X34332 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34331),esk572_3(X34331,X34332,X34333))),esk573_3(X34331,X34332,X34333))
        | ~ hBOOL(hAPP(X34333,esk570_3(X34331,X34332,X34333)))
        | X34331 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34333,X34332,X34331) )
      & ( ~ hBOOL(hAPP(X34333,esk572_3(X34331,X34332,X34333)))
        | ~ hBOOL(hAPP(X34333,esk570_3(X34331,X34332,X34333)))
        | X34331 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34333,X34332,X34331) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34331),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)),X34331))
        | ~ hBOOL(hAPP(X34333,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred2_3(X34333,X34332,X34331) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34331),esk573_3(X34331,X34332,X34333)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34331))
        | ~ hBOOL(hAPP(X34333,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred2_3(X34333,X34332,X34331) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk573_3(X34331,X34332,X34333)),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)),X34331))
        | ~ hBOOL(hAPP(X34333,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred2_3(X34333,X34332,X34331) )
      & ( X34332 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34331),esk572_3(X34331,X34332,X34333))),esk573_3(X34331,X34332,X34333))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34331))
        | ~ hBOOL(hAPP(X34333,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred2_3(X34333,X34332,X34331) )
      & ( ~ hBOOL(hAPP(X34333,esk572_3(X34331,X34332,X34333)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34331))
        | ~ hBOOL(hAPP(X34333,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred2_3(X34333,X34332,X34331) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34331),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)),esk571_3(X34331,X34332,X34333)))
        | ~ hBOOL(hAPP(X34333,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred2_3(X34333,X34332,X34331) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34331),esk573_3(X34331,X34332,X34333)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk571_3(X34331,X34332,X34333)))
        | ~ hBOOL(hAPP(X34333,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred2_3(X34333,X34332,X34331) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk573_3(X34331,X34332,X34333)),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)),esk571_3(X34331,X34332,X34333)))
        | ~ hBOOL(hAPP(X34333,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred2_3(X34333,X34332,X34331) )
      & ( X34332 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34331),esk572_3(X34331,X34332,X34333))),esk573_3(X34331,X34332,X34333))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk571_3(X34331,X34332,X34333)))
        | ~ hBOOL(hAPP(X34333,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred2_3(X34333,X34332,X34331) )
      & ( ~ hBOOL(hAPP(X34333,esk572_3(X34331,X34332,X34333)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk571_3(X34331,X34332,X34333)))
        | ~ hBOOL(hAPP(X34333,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred2_3(X34333,X34332,X34331) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34331),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk571_3(X34331,X34332,X34333)),X34331))
        | ~ hBOOL(hAPP(X34333,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred2_3(X34333,X34332,X34331) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34331),esk573_3(X34331,X34332,X34333)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk571_3(X34331,X34332,X34333)),X34331))
        | ~ hBOOL(hAPP(X34333,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred2_3(X34333,X34332,X34331) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk573_3(X34331,X34332,X34333)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk571_3(X34331,X34332,X34333)),X34331))
        | ~ hBOOL(hAPP(X34333,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred2_3(X34333,X34332,X34331) )
      & ( X34332 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34331),esk572_3(X34331,X34332,X34333))),esk573_3(X34331,X34332,X34333))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk571_3(X34331,X34332,X34333)),X34331))
        | ~ hBOOL(hAPP(X34333,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred2_3(X34333,X34332,X34331) )
      & ( ~ hBOOL(hAPP(X34333,esk572_3(X34331,X34332,X34333)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk571_3(X34331,X34332,X34333)),X34331))
        | ~ hBOOL(hAPP(X34333,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred2_3(X34333,X34332,X34331) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34331),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | X34332 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34331),esk570_3(X34331,X34332,X34333))),esk571_3(X34331,X34332,X34333))
        | ~ hBOOL(hAPP(X34333,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred2_3(X34333,X34332,X34331) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34331),esk573_3(X34331,X34332,X34333)))
        | X34332 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34331),esk570_3(X34331,X34332,X34333))),esk571_3(X34331,X34332,X34333))
        | ~ hBOOL(hAPP(X34333,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred2_3(X34333,X34332,X34331) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk573_3(X34331,X34332,X34333)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | X34332 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34331),esk570_3(X34331,X34332,X34333))),esk571_3(X34331,X34332,X34333))
        | ~ hBOOL(hAPP(X34333,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred2_3(X34333,X34332,X34331) )
      & ( X34332 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34331),esk572_3(X34331,X34332,X34333))),esk573_3(X34331,X34332,X34333))
        | X34332 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34331),esk570_3(X34331,X34332,X34333))),esk571_3(X34331,X34332,X34333))
        | ~ hBOOL(hAPP(X34333,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred2_3(X34333,X34332,X34331) )
      & ( ~ hBOOL(hAPP(X34333,esk572_3(X34331,X34332,X34333)))
        | X34332 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34331),esk570_3(X34331,X34332,X34333))),esk571_3(X34331,X34332,X34333))
        | ~ hBOOL(hAPP(X34333,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred2_3(X34333,X34332,X34331) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34331),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(X34333,esk570_3(X34331,X34332,X34333)))
        | ~ hBOOL(hAPP(X34333,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred2_3(X34333,X34332,X34331) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34331),esk573_3(X34331,X34332,X34333)))
        | ~ hBOOL(hAPP(X34333,esk570_3(X34331,X34332,X34333)))
        | ~ hBOOL(hAPP(X34333,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred2_3(X34333,X34332,X34331) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk573_3(X34331,X34332,X34333)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(X34333,esk570_3(X34331,X34332,X34333)))
        | ~ hBOOL(hAPP(X34333,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred2_3(X34333,X34332,X34331) )
      & ( X34332 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34331),esk572_3(X34331,X34332,X34333))),esk573_3(X34331,X34332,X34333))
        | ~ hBOOL(hAPP(X34333,esk570_3(X34331,X34332,X34333)))
        | ~ hBOOL(hAPP(X34333,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred2_3(X34333,X34332,X34331) )
      & ( ~ hBOOL(hAPP(X34333,esk572_3(X34331,X34332,X34333)))
        | ~ hBOOL(hAPP(X34333,esk570_3(X34331,X34332,X34333)))
        | ~ hBOOL(hAPP(X34333,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred2_3(X34333,X34332,X34331) ) ),
    inference(distribute,[status(thm)],[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_5219])])])])])]) ).

fof(i_0_7652,plain,
    ! [X24575,X24576,X24577] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24577),X24576))
      | hAPP(c_Finite__Set_Ocard(X24577),hAPP(hAPP(c_Set_Oinsert(X24577),X24575),X24576)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X24577),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24577,tc_HOL_Obool)),X24576),hAPP(hAPP(c_Set_Oinsert(X24577),X24575),c_Orderings_Obot__class_Obot(tc_fun(X24577,tc_HOL_Obool)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__insert])]) ).

cnf(i_0_7653,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_5621]) ).

cnf(i_0_7654,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_5622]) ).

cnf(i_0_7655,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_5623]) ).

cnf(i_0_7656,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_5624]) ).

fof(i_0_7657,plain,
    ! [X21540,X21541,X21542,X21543] :
      ( ~ class_Fields_Olinordered__field(X21543)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21543),X21542),X21541))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21543),c_Groups_Ozero__class_Ozero(X21543)),X21540))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21543),c_Groups_Ozero__class_Ozero(X21543)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21543),X21541),X21542)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21543),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21543),X21540),X21541)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21543),X21540),X21542))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__left__mono])]) ).

fof(i_0_7658,plain,
    ! [X21432,X21433,X21434,X21435] :
      ( ~ class_Fields_Olinordered__field(X21435)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21435),X21434),X21433))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21435),c_Groups_Ozero__class_Ozero(X21435)),X21432))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21435),c_Groups_Ozero__class_Ozero(X21435)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21435),X21433),X21434)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21435),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21435),X21432),X21433)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21435),X21432),X21434))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__strict__left__mono])]) ).

fof(i_0_7659,plain,
    ! [X23287,X23288,X23289] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X23289,X23289),tc_HOL_Obool)),X23288),X23287))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23289,tc_HOL_Obool)),hAPP(c_Relation_OField(X23289),X23288)),hAPP(c_Relation_OField(X23289),X23287))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mono__Field])]) ).

fof(i_0_7660,plain,
    ! [X23645,X23646,X23647,X23648,X23649,X23650] :
      ( ~ c_Finite__Set_Ofolding(X23650,X23649,X23648,X23647)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23650),X23646))
      | hAPP(c_Fun_Ocomp(X23649,X23649,X23649,hAPP(X23648,X23645)),hAPP(X23647,X23646)) = hAPP(c_Fun_Ocomp(X23649,X23649,X23649,hAPP(X23647,X23646)),hAPP(X23648,X23645)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__comp_H])]) ).

fof(i_0_7661,plain,
    ! [X34310,X34311,X34312,X34313,X34314,X34315,X34316,X34317,X34318,X34319] :
      ( ( X34310 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hBOOL(hAPP(X34312,X34311))
        | ~ epred1_3(X34312,X34311,X34310) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34310))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34314))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34314),X34310))
        | X34311 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34310),X34313)),X34314)
        | hBOOL(hAPP(X34312,X34314))
        | ~ epred1_3(X34312,X34311,X34310) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34310),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34310),X34316))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X34316),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | X34311 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34310),X34315)),X34316)
        | hBOOL(hAPP(X34312,X34316))
        | ~ epred1_3(X34312,X34311,X34310) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34317),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)),X34317))
        | X34317 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34319,X34318,X34317) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34317),esk569_3(X34317,X34318,X34319)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34317))
        | X34317 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34319,X34318,X34317) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk569_3(X34317,X34318,X34319)),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)),X34317))
        | X34317 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34319,X34318,X34317) )
      & ( X34318 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34317),esk568_3(X34317,X34318,X34319))),esk569_3(X34317,X34318,X34319))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34317))
        | X34317 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34319,X34318,X34317) )
      & ( ~ hBOOL(hAPP(X34319,esk569_3(X34317,X34318,X34319)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34317))
        | X34317 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34319,X34318,X34317) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34317),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)),esk567_3(X34317,X34318,X34319)))
        | X34317 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34319,X34318,X34317) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34317),esk569_3(X34317,X34318,X34319)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk567_3(X34317,X34318,X34319)))
        | X34317 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34319,X34318,X34317) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk569_3(X34317,X34318,X34319)),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)),esk567_3(X34317,X34318,X34319)))
        | X34317 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34319,X34318,X34317) )
      & ( X34318 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34317),esk568_3(X34317,X34318,X34319))),esk569_3(X34317,X34318,X34319))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk567_3(X34317,X34318,X34319)))
        | X34317 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34319,X34318,X34317) )
      & ( ~ hBOOL(hAPP(X34319,esk569_3(X34317,X34318,X34319)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk567_3(X34317,X34318,X34319)))
        | X34317 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34319,X34318,X34317) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34317),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk567_3(X34317,X34318,X34319)),X34317))
        | X34317 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34319,X34318,X34317) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34317),esk569_3(X34317,X34318,X34319)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk567_3(X34317,X34318,X34319)),X34317))
        | X34317 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34319,X34318,X34317) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk569_3(X34317,X34318,X34319)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk567_3(X34317,X34318,X34319)),X34317))
        | X34317 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34319,X34318,X34317) )
      & ( X34318 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34317),esk568_3(X34317,X34318,X34319))),esk569_3(X34317,X34318,X34319))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk567_3(X34317,X34318,X34319)),X34317))
        | X34317 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34319,X34318,X34317) )
      & ( ~ hBOOL(hAPP(X34319,esk569_3(X34317,X34318,X34319)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk567_3(X34317,X34318,X34319)),X34317))
        | X34317 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34319,X34318,X34317) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34317),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | X34318 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34317),esk566_3(X34317,X34318,X34319))),esk567_3(X34317,X34318,X34319))
        | X34317 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34319,X34318,X34317) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34317),esk569_3(X34317,X34318,X34319)))
        | X34318 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34317),esk566_3(X34317,X34318,X34319))),esk567_3(X34317,X34318,X34319))
        | X34317 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34319,X34318,X34317) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk569_3(X34317,X34318,X34319)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | X34318 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34317),esk566_3(X34317,X34318,X34319))),esk567_3(X34317,X34318,X34319))
        | X34317 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34319,X34318,X34317) )
      & ( X34318 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34317),esk568_3(X34317,X34318,X34319))),esk569_3(X34317,X34318,X34319))
        | X34318 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34317),esk566_3(X34317,X34318,X34319))),esk567_3(X34317,X34318,X34319))
        | X34317 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34319,X34318,X34317) )
      & ( ~ hBOOL(hAPP(X34319,esk569_3(X34317,X34318,X34319)))
        | X34318 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34317),esk566_3(X34317,X34318,X34319))),esk567_3(X34317,X34318,X34319))
        | X34317 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34319,X34318,X34317) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34317),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(X34319,esk567_3(X34317,X34318,X34319)))
        | X34317 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34319,X34318,X34317) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34317),esk569_3(X34317,X34318,X34319)))
        | ~ hBOOL(hAPP(X34319,esk567_3(X34317,X34318,X34319)))
        | X34317 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34319,X34318,X34317) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk569_3(X34317,X34318,X34319)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(X34319,esk567_3(X34317,X34318,X34319)))
        | X34317 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34319,X34318,X34317) )
      & ( X34318 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34317),esk568_3(X34317,X34318,X34319))),esk569_3(X34317,X34318,X34319))
        | ~ hBOOL(hAPP(X34319,esk567_3(X34317,X34318,X34319)))
        | X34317 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34319,X34318,X34317) )
      & ( ~ hBOOL(hAPP(X34319,esk569_3(X34317,X34318,X34319)))
        | ~ hBOOL(hAPP(X34319,esk567_3(X34317,X34318,X34319)))
        | X34317 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34319,X34318,X34317) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34317),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)),X34317))
        | ~ hBOOL(hAPP(X34319,X34318))
        | epred1_3(X34319,X34318,X34317) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34317),esk569_3(X34317,X34318,X34319)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34317))
        | ~ hBOOL(hAPP(X34319,X34318))
        | epred1_3(X34319,X34318,X34317) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk569_3(X34317,X34318,X34319)),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)),X34317))
        | ~ hBOOL(hAPP(X34319,X34318))
        | epred1_3(X34319,X34318,X34317) )
      & ( X34318 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34317),esk568_3(X34317,X34318,X34319))),esk569_3(X34317,X34318,X34319))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34317))
        | ~ hBOOL(hAPP(X34319,X34318))
        | epred1_3(X34319,X34318,X34317) )
      & ( ~ hBOOL(hAPP(X34319,esk569_3(X34317,X34318,X34319)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34317))
        | ~ hBOOL(hAPP(X34319,X34318))
        | epred1_3(X34319,X34318,X34317) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34317),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)),esk567_3(X34317,X34318,X34319)))
        | ~ hBOOL(hAPP(X34319,X34318))
        | epred1_3(X34319,X34318,X34317) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34317),esk569_3(X34317,X34318,X34319)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk567_3(X34317,X34318,X34319)))
        | ~ hBOOL(hAPP(X34319,X34318))
        | epred1_3(X34319,X34318,X34317) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk569_3(X34317,X34318,X34319)),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)),esk567_3(X34317,X34318,X34319)))
        | ~ hBOOL(hAPP(X34319,X34318))
        | epred1_3(X34319,X34318,X34317) )
      & ( X34318 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34317),esk568_3(X34317,X34318,X34319))),esk569_3(X34317,X34318,X34319))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk567_3(X34317,X34318,X34319)))
        | ~ hBOOL(hAPP(X34319,X34318))
        | epred1_3(X34319,X34318,X34317) )
      & ( ~ hBOOL(hAPP(X34319,esk569_3(X34317,X34318,X34319)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk567_3(X34317,X34318,X34319)))
        | ~ hBOOL(hAPP(X34319,X34318))
        | epred1_3(X34319,X34318,X34317) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34317),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk567_3(X34317,X34318,X34319)),X34317))
        | ~ hBOOL(hAPP(X34319,X34318))
        | epred1_3(X34319,X34318,X34317) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34317),esk569_3(X34317,X34318,X34319)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk567_3(X34317,X34318,X34319)),X34317))
        | ~ hBOOL(hAPP(X34319,X34318))
        | epred1_3(X34319,X34318,X34317) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk569_3(X34317,X34318,X34319)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk567_3(X34317,X34318,X34319)),X34317))
        | ~ hBOOL(hAPP(X34319,X34318))
        | epred1_3(X34319,X34318,X34317) )
      & ( X34318 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34317),esk568_3(X34317,X34318,X34319))),esk569_3(X34317,X34318,X34319))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk567_3(X34317,X34318,X34319)),X34317))
        | ~ hBOOL(hAPP(X34319,X34318))
        | epred1_3(X34319,X34318,X34317) )
      & ( ~ hBOOL(hAPP(X34319,esk569_3(X34317,X34318,X34319)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk567_3(X34317,X34318,X34319)),X34317))
        | ~ hBOOL(hAPP(X34319,X34318))
        | epred1_3(X34319,X34318,X34317) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34317),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | X34318 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34317),esk566_3(X34317,X34318,X34319))),esk567_3(X34317,X34318,X34319))
        | ~ hBOOL(hAPP(X34319,X34318))
        | epred1_3(X34319,X34318,X34317) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34317),esk569_3(X34317,X34318,X34319)))
        | X34318 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34317),esk566_3(X34317,X34318,X34319))),esk567_3(X34317,X34318,X34319))
        | ~ hBOOL(hAPP(X34319,X34318))
        | epred1_3(X34319,X34318,X34317) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk569_3(X34317,X34318,X34319)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | X34318 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34317),esk566_3(X34317,X34318,X34319))),esk567_3(X34317,X34318,X34319))
        | ~ hBOOL(hAPP(X34319,X34318))
        | epred1_3(X34319,X34318,X34317) )
      & ( X34318 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34317),esk568_3(X34317,X34318,X34319))),esk569_3(X34317,X34318,X34319))
        | X34318 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34317),esk566_3(X34317,X34318,X34319))),esk567_3(X34317,X34318,X34319))
        | ~ hBOOL(hAPP(X34319,X34318))
        | epred1_3(X34319,X34318,X34317) )
      & ( ~ hBOOL(hAPP(X34319,esk569_3(X34317,X34318,X34319)))
        | X34318 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34317),esk566_3(X34317,X34318,X34319))),esk567_3(X34317,X34318,X34319))
        | ~ hBOOL(hAPP(X34319,X34318))
        | epred1_3(X34319,X34318,X34317) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34317),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(X34319,esk567_3(X34317,X34318,X34319)))
        | ~ hBOOL(hAPP(X34319,X34318))
        | epred1_3(X34319,X34318,X34317) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34317),esk569_3(X34317,X34318,X34319)))
        | ~ hBOOL(hAPP(X34319,esk567_3(X34317,X34318,X34319)))
        | ~ hBOOL(hAPP(X34319,X34318))
        | epred1_3(X34319,X34318,X34317) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk569_3(X34317,X34318,X34319)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(X34319,esk567_3(X34317,X34318,X34319)))
        | ~ hBOOL(hAPP(X34319,X34318))
        | epred1_3(X34319,X34318,X34317) )
      & ( X34318 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34317),esk568_3(X34317,X34318,X34319))),esk569_3(X34317,X34318,X34319))
        | ~ hBOOL(hAPP(X34319,esk567_3(X34317,X34318,X34319)))
        | ~ hBOOL(hAPP(X34319,X34318))
        | epred1_3(X34319,X34318,X34317) )
      & ( ~ hBOOL(hAPP(X34319,esk569_3(X34317,X34318,X34319)))
        | ~ hBOOL(hAPP(X34319,esk567_3(X34317,X34318,X34319)))
        | ~ hBOOL(hAPP(X34319,X34318))
        | epred1_3(X34319,X34318,X34317) ) ),
    inference(distribute,[status(thm)],[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_5218])])])])])]) ).

fof(i_0_7662,plain,
    ! [X29899,X29900,X29901,X29902,X29903] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29903,tc_fun(X29902,tc_HOL_Obool)),X29901),hAPP(hAPP(c_COMBB(tc_fun(X29902,tc_HOL_Obool),tc_fun(X29902,tc_HOL_Obool),X29903),hAPP(c_Set_Oinsert(X29902),X29900)),X29899)) = hAPP(hAPP(c_Set_Oinsert(X29902),X29900),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29903,tc_fun(X29902,tc_HOL_Obool)),X29901),X29899)),
    inference(variable_rename,[status(thm)],[fact_INT__simps_I5_J]) ).

fof(i_0_7663,plain,
    ! [X29894,X29895,X29896,X29897,X29898] : hAPP(hAPP(c_Set_Oinsert(X29898),X29897),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29896,tc_fun(X29898,tc_HOL_Obool)),X29895),X29894)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29896,tc_fun(X29898,tc_HOL_Obool)),X29895),hAPP(hAPP(c_COMBB(tc_fun(X29898,tc_HOL_Obool),tc_fun(X29898,tc_HOL_Obool),X29896),hAPP(c_Set_Oinsert(X29898),X29897)),X29894)),
    inference(variable_rename,[status(thm)],[fact_INT__extend__simps_I5_J]) ).

fof(i_0_7664,plain,
    ! [X19268,X19269,X19270,X19271] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19271),X19270)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19269),X19270)),X19268)) = 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),X19271),X19269)),X19270)),X19268),
    inference(variable_rename,[status(thm)],[fact_left__add__mult__distrib]) ).

fof(i_0_7665,plain,
    ! [X31752,X31753,X31754,X31755,X31756] : hAPP(hAPP(c_List_Ozip(X31756,X31755),X31754),c_List_OtakeWhile(X31755,X31753,X31752)) = c_List_OtakeWhile(tc_prod(X31756,X31755),hAPP(c_Fun_Ocomp(X31755,tc_HOL_Obool,tc_prod(X31756,X31755),X31753),c_Product__Type_Osnd(X31756,X31755)),hAPP(hAPP(c_List_Ozip(X31756,X31755),X31754),X31752)),
    inference(variable_rename,[status(thm)],[fact_zip__takeWhile__snd]) ).

cnf(i_0_7666,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_7667,plain,
    ! [X33240,X33241,X33242,X33243,X33244] :
      ( ( X33244 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
        | hAPP(c_New__DSequence_Oneg__decr__bind(X33243,X33242,X33241,X33240),X33244) = c_Lazy__Sequence_Ohit__bound(X33242) )
      & ( X33244 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
        | hAPP(c_New__DSequence_Oneg__decr__bind(X33243,X33242,X33241,X33240),X33244) = c_Lazy__Sequence_Ohb__bind(X33243,X33242,hAPP(X33241,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X33244),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(X33243,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X33242))),X33240),X33244)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_New__DSequence_Oneg__decr__bind__def])]) ).

fof(i_0_7668,plain,
    ! [X26774,X26775,X26776,X26777] :
      ( ~ c_Fun_Oinj__on(X26777,X26776,X26775,c_Orderings_Otop__class_Otop(tc_fun(X26777,tc_HOL_Obool)))
      | c_Fun_Oinj__on(X26777,tc_fun(X26774,X26776),hAPP(hAPP(c_COMBB(X26776,tc_fun(X26774,X26776),X26777),c_COMBK(X26776,X26774)),X26775),c_Orderings_Otop__class_Otop(tc_fun(X26777,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__fun])]) ).

fof(i_0_7669,plain,
    ! [X31054,X31055,X31056] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31056,tc_HOL_Obool)),X31055),X31054) = c_Complete__Lattice_OInf__class_OInf(tc_fun(X31056,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X31056,tc_HOL_Obool)),X31055),hAPP(hAPP(c_Set_Oinsert(tc_fun(X31056,tc_HOL_Obool)),X31054),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X31056,tc_HOL_Obool),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[fact_Int__eq__Inter]) ).

fof(i_0_7670,plain,
    ! [X30922,X30923,X30924] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X30924,tc_HOL_Obool)),X30923),X30922) = c_Complete__Lattice_OSup__class_OSup(tc_fun(X30924,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X30924,tc_HOL_Obool)),X30923),hAPP(hAPP(c_Set_Oinsert(tc_fun(X30924,tc_HOL_Obool)),X30922),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X30924,tc_HOL_Obool),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[fact_Un__eq__Union]) ).

fof(i_0_7671,plain,
    ! [X21536,X21537,X21538,X21539] :
      ( ~ class_Fields_Olinordered__field__inverse__zero(X21539)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21539),X21538),X21537))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21539),X21536),c_Groups_Ozero__class_Ozero(X21539)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21539),c_Groups_Ozero__class_Ozero(X21539)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21539),X21538),X21537)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21539),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21539),X21536),X21538)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21539),X21536),X21537))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__left__mono__neg])]) ).

fof(i_0_7672,plain,
    ! [X21428,X21429,X21430,X21431] :
      ( ~ class_Fields_Olinordered__field(X21431)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21431),X21430),X21429))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21431),X21428),c_Groups_Ozero__class_Ozero(X21431)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21431),c_Groups_Ozero__class_Ozero(X21431)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21431),X21430),X21429)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21431),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21431),X21428),X21430)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21431),X21428),X21429))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__strict__left__mono__neg])]) ).

fof(i_0_7673,plain,
    ! [X33245,X33246,X33247,X33248,X33249] :
      ( ( X33249 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
        | hAPP(c_New__DSequence_Opos__decr__bind(X33248,X33247,X33246,X33245),X33249) = c_Lazy__Sequence_Oempty(X33247) )
      & ( X33249 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
        | hAPP(c_New__DSequence_Opos__decr__bind(X33248,X33247,X33246,X33245),X33249) = hAPP(c_Lazy__Sequence_Obind(X33248,X33247,hAPP(X33246,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X33249),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBC(X33248,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X33247)),X33245),X33249)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_New__DSequence_Opos__decr__bind__def])]) ).

fof(i_0_7674,plain,
    ! [X29174,X29175,X29176,X29177,X29178] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29178),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29177)),X29176)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29178),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29175)),X29174)))
      | hAPP(hAPP(c_List_Onth(tc_prod(X29177,X29175)),hAPP(hAPP(c_List_Ozip(X29177,X29175),X29176),X29174)),X29178) = hAPP(hAPP(c_Product__Type_OPair(X29177,X29175),hAPP(hAPP(c_List_Onth(X29177),X29176),X29178)),hAPP(hAPP(c_List_Onth(X29175),X29174),X29178)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__zip])]) ).

fof(i_0_7675,plain,
    ! [X19559,X19560,X19561] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19561,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19560),X19559)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19560),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19561),X19560),X19559))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19561,X19560)),
    inference(variable_rename,[status(thm)],[fact_mod__mult2__eq]) ).

cnf(i_0_7676,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_5572]) ).

fof(i_0_7677,plain,
    ! [X25652,X25653,X25654] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25654),X25653))
        | 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)),X25654)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X25652),X25653)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25652),X25654)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25653),X25654)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25652),X25653))
        | 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)),X25654)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X25652),X25653)) = 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),X25654),X25653)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25652),X25653))
        | 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)),X25654)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X25652),X25653)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25654),X25653)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5626])])]) ).

cnf(i_0_7678,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_7679,plain,
    ! [X29129,X29130,X29131,X29132,X29133] : hAPP(hAPP(c_List_Olist__update(X29133,hAPP(hAPP(c_List_Oappend(X29133),X29132),hAPP(hAPP(c_List_Olist_OCons(X29133),X29131),X29130))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29133)),X29132)),X29129) = hAPP(hAPP(c_List_Oappend(X29133),X29132),hAPP(hAPP(c_List_Olist_OCons(X29133),X29129),X29130)),
    inference(variable_rename,[status(thm)],[fact_list__update__length]) ).

cnf(i_0_7680,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_7681,plain,
    ! [X32193,X32194] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X32194),tc_List_Olist(X32194)),tc_HOL_Obool)),c_List_Olistrel1(X32194,c_Transitive__Closure_Ortrancl(X32194,X32193))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X32194),c_List_Olistrel1(X32194,X32193)))),
    inference(variable_rename,[status(thm)],[fact_listrel1__rtrancl__subset__rtrancl__listrel1]) ).

fof(i_0_7682,plain,
    ! [X32166,X32167,X32168] : c_Transitive__Closure_Ortrancl(X32168,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X32168,X32168),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X32168,X32167)),c_Transitive__Closure_Ortrancl(X32168,X32166))) = c_Transitive__Closure_Ortrancl(X32168,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X32168,X32168),tc_HOL_Obool)),X32167),X32166)),
    inference(variable_rename,[status(thm)],[fact_rtrancl__Un__rtrancl]) ).

cnf(i_0_7683,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_7684,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_7685,plain,
    ! [X30284,X30285,X30286] : hAPP(hAPP(c_List_Ozip(X30286,X30285),hAPP(hAPP(c_List_Omap(tc_prod(X30286,X30285),X30286),c_Product__Type_Ofst(X30286,X30285)),X30284)),hAPP(hAPP(c_List_Omap(tc_prod(X30286,X30285),X30285),c_Product__Type_Osnd(X30286,X30285)),X30284)) = X30284,
    inference(variable_rename,[status(thm)],[fact_zip__map__fst__snd]) ).

fof(i_0_7686,plain,
    ! [X25871,X25872,X25873,X25874,X25875,X25876,X25877,X25878] :
      ( ~ class_Groups_Ocomm__monoid__mult(X25878)
      | ~ c_Fun_Oinj__on(X25877,X25876,X25875,X25874)
      | X25873 != hAPP(c_Set_Oimage(X25877,X25876,X25875),X25874)
      | X25872 != hAPP(c_Fun_Ocomp(X25876,X25878,X25877,X25871),X25875)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25876,X25878),X25871),X25873) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25877,X25878),X25872),X25874) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__reindex__cong])]) ).

fof(i_0_7687,plain,
    ! [X19000,X19001,X19002] :
      ( ~ class_Rings_Olinordered__ring(X19002)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19002),c_Groups_Ozero__class_Ozero(X19002)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19002),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19002),X19001),X19001)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19002),X19000),X19000)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__squares__ge__zero])]) ).

fof(i_0_7688,plain,
    ! [X32272,X32273] :
      ( ( ~ 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),X32273),X32272)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X32273),X32272)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X32273),X32272))
        | 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),X32273),X32272)),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_7689,plain,
    ! [X23603,X23604,X23605,X23606,X23607,X23608] :
      ( ~ c_Finite__Set_Ofolding(X23608,X23607,X23606,X23605)
      | hAPP(c_Fun_Ocomp(X23607,X23607,X23607,hAPP(X23606,X23604)),hAPP(X23606,X23603)) = hAPP(c_Fun_Ocomp(X23607,X23607,X23607,hAPP(X23606,X23603)),hAPP(X23606,X23604)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__comp])]) ).

fof(i_0_7690,plain,
    ! [X27331,X27332,X27333,X27334,X27335] : hAPP(hAPP(c_Product__Type_OSigma(X27335,X27334),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27335,tc_HOL_Obool)),X27333),X27332)),X27331) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X27335,X27334),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X27335,X27334),X27333),X27331)),hAPP(hAPP(c_Product__Type_OSigma(X27335,X27334),X27332),X27331)),
    inference(variable_rename,[status(thm)],[fact_Sigma__Int__distrib1]) ).

fof(i_0_7691,plain,
    ! [X27305,X27306,X27307,X27308,X27309] : hAPP(hAPP(c_Product__Type_OSigma(X27309,X27308),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27309,tc_HOL_Obool)),X27307),X27306)),X27305) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X27309,X27308),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X27309,X27308),X27307),X27305)),hAPP(hAPP(c_Product__Type_OSigma(X27309,X27308),X27306),X27305)),
    inference(variable_rename,[status(thm)],[fact_Sigma__Un__distrib1]) ).

fof(i_0_7692,plain,
    ! [X27348,X27349,X27350,X27351,X27352] : hAPP(hAPP(c_Product__Type_OSigma(X27352,X27351),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27352,tc_HOL_Obool)),X27350),X27349)),X27348) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X27352,X27351),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X27352,X27351),X27350),X27348)),hAPP(hAPP(c_Product__Type_OSigma(X27352,X27351),X27349),X27348)),
    inference(variable_rename,[status(thm)],[fact_Sigma__Diff__distrib1]) ).

cnf(i_0_7693,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_7694,plain,
    ! [X29612,X29613,X29614,X29615] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X29615),X29614),hAPP(c_List_Oset(X29615),c_List_Obutlast(X29615,X29613))))
        | hBOOL(hAPP(hAPP(c_member(X29615),X29614),hAPP(c_List_Oset(X29615),c_List_Obutlast(X29615,hAPP(hAPP(c_List_Oappend(X29615),X29613),X29612))))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X29615),X29614),hAPP(c_List_Oset(X29615),c_List_Obutlast(X29615,X29612))))
        | hBOOL(hAPP(hAPP(c_member(X29615),X29614),hAPP(c_List_Oset(X29615),c_List_Obutlast(X29615,hAPP(hAPP(c_List_Oappend(X29615),X29613),X29612))))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__set__butlast__appendI])])]) ).

fof(i_0_7695,plain,
    ! [X23470,X23471,X23472] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X23472,X23472),tc_HOL_Obool)),X23471),X23470))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23472,tc_HOL_Obool)),c_Wellfounded_Oacc(X23472,X23470)),c_Wellfounded_Oacc(X23472,X23471))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc__subset])]) ).

fof(i_0_7696,plain,
    ! [X30543,X30544,X30545,X30546,X30547,X30548] :
      ( ~ class_Orderings_Olinorder(X30548)
      | hAPP(X30547,X30546) = hAPP(X30547,X30545)
      | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30544,X30548,X30547),X30545),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30544,X30548,X30547),X30546),X30543)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30544,X30548,X30547),X30546),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30544,X30548,X30547),X30545),X30543)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insort__key__left__comm])]) ).

fof(i_0_7697,plain,
    ! [X34004,X34005,X34006,X34007] :
      ( hAPP(c_Set_Oimage(X34007,X34006,X34005),c_Orderings_Otop__class_Otop(tc_fun(X34007,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X34006,tc_HOL_Obool))
      | hAPP(X34005,hAPP(c_Hilbert__Choice_Oinv__into(X34007,X34006,c_Orderings_Otop__class_Otop(tc_fun(X34007,tc_HOL_Obool)),X34005),X34004)) = X34004 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_surj__f__inv__f])]) ).

fof(i_0_7698,plain,
    ! [X22104,X22105] :
      ( X22105 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22104,X22105),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X22104),X22105)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X22104,X22105)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__int__rel__div__mod])]) ).

fof(i_0_7699,plain,
    ! [X29908,X29909,X29910,X29911,X29912,X29913] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29913,tc_fun(X29912,tc_HOL_Obool)),X29911),hAPP(hAPP(c_COMBB(X29910,tc_fun(X29912,tc_HOL_Obool),X29913),X29909),X29908)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29910,tc_fun(X29912,tc_HOL_Obool)),hAPP(c_Set_Oimage(X29913,X29910,X29908),X29911)),X29909),
    inference(variable_rename,[status(thm)],[fact_INT__extend__simps_I10_J]) ).

fof(i_0_7700,plain,
    ! [X25089,X25090,X25091,X25092,X25093,X25094] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25094,tc_fun(X25093,tc_HOL_Obool)),X25092),hAPP(hAPP(c_COMBB(X25091,tc_fun(X25093,tc_HOL_Obool),X25094),X25090),X25089)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25091,tc_fun(X25093,tc_HOL_Obool)),hAPP(c_Set_Oimage(X25094,X25091,X25089),X25092)),X25090),
    inference(variable_rename,[status(thm)],[fact_UN__extend__simps_I10_J]) ).

fof(i_0_7701,plain,
    ! [X29914,X29915,X29916,X29917,X29918,X29919] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29919,tc_fun(X29918,tc_HOL_Obool)),hAPP(c_Set_Oimage(X29917,X29919,X29916),X29915)),X29914) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29917,tc_fun(X29918,tc_HOL_Obool)),X29915),hAPP(hAPP(c_COMBB(X29919,tc_fun(X29918,tc_HOL_Obool),X29917),X29914),X29916)),
    inference(variable_rename,[status(thm)],[fact_INT__simps_I10_J]) ).

fof(i_0_7702,plain,
    ! [X25101,X25102,X25103,X25104,X25105,X25106] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25106,tc_fun(X25105,tc_HOL_Obool)),hAPP(c_Set_Oimage(X25104,X25106,X25103),X25102)),X25101) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25104,tc_fun(X25105,tc_HOL_Obool)),X25102),hAPP(hAPP(c_COMBB(X25106,tc_fun(X25105,tc_HOL_Obool),X25104),X25101),X25103)),
    inference(variable_rename,[status(thm)],[fact_UN__simps_I10_J]) ).

fof(i_0_7703,plain,
    ! [X21889,X21890] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X21890,X21889),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X21890),X21889)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21890,X21889)))),
    inference(variable_rename,[status(thm)],[fact_divmod__nat__rel]) ).

cnf(i_0_7704,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_7705,plain,
    ! [X19296,X19297,X19298] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19298,tc_HOL_Obool)),X19297),X19296))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19298,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X19298,tc_HOL_Obool)),X19296)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X19298,tc_HOL_Obool)),X19297))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Compl__anti__mono])]) ).

fof(i_0_7706,plain,
    ! [X25828,X25829,X25830] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25830),X25829))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25830,tc_HOL_Obool)),X25829),hAPP(c_Set_Oimage(X25830,X25830,X25828),X25829)))
      | c_Fun_Oinj__on(X25830,X25830,X25828,X25829) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__surj__inj])]) ).

fof(i_0_7707,plain,
    ! [X27286,X27287,X27288] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(X27288,X27287),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X27288,X27287),c_Orderings_Otop__class_Otop(tc_fun(X27288,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X27287,tc_HOL_Obool),X27288),X27286))) = hAPP(hAPP(c_Product__Type_OSigma(X27288,X27287),c_Orderings_Otop__class_Otop(tc_fun(X27288,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X27287,tc_HOL_Obool),X27288),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X27287,tc_HOL_Obool)),X27286))),
    inference(variable_rename,[status(thm)],[fact_Compl__Times__UNIV1]) ).

fof(i_0_7708,plain,
    ! [X27283,X27284,X27285] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(X27285,X27284),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X27285,X27284),X27283),hAPP(c_COMBK(tc_fun(X27284,tc_HOL_Obool),X27285),c_Orderings_Otop__class_Otop(tc_fun(X27284,tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(X27285,X27284),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X27285,tc_HOL_Obool)),X27283)),hAPP(c_COMBK(tc_fun(X27284,tc_HOL_Obool),X27285),c_Orderings_Otop__class_Otop(tc_fun(X27284,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_Compl__Times__UNIV2]) ).

fof(i_0_7709,plain,
    ! [X28511,X28512,X28513,X28514] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X28514),X28513),c_Wellfounded_Oacc(X28514,X28512)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X28514)),X28511),c_Wellfounded_Oacc(tc_List_Olist(X28514),c_List_Olistrel1(X28514,X28512))))
      | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X28514)),hAPP(hAPP(c_List_Olist_OCons(X28514),X28513),X28511)),c_Wellfounded_Oacc(tc_List_Olist(X28514),c_List_Olistrel1(X28514,X28512)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cons__acc__listrel1I])]) ).

fof(i_0_7710,plain,
    ! [X21544,X21545,X21546,X21547] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21547),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21547),X21545),X21546)),X21544))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21547),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21547),X21544),X21546)),X21545))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21547),X21546),c_Groups_Ozero__class_Ozero(X21547)))
        | ~ class_Fields_Olinordered__field(X21547) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21547),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21547),X21544),X21546)),X21545))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21547),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21547),X21545),X21546)),X21544))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21547),X21546),c_Groups_Ozero__class_Ozero(X21547)))
        | ~ class_Fields_Olinordered__field(X21547) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__divide__le__eq])])]) ).

fof(i_0_7711,plain,
    ! [X21436,X21437,X21438,X21439] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21439),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21439),X21437),X21438)),X21436))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21439),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21439),X21436),X21438)),X21437))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21439),X21438),c_Groups_Ozero__class_Ozero(X21439)))
        | ~ class_Fields_Olinordered__field(X21439) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21439),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21439),X21436),X21438)),X21437))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21439),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21439),X21437),X21438)),X21436))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21439),X21438),c_Groups_Ozero__class_Ozero(X21439)))
        | ~ class_Fields_Olinordered__field(X21439) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__divide__less__eq])])]) ).

cnf(i_0_7712,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_5562]) ).

fof(i_0_7713,plain,
    ! [X22067,X22068,X22069] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22069,tc_fun(X22069,tc_HOL_Obool))),X22068),X22067))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22069,tc_HOL_Obool)),c_Wellfounded_Oaccp(X22069,X22067)),c_Wellfounded_Oaccp(X22069,X22068))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_accp__subset])]) ).

fof(i_0_7714,plain,
    ! [X24405,X24406,X24407,X24408,X24409,X24410] :
      ( ~ c_Finite__Set_Ofolding__idem(X24410,X24409,X24408,X24407)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24410),X24406))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24410,tc_HOL_Obool)),X24405),X24406))
      | hAPP(c_Fun_Ocomp(X24409,X24409,X24409,hAPP(X24407,X24406)),hAPP(X24407,X24405)) = hAPP(X24407,X24406) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__idem_Osubset__comp__idem])]) ).

fof(i_0_7715,plain,
    ! [X30594,X30595,X30596] :
      ( ~ class_Orderings_Olinorder(X30596)
      | ~ hBOOL(hAPP(hAPP(c_member(X30596),X30595),hAPP(c_List_Oset(X30596),X30594)))
      | c_List_Olinorder__class_Oinsort__insert__key(X30596,X30596,c_COMBI(X30596),X30595,X30594) = X30594 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insort__insert__triv])]) ).

fof(i_0_7716,plain,
    ! [X19786,X19787,X19788] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19788),X19787)),X19786))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19786),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19788),hAPP(c_Nat_OSuc,X19787))))
        | X19787 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19786),X19788)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19788)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19788),X19787)),X19786))
        | X19787 != hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19786),X19788)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19788)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19786),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19788),hAPP(c_Nat_OSuc,X19787))))
        | X19787 != hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19786),X19788)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19788)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__div__lemma])])]) ).

fof(i_0_7717,plain,
    ! [X26333,X26334,X26335,X26336,X26337] :
      ( ~ class_Groups_Oab__group__add(X26337)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26336),X26335))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26336,tc_HOL_Obool)),X26334),X26335))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26336,X26337),X26333),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26336,tc_HOL_Obool)),X26335),X26334)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X26337),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26336,X26337),X26333),X26335)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26336,X26337),X26333),X26334)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__diff])]) ).

cnf(i_0_7718,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_7719,plain,
    ! [X28808,X28809,X28810] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X28810),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28809)),X28808)))
      | X28808 = hAPP(hAPP(c_List_Oappend(X28809),hAPP(hAPP(c_List_Otake(X28809),X28810),X28808)),hAPP(hAPP(c_List_Olist_OCons(X28809),hAPP(hAPP(c_List_Onth(X28809),X28808),X28810)),hAPP(hAPP(c_List_Odrop(X28809),hAPP(c_Nat_OSuc,X28810)),X28808))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_id__take__nth__drop])]) ).

cnf(i_0_7720,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_5567]) ).

cnf(i_0_7721,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_5568]) ).

cnf(i_0_7722,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_7723,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]) ).

fof(i_0_7724,plain,
    ! [X22789,X22790] :
      ( ( ~ 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),X22790),X22789)),c_Wellfounded_Oless__than))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22790),X22789)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22790),X22789))
        | 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),X22790),X22789)),c_Wellfounded_Oless__than)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__than__iff])]) ).

cnf(i_0_7725,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_7726,plain,
    ! [X23185,X23186,X23187,X23188,X23189,X23190] : hAPP(c_Set_Oimage(X23190,X23189,X23188),hAPP(c_Set_Oimage(X23187,X23190,X23186),X23185)) = hAPP(c_Set_Oimage(X23187,X23189,hAPP(hAPP(c_COMBB(X23190,X23189,X23187),X23188),X23186)),X23185),
    inference(variable_rename,[status(thm)],[fact_image__image]) ).

fof(i_0_7727,plain,
    ! [X24779,X24780,X24781,X24782,X24783] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X24782),X24779),X24781))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24782,X24783),X24780),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24782,tc_HOL_Obool)),X24781),hAPP(hAPP(c_Set_Oinsert(X24782),X24779),c_Orderings_Obot__class_Obot(tc_fun(X24782,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24783),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24782,X24783),X24780),X24781)),hAPP(X24780,X24779))
        | hAPP(X24780,X24779) = c_Groups_Ozero__class_Ozero(X24783)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24782),X24781))
        | ~ class_Fields_Ofield(X24783) )
      & ( hBOOL(hAPP(hAPP(c_member(X24782),X24779),X24781))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24782,X24783),X24780),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24782,tc_HOL_Obool)),X24781),hAPP(hAPP(c_Set_Oinsert(X24782),X24779),c_Orderings_Obot__class_Obot(tc_fun(X24782,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24782,X24783),X24780),X24781)
        | hAPP(X24780,X24779) = c_Groups_Ozero__class_Ozero(X24783)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24782),X24781))
        | ~ class_Fields_Ofield(X24783) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5635])])]) ).

cnf(i_0_7728,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_5574]) ).

fof(i_0_7729,plain,
    ! [X30121,X30122,X30123,X30124,X30125] :
      ( hAPP(hAPP(c_List_Omap(X30125,X30124),X30123),X30122) != hAPP(hAPP(c_List_Omap(X30125,X30124),X30123),X30121)
      | ~ c_Fun_Oinj__on(X30125,X30124,X30123,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X30125,tc_HOL_Obool)),hAPP(c_List_Oset(X30125),X30122)),hAPP(c_List_Oset(X30125),X30121)))
      | X30122 = X30121 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__inj__on])]) ).

fof(i_0_7730,plain,
    ! [X30116,X30117,X30118,X30119,X30120] :
      ( ( hAPP(hAPP(c_List_Omap(X30120,X30119),X30118),X30117) != hAPP(hAPP(c_List_Omap(X30120,X30119),X30118),X30116)
        | X30117 = X30116
        | ~ c_Fun_Oinj__on(X30120,X30119,X30118,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X30120,tc_HOL_Obool)),hAPP(c_List_Oset(X30120),X30117)),hAPP(c_List_Oset(X30120),X30116))) )
      & ( X30117 != X30116
        | hAPP(hAPP(c_List_Omap(X30120,X30119),X30118),X30117) = hAPP(hAPP(c_List_Omap(X30120,X30119),X30118),X30116)
        | ~ c_Fun_Oinj__on(X30120,X30119,X30118,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X30120,tc_HOL_Obool)),hAPP(c_List_Oset(X30120),X30117)),hAPP(c_List_Oset(X30120),X30116))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__map__eq__map])])]) ).

fof(i_0_7731,plain,
    ! [X19953,X19954,X19955] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19953),X19954))
        | hBOOL(hAPP(X19955,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19954)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19953))))
        | ~ hBOOL(hAPP(X19955,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19954),X19953)))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19954),X19953))
        | hBOOL(hAPP(X19955,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(X19955,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19954),X19953)))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19954),X19953))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19953),X19954))
        | hBOOL(hAPP(X19955,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19954),X19953)))) )
      & ( ~ hBOOL(hAPP(X19955,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19953),X19954))
        | hBOOL(hAPP(X19955,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19954),X19953)))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19954),X19953))
        | ~ hBOOL(hAPP(X19955,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19954)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19953))))
        | hBOOL(hAPP(X19955,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19954),X19953)))) )
      & ( ~ hBOOL(hAPP(X19955,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(X19955,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19954)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19953))))
        | hBOOL(hAPP(X19955,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19954),X19953)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiff__int__split])])]) ).

fof(i_0_7732,plain,
    ! [X30528,X30529,X30530,X30531] :
      ( ~ hBOOL(hAPP(c_List_Olistsp(X30531,X30530),X30529))
      | ~ hBOOL(hAPP(c_List_Olistsp(X30531,X30528),X30529))
      | hBOOL(hAPP(c_List_Olistsp(X30531,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X30531,tc_HOL_Obool)),X30530),X30528)),X30529)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsp__infI])]) ).

cnf(i_0_7733,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_7734,plain,
    ! [X32528,X32529,X32530,X32531,X32532] :
      ( ~ c_Relation_Osingle__valued(X32532,X32531,hAPP(c_Relation_Oconverse(X32531,X32532),X32530))
      | hAPP(c_Relation_OImage(X32531,X32532,X32530),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X32531,tc_HOL_Obool)),X32529),X32528)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X32532,tc_HOL_Obool)),hAPP(c_Relation_OImage(X32531,X32532,X32530),X32529)),hAPP(c_Relation_OImage(X32531,X32532,X32530),X32528)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Image__Int__eq])]) ).

fof(i_0_7735,plain,
    ! [X21407,X21408,X21409,X21410,X21411] :
      ( ~ class_Fields_Olinordered__field(X21411)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21411),c_Groups_Ozero__class_Ozero(X21411)),X21410))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21411),X21410),X21409))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21411),c_Groups_Ozero__class_Ozero(X21411)),X21408))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21411),X21408),X21407))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21411),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21411),X21410),X21407)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21411),X21409),X21408))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_frac__le])]) ).

fof(i_0_7736,plain,
    ! [X18806,X18807,X18808,X18809,X18810] :
      ( ~ class_Rings_Oordered__semiring(X18810)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18810),X18809),X18808))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18810),X18807),X18806))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18810),c_Groups_Ozero__class_Ozero(X18810)),X18809))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18810),c_Groups_Ozero__class_Ozero(X18810)),X18807))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18810),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18810),X18809),X18807)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18810),X18808),X18806))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__mono_H])]) ).

fof(i_0_7737,plain,
    ! [X18811,X18812,X18813,X18814,X18815] :
      ( ~ class_Rings_Oordered__semiring(X18815)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18815),X18814),X18813))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18815),X18812),X18811))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18815),c_Groups_Ozero__class_Ozero(X18815)),X18813))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18815),c_Groups_Ozero__class_Ozero(X18815)),X18812))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18815),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18815),X18814),X18812)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18815),X18813),X18811))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__mono])]) ).

fof(i_0_7738,plain,
    ! [X21412,X21413,X21414,X21415,X21416] :
      ( ~ class_Fields_Olinordered__field(X21416)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21416),c_Groups_Ozero__class_Ozero(X21416)),X21415))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21416),X21415),X21414))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21416),c_Groups_Ozero__class_Ozero(X21416)),X21413))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21416),X21413),X21412))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21416),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21416),X21415),X21412)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21416),X21414),X21413))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_frac__less])]) ).

fof(i_0_7739,plain,
    ! [X21417,X21418,X21419,X21420,X21421] :
      ( ~ class_Fields_Olinordered__field(X21421)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21421),c_Groups_Ozero__class_Ozero(X21421)),X21420))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21421),X21420),X21419))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21421),c_Groups_Ozero__class_Ozero(X21421)),X21418))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21421),X21418),X21417))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21421),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21421),X21420),X21417)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21421),X21419),X21418))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_frac__less2])]) ).

fof(i_0_7740,plain,
    ! [X18974,X18975,X18976,X18977,X18978] :
      ( ~ class_Rings_Olinordered__semiring__strict(X18978)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18978),X18977),X18976))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18978),X18975),X18974))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18978),c_Groups_Ozero__class_Ozero(X18978)),X18977))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18978),c_Groups_Ozero__class_Ozero(X18978)),X18975))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18978),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18978),X18977),X18975)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18978),X18976),X18974))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__le__imp__less])]) ).

fof(i_0_7741,plain,
    ! [X18969,X18970,X18971,X18972,X18973] :
      ( ~ class_Rings_Olinordered__semiring__strict(X18973)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18973),X18972),X18971))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18973),X18970),X18969))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18973),c_Groups_Ozero__class_Ozero(X18973)),X18972))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18973),c_Groups_Ozero__class_Ozero(X18973)),X18970))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18973),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18973),X18972),X18970)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18973),X18971),X18969))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__less__imp__less])]) ).

fof(i_0_7742,plain,
    ! [X18979,X18980,X18981,X18982,X18983] :
      ( ~ class_Rings_Olinordered__semiring__strict(X18983)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18983),X18982),X18981))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18983),X18980),X18979))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18983),c_Groups_Ozero__class_Ozero(X18983)),X18982))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18983),c_Groups_Ozero__class_Ozero(X18983)),X18980))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18983),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18983),X18982),X18980)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18983),X18981),X18979))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__mono_H])]) ).

fof(i_0_7743,plain,
    ! [X18984,X18985,X18986,X18987,X18988] :
      ( ~ class_Rings_Olinordered__semiring__strict(X18988)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18988),X18987),X18986))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18988),X18985),X18984))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18988),c_Groups_Ozero__class_Ozero(X18988)),X18986))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18988),c_Groups_Ozero__class_Ozero(X18988)),X18985))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18988),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18988),X18987),X18985)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18988),X18986),X18984))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__mono])]) ).

cnf(i_0_7744,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_7745,plain,
    ! [X26436,X26437,X26438,X26439,X26440] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X26439),X26437),X26438))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26439,X26440),X26436),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26439,tc_HOL_Obool)),X26438),hAPP(hAPP(c_Set_Oinsert(X26439),X26437),c_Orderings_Obot__class_Obot(tc_fun(X26439,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X26440),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26439,X26440),X26436),X26438)),hAPP(X26436,X26437))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26439),X26438))
        | ~ class_Groups_Oab__group__add(X26440) )
      & ( hBOOL(hAPP(hAPP(c_member(X26439),X26437),X26438))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26439,X26440),X26436),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26439,tc_HOL_Obool)),X26438),hAPP(hAPP(c_Set_Oinsert(X26439),X26437),c_Orderings_Obot__class_Obot(tc_fun(X26439,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26439,X26440),X26436),X26438)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26439),X26438))
        | ~ class_Groups_Oab__group__add(X26440) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5638])])]) ).

fof(i_0_7746,plain,
    ! [X26431,X26432,X26433,X26434,X26435] :
      ( ~ class_Rings_Oring(X26435)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26434),X26433))
      | ~ hBOOL(hAPP(hAPP(c_member(X26434),X26432),X26433))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26434,X26435),X26431),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26434,tc_HOL_Obool)),X26433),hAPP(hAPP(c_Set_Oinsert(X26434),X26432),c_Orderings_Obot__class_Obot(tc_fun(X26434,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X26435),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26434,X26435),X26431),X26433)),hAPP(X26431,X26432)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__diff1__ring])]) ).

fof(i_0_7747,plain,
    ! [X26445,X26446,X26447] :
      ( ~ class_Fields_Ofield(X26447)
      | X26446 = c_Groups_Oone__class_Oone(X26447)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26447),hAPP(c_Power_Opower__class_Opower(X26447),X26446)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X26445)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X26447),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X26447),hAPP(hAPP(c_Power_Opower__class_Opower(X26447),X26446),X26445)),c_Groups_Oone__class_Oone(X26447))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X26447),X26446),c_Groups_Oone__class_Oone(X26447))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_geometric__sum])]) ).

fof(i_0_7748,plain,
    ! [X30141,X30142] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X30142)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X30142),hAPP(c_Groups_Oabs__class_Oabs(X30142),hAPP(c_List_Omonoid__add__class_Olistsum(X30142),X30141))),hAPP(c_List_Omonoid__add__class_Olistsum(X30142),hAPP(hAPP(c_List_Omap(X30142,X30142),c_Groups_Oabs__class_Oabs(X30142)),X30141)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__abs])]) ).

cnf(i_0_7749,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_7750,plain,
    ! [X25832,X25833,X25834] : 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)),X25834)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X25833),X25832)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25833),X25834)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25832),X25834)),
    inference(variable_rename,[status(thm)],[fact_image__add__atLeastLessThan]) ).

fof(i_0_7751,plain,
    ! [X26286,X26287,X26288,X26289,X26290] :
      ( ~ class_Groups_Oab__group__add(X26290)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X26289),X26288))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X26288),X26287))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X26290),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26290),X26286),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X26289),X26287))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26290),X26286),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X26289),X26288))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26290),X26286),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X26288),X26287)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__diff__nat__ivl])]) ).

fof(i_0_7752,plain,
    ! [X26281,X26282,X26283,X26284,X26285] :
      ( ~ class_Groups_Ocomm__monoid__add(X26285)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X26284),X26283))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X26283),X26282))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26285),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26285),X26281),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X26284),X26283))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26285),X26281),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X26283),X26282))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26285),X26281),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X26284),X26282)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__add__nat__ivl])]) ).

fof(i_0_7753,plain,
    ! [X18949,X18950,X18951,X18952] :
      ( ~ class_Rings_Olinordered__semiring__strict(X18952)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18952),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18952),X18951),X18950)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18952),X18949),X18950)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18952),c_Groups_Ozero__class_Ozero(X18952)),X18950))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18952),X18951),X18949)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__le__imp__le])]) ).

fof(i_0_7754,plain,
    ! [X18945,X18946,X18947,X18948] :
      ( ~ class_Rings_Olinordered__semiring__strict(X18948)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18948),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18948),X18947),X18946)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18948),X18947),X18945)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18948),c_Groups_Ozero__class_Ozero(X18948)),X18947))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18948),X18946),X18945)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__le__imp__le])]) ).

fof(i_0_7755,plain,
    ! [X18993,X18994,X18995,X18996] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18996),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18996),X18995),X18994)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18996),X18995),X18993)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18996),X18994),X18993))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18996),c_Groups_Ozero__class_Ozero(X18996)),X18995))
        | ~ class_Rings_Olinordered__ring__strict(X18996) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18996),X18994),X18993))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18996),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18996),X18995),X18994)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18996),X18995),X18993)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18996),c_Groups_Ozero__class_Ozero(X18996)),X18995))
        | ~ class_Rings_Olinordered__ring__strict(X18996) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__cancel__left__pos])])]) ).

fof(i_0_7756,plain,
    ! [X18965,X18966,X18967,X18968] :
      ( ~ class_Rings_Olinordered__semiring(X18968)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18968),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18968),X18967),X18966)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18968),X18965),X18966)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18968),c_Groups_Ozero__class_Ozero(X18968)),X18966))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18968),X18967),X18965)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__less__imp__less])]) ).

fof(i_0_7757,plain,
    ! [X18961,X18962,X18963,X18964] :
      ( ~ class_Rings_Olinordered__semiring__strict(X18964)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18964),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18964),X18963),X18962)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18964),X18961),X18962)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18964),c_Groups_Ozero__class_Ozero(X18964)),X18962))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18964),X18963),X18961)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__imp__less__right])]) ).

fof(i_0_7758,plain,
    ! [X20584,X20585,X20586,X20587] :
      ( ~ class_Rings_Olinordered__semidom(X20587)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20587),hAPP(hAPP(c_Power_Opower__class_Opower(X20587),X20586),X20585)),hAPP(hAPP(c_Power_Opower__class_Opower(X20587),X20584),X20585)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20587),c_Groups_Ozero__class_Ozero(X20587)),X20584))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20587),X20586),X20584)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__less__imp__less__base])]) ).

fof(i_0_7759,plain,
    ! [X18957,X18958,X18959,X18960] :
      ( ~ class_Rings_Olinordered__semiring(X18960)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18960),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18960),X18959),X18958)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18960),X18959),X18957)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18960),c_Groups_Ozero__class_Ozero(X18960)),X18959))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18960),X18958),X18957)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__less__imp__less])]) ).

fof(i_0_7760,plain,
    ! [X18953,X18954,X18955,X18956] :
      ( ~ class_Rings_Olinordered__semiring__strict(X18956)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18956),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18956),X18955),X18954)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18956),X18955),X18953)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18956),c_Groups_Ozero__class_Ozero(X18956)),X18955))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18956),X18954),X18953)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__imp__less__left])]) ).

fof(i_0_7761,plain,
    ! [X18338,X18339,X18340,X18341] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18341),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18341),X18340),X18339)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18341),X18340),X18338)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18341),X18339),X18338))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18341),c_Groups_Ozero__class_Ozero(X18341)),X18340))
        | ~ class_Rings_Olinordered__ring__strict(X18341) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18341),X18339),X18338))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18341),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18341),X18340),X18339)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18341),X18340),X18338)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18341),c_Groups_Ozero__class_Ozero(X18341)),X18340))
        | ~ class_Rings_Olinordered__ring__strict(X18341) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__pos])])]) ).

cnf(i_0_7762,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_7763,plain,
    ! [X26501,X26502,X26503,X26504] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26504),X26503))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26504,tc_HOL_Obool)),X26503),X26502))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26504,tc_Nat_Onat),X26501),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26504,tc_HOL_Obool)),X26502),X26503)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26504,tc_Nat_Onat),X26501),X26502)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26504,tc_Nat_Onat),X26501),X26503)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__diff__nat])]) ).

fof(i_0_7764,plain,
    ! [X27067,X27068,X27069,X27071] :
      ( ( hBOOL(hAPP(hAPP(c_member(X27069),esk265_3(X27067,X27068,X27069)),X27068))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27069),hAPP(c_Finite__Set_Ofold1(X27069,c_Orderings_Oord__class_Omin(X27069)),X27068)),X27067))
        | X27068 = c_Orderings_Obot__class_Obot(tc_fun(X27069,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27069),X27068))
        | ~ class_Orderings_Olinorder(X27069) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27069),esk265_3(X27067,X27068,X27069)),X27067))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27069),hAPP(c_Finite__Set_Ofold1(X27069,c_Orderings_Oord__class_Omin(X27069)),X27068)),X27067))
        | X27068 = c_Orderings_Obot__class_Obot(tc_fun(X27069,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27069),X27068))
        | ~ class_Orderings_Olinorder(X27069) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X27069),X27071),X27068))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27069),X27071),X27067))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27069),hAPP(c_Finite__Set_Ofold1(X27069,c_Orderings_Oord__class_Omin(X27069)),X27068)),X27067))
        | X27068 = c_Orderings_Obot__class_Obot(tc_fun(X27069,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27069),X27068))
        | ~ class_Orderings_Olinorder(X27069) ) ),
    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_7765,plain,
    ! [X27054,X27055,X27056,X27058] :
      ( ( hBOOL(hAPP(hAPP(c_member(X27056),esk263_3(X27054,X27055,X27056)),X27055))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27056),hAPP(c_Finite__Set_Ofold1(X27056,c_Orderings_Oord__class_Omin(X27056)),X27055)),X27054))
        | X27055 = c_Orderings_Obot__class_Obot(tc_fun(X27056,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27056),X27055))
        | ~ class_Orderings_Olinorder(X27056) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27056),esk263_3(X27054,X27055,X27056)),X27054))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27056),hAPP(c_Finite__Set_Ofold1(X27056,c_Orderings_Oord__class_Omin(X27056)),X27055)),X27054))
        | X27055 = c_Orderings_Obot__class_Obot(tc_fun(X27056,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27056),X27055))
        | ~ class_Orderings_Olinorder(X27056) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X27056),X27058),X27055))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27056),X27058),X27054))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27056),hAPP(c_Finite__Set_Ofold1(X27056,c_Orderings_Oord__class_Omin(X27056)),X27055)),X27054))
        | X27055 = c_Orderings_Obot__class_Obot(tc_fun(X27056,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27056),X27055))
        | ~ class_Orderings_Olinorder(X27056) ) ),
    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_7766,plain,
    ! [X29660,X29661,X29662,X29663,X29664,X29665] :
      ( ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29665,tc_fun(X29664,tc_HOL_Obool)),X29663),X29662),X29661))
      | hBOOL(hAPP(hAPP(X29662,X29660),X29661))
      | ~ hBOOL(hAPP(hAPP(c_member(X29665),X29660),X29663)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5641])]) ).

fof(i_0_7767,plain,
    ! [X29654,X29655,X29656,X29657,X29658,X29659] :
      ( ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29659,tc_fun(X29658,tc_HOL_Obool)),X29657),X29656),X29655))
      | ~ hBOOL(hAPP(hAPP(c_member(X29659),X29654),X29657))
      | hBOOL(hAPP(hAPP(X29656,X29654),X29655)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF1__D])]) ).

fof(i_0_7768,plain,
    ! [X20465,X20466,X20467,X20468] :
      ( ~ class_Rings_Olinordered__semidom(X20468)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20468),c_Groups_Oone__class_Oone(X20468)),X20467))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20468),hAPP(hAPP(c_Power_Opower__class_Opower(X20468),X20467),X20466)),hAPP(hAPP(c_Power_Opower__class_Opower(X20468),X20467),X20465)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20466),X20465)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__le__imp__le__exp])]) ).

fof(i_0_7769,plain,
    ! [X20461,X20462,X20463,X20464] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20464),hAPP(hAPP(c_Power_Opower__class_Opower(X20464),X20463),X20462)),hAPP(hAPP(c_Power_Opower__class_Opower(X20464),X20463),X20461)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20462),X20461))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20464),c_Groups_Oone__class_Oone(X20464)),X20463))
        | ~ class_Rings_Olinordered__semidom(X20464) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20462),X20461))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20464),hAPP(hAPP(c_Power_Opower__class_Opower(X20464),X20463),X20462)),hAPP(hAPP(c_Power_Opower__class_Opower(X20464),X20463),X20461)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20464),c_Groups_Oone__class_Oone(X20464)),X20463))
        | ~ class_Rings_Olinordered__semidom(X20464) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__increasing__iff])])]) ).

fof(i_0_7770,plain,
    ! [X20615,X20616,X20617,X20618] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20618),hAPP(hAPP(c_Power_Opower__class_Opower(X20618),X20617),X20616)),hAPP(hAPP(c_Power_Opower__class_Opower(X20618),X20617),X20615)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20616),X20615))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20618),c_Groups_Oone__class_Oone(X20618)),X20617))
        | ~ class_Rings_Olinordered__semidom(X20618) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20616),X20615))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20618),hAPP(hAPP(c_Power_Opower__class_Opower(X20618),X20617),X20616)),hAPP(hAPP(c_Power_Opower__class_Opower(X20618),X20617),X20615)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20618),c_Groups_Oone__class_Oone(X20618)),X20617))
        | ~ class_Rings_Olinordered__semidom(X20618) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__strict__increasing__iff])])]) ).

fof(i_0_7771,plain,
    ! [X20611,X20612,X20613,X20614] :
      ( ~ class_Rings_Olinordered__semidom(X20614)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20614),c_Groups_Oone__class_Oone(X20614)),X20613))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20614),hAPP(hAPP(c_Power_Opower__class_Opower(X20614),X20613),X20612)),hAPP(hAPP(c_Power_Opower__class_Opower(X20614),X20613),X20611)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20612),X20611)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__less__imp__less__exp])]) ).

fof(i_0_7772,plain,
    ! [X28994,X28995,X28996] :
      ( X28996 = c_List_Olist_ONil(X28995)
      | hBOOL(hAPP(hAPP(c_member(X28995),hAPP(c_Product__Type_Ofst(X28995,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect(X28995,X28996),X28994))),hAPP(c_List_Oset(X28995),X28996))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_select])]) ).

fof(i_0_7773,plain,
    ! [X27379,X27380,X27381,X27382] : hAPP(c_Finite__Set_Ocard(tc_prod(X27382,X27381)),hAPP(hAPP(c_Product__Type_OSigma(X27382,X27381),hAPP(hAPP(c_Set_Oinsert(X27382),X27380),c_Orderings_Obot__class_Obot(tc_fun(X27382,tc_HOL_Obool)))),hAPP(c_COMBK(tc_fun(X27381,tc_HOL_Obool),X27382),X27379))) = hAPP(c_Finite__Set_Ocard(X27381),X27379),
    inference(variable_rename,[status(thm)],[fact_card__cartesian__product__singleton]) ).

fof(i_0_7774,plain,
    ! [X17104,X17105,X17106] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X17106)),X17105),X17104))
        | hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X17106))),X17105),X17104)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X17106))),X17105),X17104))
        | hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X17106)),X17105),X17104)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evalc_Oequations_I9_J])]) ).

fof(i_0_7775,plain,
    ! [X17067,X17068,X17069] :
      ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X17069))),X17068),X17067))
      | hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X17069)),X17068),X17067)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evalc_OBody])]) ).

cnf(i_0_7776,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_7777,plain,
    ! [X21979,X21980,X21981,X21982,X21983] :
      ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X21983,X21982,tc_HOL_Obool),X21981),hAPP(hAPP(c_Product__Type_OPair(X21983,X21982),X21980),X21979)))
      | hBOOL(hAPP(hAPP(X21981,X21980),X21979)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_splitD])]) ).

fof(i_0_7778,plain,
    ! [X26027,X26028,X26029] : c_Fun_Oinj__on(tc_prod(X26029,X26028),tc_prod(X26028,X26029),hAPP(c_Product__Type_Oprod_Oprod__case(X26029,X26028,tc_prod(X26028,X26029)),hAPP(c_COMBC(X26028,X26029,tc_prod(X26028,X26029)),c_Product__Type_OPair(X26028,X26029))),X26027),
    inference(variable_rename,[status(thm)],[fact_swap__inj__on]) ).

fof(i_0_7779,plain,
    ! [X27103,X27104,X27105] :
      ( ( hBOOL(hAPP(hAPP(c_member(X27105),esk271_3(X27103,X27104,X27105)),X27104))
        | 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(X27105,tc_Nat_Onat),X27103),X27104)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27105),X27104)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X27103,esk271_3(X27103,X27104,X27105))))
        | 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(X27105,tc_Nat_Onat),X27103),X27104)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27105),X27104)) ) ),
    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_7780,plain,
    ! [X24716,X24717,X24718,X24719] :
      ( ( ~ 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(X24718,tc_Nat_Onat),X24716),X24717)))
        | ~ hBOOL(hAPP(hAPP(c_member(X24718),X24719),X24717))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X24716,X24719)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24718),X24717)) )
      & ( hBOOL(hAPP(hAPP(c_member(X24718),esk143_3(X24716,X24717,X24718)),X24717))
        | 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(X24718,tc_Nat_Onat),X24716),X24717)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24718),X24717)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X24716,esk143_3(X24716,X24717,X24718))))
        | 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(X24718,tc_Nat_Onat),X24716),X24717)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24718),X24717)) ) ),
    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_7781,plain,
    ! [X26266,X26267,X26268,X26269] :
      ( ~ class_Groups_Ocomm__monoid__add(X26269)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26269),X26268),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X26267),hAPP(c_Nat_OSuc,X26266))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26269),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X26269,tc_Nat_Onat),X26268),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X26267,X26266)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__shift__bounds__cl__Suc__ivl])]) ).

fof(i_0_7782,plain,
    ! [X18989,X18990,X18991,X18992] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18992),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18992),X18991),X18990)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18992),X18991),X18989)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18992),X18989),X18990))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18992),X18991),c_Groups_Ozero__class_Ozero(X18992)))
        | ~ class_Rings_Olinordered__ring__strict(X18992) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18992),X18989),X18990))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18992),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18992),X18991),X18990)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18992),X18991),X18989)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18992),X18991),c_Groups_Ozero__class_Ozero(X18992)))
        | ~ class_Rings_Olinordered__ring__strict(X18992) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__cancel__left__neg])])]) ).

fof(i_0_7783,plain,
    ! [X18357,X18358,X18359,X18360] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18360),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18360),X18359),X18358)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18360),X18359),X18357)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18360),X18357),X18358))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18360),X18359),c_Groups_Ozero__class_Ozero(X18360)))
        | ~ class_Rings_Olinordered__ring__strict(X18360) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18360),X18357),X18358))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18360),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18360),X18359),X18358)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18360),X18359),X18357)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18360),X18359),c_Groups_Ozero__class_Ozero(X18360)))
        | ~ class_Rings_Olinordered__ring__strict(X18360) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__neg])])]) ).

fof(i_0_7784,plain,
    ! [X23816,X23817,X23818] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23818,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23818,tc_HOL_Obool)),X23817),X23816)),X23817)),
    inference(variable_rename,[status(thm)],[fact_Int__lower1]) ).

fof(i_0_7785,plain,
    ! [X23813,X23814,X23815] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23815,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23815,tc_HOL_Obool)),X23814),X23813)),X23813)),
    inference(variable_rename,[status(thm)],[fact_Int__lower2]) ).

fof(i_0_7786,plain,
    ! [X20263,X20264,X20265] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20265,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20265,tc_HOL_Obool)),X20264),X20263)),X20264)),
    inference(variable_rename,[status(thm)],[fact_Diff__subset]) ).

fof(i_0_7787,plain,
    ! [X30427,X30428,X30429,X30430,X30431] :
      ( ~ class_Groups_Ocomm__monoid__add(X30431)
      | ~ hBOOL(hAPP(hAPP(c_member(X30430),X30429),hAPP(c_List_Oset(X30430),X30428)))
      | hAPP(c_List_Omonoid__add__class_Olistsum(X30431),hAPP(hAPP(c_List_Omap(X30430,X30431),X30427),X30428)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X30431),hAPP(X30427,X30429)),hAPP(c_List_Omonoid__add__class_Olistsum(X30431),hAPP(hAPP(c_List_Omap(X30430,X30431),X30427),c_List_Oremove1(X30430,X30429,X30428)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__map__remove1])]) ).

fof(i_0_7788,plain,
    ! [X23954,X23955,X23956,X23957] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23957,tc_HOL_Obool)),X23956),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23957,tc_HOL_Obool)),X23955),X23954)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23957,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23957,tc_HOL_Obool)),X23956),X23955)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23957,tc_HOL_Obool)),X23956),X23954)),
    inference(variable_rename,[status(thm)],[fact_Int__Un__distrib]) ).

fof(i_0_7789,plain,
    ! [X23950,X23951,X23952,X23953] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23953,tc_HOL_Obool)),X23952),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23953,tc_HOL_Obool)),X23951),X23950)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23953,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23953,tc_HOL_Obool)),X23952),X23951)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23953,tc_HOL_Obool)),X23952),X23950)),
    inference(variable_rename,[status(thm)],[fact_Diff__Int__distrib]) ).

fof(i_0_7790,plain,
    ! [X23958,X23959,X23960,X23961] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23961,tc_HOL_Obool)),X23960),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23961,tc_HOL_Obool)),X23959),X23958)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23961,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23961,tc_HOL_Obool)),X23960),X23959)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23961,tc_HOL_Obool)),X23960),X23958)),
    inference(variable_rename,[status(thm)],[fact_Un__Int__distrib]) ).

fof(i_0_7791,plain,
    ! [X24075,X24076,X24077,X24078] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24078,tc_HOL_Obool)),X24077),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24078,tc_HOL_Obool)),X24076),X24075)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24078,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24078,tc_HOL_Obool)),X24077),X24076)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24078,tc_HOL_Obool)),X24077),X24075)),
    inference(variable_rename,[status(thm)],[fact_Diff__Int]) ).

fof(i_0_7792,plain,
    ! [X24071,X24072,X24073,X24074] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24074,tc_HOL_Obool)),X24073),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24074,tc_HOL_Obool)),X24072),X24071)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24074,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24074,tc_HOL_Obool)),X24073),X24072)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24074,tc_HOL_Obool)),X24073),X24071)),
    inference(variable_rename,[status(thm)],[fact_Diff__Un]) ).

fof(i_0_7793,plain,
    ! [X22361,X22362,X22363,X22364,X22365,X22366] : c_Product__Type_Oprod_Oprod__rec(X22366,X22365,X22364,X22363,hAPP(hAPP(c_Product__Type_OPair(X22366,X22365),X22362),X22361)) = hAPP(hAPP(X22363,X22362),X22361),
    inference(variable_rename,[status(thm)],[fact_prod_Orecs]) ).

fof(i_0_7794,plain,
    ! [X33264,X33265,X33266,X33267,X33268] : hAPP(c_New__DSequence_Oneg__bind(X33268,X33267,X33266,X33265),X33264) = c_Lazy__Sequence_Ohb__bind(X33268,X33267,hAPP(X33266,X33264),hAPP(hAPP(c_COMBC(X33268,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X33267))),X33265),X33264)),
    inference(variable_rename,[status(thm)],[fact_New__DSequence_Oneg__bind__def]) ).

fof(i_0_7795,plain,
    ! [X26257,X26258,X26259,X26260] :
      ( ~ class_Groups_Ocomm__monoid__add(X26260)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26260),X26259),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X26258)),hAPP(c_Nat_OSuc,X26257))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26260),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X26260,tc_Nat_Onat),X26259),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X26258),X26257)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__shift__bounds__Suc__ivl])]) ).

fof(i_0_7796,plain,
    ! [X25435,X25436,X25437] : 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)),X25437)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X25436,X25435)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25436),X25437),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25435),X25437)),
    inference(variable_rename,[status(thm)],[fact_image__add__atLeastAtMost]) ).

cnf(i_0_7797,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_7798,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_5571]) ).

cnf(i_0_7799,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_7800,plain,
    ! [X27752,X27753,X27754,X27755] :
      ( ( hBOOL(hAPP(hAPP(c_member(X27755),X27754),X27753))
        | ~ hBOOL(hAPP(hAPP(c_member(X27755),X27754),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27755,tc_HOL_Obool)),X27753),hAPP(c_Set_OCollect(X27755),X27752)))) )
      & ( hBOOL(hAPP(X27752,X27754))
        | ~ hBOOL(hAPP(hAPP(c_member(X27755),X27754),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27755,tc_HOL_Obool)),X27753),hAPP(c_Set_OCollect(X27755),X27752)))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X27755),X27754),X27753))
        | ~ hBOOL(hAPP(X27752,X27754))
        | hBOOL(hAPP(hAPP(c_member(X27755),X27754),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27755,tc_HOL_Obool)),X27753),hAPP(c_Set_OCollect(X27755),X27752)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__Collect])])]) ).

fof(i_0_7801,plain,
    ! [X31260,X31261,X31262,X31263] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X31263),X31262),hAPP(c_List_Oset(X31263),X31261)))
      | hBOOL(hAPP(X31260,X31262))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31263)),hAPP(c_List_Ofilter(X31263,X31260),X31261))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31263)),X31261))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5645])]) ).

fof(i_0_7802,plain,
    ! [X25806,X25807,X25808,X25809,X25810] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25810),X25807),X25809))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25810),X25808),X25809))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25810,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X25810,X25809),X25808)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X25810,X25807),X25806)))
        | ~ class_Orderings_Olinorder(X25810) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25810),X25808),X25806))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25810),X25808),X25809))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25810,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X25810,X25809),X25808)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X25810,X25807),X25806)))
        | ~ class_Orderings_Olinorder(X25810) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__subset__iff])])]) ).

fof(i_0_7803,plain,
    ! [X24399,X24400,X24401,X24402,X24403,X24404] :
      ( ~ c_Finite__Set_Ofolding__idem(X24404,X24403,X24402,X24401)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24404),X24400))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24404),X24399))
      | hAPP(X24401,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24404,tc_HOL_Obool)),X24400),X24399)) = hAPP(c_Fun_Ocomp(X24403,X24403,X24403,hAPP(X24401,X24400)),hAPP(X24401,X24399)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__idem_Ounion__idem])]) ).

cnf(i_0_7804,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_7805,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_7806,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_7807,plain,
    ! [X30775,X30776,X30777] :
      ( ~ c_Wellfounded_Owf(X30777,X30776)
      | ~ c_Wellfounded_Owf(X30777,X30775)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X30777,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X30777,X30777),X30776)),hAPP(c_Relation_ORange(X30777,X30777),X30775)) != c_Orderings_Obot__class_Obot(tc_fun(X30777,tc_HOL_Obool))
      | c_Wellfounded_Owf(X30777,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X30777,X30777),tc_HOL_Obool)),X30776),X30775)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__Un])]) ).

fof(i_0_7808,plain,
    ! [X33011,X33012,X33013,X33014,X33015] :
      ( ~ c_Finite__Set_Ofun__left__comm(X33015,X33014,X33013)
      | hAPP(hAPP(c_Finite__Set_Ofold(X33015,X33014,X33013),X33012),hAPP(c_List_Oset(X33015),X33011)) = hAPP(c_List_Ofoldl(X33014,X33015,hAPP(c_COMBC(X33015,X33014,X33014),X33013),X33012),c_List_Oremdups(X33015,X33011)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__set__remdups])]) ).

fof(i_0_7809,plain,
    ! [X33335,X33336,X33337,X33338] : c_Predicate_Oconversep(X33338,X33337,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X33338,tc_fun(X33337,tc_HOL_Obool))),X33336),X33335)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X33337,tc_fun(X33338,tc_HOL_Obool))),c_Predicate_Oconversep(X33338,X33337,X33336)),c_Predicate_Oconversep(X33338,X33337,X33335)),
    inference(variable_rename,[status(thm)],[fact_converse__meet]) ).

fof(i_0_7810,plain,
    ! [X33344,X33345,X33346,X33347] : c_Predicate_Oconversep(X33347,X33346,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X33347,tc_fun(X33346,tc_HOL_Obool))),X33345),X33344)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X33346,tc_fun(X33347,tc_HOL_Obool))),c_Predicate_Oconversep(X33347,X33346,X33345)),c_Predicate_Oconversep(X33347,X33346,X33344)),
    inference(variable_rename,[status(thm)],[fact_converse__join]) ).

fof(i_0_7811,plain,
    ! [X19912,X19913,X19914] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19913),X19914)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19912),X19914)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19913),X19912))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19914),X19912))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19914),X19913)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19913),X19912))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19913),X19914)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19912),X19914)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19914),X19912))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19914),X19913)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__diff__iff])])]) ).

fof(i_0_7812,plain,
    ! [X20009,X20010,X20011] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20010),X20011)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20009),X20011)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20010),X20009))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20011),X20009))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20011),X20010)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20010),X20009))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20010),X20011)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20009),X20011)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20011),X20009))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20011),X20010)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__diff__iff])])]) ).

cnf(i_0_7813,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_7814,plain,
    ! [X18334,X18335,X18336,X18337] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18337),X18336),c_Groups_Ozero__class_Ozero(X18337)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18337),c_Groups_Ozero__class_Ozero(X18337)),X18336))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18337),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18337),X18336),X18335)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18337),X18336),X18334)))
        | ~ class_Rings_Olinordered__ring__strict(X18337) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18337),X18334),X18335))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18337),c_Groups_Ozero__class_Ozero(X18337)),X18336))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18337),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18337),X18336),X18335)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18337),X18336),X18334)))
        | ~ class_Rings_Olinordered__ring__strict(X18337) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18337),X18336),c_Groups_Ozero__class_Ozero(X18337)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18337),X18335),X18334))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18337),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18337),X18336),X18335)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18337),X18336),X18334)))
        | ~ class_Rings_Olinordered__ring__strict(X18337) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18337),X18334),X18335))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18337),X18335),X18334))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18337),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18337),X18336),X18335)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18337),X18336),X18334)))
        | ~ class_Rings_Olinordered__ring__strict(X18337) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18337),c_Groups_Ozero__class_Ozero(X18337)),X18336))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18337),X18335),X18334))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18337),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18337),X18336),X18335)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18337),X18336),X18334)))
        | ~ class_Rings_Olinordered__ring__strict(X18337) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18337),X18336),c_Groups_Ozero__class_Ozero(X18337)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18337),X18334),X18335))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18337),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18337),X18336),X18335)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18337),X18336),X18334)))
        | ~ class_Rings_Olinordered__ring__strict(X18337) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__disj])])]) ).

fof(i_0_7815,plain,
    ! [X18330,X18331,X18332,X18333] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18333),X18331),c_Groups_Ozero__class_Ozero(X18333)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18333),c_Groups_Ozero__class_Ozero(X18333)),X18331))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18333),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18333),X18332),X18331)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18333),X18330),X18331)))
        | ~ class_Rings_Olinordered__ring__strict(X18333) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18333),X18330),X18332))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18333),c_Groups_Ozero__class_Ozero(X18333)),X18331))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18333),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18333),X18332),X18331)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18333),X18330),X18331)))
        | ~ class_Rings_Olinordered__ring__strict(X18333) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18333),X18331),c_Groups_Ozero__class_Ozero(X18333)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18333),X18332),X18330))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18333),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18333),X18332),X18331)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18333),X18330),X18331)))
        | ~ class_Rings_Olinordered__ring__strict(X18333) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18333),X18330),X18332))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18333),X18332),X18330))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18333),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18333),X18332),X18331)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18333),X18330),X18331)))
        | ~ class_Rings_Olinordered__ring__strict(X18333) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18333),c_Groups_Ozero__class_Ozero(X18333)),X18331))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18333),X18332),X18330))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18333),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18333),X18332),X18331)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18333),X18330),X18331)))
        | ~ class_Rings_Olinordered__ring__strict(X18333) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18333),X18331),c_Groups_Ozero__class_Ozero(X18333)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18333),X18330),X18332))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18333),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18333),X18332),X18331)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18333),X18330),X18331)))
        | ~ class_Rings_Olinordered__ring__strict(X18333) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__right__disj])])]) ).

fof(i_0_7816,plain,
    ! [X20839,X20840,X20841,X20842] :
      ( ( hBOOL(hAPP(hAPP(c_member(X20842),X20841),X20839))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20842,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X20842),X20841),X20840)),X20839)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20842,tc_HOL_Obool)),X20840),X20839))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20842,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X20842),X20841),X20840)),X20839)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X20842),X20841),X20839))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20842,tc_HOL_Obool)),X20840),X20839))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20842,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X20842),X20841),X20840)),X20839)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__subset])])]) ).

fof(i_0_7817,plain,
    ! [X26516,X26517,X26518] :
      ( ~ class_Groups_Ocomm__monoid__add(X26518)
      | ~ class_Groups_Ocomm__monoid__mult(X26518)
      | ~ c_Nat__Transfer_Onat__set(X26517)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X26518),X26516),X26517) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26518),hAPP(hAPP(c_COMBB(tc_Int_Oint,X26518,tc_Nat_Onat),X26516),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X26517)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__sum__prod_I1_J])]) ).

fof(i_0_7818,plain,
    ! [X24703,X24704,X24705] :
      ( ~ class_Groups_Ocomm__monoid__add(X24705)
      | ~ class_Groups_Ocomm__monoid__mult(X24705)
      | ~ c_Nat__Transfer_Onat__set(X24704)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X24705),X24703),X24704) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,X24705),hAPP(hAPP(c_COMBB(tc_Int_Oint,X24705,tc_Nat_Onat),X24703),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X24704)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__sum__prod_I2_J])]) ).

fof(i_0_7819,plain,
    ! [X26372,X26373,X26374,X26375,X26376] :
      ( ~ class_Groups_Ocomm__monoid__add(X26376)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26375),X26374))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26375),X26373))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26375,tc_HOL_Obool)),X26374),X26373) != c_Orderings_Obot__class_Obot(tc_fun(X26375,tc_HOL_Obool))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26375,X26376),X26372),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26375,tc_HOL_Obool)),X26374),X26373)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26376),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26375,X26376),X26372),X26374)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26375,X26376),X26372),X26373)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__Un__disjoint])]) ).

fof(i_0_7820,plain,
    ! [X24765,X24766,X24767,X24768,X24769] :
      ( ~ class_Groups_Ocomm__monoid__mult(X24769)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24768),X24767))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24768),X24766))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24768,tc_HOL_Obool)),X24767),X24766) != c_Orderings_Obot__class_Obot(tc_fun(X24768,tc_HOL_Obool))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24768,X24769),X24765),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24768,tc_HOL_Obool)),X24767),X24766)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24769),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24768,X24769),X24765),X24767)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24768,X24769),X24765),X24766)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod_Ounion__disjoint])]) ).

fof(i_0_7821,plain,
    ! [X24760,X24761,X24762,X24763,X24764] :
      ( ~ class_Groups_Ocomm__monoid__mult(X24764)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24763),X24762))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24763),X24761))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24763,tc_HOL_Obool)),X24762),X24761) != c_Orderings_Obot__class_Obot(tc_fun(X24763,tc_HOL_Obool))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24763,X24764),X24760),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24763,tc_HOL_Obool)),X24762),X24761)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24764),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24763,X24764),X24760),X24762)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24763,X24764),X24760),X24761)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__Un__disjoint])]) ).

fof(i_0_7822,plain,
    ! [X26505,X26506,X26507] :
      ( ~ class_Groups_Ocomm__monoid__add(X26507)
      | ~ class_Groups_Ocomm__monoid__mult(X26507)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26507),X26506),X26505) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X26507),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X26507,tc_Int_Oint),X26506),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X26505)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__sum__prod_I1_J])]) ).

fof(i_0_7823,plain,
    ! [X24654,X24655,X24656] :
      ( ~ class_Groups_Ocomm__monoid__add(X24656)
      | ~ class_Groups_Ocomm__monoid__mult(X24656)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,X24656),X24655),X24654) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X24656),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X24656,tc_Int_Oint),X24655),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X24654)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__sum__prod_I2_J])]) ).

cnf(i_0_7824,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_7825,plain,
    ! [X32228,X32229] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X32229),tc_List_Olist(X32229)),tc_HOL_Obool)),c_List_Olistrel(X32229,X32228)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X32229),c_List_Olistrel1(X32229,X32228)))),
    inference(variable_rename,[status(thm)],[fact_listrel__subset__rtrancl__listrel1]) ).

fof(i_0_7826,plain,
    ! [X22121,X22122,X22123,X22124] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22123))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22123))
        | hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22124,X22123),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22122),X22121)))
        | X22124 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22123),X22122)),X22121) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22123),X22121))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22121),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)),X22123))
        | hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22124,X22123),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22122),X22121)))
        | X22124 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22123),X22122)),X22121) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22123))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22121))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22121),X22123))
        | hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22124,X22123),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22122),X22121)))
        | X22124 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22123),X22122)),X22121) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22123),X22121))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22121),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)),X22121))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22121),X22123))
        | hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22124,X22123),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22122),X22121)))
        | X22124 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22123),X22122)),X22121) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5651])])]) ).

fof(i_0_7827,plain,
    ! [X26060,X26061] : 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)),X26061)),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),X26060),X26061))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X26061),X26060),
    inference(variable_rename,[status(thm)],[fact_image__add__int__atLeastLessThan]) ).

fof(i_0_7828,plain,
    ! [X28920,X28921,X28922,X28923] : hAPP(hAPP(c_List_Odrop(X28923),X28922),hAPP(hAPP(c_List_Oappend(X28923),X28921),X28920)) = hAPP(hAPP(c_List_Oappend(X28923),hAPP(hAPP(c_List_Odrop(X28923),X28922),X28921)),hAPP(hAPP(c_List_Odrop(X28923),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X28922),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28923)),X28921))),X28920)),
    inference(variable_rename,[status(thm)],[fact_drop__append]) ).

fof(i_0_7829,plain,
    ! [X28790,X28791,X28792,X28793] : hAPP(hAPP(c_List_Otake(X28793),X28792),hAPP(hAPP(c_List_Oappend(X28793),X28791),X28790)) = hAPP(hAPP(c_List_Oappend(X28793),hAPP(hAPP(c_List_Otake(X28793),X28792),X28791)),hAPP(hAPP(c_List_Otake(X28793),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X28792),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28793)),X28791))),X28790)),
    inference(variable_rename,[status(thm)],[fact_take__append]) ).

fof(i_0_7830,plain,
    ! [X30459,X30460,X30461] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X30461,tc_HOL_Obool)),hAPP(c_List_Oset(X30461),c_List_Oremove1(X30461,X30460,X30459))),hAPP(c_List_Oset(X30461),X30459))),
    inference(variable_rename,[status(thm)],[fact_set__remove1__subset]) ).

fof(i_0_7831,plain,
    ! [X28895,X28896,X28897] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28897,tc_HOL_Obool)),hAPP(c_List_Oset(X28897),c_List_Osublist(X28897,X28896,X28895))),hAPP(c_List_Oset(X28897),X28896))),
    inference(variable_rename,[status(thm)],[fact_set__sublist__subset]) ).

fof(i_0_7832,plain,
    ! [X26050,X26051,X26052,X26053] :
      ( ~ c_Fun_Oinj__on(X26053,X26052,X26051,X26050)
      | c_Fun_Oinj__on(X26052,X26053,c_Fun_Othe__inv__into(X26053,X26052,X26050,X26051),hAPP(c_Set_Oimage(X26053,X26052,X26051),X26050)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__the__inv__into])]) ).

fof(i_0_7833,plain,
    ! [X30953,X30954,X30955] : hAPP(c_Relation_ODomain(X30955,X30954),hAPP(c_Set_OCollect(tc_prod(X30955,X30954)),hAPP(c_Product__Type_Oprod_Oprod__case(X30955,X30954,tc_HOL_Obool),X30953))) = hAPP(c_Set_OCollect(X30955),hAPP(hAPP(c_COMBB(tc_fun(X30954,tc_HOL_Obool),tc_HOL_Obool,X30955),c_HOL_OEx(X30954)),X30953)),
    inference(variable_rename,[status(thm)],[fact_Domain__Collect__split]) ).

cnf(i_0_7834,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_7835,plain,
    ! [X32865,X32866,X32867,X32868,X32869] :
      ( ~ c_Finite__Set_Ofun__left__comm__idem(X32869,X32868,X32867)
      | hAPP(hAPP(c_Finite__Set_Ofold(X32869,X32868,X32867),X32866),hAPP(c_List_Oset(X32869),X32865)) = hAPP(c_List_Ofoldl(X32868,X32869,hAPP(c_COMBC(X32869,X32868,X32868),X32867),X32866),X32865) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofold__set])]) ).

fof(i_0_7836,plain,
    ! [X26508,X26509,X26510,X26511] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X26511),X26510),X26509))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26511,tc_Nat_Onat),X26508),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26511,tc_HOL_Obool)),X26509),hAPP(hAPP(c_Set_Oinsert(X26511),X26510),c_Orderings_Obot__class_Obot(tc_fun(X26511,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26511,tc_Nat_Onat),X26508),X26509)),hAPP(X26508,X26510)) )
      & ( hBOOL(hAPP(hAPP(c_member(X26511),X26510),X26509))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26511,tc_Nat_Onat),X26508),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26511,tc_HOL_Obool)),X26509),hAPP(hAPP(c_Set_Oinsert(X26511),X26510),c_Orderings_Obot__class_Obot(tc_fun(X26511,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26511,tc_Nat_Onat),X26508),X26509) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5653])]) ).

fof(i_0_7837,plain,
    ! [X26178,X26179,X26180,X26181] :
      ( ~ class_Groups_Oab__group__add(X26181)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26180,X26181),hAPP(hAPP(c_COMBB(X26181,X26181,X26180),c_Groups_Ouminus__class_Ouminus(X26181)),X26179)),X26178) = hAPP(c_Groups_Ouminus__class_Ouminus(X26181),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26180,X26181),X26179),X26178)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__negf])]) ).

fof(i_0_7838,plain,
    ! [X24628,X24629,X24630,X24631] :
      ( ~ class_Fields_Olinordered__field(X24631)
      | hAPP(c_Groups_Oabs__class_Oabs(X24631),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24630,X24631),X24629),X24628)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24630,X24631),hAPP(hAPP(c_COMBB(X24631,X24631,X24630),c_Groups_Oabs__class_Oabs(X24631)),X24629)),X24628) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__setprod])]) ).

fof(i_0_7839,plain,
    ! [X28900,X28901,X28902,X28904,X28905,X28906,X28907,X28909] :
      ( ( hBOOL(hAPP(hAPP(c_member(X28902),esk323_3(X28900,X28901,X28902)),hAPP(c_List_Oset(X28902),X28901)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X28904),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28902)),X28901)))
        | hBOOL(hAPP(X28900,hAPP(hAPP(c_List_Onth(X28902),X28901),X28904))) )
      & ( ~ hBOOL(hAPP(X28900,esk323_3(X28900,X28901,X28902)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X28904),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28902)),X28901)))
        | hBOOL(hAPP(X28900,hAPP(hAPP(c_List_Onth(X28902),X28901),X28904))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk324_3(X28905,X28906,X28907)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28907)),X28906)))
        | ~ hBOOL(hAPP(hAPP(c_member(X28907),X28909),hAPP(c_List_Oset(X28907),X28906)))
        | hBOOL(hAPP(X28905,X28909)) )
      & ( ~ hBOOL(hAPP(X28905,hAPP(hAPP(c_List_Onth(X28907),X28906),esk324_3(X28905,X28906,X28907))))
        | ~ hBOOL(hAPP(hAPP(c_member(X28907),X28909),hAPP(c_List_Oset(X28907),X28906)))
        | hBOOL(hAPP(X28905,X28909)) ) ),
    inference(distribute,[status(thm)],[inference(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_7840,plain,
    ! [X19090,X19091,X19092,X19093] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19093,tc_HOL_Obool)),X19092),X19091))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19093,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X19093),X19090),X19092)),hAPP(hAPP(c_Set_Oinsert(X19093),X19090),X19091))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__mono])]) ).

cnf(i_0_7841,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_5605]) ).

cnf(i_0_7842,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_5606]) ).

cnf(i_0_7843,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_7844,plain,
    ! [X31555,X31556,X31557,X31558,X31559] :
      ( ( c_List_Olinorder__class_Osorted(X31557,X31556)
        | ~ c_List_Olinorder__class_Osorted(X31557,hAPP(hAPP(c_List_Oappend(X31557),X31556),X31555))
        | ~ class_Orderings_Olinorder(X31557) )
      & ( c_List_Olinorder__class_Osorted(X31557,X31555)
        | ~ c_List_Olinorder__class_Osorted(X31557,hAPP(hAPP(c_List_Oappend(X31557),X31556),X31555))
        | ~ class_Orderings_Olinorder(X31557) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X31557),X31558),hAPP(c_List_Oset(X31557),X31556)))
        | ~ hBOOL(hAPP(hAPP(c_member(X31557),X31559),hAPP(c_List_Oset(X31557),X31555)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31557),X31558),X31559))
        | ~ c_List_Olinorder__class_Osorted(X31557,hAPP(hAPP(c_List_Oappend(X31557),X31556),X31555))
        | ~ class_Orderings_Olinorder(X31557) )
      & ( hBOOL(hAPP(hAPP(c_member(X31557),esk392_3(X31555,X31556,X31557)),hAPP(c_List_Oset(X31557),X31556)))
        | ~ c_List_Olinorder__class_Osorted(X31557,X31556)
        | ~ c_List_Olinorder__class_Osorted(X31557,X31555)
        | c_List_Olinorder__class_Osorted(X31557,hAPP(hAPP(c_List_Oappend(X31557),X31556),X31555))
        | ~ class_Orderings_Olinorder(X31557) )
      & ( hBOOL(hAPP(hAPP(c_member(X31557),esk393_3(X31555,X31556,X31557)),hAPP(c_List_Oset(X31557),X31555)))
        | ~ c_List_Olinorder__class_Osorted(X31557,X31556)
        | ~ c_List_Olinorder__class_Osorted(X31557,X31555)
        | c_List_Olinorder__class_Osorted(X31557,hAPP(hAPP(c_List_Oappend(X31557),X31556),X31555))
        | ~ class_Orderings_Olinorder(X31557) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31557),esk392_3(X31555,X31556,X31557)),esk393_3(X31555,X31556,X31557)))
        | ~ c_List_Olinorder__class_Osorted(X31557,X31556)
        | ~ c_List_Olinorder__class_Osorted(X31557,X31555)
        | c_List_Olinorder__class_Osorted(X31557,hAPP(hAPP(c_List_Oappend(X31557),X31556),X31555))
        | ~ class_Orderings_Olinorder(X31557) ) ),
    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_7845,plain,
    ! [X20596,X20597,X20598] :
      ( ~ class_Rings_Olinordered__semidom(X20598)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20598),c_Groups_Oone__class_Oone(X20598)),X20597))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20598),hAPP(hAPP(c_Power_Opower__class_Opower(X20598),X20597),X20596)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20598),X20597),hAPP(hAPP(c_Power_Opower__class_Opower(X20598),X20597),X20596)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__less__power__Suc])]) ).

fof(i_0_7846,plain,
    ! [X20254,X20255,X20256,X20257] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20257,tc_HOL_Obool)),X20256),X20255))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20257,tc_HOL_Obool)),X20255),X20254))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20257,tc_HOL_Obool)),X20255),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20257,tc_HOL_Obool)),X20254),X20256)) = X20256 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__diff])]) ).

fof(i_0_7847,plain,
    ! [X25440,X25441,X25442] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25442,tc_HOL_Obool)),X25441),X25440))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X25442,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X25442),X25441)),hAPP(c_Set_OPow(X25442),X25440))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pow__mono])]) ).

fof(i_0_7848,plain,
    ! [X21706,X21707,X21708,X21709,X21710,X21711] : hAPP(hAPP(c_Fun_Ocomp(X21711,X21710,X21709,hAPP(c_COMBK(X21710,X21711),X21708)),X21707),X21706) = X21708,
    inference(variable_rename,[status(thm)],[fact_K__record__comp]) ).

fof(i_0_7849,plain,
    ! [X17073,X17074,X17075,X17076,X17077] :
      ( ( ~ c_Hoare__Mirabelle_Otriple__valid(X17077,X17076,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17077),X17075),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X17074))),X17073))
        | c_Hoare__Mirabelle_Otriple__valid(X17077,hAPP(c_Nat_OSuc,X17076),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17077),X17075),hAPP(c_Com_Ocom_OBODY,X17074)),X17073)) )
      & ( ~ c_Hoare__Mirabelle_Otriple__valid(X17077,hAPP(c_Nat_OSuc,X17076),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17077),X17075),hAPP(c_Com_Ocom_OBODY,X17074)),X17073))
        | c_Hoare__Mirabelle_Otriple__valid(X17077,X17076,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17077),X17075),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X17074))),X17073)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Body__triple__valid__Suc])]) ).

fof(i_0_7850,plain,
    ! [X28877,X28878,X28879] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28879,tc_HOL_Obool)),hAPP(c_List_Oset(X28879),hAPP(hAPP(c_List_Odrop(X28879),X28878),X28877))),hAPP(c_List_Oset(X28879),X28877))),
    inference(variable_rename,[status(thm)],[fact_set__drop__subset]) ).

fof(i_0_7851,plain,
    ! [X28813,X28814,X28815] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28815,tc_HOL_Obool)),hAPP(c_List_Oset(X28815),hAPP(hAPP(c_List_Otake(X28815),X28814),X28813))),hAPP(c_List_Oset(X28815),X28813))),
    inference(variable_rename,[status(thm)],[fact_set__take__subset]) ).

fof(i_0_7852,plain,
    ! [X21564,X21565,X21566,X21567] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21567),X21565),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21567),X21564),X21566)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21567),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21567),X21565),X21566)),X21564))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21567),c_Groups_Ozero__class_Ozero(X21567)),X21566))
        | ~ class_Fields_Olinordered__field(X21567) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21567),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21567),X21565),X21566)),X21564))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21567),X21565),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21567),X21564),X21566)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21567),c_Groups_Ozero__class_Ozero(X21567)),X21566))
        | ~ class_Fields_Olinordered__field(X21567) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__le__divide__eq])])]) ).

fof(i_0_7853,plain,
    ! [X21560,X21561,X21562,X21563] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21563),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21563),X21561),X21562)),X21560))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21563),X21561),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21563),X21560),X21562)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21563),c_Groups_Ozero__class_Ozero(X21563)),X21562))
        | ~ class_Fields_Olinordered__field(X21563) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21563),X21561),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21563),X21560),X21562)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21563),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21563),X21561),X21562)),X21560))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21563),c_Groups_Ozero__class_Ozero(X21563)),X21562))
        | ~ class_Fields_Olinordered__field(X21563) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__divide__le__eq])])]) ).

fof(i_0_7854,plain,
    ! [X21552,X21553,X21554,X21555] :
      ( ~ class_Fields_Olinordered__field(X21555)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21555),c_Groups_Ozero__class_Ozero(X21555)),X21554))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21555),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21555),X21553),X21554)),X21552))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21555),X21553),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21555),X21552),X21554))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__imp__le__div__pos])]) ).

fof(i_0_7855,plain,
    ! [X21456,X21457,X21458,X21459] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21459),X21457),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21459),X21456),X21458)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21459),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21459),X21457),X21458)),X21456))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21459),c_Groups_Ozero__class_Ozero(X21459)),X21458))
        | ~ class_Fields_Olinordered__field(X21459) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21459),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21459),X21457),X21458)),X21456))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21459),X21457),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21459),X21456),X21458)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21459),c_Groups_Ozero__class_Ozero(X21459)),X21458))
        | ~ class_Fields_Olinordered__field(X21459) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__less__divide__eq])])]) ).

fof(i_0_7856,plain,
    ! [X21452,X21453,X21454,X21455] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21455),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21455),X21453),X21454)),X21452))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21455),X21453),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21455),X21452),X21454)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21455),c_Groups_Ozero__class_Ozero(X21455)),X21454))
        | ~ class_Fields_Olinordered__field(X21455) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21455),X21453),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21455),X21452),X21454)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21455),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21455),X21453),X21454)),X21452))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21455),c_Groups_Ozero__class_Ozero(X21455)),X21454))
        | ~ class_Fields_Olinordered__field(X21455) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__divide__less__eq])])]) ).

fof(i_0_7857,plain,
    ! [X21444,X21445,X21446,X21447] :
      ( ~ class_Fields_Olinordered__field(X21447)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21447),c_Groups_Ozero__class_Ozero(X21447)),X21446))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21447),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21447),X21445),X21446)),X21444))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21447),X21445),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21447),X21444),X21446))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__imp__less__div__pos])]) ).

fof(i_0_7858,plain,
    ! [X31774,X31775,X31776,X31777] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31777),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31776)),c_List_OtakeWhile(X31776,X31775,X31774))))
      | hAPP(hAPP(c_List_Onth(X31776),c_List_OtakeWhile(X31776,X31775,X31774)),X31777) = hAPP(hAPP(c_List_Onth(X31776),X31774),X31777) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_takeWhile__nth])]) ).

fof(i_0_7859,plain,
    ! [X24635,X24636,X24637,X24638] :
      ( ~ class_Groups_Ocomm__monoid__mult(X24638)
      | ~ class_Rings_Oring__1(X24638)
      | hAPP(c_Int_Oring__1__class_Oof__int(X24638),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24637,tc_Int_Oint),X24636),X24635)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24637,X24638),hAPP(hAPP(c_COMBB(tc_Int_Oint,X24638,X24637),c_Int_Oring__1__class_Oof__int(X24638)),X24636)),X24635) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__setprod])]) ).

fof(i_0_7860,plain,
    ! [X24642,X24643,X24644,X24645] :
      ( ~ class_Groups_Ocomm__monoid__mult(X24645)
      | ~ class_Rings_Osemiring__1(X24645)
      | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X24645),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24644,tc_Nat_Onat),X24643),X24642)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24644,X24645),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X24645,X24644),c_Nat_Osemiring__1__class_Oof__nat(X24645)),X24643)),X24642) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__setprod])]) ).

cnf(i_0_7861,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_5582]) ).

cnf(i_0_7862,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_7863,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_7864,plain,
    ! [X32472,X32473,X32474,X32475] : hAPP(c_Relation_Oconverse(X32475,X32474),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X32475,X32474),tc_HOL_Obool)),X32473),X32472)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X32474,X32475),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X32475,X32474),X32473)),hAPP(c_Relation_Oconverse(X32475,X32474),X32472)),
    inference(variable_rename,[status(thm)],[fact_converse__Int]) ).

fof(i_0_7865,plain,
    ! [X32455,X32456,X32457,X32458] : hAPP(c_Relation_Oconverse(X32458,X32457),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X32458,X32457),tc_HOL_Obool)),X32456),X32455)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X32457,X32458),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X32458,X32457),X32456)),hAPP(c_Relation_Oconverse(X32458,X32457),X32455)),
    inference(variable_rename,[status(thm)],[fact_converse__Un]) ).

fof(i_0_7866,plain,
    ! [X31762,X31763,X31764] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31764)),c_List_OtakeWhile(X31764,X31763,X31762))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31764)),X31762))),
    inference(variable_rename,[status(thm)],[fact_length__takeWhile__le]) ).

fof(i_0_7867,plain,
    ! [X18119,X18120,X18121,X18122] : hAPP(hAPP(c_Nat_Ocompow(X18122,X18122),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18121),X18120)),X18119) = hAPP(c_Fun_Ocomp(X18122,X18122,X18122,hAPP(hAPP(c_Nat_Ocompow(X18122,X18122),X18121),X18119)),hAPP(hAPP(c_Nat_Ocompow(X18122,X18122),X18120),X18119)),
    inference(variable_rename,[status(thm)],[fact_funpow__add]) ).

fof(i_0_7868,plain,
    ! [X26192,X26193,X26194,X26195] :
      ( ~ class_Rings_Oring__1(X26195)
      | hAPP(c_Int_Oring__1__class_Oof__int(X26195),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26194,tc_Int_Oint),X26193),X26192)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26194,X26195),hAPP(hAPP(c_COMBB(tc_Int_Oint,X26195,X26194),c_Int_Oring__1__class_Oof__int(X26195)),X26193)),X26192) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__setsum])]) ).

fof(i_0_7869,plain,
    ! [X26188,X26189,X26190,X26191] :
      ( ~ class_Rings_Osemiring__1(X26191)
      | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X26191),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26190,tc_Nat_Onat),X26189),X26188)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26190,X26191),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X26191,X26190),c_Nat_Osemiring__1__class_Oof__nat(X26191)),X26189)),X26188) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__setsum])]) ).

fof(i_0_7870,plain,
    ! [X26827] : c_Fun_Oinj__on(X26827,tc_fun(X26827,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X26827,tc_fun(X26827,tc_HOL_Obool),tc_fun(X26827,tc_HOL_Obool)),c_Set_Oinsert(X26827)),c_Orderings_Obot__class_Obot(tc_fun(X26827,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X26827,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_inj__singleton]) ).

fof(i_0_7871,plain,
    ! [X27314,X27315,X27316,X27317] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27317),X27316))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27315),X27314))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X27317,X27315)),hAPP(hAPP(c_Product__Type_OSigma(X27317,X27315),X27316),hAPP(c_COMBK(tc_fun(X27315,tc_HOL_Obool),X27317),X27314)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__cartesian__product])]) ).

fof(i_0_7872,plain,
    ! [X24572,X24573,X24574] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24574),X24573))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24574,tc_HOL_Obool)),X24572),X24573))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X24574),X24572)),hAPP(c_Finite__Set_Ocard(X24574),X24573)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X24574,tc_HOL_Obool)),X24572),X24573)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__psubset])]) ).

fof(i_0_7873,plain,
    ! [X23561,X23562,X23563,X23564,X23565] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23565),X23564))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23563,tc_HOL_Obool)),X23562),hAPP(c_Set_Oimage(X23565,X23563,X23561),X23564)))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X23563),X23562)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__surj])]) ).

cnf(i_0_7874,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_7875,plain,
    ! [X34178] : c_Fun_Obij__betw(X34178,X34178,c_Fun_Oid(X34178),c_Orderings_Otop__class_Otop(tc_fun(X34178,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X34178,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_bij__id]) ).

fof(i_0_7876,plain,
    ! [X25667,X25668,X25669,X25670,X25671] :
      ( ~ c_Fun_Oinj__on(X25671,X25670,X25669,X25668)
      | ~ c_Fun_Oinj__on(X25671,X25670,X25669,X25667)
      | c_Fun_Oinj__on(X25671,X25670,X25669,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25671,tc_HOL_Obool)),X25668),X25667)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__Int])]) ).

fof(i_0_7877,plain,
    ! [X28966,X28967,X28968,X28969] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X28969),X28968)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28967)),X28966)))
      | hAPP(hAPP(c_List_Onth(X28967),hAPP(hAPP(c_List_Odrop(X28967),X28969),X28966)),X28968) = hAPP(hAPP(c_List_Onth(X28967),X28966),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X28969),X28968)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__drop])]) ).

fof(i_0_7878,plain,
    ! [X26400,X26401,X26402,X26403] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X26402)),X26401))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26403),X26400),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X26401,hAPP(c_Nat_OSuc,X26402))) = c_Groups_Ozero__class_Ozero(X26403)
        | ~ class_Groups_Ocomm__monoid__add(X26403) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X26402)),X26401))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26403),X26400),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X26401,hAPP(c_Nat_OSuc,X26402))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26403),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26403),X26400),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X26401,X26402))),hAPP(X26400,hAPP(c_Nat_OSuc,X26402)))
        | ~ class_Groups_Ocomm__monoid__add(X26403) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5658])])]) ).

fof(i_0_7879,plain,
    ! [X31701,X31702,X31703,X31704] :
      ( ~ class_Orderings_Olinorder(X31704)
      | ~ c_List_Olinorder__class_Osorted(X31704,hAPP(c_List_Orev(X31704),X31703))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31702),X31701))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31701),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31704)),X31703)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31704),hAPP(hAPP(c_List_Onth(X31704),X31703),X31701)),hAPP(hAPP(c_List_Onth(X31704),X31703),X31702))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__rev__nth__mono])]) ).

fof(i_0_7880,plain,
    ! [X29086,X29087,X29088,X29089,X29090,X29091] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29091)),X29090) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29089)),X29088)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29091)),X29087) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29089)),X29086)
      | hAPP(hAPP(c_List_Ozip(X29091,X29089),hAPP(hAPP(c_List_Oappend(X29091),X29090),X29087)),hAPP(hAPP(c_List_Oappend(X29089),X29088),X29086)) = hAPP(hAPP(c_List_Oappend(tc_prod(X29091,X29089)),hAPP(hAPP(c_List_Ozip(X29091,X29089),X29090),X29088)),hAPP(hAPP(c_List_Ozip(X29091,X29089),X29087),X29086)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zip__append])]) ).

fof(i_0_7881,plain,
    ! [X30187,X30188,X30189,X30190,X30191] : c_List_Olist_Olist__size(X30191,X30190,hAPP(hAPP(c_List_Omap(X30189,X30191),X30188),X30187)) = c_List_Olist_Olist__size(X30189,hAPP(c_Fun_Ocomp(X30191,tc_Nat_Onat,X30189,X30190),X30188),X30187),
    inference(variable_rename,[status(thm)],[fact_list__size__map]) ).

fof(i_0_7882,plain,
    ! [X27626,X27627,X27628,X27629] :
      ( ~ c_Relation_Orefl__on(X27629,X27628,X27627)
      | ~ hBOOL(hAPP(hAPP(c_member(X27629),X27626),X27628))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X27629,X27629)),hAPP(hAPP(c_Product__Type_OPair(X27629,X27629),X27626),X27626)),X27627)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__onD])]) ).

fof(i_0_7883,plain,
    ! [X25181,X25182,X25183,X25184,X25185] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X25185),X25184),X25183))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25182,tc_HOL_Obool)),hAPP(X25181,X25184)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25185,tc_fun(X25182,tc_HOL_Obool)),X25183),X25181))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__upper])]) ).

fof(i_0_7884,plain,
    ! [X28801,X28802,X28803,X28804] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X28804) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Otake(X28803),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X28804)),hAPP(hAPP(c_List_Olist_OCons(X28803),X28802),X28801)) = c_List_Olist_ONil(X28803) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X28804) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Otake(X28803),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X28804)),hAPP(hAPP(c_List_Olist_OCons(X28803),X28802),X28801)) = hAPP(hAPP(c_List_Olist_OCons(X28803),X28802),hAPP(hAPP(c_List_Otake(X28803),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X28804)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X28801)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__Cons__number__of])]) ).

fof(i_0_7885,plain,
    ! [X17943,X17944,X17945,X17947,X17948,X17949,X17950] :
      ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17944),X17943),esk34_3(X17943,X17944,X17945)))
        | ~ hBOOL(hAPP(X17945,X17943))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X17945,X17944)),X17943),X17943)) )
      & ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X17945,X17944)),esk34_3(X17943,X17944,X17945)),X17943))
        | ~ hBOOL(hAPP(X17945,X17943))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X17945,X17944)),X17943),X17943)) )
      & ( hBOOL(hAPP(X17949,X17947))
        | hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X17949,X17948)),X17947),X17947)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17948),X17947),X17950))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X17949,X17948)),X17950),X17947))
        | hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X17949,X17948)),X17947),X17947)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evalc_Oequations_I7_J])])])])])]) ).

fof(i_0_7886,plain,
    ! [X22291,X22292,X22293,X22294,X22295,X22296] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22296,tc_fun(X22295,tc_HOL_Obool))),X22294),X22293))
      | ~ hBOOL(hAPP(hAPP(X22294,X22292),X22291))
      | hBOOL(hAPP(hAPP(X22293,X22292),X22291)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_predicate2D])]) ).

fof(i_0_7887,plain,
    ! [X22297,X22298,X22299,X22300,X22301,X22302] :
      ( ~ hBOOL(hAPP(hAPP(X22302,X22301),X22300))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22299,tc_fun(X22298,tc_HOL_Obool))),X22302),X22297))
      | hBOOL(hAPP(hAPP(X22297,X22301),X22300)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__predicate2D])]) ).

fof(i_0_7888,plain,
    ! [X26997,X26998,X26999] :
      ( ~ class_Orderings_Olinorder(X26999)
      | X26998 = c_Orderings_Obot__class_Obot(tc_fun(X26999,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26999,tc_HOL_Obool)),X26998),X26997))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26999),X26997))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26999),hAPP(c_Finite__Set_Ofold1(X26999,c_Orderings_Oord__class_Omin(X26999)),X26997)),hAPP(c_Finite__Set_Ofold1(X26999,c_Orderings_Oord__class_Omin(X26999)),X26998))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1__antimono])]) ).

fof(i_0_7889,plain,
    ! [X23042,X23043,X23044,X23045] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X23045),X23044),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23045,tc_HOL_Obool)),X23043),X23042)))
        | hBOOL(hAPP(hAPP(c_member(X23045),X23044),X23043))
        | hBOOL(hAPP(hAPP(c_member(X23045),X23044),X23042)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X23045),X23044),X23043))
        | hBOOL(hAPP(hAPP(c_member(X23045),X23044),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23045,tc_HOL_Obool)),X23043),X23042))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X23045),X23044),X23042))
        | hBOOL(hAPP(hAPP(c_member(X23045),X23044),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23045,tc_HOL_Obool)),X23043),X23042))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Un__iff])])]) ).

fof(i_0_7890,plain,
    ! [X22809,X22810,X22811,X22812] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X22812),X22811),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22812,tc_HOL_Obool)),X22810),X22809)))
      | hBOOL(hAPP(hAPP(c_member(X22812),X22811),X22810))
      | hBOOL(hAPP(hAPP(c_member(X22812),X22811),X22809)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5659])]) ).

cnf(i_0_7891,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_7892,plain,
    ! [X20196,X20197,X20198] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20198),c_Groups_Ozero__class_Ozero(X20198)),esk69_3(X20196,X20197,X20198)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20198),X20197),X20196))
        | ~ class_Fields_Olinordered__field(X20198) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20198),X20197),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20198),X20196),esk69_3(X20196,X20197,X20198))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20198),X20197),X20196))
        | ~ class_Fields_Olinordered__field(X20198) ) ),
    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_7893,plain,
    ! [X29441,X29442,X29443,X29444,X29445,X29446] : hAPP(c_List_Ofoldl(X29446,X29445,X29444,X29443),hAPP(hAPP(c_List_Olist_OCons(X29445),X29442),X29441)) = hAPP(c_List_Ofoldl(X29446,X29445,X29444,hAPP(hAPP(X29444,X29443),X29442)),X29441),
    inference(variable_rename,[status(thm)],[fact_foldl__Cons]) ).

fof(i_0_7894,plain,
    ! [X31708,X31709] :
      ( ( X31708 != c_List_Olist_ONil(tc_List_Olist(X31709))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31709))),c_List_Otranspose(X31709,X31708)) = 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(X31709),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X31709))),X31708))) )
      & ( X31708 = c_List_Olist_ONil(tc_List_Olist(X31709))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31709))),c_List_Otranspose(X31709,X31708)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31709)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X31709)),X31708),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(X31709),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X31709))),X31708))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_length__transpose__sorted])])]) ).

fof(i_0_7895,plain,
    ! [X20454,X20455,X20456,X20457] :
      ( ~ class_Rings_Olinordered__semidom(X20457)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20457),X20456),X20455))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20457),c_Groups_Ozero__class_Ozero(X20457)),X20456))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20454))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20457),hAPP(hAPP(c_Power_Opower__class_Opower(X20457),X20456),X20454)),hAPP(hAPP(c_Power_Opower__class_Opower(X20457),X20455),X20454))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__strict__mono])]) ).

fof(i_0_7896,plain,
    ! [X20469,X20470,X20471,X20472] :
      ( ~ class_Rings_Olinordered__semidom(X20472)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20471),X20470))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20472),c_Groups_Ozero__class_Ozero(X20472)),X20469))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20472),X20469),c_Groups_Oone__class_Oone(X20472)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20472),hAPP(hAPP(c_Power_Opower__class_Opower(X20472),X20469),X20470)),hAPP(hAPP(c_Power_Opower__class_Opower(X20472),X20469),X20471))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__decreasing])]) ).

fof(i_0_7897,plain,
    ! [X20473,X20474,X20475,X20476] :
      ( ~ class_Rings_Olinordered__semidom(X20476)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20475),X20474))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20476),c_Groups_Ozero__class_Ozero(X20476)),X20473))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20476),X20473),c_Groups_Oone__class_Oone(X20476)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20476),hAPP(hAPP(c_Power_Opower__class_Opower(X20476),X20473),X20474)),hAPP(hAPP(c_Power_Opower__class_Opower(X20476),X20473),X20475))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__strict__decreasing])]) ).

fof(i_0_7898,plain,
    ! [X27113,X27114,X27115,X27116,X27117] : hAPP(c_Set_Ovimage(X27117,X27116,X27115),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27116,tc_HOL_Obool)),X27114),X27113)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27117,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X27117,X27116,X27115),X27114)),hAPP(c_Set_Ovimage(X27117,X27116,X27115),X27113)),
    inference(variable_rename,[status(thm)],[fact_vimage__Int]) ).

fof(i_0_7899,plain,
    ! [X27118,X27119,X27120,X27121,X27122] : hAPP(c_Set_Ovimage(X27122,X27121,X27120),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27121,tc_HOL_Obool)),X27119),X27118)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27122,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X27122,X27121,X27120),X27119)),hAPP(c_Set_Ovimage(X27122,X27121,X27120),X27118)),
    inference(variable_rename,[status(thm)],[fact_vimage__Un]) ).

fof(i_0_7900,plain,
    ! [X27148,X27149,X27150,X27151,X27152] : hAPP(c_Set_Ovimage(X27152,X27151,X27150),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27151,tc_HOL_Obool)),X27149),X27148)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27152,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X27152,X27151,X27150),X27149)),hAPP(c_Set_Ovimage(X27152,X27151,X27150),X27148)),
    inference(variable_rename,[status(thm)],[fact_vimage__Diff]) ).

fof(i_0_7901,plain,
    ! [X23163,X23164,X23165,X23166,X23167] : hAPP(c_Relation_OImage(X23167,X23166,X23165),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23167,tc_HOL_Obool)),X23164),X23163)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23166,tc_HOL_Obool)),hAPP(c_Relation_OImage(X23167,X23166,X23165),X23164)),hAPP(c_Relation_OImage(X23167,X23166,X23165),X23163)),
    inference(variable_rename,[status(thm)],[fact_Image__Un]) ).

fof(i_0_7902,plain,
    ! [X23158,X23159,X23160,X23161,X23162] : hAPP(c_Set_Oimage(X23162,X23161,X23160),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23162,tc_HOL_Obool)),X23159),X23158)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23161,tc_HOL_Obool)),hAPP(c_Set_Oimage(X23162,X23161,X23160),X23159)),hAPP(c_Set_Oimage(X23162,X23161,X23160),X23158)),
    inference(variable_rename,[status(thm)],[fact_image__Un]) ).

fof(i_0_7903,plain,
    ! [X28652,X28653,X28654,X28655] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X28655)),X28654),c_List_Olists(X28655,X28652)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X28655)),hAPP(hAPP(c_List_Oappend(X28655),X28654),X28653)),c_List_Olists(X28655,X28652))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X28655)),X28653),c_List_Olists(X28655,X28652)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X28655)),hAPP(hAPP(c_List_Oappend(X28655),X28654),X28653)),c_List_Olists(X28655,X28652))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X28655)),X28654),c_List_Olists(X28655,X28652)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X28655)),X28653),c_List_Olists(X28655,X28652)))
        | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X28655)),hAPP(hAPP(c_List_Oappend(X28655),X28654),X28653)),c_List_Olists(X28655,X28652))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__in__lists__conv])])]) ).

cnf(i_0_7904,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_7905,plain,
    ! [X25573,X25574,X25575] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25575,tc_HOL_Obool)),X25574),X25573))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X25575,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(X25575,X25574)),c_Predicate_OPowp(X25575,X25573))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Powp__mono])]) ).

fof(i_0_7906,plain,
    ! [X30728,X30729,X30730,X30731] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X30731),X30730))
      | ~ hBOOL(hAPP(c_List_Odistinct(X30729),X30728))
      | hBOOL(hAPP(c_List_Odistinct(tc_prod(X30731,X30729)),c_Enum_Oproduct(X30731,X30729,X30730,X30728))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__product])]) ).

fof(i_0_7907,plain,
    ! [X24695,X24696,X24697,X24698] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24698),X24697))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24696),X24695))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X24698,X24696)),c_Sum__Type_OPlus(X24698,X24696,X24697,X24695))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Plus])]) ).

cnf(i_0_7908,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_7909,plain,
    ! [X23663,X23664,X23665,X23666,X23667,X23668] :
      ( ~ c_Finite__Set_Ofolding(X23668,X23667,X23666,X23665)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23668),X23664))
      | hBOOL(hAPP(hAPP(c_member(X23668),X23663),X23664))
      | hAPP(X23665,hAPP(hAPP(c_Set_Oinsert(X23668),X23663),X23664)) = hAPP(c_Fun_Ocomp(X23667,X23667,X23667,hAPP(X23665,X23664)),hAPP(X23666,X23663)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5662])]) ).

fof(i_0_7910,plain,
    ! [X25343,X25344,X25345,X25346] :
      ( X25346 != X25345
      | ~ hBOOL(hAPP(hAPP(c_member(X25344),X25346),X25343))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X25344,X25344)),hAPP(hAPP(c_Product__Type_OPair(X25344,X25344),X25346),X25345)),c_Relation_OId__on(X25344,X25343))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Id__on__eqI])]) ).

fof(i_0_7911,plain,
    ! [X27248,X27249] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X27249),c_Int_OInteg))
      | ~ hBOOL(hAPP(X27248,hAPP(c_Int_ORep__Integ,esk274_2(X27248,X27249))))
      | hBOOL(hAPP(X27248,X27249)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Rep__Integ__induct])])]) ).

fof(i_0_7912,plain,
    ! [X29124,X29125,X29126,X29127,X29128] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29128),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29127)),X29126)))
      | hAPP(hAPP(c_List_Olist__update(X29127,hAPP(hAPP(c_List_Oappend(X29127),X29126),X29125)),X29128),X29124) = hAPP(hAPP(c_List_Oappend(X29127),hAPP(hAPP(c_List_Olist__update(X29127,X29126),X29128),X29124)),X29125) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__update__append1])]) ).

fof(i_0_7913,plain,
    ! [X19258,X19259,X19260] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19260),X19259)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19258),X19259)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19259))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19260),X19258)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19259))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19260),X19259)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19258),X19259))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19260),X19258))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19260),X19259)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19258),X19259))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__cancel2])])]) ).

fof(i_0_7914,plain,
    ! [X19255,X19256,X19257] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19257),X19256)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19257),X19255)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19257))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19256),X19255)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19257))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19257),X19256)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19257),X19255))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19256),X19255))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19257),X19256)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19257),X19255))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__cancel1])])]) ).

fof(i_0_7915,plain,
    ! [X19225,X19226,X19227] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19227),X19226)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19227),X19225)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19226),X19225))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19227)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19226),X19225))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19227),X19226)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19227),X19225)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19227)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__le__cancel1])])]) ).

fof(i_0_7916,plain,
    ! [X20496,X20497,X20498] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20498))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X20498),X20497)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X20498),X20496)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20497),X20496)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__power__less__imp__less])]) ).

fof(i_0_7917,plain,
    ! [X19065,X19066,X19067] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19067),X19066)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19067),X19065)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19066),X19065))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19067)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19066),X19065))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19067),X19066)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19067),X19065)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19067)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__less__cancel1])])]) ).

fof(i_0_7918,plain,
    ! [X28228,X28229,X28230] :
      ( ~ c_Wellfounded_Owf(X28230,X28229)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28230,tc_HOL_Obool)),X28228),hAPP(c_Relation_OImage(X28230,X28230,X28229),X28228)))
      | X28228 = c_Orderings_Obot__class_Obot(tc_fun(X28230,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wfE__pf])]) ).

fof(i_0_7919,plain,
    ! [X26479,X26480,X26481] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26481,tc_Nat_Onat),X26480),X26479)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26481,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X26481),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X26480)),X26479),
    inference(variable_rename,[status(thm)],[fact_int__setsum]) ).

fof(i_0_7920,plain,
    ! [X24639,X24640,X24641] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24641,tc_Nat_Onat),X24640),X24639)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24641,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X24641),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X24640)),X24639),
    inference(variable_rename,[status(thm)],[fact_int__setprod]) ).

fof(i_0_7921,plain,
    ! [X32957,X32958,X32959,X32960,X32961] :
      ( ~ c_Finite__Set_Ofun__left__comm(X32961,X32960,X32959)
      | hAPP(c_Fun_Ocomp(X32960,X32960,X32960,hAPP(X32959,X32958)),hAPP(X32959,X32957)) = hAPP(c_Fun_Ocomp(X32960,X32960,X32960,hAPP(X32959,X32957)),hAPP(X32959,X32958)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofun__comp__comm])]) ).

fof(i_0_7922,plain,
    ! [X17010,X17011,X17012] : c_Hoare__Mirabelle_Ohoare__derivs(X17012,X17011,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X17012)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17012),X17010),c_Com_Ocom_OSKIP),X17010)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X17012),tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_hoare__derivs_Oequations_I7_J]) ).

fof(i_0_7923,plain,
    ! [X17007,X17008,X17009] : c_Hoare__Mirabelle_Ohoare__derivs(X17009,X17008,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X17009)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17009),X17007),c_Com_Ocom_OSKIP),X17007)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X17009),tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_hoare__derivs_OSkip]) ).

fof(i_0_7924,plain,
    ! [X29189,X29190,X29191,X29192] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29192),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29191)),X29190)))
      | hBOOL(hAPP(hAPP(c_member(X29191),X29189),hAPP(c_List_Oset(X29191),hAPP(hAPP(c_List_Olist__update(X29191,X29190),X29192),X29189)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__update__memI])]) ).

fof(i_0_7925,plain,
    ! [X24917,X24918,X24919,X24920,X24921,X24922] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X24922),X24921),X24920))
      | ~ hBOOL(hAPP(hAPP(c_member(X24919),X24918),hAPP(X24917,X24921)))
      | hBOOL(hAPP(hAPP(c_member(X24919),X24918),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24922,tc_fun(X24919,tc_HOL_Obool)),X24920),X24917))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__I])]) ).

fof(i_0_7926,plain,
    ! [X22076,X22077,X22078,X22079,X22080,X22081] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22081,X22080),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22079),X22078)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22081,X22080),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22077),X22076)))
      | X22080 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | X22079 = X22077 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_unique__quotient])]) ).

fof(i_0_7927,plain,
    ! [X22070,X22071,X22072,X22073,X22074,X22075] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22075,X22074),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22073),X22072)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22075,X22074),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22071),X22070)))
      | X22074 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | X22072 = X22070 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_unique__remainder])]) ).

fof(i_0_7928,plain,
    ! [X25738,X25739,X25740,X25741] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25741),hAPP(c_Set_Oimage(X25740,X25741,X25739),X25738)))
      | ~ c_Fun_Oinj__on(X25740,X25741,X25739,X25738)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X25740),X25738)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__imageD])]) ).

cnf(i_0_7929,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_7930,plain,
    ! [X32538,X32539,X32540,X32541] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X32541,X32540),tc_HOL_Obool)),X32539),X32538))
      | ~ c_Relation_Osingle__valued(X32541,X32540,X32538)
      | c_Relation_Osingle__valued(X32541,X32540,X32539) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_single__valued__subset])]) ).

fof(i_0_7931,plain,
    ! [X32771,X32772,X32773,X32776,X32777,X32778,X32779,X32780] :
      ( ( X32771 = hAPP(hAPP(c_List_Oappend(X32773),esk483_3(X32771,X32772,X32773)),hAPP(hAPP(c_List_Olist_OCons(X32773),X32772),esk484_3(X32771,X32772,X32773)))
        | ~ hBOOL(hAPP(hAPP(c_member(X32773),X32772),hAPP(c_List_Oset(X32773),X32771))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X32773),X32772),hAPP(c_List_Oset(X32773),esk484_3(X32771,X32772,X32773))))
        | ~ hBOOL(hAPP(hAPP(c_member(X32773),X32772),hAPP(c_List_Oset(X32773),X32771))) )
      & ( X32776 != hAPP(hAPP(c_List_Oappend(X32778),X32779),hAPP(hAPP(c_List_Olist_OCons(X32778),X32777),X32780))
        | hBOOL(hAPP(hAPP(c_member(X32778),X32777),hAPP(c_List_Oset(X32778),X32780)))
        | hBOOL(hAPP(hAPP(c_member(X32778),X32777),hAPP(c_List_Oset(X32778),X32776))) ) ),
    inference(distribute,[status(thm)],[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_7932,plain,
    ! [X32761,X32762,X32763,X32766,X32767,X32768,X32769,X32770] :
      ( ( X32761 = hAPP(hAPP(c_List_Oappend(X32763),esk481_3(X32761,X32762,X32763)),hAPP(hAPP(c_List_Olist_OCons(X32763),X32762),esk482_3(X32761,X32762,X32763)))
        | ~ hBOOL(hAPP(hAPP(c_member(X32763),X32762),hAPP(c_List_Oset(X32763),X32761))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X32763),X32762),hAPP(c_List_Oset(X32763),esk481_3(X32761,X32762,X32763))))
        | ~ hBOOL(hAPP(hAPP(c_member(X32763),X32762),hAPP(c_List_Oset(X32763),X32761))) )
      & ( X32766 != hAPP(hAPP(c_List_Oappend(X32768),X32769),hAPP(hAPP(c_List_Olist_OCons(X32768),X32767),X32770))
        | hBOOL(hAPP(hAPP(c_member(X32768),X32767),hAPP(c_List_Oset(X32768),X32769)))
        | hBOOL(hAPP(hAPP(c_member(X32768),X32767),hAPP(c_List_Oset(X32768),X32766))) ) ),
    inference(distribute,[status(thm)],[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_7933,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_7934,plain,
    ! [X18651,X18652,X18653,X18654] :
      ( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X18654)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18654),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18654),X18653),X18652)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18654),X18651),X18652)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18654),X18653),X18651)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__right])]) ).

fof(i_0_7935,plain,
    ! [X18630,X18631,X18632,X18633] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18633),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18633),X18632),X18631)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18633),X18630),X18631)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18633),X18632),X18630))
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X18633) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18633),X18632),X18630))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18633),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18633),X18632),X18631)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18633),X18630),X18631)))
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X18633) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__cancel__right])])]) ).

fof(i_0_7936,plain,
    ! [X18655,X18656,X18657,X18658] :
      ( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X18658)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18658),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18658),X18657),X18656)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18658),X18657),X18655)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18658),X18656),X18655)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__left])]) ).

fof(i_0_7937,plain,
    ! [X18634,X18635,X18636,X18637] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18637),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18637),X18636),X18635)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18637),X18636),X18634)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18637),X18635),X18634))
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X18637) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18637),X18635),X18634))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18637),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18637),X18636),X18635)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18637),X18636),X18634)))
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X18637) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__cancel__left])])]) ).

fof(i_0_7938,plain,
    ! [X17309,X17310,X17311,X17312] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17312),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17312),X17311),X17310)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17312),X17309),X17310)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17312),X17311),X17309))
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X17312) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17312),X17311),X17309))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17312),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17312),X17311),X17310)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17312),X17309),X17310)))
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X17312) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__cancel__right])])]) ).

fof(i_0_7939,plain,
    ! [X17276,X17277,X17278,X17279] :
      ( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X17279)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17279),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17279),X17278),X17277)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17279),X17276),X17277)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17279),X17278),X17276)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__right])]) ).

fof(i_0_7940,plain,
    ! [X17305,X17306,X17307,X17308] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17308),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17308),X17307),X17306)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17308),X17307),X17305)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17308),X17306),X17305))
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X17308) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17308),X17306),X17305))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17308),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17308),X17307),X17306)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17308),X17307),X17305)))
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X17308) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__cancel__left])])]) ).

fof(i_0_7941,plain,
    ! [X17272,X17273,X17274,X17275] :
      ( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X17275)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17275),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17275),X17274),X17273)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17275),X17274),X17272)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17275),X17273),X17272)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__left])]) ).

fof(i_0_7942,plain,
    ! [X17933,X17934,X17935,X17936,X17938,X17939,X17940,X17941,X17942] :
      ( ( c_Natural_Oevaln(X17935,X17934,X17933,esk33_4(X17933,X17934,X17935,X17936))
        | ~ hBOOL(hAPP(X17936,X17934))
        | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X17936,X17935),X17934,X17933,X17934) )
      & ( c_Natural_Oevaln(c_Com_Ocom_OWhile(X17936,X17935),esk33_4(X17933,X17934,X17935,X17936),X17933,X17934)
        | ~ hBOOL(hAPP(X17936,X17934))
        | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X17936,X17935),X17934,X17933,X17934) )
      & ( hBOOL(hAPP(X17941,X17939))
        | c_Natural_Oevaln(c_Com_Ocom_OWhile(X17941,X17940),X17939,X17938,X17939) )
      & ( ~ c_Natural_Oevaln(X17940,X17939,X17938,X17942)
        | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X17941,X17940),X17942,X17938,X17939)
        | c_Natural_Oevaln(c_Com_Ocom_OWhile(X17941,X17940),X17939,X17938,X17939) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evaln_Oequations_I7_J])])])])])]) ).

fof(i_0_7943,plain,
    ! [X17130,X17131,X17132,X17133] :
      ( ( X17131 = hAPP(c_Nat_OSuc,esk8_4(X17130,X17131,X17132,X17133))
        | ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X17133),X17132,X17131,X17130) )
      & ( c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X17133)),X17132,esk8_4(X17130,X17131,X17132,X17133),X17130)
        | ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X17133),X17132,X17131,X17130) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5667])])])]) ).

fof(i_0_7944,plain,
    ! [X31589,X31590,X31591,X31592] :
      ( ~ class_Orderings_Olinorder(X31592)
      | ~ c_List_Olinorder__class_Osorted(X31592,X31591)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31590),X31589))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31589),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31592)),X31591)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31592),hAPP(hAPP(c_List_Onth(X31592),X31591),X31590)),hAPP(hAPP(c_List_Onth(X31592),X31591),X31589))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__nth__mono])]) ).

fof(i_0_7945,plain,
    ! [X28055,X28056,X28057] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28057,X28057),tc_HOL_Obool),hAPP(c_Nat_OSuc,X28056)),X28055) = hAPP(hAPP(c_Relation_Orel__comp(X28057,X28057,X28057),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28057,X28057),tc_HOL_Obool),X28056),X28055)),X28055),
    inference(variable_rename,[status(thm)],[fact_relpow_Osimps_I2_J]) ).

fof(i_0_7946,plain,
    ! [X21499,X21500,X21501,X21502] :
      ( ~ class_Fields_Ofield(X21502)
      | X21501 = c_Groups_Ozero__class_Ozero(X21502)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21502),X21500),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21502),X21499),X21501)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21502),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21502),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21502),X21501),X21500)),X21499)),X21501) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__divide__eq__iff])]) ).

fof(i_0_7947,plain,
    ! [X21482,X21483,X21484,X21485] :
      ( ~ class_Fields_Ofield(X21485)
      | X21484 = c_Groups_Ozero__class_Ozero(X21485)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21485),X21483),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21485),X21482),X21484)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21485),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21485),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21485),X21484),X21483)),X21482)),X21484) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__divide__eq__iff])]) ).

fof(i_0_7948,plain,
    ! [X31562,X31563,X31564,X31565,X31566,X31567] :
      ( ~ class_Orderings_Olinorder(X31567)
      | ~ c_List_Olinorder__class_Osorted(X31567,hAPP(hAPP(c_List_Omap(X31566,X31567),X31565),X31564))
      | ~ hBOOL(hAPP(X31563,X31562))
      | hAPP(c_List_Ofilter(X31566,X31563),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X31566,X31567,X31565),X31562),X31564)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X31566,X31567,X31565),X31562),hAPP(c_List_Ofilter(X31566,X31563),X31564)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_filter__insort])]) ).

cnf(i_0_7949,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_5668]) ).

cnf(i_0_7950,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_5429]) ).

fof(i_0_7951,plain,
    ! [X19222,X19223,X19224] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19224,tc_HOL_Obool)),X19223),hAPP(hAPP(c_Set_Oinsert(X19224),X19222),c_Orderings_Obot__class_Obot(tc_fun(X19224,tc_HOL_Obool)))))
      | X19223 = c_Orderings_Obot__class_Obot(tc_fun(X19224,tc_HOL_Obool))
      | X19223 = hAPP(hAPP(c_Set_Oinsert(X19224),X19222),c_Orderings_Obot__class_Obot(tc_fun(X19224,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__singletonD])]) ).

fof(i_0_7952,plain,
    ! [X20804,X20805,X20806,X20807] :
      ( ( hBOOL(hAPP(hAPP(c_member(X20807),X20806),X20805))
        | ~ hBOOL(hAPP(hAPP(c_member(X20807),X20806),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20807,tc_HOL_Obool)),X20805),X20804))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X20807),X20806),X20804))
        | ~ hBOOL(hAPP(hAPP(c_member(X20807),X20806),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20807,tc_HOL_Obool)),X20805),X20804))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X20807),X20806),X20805))
        | hBOOL(hAPP(hAPP(c_member(X20807),X20806),X20804))
        | hBOOL(hAPP(hAPP(c_member(X20807),X20806),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20807,tc_HOL_Obool)),X20805),X20804))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5669])])]) ).

fof(i_0_7953,plain,
    ! [X20734,X20735,X20736,X20737] :
      ( ( hBOOL(hAPP(hAPP(c_member(X20737),X20736),X20735))
        | ~ hBOOL(hAPP(hAPP(c_member(X20737),X20736),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20737,tc_HOL_Obool)),X20735),X20734))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X20737),X20736),X20734))
        | ~ hBOOL(hAPP(hAPP(c_member(X20737),X20736),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20737,tc_HOL_Obool)),X20735),X20734))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DiffE])])]) ).

fof(i_0_7954,plain,
    ! [X20812,X20813,X20814,X20815] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X20815),X20814),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20815,tc_HOL_Obool)),X20813),X20812)))
      | ~ hBOOL(hAPP(hAPP(c_member(X20815),X20814),X20812)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5670])]) ).

fof(i_0_7955,plain,
    ! [X23364,X23365,X23366,X23367] : c_Fun_Ofun__upd(X23367,X23366,X23365,X23364,hAPP(X23365,X23364)) = X23365,
    inference(variable_rename,[status(thm)],[fact_fun__upd__triv]) ).

cnf(i_0_7956,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_5671]) ).

cnf(i_0_7957,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_5672]) ).

cnf(i_0_7958,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_5673]) ).

cnf(i_0_7959,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_5674]) ).

fof(i_0_7960,plain,
    ! [X23405,X23406,X23407,X23408,X23409] :
      ( hAPP(X23409,X23408) != X23407
      | c_Fun_Ofun__upd(X23406,X23405,X23409,X23408,X23407) = X23409 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__upd__idem])]) ).

fof(i_0_7961,plain,
    ! [X24608,X24609,X24610,X24613,X24614,X24615,X24616,X24617] :
      ( ( X24609 = hAPP(hAPP(c_Set_Oinsert(X24610),esk139_3(X24608,X24609,X24610)),esk140_3(X24608,X24609,X24610))
        | hAPP(c_Finite__Set_Ocard(X24610),X24609) != hAPP(c_Nat_OSuc,X24608) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X24610),esk139_3(X24608,X24609,X24610)),esk140_3(X24608,X24609,X24610)))
        | hAPP(c_Finite__Set_Ocard(X24610),X24609) != hAPP(c_Nat_OSuc,X24608) )
      & ( hAPP(c_Finite__Set_Ocard(X24610),esk140_3(X24608,X24609,X24610)) = X24608
        | hAPP(c_Finite__Set_Ocard(X24610),X24609) != hAPP(c_Nat_OSuc,X24608) )
      & ( X24608 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | esk140_3(X24608,X24609,X24610) = c_Orderings_Obot__class_Obot(tc_fun(X24610,tc_HOL_Obool))
        | hAPP(c_Finite__Set_Ocard(X24610),X24609) != hAPP(c_Nat_OSuc,X24608) )
      & ( X24613 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X24614 != hAPP(hAPP(c_Set_Oinsert(X24615),X24616),X24617)
        | hBOOL(hAPP(hAPP(c_member(X24615),X24616),X24617))
        | hAPP(c_Finite__Set_Ocard(X24615),X24617) != X24613
        | hAPP(c_Finite__Set_Ocard(X24615),X24614) = hAPP(c_Nat_OSuc,X24613) )
      & ( X24617 != c_Orderings_Obot__class_Obot(tc_fun(X24615,tc_HOL_Obool))
        | X24614 != hAPP(hAPP(c_Set_Oinsert(X24615),X24616),X24617)
        | hBOOL(hAPP(hAPP(c_member(X24615),X24616),X24617))
        | hAPP(c_Finite__Set_Ocard(X24615),X24617) != X24613
        | hAPP(c_Finite__Set_Ocard(X24615),X24614) = hAPP(c_Nat_OSuc,X24613) ) ),
    inference(distribute,[status(thm)],[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_5675])])])])])]) ).

fof(i_0_7962,plain,
    ! [X24455,X24456,X24457,X24458,X24459,X24460] :
      ( ~ c_Finite__Set_Ofolding__idem(X24460,X24459,X24458,X24457)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24460),X24456))
      | ~ hBOOL(hAPP(hAPP(c_member(X24460),X24455),X24456))
      | hAPP(c_Fun_Ocomp(X24459,X24459,X24459,hAPP(X24457,X24456)),hAPP(X24458,X24455)) = hAPP(X24457,X24456) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__idem_Oin__comp__idem])]) ).

fof(i_0_7963,plain,
    ! [X28751,X28752,X28753] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X28753),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28752)),X28751)))
      | hAPP(hAPP(c_List_Otake(X28752),hAPP(c_Nat_OSuc,X28753)),X28751) = hAPP(hAPP(c_List_Oappend(X28752),hAPP(hAPP(c_List_Otake(X28752),X28753),X28751)),hAPP(hAPP(c_List_Olist_OCons(X28752),hAPP(hAPP(c_List_Onth(X28752),X28751),X28753)),c_List_Olist_ONil(X28752))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__Suc__conv__app__nth])]) ).

fof(i_0_7964,plain,
    ! [X24508,X24509,X24510] :
      ( ~ class_Orderings_Olinorder(X24510)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24510),X24509))
      | X24509 = c_Orderings_Obot__class_Obot(tc_fun(X24510,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24510),X24508))
      | X24508 = c_Orderings_Obot__class_Obot(tc_fun(X24510,tc_HOL_Obool))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24510,tc_HOL_Obool)),X24509),X24508) != c_Orderings_Obot__class_Obot(tc_fun(X24510,tc_HOL_Obool))
      | c_Big__Operators_Olattice_OInf__fin(X24510,c_Orderings_Oord__class_Omin(X24510),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24510,tc_HOL_Obool)),X24509),X24508)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X24510),c_Big__Operators_Olattice_OInf__fin(X24510,c_Orderings_Oord__class_Omin(X24510),X24509)),c_Big__Operators_Olattice_OInf__fin(X24510,c_Orderings_Oord__class_Omin(X24510),X24508)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Ounion__disjoint])]) ).

fof(i_0_7965,plain,
    ! [X24452,X24453,X24454] :
      ( ~ class_Orderings_Olinorder(X24454)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24454),X24453))
      | X24453 = c_Orderings_Obot__class_Obot(tc_fun(X24454,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24454),X24452))
      | X24452 = c_Orderings_Obot__class_Obot(tc_fun(X24454,tc_HOL_Obool))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24454,tc_HOL_Obool)),X24453),X24452) != c_Orderings_Obot__class_Obot(tc_fun(X24454,tc_HOL_Obool))
      | c_Big__Operators_Olattice_OSup__fin(X24454,c_Orderings_Oord__class_Omax(X24454),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24454,tc_HOL_Obool)),X24453),X24452)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X24454),c_Big__Operators_Olattice_OSup__fin(X24454,c_Orderings_Oord__class_Omax(X24454),X24453)),c_Big__Operators_Olattice_OSup__fin(X24454,c_Orderings_Oord__class_Omax(X24454),X24452)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Ounion__disjoint])]) ).

fof(i_0_7966,plain,
    ! [X18215,X18216,X18217,X18218] : hAPP(hAPP(c_Nat_Ocompow(tc_fun(X18218,X18217),tc_fun(X18218,X18217)),X18216),c_Fun_Ocomp(X18217,X18217,X18218,X18215)) = c_Fun_Ocomp(X18217,X18217,X18218,hAPP(hAPP(c_Nat_Ocompow(X18217,X18217),X18216),X18215)),
    inference(variable_rename,[status(thm)],[fact_comp__funpow]) ).

fof(i_0_7967,plain,
    ! [X33282,X33283,X33284,X33285,X33286] : hAPP(c_New__DSequence_Opos__bind(X33286,X33285,X33284,X33283),X33282) = hAPP(c_Lazy__Sequence_Obind(X33286,X33285,hAPP(X33284,X33282)),hAPP(hAPP(c_COMBC(X33286,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X33285)),X33283),X33282)),
    inference(variable_rename,[status(thm)],[fact_New__DSequence_Opos__bind__def]) ).

fof(i_0_7968,plain,
    ! [X34110,X34111,X34112,X34113,X34114,X34115] : hAPP(hAPP(c_Product__Type_Ocurry(X34115,X34114,X34113,X34112),X34111),X34110) = hAPP(X34112,hAPP(hAPP(c_Product__Type_OPair(X34115,X34114),X34111),X34110)),
    inference(variable_rename,[status(thm)],[fact_curry__def]) ).

fof(i_0_7969,plain,
    ! [X25742,X25743,X25744,X25745,X25746] :
      ( ( hAPP(c_Set_Oimage(X25746,X25745,X25744),X25743) != hAPP(c_Set_Oimage(X25746,X25745,X25744),X25742)
        | X25743 = X25742
        | ~ c_Fun_Oinj__on(X25746,X25745,X25744,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25746,tc_HOL_Obool)),X25743),X25742)) )
      & ( X25743 != X25742
        | hAPP(c_Set_Oimage(X25746,X25745,X25744),X25743) = hAPP(c_Set_Oimage(X25746,X25745,X25744),X25742)
        | ~ c_Fun_Oinj__on(X25746,X25745,X25744,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25746,tc_HOL_Obool)),X25743),X25742)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__Un__image__eq__iff])])]) ).

cnf(i_0_7970,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk398_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_7971,plain,
    ! [X21556,X21557,X21558,X21559] :
      ( ~ class_Fields_Olinordered__field(X21559)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21559),c_Groups_Ozero__class_Ozero(X21559)),X21558))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21559),X21557),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21559),X21556),X21558)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21559),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21559),X21557),X21558)),X21556)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__imp__div__pos__le])]) ).

fof(i_0_7972,plain,
    ! [X21448,X21449,X21450,X21451] :
      ( ~ class_Fields_Olinordered__field(X21451)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21451),c_Groups_Ozero__class_Ozero(X21451)),X21450))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21451),X21449),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21451),X21448),X21450)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21451),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21451),X21449),X21450)),X21448)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__imp__div__pos__less])]) ).

fof(i_0_7973,plain,
    ! [X27621,X27622,X27623,X27624,X27625] :
      ( ~ c_Relation_Orefl__on(X27625,X27624,X27623)
      | ~ c_Relation_Orefl__on(X27625,X27622,X27621)
      | c_Relation_Orefl__on(X27625,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27625,tc_HOL_Obool)),X27624),X27622),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X27625,X27625),tc_HOL_Obool)),X27623),X27621)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__on__Int])]) ).

fof(i_0_7974,plain,
    ! [X27615,X27616,X27617,X27618,X27619] :
      ( ~ c_Relation_Orefl__on(X27619,X27618,X27617)
      | ~ c_Relation_Orefl__on(X27619,X27616,X27615)
      | c_Relation_Orefl__on(X27619,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27619,tc_HOL_Obool)),X27618),X27616),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X27619,X27619),tc_HOL_Obool)),X27617),X27615)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__on__Un])]) ).

fof(i_0_7975,plain,
    ! [X34093,X34094,X34095,X34096] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X34096,X34095,X34094,X34093,c_Lazy__Sequence_Olazy__sequence_OEmpty(X34095)) = X34094,
    inference(variable_rename,[status(thm)],[fact_lazy__sequence_Orecs_I1_J]) ).

fof(i_0_7976,plain,
    ! [X33987,X33988,X33989] :
      ( hAPP(c_Set_Oimage(X33989,X33988,X33987),c_Orderings_Otop__class_Otop(tc_fun(X33989,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X33988,tc_HOL_Obool))
      | c_Fun_Oinj__on(X33988,X33989,c_Hilbert__Choice_Oinv__into(X33989,X33988,c_Orderings_Otop__class_Otop(tc_fun(X33989,tc_HOL_Obool)),X33987),c_Orderings_Otop__class_Otop(tc_fun(X33988,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_surj__imp__inj__inv])]) ).

fof(i_0_7977,plain,
    ! [X34121,X34122] : c_Fun_Obij__betw(X34122,X34122,c_Fun_Oid(X34122),X34121,X34121),
    inference(variable_rename,[status(thm)],[fact_bij__betw__id]) ).

fof(i_0_7978,plain,
    ! [X30930,X30931,X30932,X30933,X30934] : hAPP(c_Relation_ODomain(X30934,X30933),hAPP(hAPP(c_Set_Oinsert(tc_prod(X30934,X30933)),hAPP(hAPP(c_Product__Type_OPair(X30934,X30933),X30932),X30931)),X30930)) = hAPP(hAPP(c_Set_Oinsert(X30934),X30932),hAPP(c_Relation_ODomain(X30934,X30933),X30930)),
    inference(variable_rename,[status(thm)],[fact_Domain__insert]) ).

fof(i_0_7979,plain,
    ! [X28288,X28289,X28290,X28291,X28292] : hAPP(c_Relation_ORange(X28292,X28291),hAPP(hAPP(c_Set_Oinsert(tc_prod(X28292,X28291)),hAPP(hAPP(c_Product__Type_OPair(X28292,X28291),X28290),X28289)),X28288)) = hAPP(hAPP(c_Set_Oinsert(X28291),X28289),hAPP(c_Relation_ORange(X28292,X28291),X28288)),
    inference(variable_rename,[status(thm)],[fact_Range__insert]) ).

cnf(i_0_7980,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_5676]) ).

fof(i_0_7981,plain,
    ! [X19313,X19314,X19315,X19316] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19316,tc_HOL_Obool)),X19315),X19314))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19316,tc_HOL_Obool)),X19314),X19313))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19316,tc_HOL_Obool)),X19315),X19313)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__trans])]) ).

fof(i_0_7982,plain,
    ! [X19209,X19210,X19211,X19212] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X19212,tc_HOL_Obool)),X19211),X19210))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19212,tc_HOL_Obool)),X19210),X19209))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X19212,tc_HOL_Obool)),X19211),X19209)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__subset__trans])]) ).

fof(i_0_7983,plain,
    ! [X19205,X19206,X19207,X19208] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19208,tc_HOL_Obool)),X19207),X19206))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X19208,tc_HOL_Obool)),X19206),X19205))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X19208,tc_HOL_Obool)),X19207),X19205)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__psubset__trans])]) ).

fof(i_0_7984,plain,
    ! [X17884,X17885,X17886,X17887] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X17887,tc_HOL_Obool)),X17886),X17885))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X17887,tc_HOL_Obool)),X17885),X17884))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X17887,tc_HOL_Obool)),X17886),X17884)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__trans])]) ).

fof(i_0_7985,plain,
    ! [X23334,X23335] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X23335),X23334))
        | hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23335)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X23334))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23335)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X23334)))
        | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X23335),X23334)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__relations_I2_J])]) ).

fof(i_0_7986,plain,
    ! [X30340,X30341,X30342,X30343,X30344] : hAPP(hAPP(c_Product__Type_Oscomp(X30344,X30343,X30344,X30342),hAPP(c_Product__Type_OPair(X30343,X30344),X30341)),X30340) = hAPP(X30340,X30341),
    inference(variable_rename,[status(thm)],[fact_Pair__scomp]) ).

cnf(i_0_7987,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_5677]) ).

fof(i_0_7988,plain,
    ! [X19747,X19748,X19749] :
      ( ~ class_Divides_Osemiring__div(X19749)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19749),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19749),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X19749),X19748),X19747)),X19747)),c_Divides_Odiv__class_Omod(X19749,X19748,X19747)) = X19748 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__div__equality])]) ).

fof(i_0_7989,plain,
    ! [X19797,X19798,X19799] :
      ( ~ class_Divides_Osemiring__div(X19799)
      | X19798 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19799),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19799),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X19799),X19798),X19797)),X19797)),c_Divides_Odiv__class_Omod(X19799,X19798,X19797)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__div__decomp])]) ).

fof(i_0_7990,plain,
    ! [X31884,X31885,X31886,X31887] :
      ( ~ class_Orderings_Olinorder(X31887)
      | c_List_Olinorder__class_Osorted(X31887,hAPP(hAPP(c_List_Omap(X31886,X31887),X31885),c_List_Olinorder__class_Osort__key(X31886,X31887,X31885,X31884))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__sort__key])]) ).

cnf(i_0_7991,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_5678]) ).

cnf(i_0_7992,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_5679]) ).

fof(i_0_7993,plain,
    ! [X17070,X17071,X17072] :
      ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X17072)),X17071),X17070))
      | hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X17072))),X17071),X17070)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evalc__elim__cases_I6_J])]) ).

fof(i_0_7994,plain,
    ! [X25196,X25197] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25197,tc_fun(X25197,tc_HOL_Obool)),X25196),hAPP(hAPP(c_COMBC(X25197,tc_fun(X25197,tc_HOL_Obool),tc_fun(X25197,tc_HOL_Obool)),c_Set_Oinsert(X25197)),c_Orderings_Obot__class_Obot(tc_fun(X25197,tc_HOL_Obool)))) = X25196,
    inference(variable_rename,[status(thm)],[fact_UN__singleton]) ).

fof(i_0_7995,plain,
    ! [X29016,X29017,X29018,X29019] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29019),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29018)),X29017)))
      | hAPP(hAPP(c_List_Olist__update(X29018,X29017),X29019),X29016) = hAPP(hAPP(c_List_Oappend(X29018),hAPP(hAPP(c_List_Otake(X29018),X29019),X29017)),hAPP(hAPP(c_List_Olist_OCons(X29018),X29016),hAPP(hAPP(c_List_Odrop(X29018),hAPP(c_Nat_OSuc,X29019)),X29017))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_upd__conv__take__nth__drop])]) ).

fof(i_0_7996,plain,
    ! [X30500,X30501,X30502,X30503,X30504,X30505] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X30505),hAPP(X30504,X30503)),hAPP(X30504,X30502)))
        | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30501,X30505,X30504),X30503),hAPP(hAPP(c_List_Olist_OCons(X30501),X30502),X30500)) = hAPP(hAPP(c_List_Olist_OCons(X30501),X30503),hAPP(hAPP(c_List_Olist_OCons(X30501),X30502),X30500))
        | ~ class_Orderings_Olinorder(X30505) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X30505),hAPP(X30504,X30503)),hAPP(X30504,X30502)))
        | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30501,X30505,X30504),X30503),hAPP(hAPP(c_List_Olist_OCons(X30501),X30502),X30500)) = hAPP(hAPP(c_List_Olist_OCons(X30501),X30502),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30501,X30505,X30504),X30503),X30500))
        | ~ class_Orderings_Olinorder(X30505) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5680])])]) ).

fof(i_0_7997,plain,
    ! [X30744,X30745] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X30745),X30744))
      | hBOOL(hAPP(c_List_Odistinct(tc_fun(X30745,tc_HOL_Obool)),hAPP(hAPP(c_List_Omap(tc_List_Olist(X30745),tc_fun(X30745,tc_HOL_Obool)),c_List_Oset(X30745)),c_Enum_Osublists(X30745,X30744)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__set__sublists])]) ).

fof(i_0_7998,plain,
    ! [X29537,X29538] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X29538)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X29537)))
        | c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X29538),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X29537)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X29538)),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X29538)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X29537))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X29538)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X29537)))
        | c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X29538),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X29537)) = c_List_Olist_ONil(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5681])]) ).

fof(i_0_7999,plain,
    ! [X25428,X25429,X25430] : hAPP(c_Set_OPow(X25430),hAPP(hAPP(c_Set_Oinsert(X25430),X25429),X25428)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X25430,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X25430),X25428)),hAPP(c_Set_Oimage(tc_fun(X25430,tc_HOL_Obool),tc_fun(X25430,tc_HOL_Obool),hAPP(c_Set_Oinsert(X25430),X25429)),hAPP(c_Set_OPow(X25430),X25428))),
    inference(variable_rename,[status(thm)],[fact_Pow__insert]) ).

fof(i_0_8000,plain,
    ! [X17653,X17654,X17655,X17656,X17657] :
      ( ~ hBOOL(hAPP(X17657,X17656))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17655),X17656),X17654))
      | hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X17657,X17655,X17653)),X17656),X17654)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evalc_OIfTrue])]) ).

fof(i_0_8001,plain,
    ! [X27195,X27196,X27197,X27198] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27198),hAPP(c_Set_Ovimage(X27198,X27197,X27196),X27195)))
      | hAPP(c_Set_Oimage(X27198,X27197,X27196),c_Orderings_Otop__class_Otop(tc_fun(X27198,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X27197,tc_HOL_Obool))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X27197),X27195)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__vimageD])]) ).

fof(i_0_8002,plain,
    ! [X28664,X28665,X28666,X28667] :
      ( ( hBOOL(hAPP(hAPP(c_member(X28667),X28666),X28664))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X28667)),hAPP(hAPP(c_List_Olist_OCons(X28667),X28666),X28665)),c_List_Olists(X28667,X28664))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X28667)),X28665),c_List_Olists(X28667,X28664)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X28667)),hAPP(hAPP(c_List_Olist_OCons(X28667),X28666),X28665)),c_List_Olists(X28667,X28664))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X28667),X28666),X28664))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X28667)),X28665),c_List_Olists(X28667,X28664)))
        | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X28667)),hAPP(hAPP(c_List_Olist_OCons(X28667),X28666),X28665)),c_List_Olists(X28667,X28664))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cons__in__lists__iff])])]) ).

fof(i_0_8003,plain,
    ! [X20843,X20844,X20845,X20846] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20846,tc_HOL_Obool)),X20844),hAPP(hAPP(c_Set_Oinsert(X20846),X20845),X20843)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20846,tc_HOL_Obool)),X20844),X20843))
        | hBOOL(hAPP(hAPP(c_member(X20846),X20845),X20844)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20846,tc_HOL_Obool)),X20844),X20843))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20846,tc_HOL_Obool)),X20844),hAPP(hAPP(c_Set_Oinsert(X20846),X20845),X20843)))
        | hBOOL(hAPP(hAPP(c_member(X20846),X20845),X20844)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5682])])]) ).

fof(i_0_8004,plain,
    ! [X22355,X22356] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),X22356))
      | 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(X22356),X22355))),X22356)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_range])]) ).

fof(i_0_8005,plain,
    ! [X23845,X23846,X23847,X23848] :
      ( ( hBOOL(hAPP(hAPP(c_member(X23848),X23847),X23846))
        | ~ hBOOL(hAPP(hAPP(c_member(X23848),X23847),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23848,tc_HOL_Obool)),X23846),X23845))) )
      & ( hBOOL(hAPP(hAPP(c_member(X23848),X23847),X23845))
        | ~ hBOOL(hAPP(hAPP(c_member(X23848),X23847),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23848,tc_HOL_Obool)),X23846),X23845))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X23848),X23847),X23846))
        | ~ hBOOL(hAPP(hAPP(c_member(X23848),X23847),X23845))
        | hBOOL(hAPP(hAPP(c_member(X23848),X23847),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23848,tc_HOL_Obool)),X23846),X23845))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__iff])])]) ).

fof(i_0_8006,plain,
    ! [X23841,X23842,X23843,X23844] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X23844),X23843),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23844,tc_HOL_Obool)),X23842),X23841)))
      | hBOOL(hAPP(hAPP(c_member(X23844),X23843),X23842)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_IntD1])]) ).

fof(i_0_8007,plain,
    ! [X23728,X23729,X23730,X23731] :
      ( ( hBOOL(hAPP(hAPP(c_member(X23731),X23730),X23729))
        | ~ hBOOL(hAPP(hAPP(c_member(X23731),X23730),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23731,tc_HOL_Obool)),X23729),X23728))) )
      & ( hBOOL(hAPP(hAPP(c_member(X23731),X23730),X23728))
        | ~ hBOOL(hAPP(hAPP(c_member(X23731),X23730),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23731,tc_HOL_Obool)),X23729),X23728))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5683])])]) ).

fof(i_0_8008,plain,
    ! [X20808,X20809,X20810,X20811] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X20811),X20810),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20811,tc_HOL_Obool)),X20809),X20808)))
      | hBOOL(hAPP(hAPP(c_member(X20811),X20810),X20809)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DiffD1])]) ).

fof(i_0_8009,plain,
    ! [X23837,X23838,X23839,X23840] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X23840),X23839),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23840,tc_HOL_Obool)),X23838),X23837)))
      | hBOOL(hAPP(hAPP(c_member(X23840),X23839),X23837)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_IntD2])]) ).

fof(i_0_8010,plain,
    ! [X20384,X20385,X20386,X20387] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20387,tc_HOL_Obool)),X20386),hAPP(hAPP(c_Set_Oinsert(X20387),X20385),X20384)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20387,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20387,tc_HOL_Obool)),X20386),X20384)),hAPP(hAPP(c_Set_Oinsert(X20387),X20385),c_Orderings_Obot__class_Obot(tc_fun(X20387,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_Diff__insert]) ).

fof(i_0_8011,plain,
    ! [X29541,X29542] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X29542),X29541))
        | c_List_Oupto(X29542,X29541) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),X29542),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X29542),c_Groups_Oone__class_Oone(tc_Int_Oint)),X29541))
        | ~ 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),X29542),X29541))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X29542),X29541))
        | c_List_Oupto(X29542,X29541) = 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),X29542),X29541))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5684])])]) ).

fof(i_0_8012,plain,
    ! [X26994,X26995,X26996] :
      ( ~ class_Groups_Oab__semigroup__mult(X26996)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26996),X26995))
      | X26995 = c_Orderings_Obot__class_Obot(tc_fun(X26996,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26996),X26994))
      | X26994 = c_Orderings_Obot__class_Obot(tc_fun(X26996,tc_HOL_Obool))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26996,tc_HOL_Obool)),X26995),X26994) != c_Orderings_Obot__class_Obot(tc_fun(X26996,tc_HOL_Obool))
      | hAPP(c_Finite__Set_Ofold1(X26996,c_Groups_Otimes__class_Otimes(X26996)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26996,tc_HOL_Obool)),X26995),X26994)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26996),hAPP(c_Finite__Set_Ofold1(X26996,c_Groups_Otimes__class_Otimes(X26996)),X26995)),hAPP(c_Finite__Set_Ofold1(X26996,c_Groups_Otimes__class_Otimes(X26996)),X26994)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1__Un])]) ).

fof(i_0_8013,plain,
    ! [X33005,X33006,X33007,X33008,X33009,X33010] :
      ( ~ c_Finite__Set_Ofun__left__comm(X33010,X33009,X33008)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33010),X33007))
      | hBOOL(hAPP(hAPP(c_member(X33010),X33006),X33007))
      | hAPP(hAPP(c_Finite__Set_Ofold(X33010,X33009,X33008),X33005),hAPP(hAPP(c_Set_Oinsert(X33010),X33006),X33007)) = hAPP(hAPP(X33008,X33006),hAPP(hAPP(c_Finite__Set_Ofold(X33010,X33009,X33008),X33005),X33007)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5685])]) ).

cnf(i_0_8014,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_5446]) ).

fof(i_0_8015,plain,
    ! [X17658,X17659,X17660,X17661,X17662] :
      ( hBOOL(hAPP(X17662,X17661))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17660),X17661),X17659))
      | hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X17662,X17658,X17660)),X17661),X17659)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5686])]) ).

fof(i_0_8016,plain,
    ! [X24461,X24462,X24463,X24464,X24465,X24466] :
      ( ~ c_Finite__Set_Ofolding__idem(X24466,X24465,X24464,X24463)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24466),X24462))
      | hAPP(X24463,hAPP(hAPP(c_Set_Oinsert(X24466),X24461),X24462)) = hAPP(c_Fun_Ocomp(X24465,X24465,X24465,hAPP(X24463,X24462)),hAPP(X24464,X24461)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__idem_Oinsert__idem])]) ).

fof(i_0_8017,plain,
    ! [X30336,X30337,X30338,X30339] : hAPP(hAPP(c_Product__Type_Oscomp(X30339,X30338,X30337,tc_prod(X30338,X30337)),X30336),c_Product__Type_OPair(X30338,X30337)) = X30336,
    inference(variable_rename,[status(thm)],[fact_scomp__Pair]) ).

fof(i_0_8018,plain,
    ! [X27844,X27845] : hAPP(c_Set_OPow(X27845),X27844) = hAPP(c_Set_OCollect(tc_fun(X27845,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(X27845,tc_HOL_Obool),tc_fun(X27845,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(X27845,tc_HOL_Obool))),X27844)),
    inference(variable_rename,[status(thm)],[fact_Pow__def]) ).

fof(i_0_8019,plain,
    ! [X31683,X31684] : hAPP(c_List_Orev(X31684),X31683) = hAPP(c_List_Ofoldl(tc_List_Olist(X31684),X31684,hAPP(c_COMBC(X31684,tc_List_Olist(X31684),tc_List_Olist(X31684)),c_List_Olist_OCons(X31684)),c_List_Olist_ONil(X31684)),X31683),
    inference(variable_rename,[status(thm)],[fact_rev__foldl__cons]) ).

fof(i_0_8020,plain,
    ! [X33537,X33538] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X33538),X33537))
        | c_Lazy__Sequence_Osmall__lazy_H(X33538,X33537) = 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),X33538),X33537))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X33538),X33537))
        | c_Lazy__Sequence_Osmall__lazy_H(X33538,X33537) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),X33537),c_Lazy__Sequence_Osmall__lazy_H(X33538,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X33537),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),X33538),X33537))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5687])])]) ).

cnf(i_0_8021,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_8022,plain,
    ! [X26448,X26449] :
      ( ~ class_Rings_Ocomm__semiring__1(X26449)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26449),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26449),c_Groups_Oone__class_Oone(X26449)),c_Groups_Oone__class_Oone(X26449))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26449),c_Nat_Osemiring__1__class_Oof__nat(X26449)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X26448))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26449),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X26449),X26448)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26449),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X26449),X26448)),c_Groups_Oone__class_Oone(X26449))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gauss__sum])]) ).

fof(i_0_8023,plain,
    ! [X30764,X30765,X30766,X30767] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X30767)),X30766),hAPP(c_List_Oset(tc_List_Olist(X30767)),c_Enum_On__lists(X30767,X30765,X30764))))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30767)),X30766) = X30765 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_length__n__lists__elem])]) ).

cnf(i_0_8024,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_5460]) ).

fof(i_0_8025,plain,
    ! [X33836,X33837,X33838] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X33838,X33838),tc_HOL_Obool)),X33837),X33836))
      | ~ c_Relation_Oantisym(X33838,X33836)
      | c_Relation_Oantisym(X33838,X33837) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_antisym__subset])]) ).

fof(i_0_8026,plain,
    ! [X31999,X32000,X32001] :
      ( ~ c_Wellfounded_Oacyclic(X32001,X32000)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X32001,X32001),tc_HOL_Obool)),X31999),X32000))
      | c_Wellfounded_Oacyclic(X32001,X31999) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acyclic__subset])]) ).

fof(i_0_8027,plain,
    ! [X28125,X28126,X28127] :
      ( ~ c_Wellfounded_Owf(X28127,X28126)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28127,X28127),tc_HOL_Obool)),X28125),X28126))
      | c_Wellfounded_Owf(X28127,X28125) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__subset])]) ).

fof(i_0_8028,plain,
    ! [X30455,X30456,X30457,X30458] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X30456),X30458),hAPP(c_List_Oset(X30456),c_List_Oremove1(X30456,X30457,X30455))))
        | hBOOL(hAPP(hAPP(c_member(X30456),X30458),hAPP(c_List_Oset(X30456),X30455)))
        | X30458 = X30457 )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X30456),X30458),hAPP(c_List_Oset(X30456),X30455)))
        | hBOOL(hAPP(hAPP(c_member(X30456),X30458),hAPP(c_List_Oset(X30456),c_List_Oremove1(X30456,X30457,X30455))))
        | X30458 = X30457 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__set__remove1])])]) ).

fof(i_0_8029,plain,
    ! [X23910,X23911,X23912,X23913] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23913,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23913,tc_HOL_Obool)),X23912),X23911)),X23910) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23913,tc_HOL_Obool)),X23912),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23913,tc_HOL_Obool)),X23911),X23910)),
    inference(variable_rename,[status(thm)],[fact_Int__assoc]) ).

fof(i_0_8030,plain,
    ! [X22946,X22947,X22948,X22949] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22949,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22949,tc_HOL_Obool)),X22948),X22947)),X22946) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22949,tc_HOL_Obool)),X22948),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22949,tc_HOL_Obool)),X22947),X22946)),
    inference(variable_rename,[status(thm)],[fact_Un__assoc]) ).

fof(i_0_8031,plain,
    ! [X23946,X23947,X23948,X23949] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23949,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23949,tc_HOL_Obool)),X23948),X23947)),X23946) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23949,tc_HOL_Obool)),X23948),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23949,tc_HOL_Obool)),X23947),X23946)),
    inference(variable_rename,[status(thm)],[fact_Int__Diff]) ).

fof(i_0_8032,plain,
    ! [X20037,X20038,X20039] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20039),X20038))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20037),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20038),X20037)),X20039))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__diff])]) ).

fof(i_0_8033,plain,
    ! [X31740,X31741,X31742,X31743] :
      ( ( hBOOL(hAPP(hAPP(c_member(X31743),X31742),hAPP(c_List_Oset(X31743),X31740)))
        | ~ hBOOL(hAPP(hAPP(c_member(X31743),X31742),hAPP(c_List_Oset(X31743),c_List_OtakeWhile(X31743,X31741,X31740)))) )
      & ( hBOOL(hAPP(X31741,X31742))
        | ~ hBOOL(hAPP(hAPP(c_member(X31743),X31742),hAPP(c_List_Oset(X31743),c_List_OtakeWhile(X31743,X31741,X31740)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__takeWhileD])])]) ).

fof(i_0_8034,plain,
    ! [X30451,X30452,X30453,X30454] :
      ( hBOOL(hAPP(hAPP(c_member(X30454),X30453),hAPP(c_List_Oset(X30454),X30452)))
      | ~ hBOOL(hAPP(hAPP(c_member(X30454),X30453),hAPP(c_List_Oset(X30454),c_List_Oremove1(X30454,X30451,X30452)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5688])]) ).

fof(i_0_8035,plain,
    ! [X28891,X28892,X28893,X28894] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X28894),X28893),hAPP(c_List_Oset(X28894),c_List_Osublist(X28894,X28892,X28891))))
      | hBOOL(hAPP(hAPP(c_member(X28894),X28893),hAPP(c_List_Oset(X28894),X28892))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__set__sublistD])]) ).

fof(i_0_8036,plain,
    ! [X28887,X28888,X28889,X28890] :
      ( hBOOL(hAPP(hAPP(c_member(X28890),X28889),hAPP(c_List_Oset(X28890),X28888)))
      | ~ hBOOL(hAPP(hAPP(c_member(X28890),X28889),hAPP(c_List_Oset(X28890),c_List_Osublist(X28890,X28888,X28887)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5689])]) ).

fof(i_0_8037,plain,
    ! [X17866,X17867,X17868,X17869,X17870,X17871] :
      ( ~ hBOOL(hAPP(X17871,X17870))
      | ~ c_Natural_Oevaln(X17869,X17870,X17868,X17867)
      | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X17871,X17869),X17867,X17868,X17866)
      | c_Natural_Oevaln(c_Com_Ocom_OWhile(X17871,X17869),X17870,X17868,X17866) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evaln_OWhileTrue])]) ).

fof(i_0_8038,plain,
    ! [X31199,X31200,X31201] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X31201,tc_HOL_Obool)),hAPP(c_List_Oset(X31201),hAPP(c_List_Ofilter(X31201,X31200),X31199))),hAPP(c_List_Oset(X31201),X31199))),
    inference(variable_rename,[status(thm)],[fact_filter__is__subset]) ).

fof(i_0_8039,plain,
    ! [X18272,X18273,X18274,X18275,X18276] :
      ( ( X18275 = X18274
        | X18273 = X18272
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18276),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18276),X18275),X18273)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18276),X18274),X18272)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18276),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18276),X18275),X18272)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18276),X18274),X18273))
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X18276) )
      & ( X18275 != X18274
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18276),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18276),X18275),X18273)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18276),X18274),X18272)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18276),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18276),X18275),X18272)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18276),X18274),X18273))
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X18276) )
      & ( X18273 != X18272
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18276),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18276),X18275),X18273)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18276),X18274),X18272)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18276),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18276),X18275),X18272)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18276),X18274),X18273))
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X18276) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_crossproduct__noteq])])]) ).

fof(i_0_8040,plain,
    ! [X18294,X18295,X18296,X18297,X18298] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18298),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18298),X18297),X18296)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18298),X18295),X18294)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18298),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18298),X18297),X18294)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18298),X18295),X18296))
        | X18297 = X18295
        | X18296 = X18294
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X18298) )
      & ( X18297 != X18295
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18298),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18298),X18297),X18296)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18298),X18295),X18294)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18298),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18298),X18297),X18294)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18298),X18295),X18296))
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X18298) )
      & ( X18296 != X18294
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18298),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18298),X18297),X18296)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18298),X18295),X18294)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18298),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18298),X18297),X18294)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18298),X18295),X18296))
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X18298) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_crossproduct__eq])])]) ).

cnf(i_0_8041,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_5690]) ).

fof(i_0_8042,plain,
    ! [X27896,X27897] :
      ( ( ~ c_Predicate_Oreflp(X27897,X27896)
        | c_Relation_Orefl__on(X27897,c_Orderings_Otop__class_Otop(tc_fun(X27897,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(X27897,X27897)),hAPP(c_Product__Type_Oprod_Oprod__case(X27897,X27897,tc_HOL_Obool),X27896))) )
      & ( ~ c_Relation_Orefl__on(X27897,c_Orderings_Otop__class_Otop(tc_fun(X27897,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(X27897,X27897)),hAPP(c_Product__Type_Oprod_Oprod__case(X27897,X27897,tc_HOL_Obool),X27896)))
        | c_Predicate_Oreflp(X27897,X27896) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_reflp__def])]) ).

fof(i_0_8043,plain,
    ! [X20029,X20030,X20031] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20029),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20030),X20031)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20029),X20031)),X20030))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20031),X20030)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20029),X20031)),X20030))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20029),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20030),X20031)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20031),X20030)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__diff__conv2])])]) ).

cnf(i_0_8044,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_5691]) ).

fof(i_0_8045,plain,
    ! [X33599,X33600,X33601,X33602,X33604,X33605,X33606,X33608] :
      ( ( hBOOL(hAPP(X33601,esk527_4(X33599,X33600,X33601,X33602)))
        | ~ hBOOL(hAPP(X33601,X33602))
        | c_FunDef_OTHE__default(X33600,X33599,X33601) = c_HOL_OThe(X33600,X33601) )
      & ( esk527_4(X33599,X33600,X33601,X33602) != X33602
        | ~ hBOOL(hAPP(X33601,X33602))
        | c_FunDef_OTHE__default(X33600,X33599,X33601) = c_HOL_OThe(X33600,X33601) )
      & ( hBOOL(hAPP(X33606,esk528_3(X33604,X33605,X33606)))
        | c_FunDef_OTHE__default(X33605,X33604,X33606) = X33604 )
      & ( ~ hBOOL(hAPP(X33606,X33608))
        | X33608 = esk528_3(X33604,X33605,X33606)
        | c_FunDef_OTHE__default(X33605,X33604,X33606) = X33604 ) ),
    inference(distribute,[status(thm)],[inference(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_8046,plain,
    ! [X27172,X27173,X27174,X27175,X27176] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X27176),X27175),hAPP(c_Set_Ovimage(X27176,X27174,X27173),X27172)))
        | hBOOL(hAPP(hAPP(c_member(X27174),hAPP(X27173,X27175)),X27172)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X27174),hAPP(X27173,X27175)),X27172))
        | hBOOL(hAPP(hAPP(c_member(X27176),X27175),hAPP(c_Set_Ovimage(X27176,X27174,X27173),X27172))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vimage__eq])]) ).

fof(i_0_8047,plain,
    ! [X27167,X27168,X27169,X27170,X27171] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X27171),X27170),hAPP(c_Set_Ovimage(X27171,X27169,X27168),X27167)))
      | hBOOL(hAPP(hAPP(c_member(X27169),hAPP(X27168,X27170)),X27167)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vimageD])]) ).

fof(i_0_8048,plain,
    ! [X19185,X19186,X19187,X19188] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19187,X19188)),X19186),X19185))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X19187,X19188)),X19186),X19185))
        | ~ class_Orderings_Oord(X19188) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19187,X19188)),X19185),X19186))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X19187,X19188)),X19186),X19185))
        | ~ class_Orderings_Oord(X19188) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19187,X19188)),X19186),X19185))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19187,X19188)),X19185),X19186))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X19187,X19188)),X19186),X19185))
        | ~ class_Orderings_Oord(X19188) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5692])])]) ).

fof(i_0_8049,plain,
    ! [X28850,X28851,X28852,X28853] : hAPP(hAPP(c_List_Odrop(X28853),X28852),hAPP(hAPP(c_List_Olist_OCons(X28853),X28851),X28850)) = c_Nat_Onat_Onat__case(tc_List_Olist(X28853),hAPP(hAPP(c_List_Olist_OCons(X28853),X28851),X28850),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(X28853),tc_List_Olist(X28853)),c_List_Odrop(X28853)),X28850),X28852),
    inference(variable_rename,[status(thm)],[fact_drop__Cons]) ).

fof(i_0_8050,plain,
    ! [X18539,X18540,X18541] :
      ( ~ class_Rings_Olinordered__idom(X18541)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18541),c_Groups_Ozero__class_Ozero(X18541)),X18540))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18541),c_Groups_Ozero__class_Ozero(X18541)),X18539))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18541),X18539),c_Groups_Oone__class_Oone(X18541)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18541),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18541),X18540),X18539)),X18540)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__le__one__le])]) ).

fof(i_0_8051,plain,
    ! [X18536,X18537,X18538] :
      ( ~ class_Rings_Olinordered__idom(X18538)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18538),c_Groups_Ozero__class_Ozero(X18538)),X18537))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18538),c_Groups_Ozero__class_Ozero(X18538)),X18536))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18538),X18536),c_Groups_Oone__class_Oone(X18538)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18538),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18538),X18536),X18537)),X18537)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__le__one__le])]) ).

fof(i_0_8052,plain,
    ! [X28405,X28406,X28407,X28408] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X28408),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X28407),X28406)))
        | hAPP(c_Random_Opick(X28407,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X28407)),X28406),X28405)),X28408) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X28407),X28406) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X28408),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X28407),X28406)))
        | hAPP(c_Random_Opick(X28407,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X28407)),X28406),X28405)),X28408) = hAPP(c_Random_Opick(X28407,X28405),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X28408),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X28407),X28406))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5693])]) ).

cnf(i_0_8053,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_5621]) ).

cnf(i_0_8054,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_5623]) ).

cnf(i_0_8055,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_5622]) ).

cnf(i_0_8056,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_5624]) ).

fof(i_0_8057,plain,
    ! [X30866,X30867,X30868,X30869,X30870,X30871,X30872] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X30868,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X30868,tc_HOL_Obool),X30867)),X30866) != c_Orderings_Obot__class_Obot(tc_fun(X30868,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X30868,tc_HOL_Obool)),X30869),X30867))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X30868,tc_HOL_Obool)),X30869),X30866) = c_Orderings_Obot__class_Obot(tc_fun(X30868,tc_HOL_Obool)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_fun(X30872,tc_HOL_Obool)),esk369_3(X30870,X30871,X30872)),X30871))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X30872,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X30872,tc_HOL_Obool),X30871)),X30870) = c_Orderings_Obot__class_Obot(tc_fun(X30872,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X30872,tc_HOL_Obool)),esk369_3(X30870,X30871,X30872)),X30870) != c_Orderings_Obot__class_Obot(tc_fun(X30872,tc_HOL_Obool))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X30872,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X30872,tc_HOL_Obool),X30871)),X30870) = c_Orderings_Obot__class_Obot(tc_fun(X30872,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_8058,plain,
    ! [X19693,X19694,X19695] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19695))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19694))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19694),X19693))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19695),X19693)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19695),X19694))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono2])]) ).

fof(i_0_8059,plain,
    ! [X30883,X30884,X30885,X30886] : hAPP(c_Relation_ODomain(X30886,X30885),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X30886,X30885),tc_HOL_Obool)),X30884),X30883)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X30886,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X30886,X30885),X30884)),hAPP(c_Relation_ODomain(X30886,X30885),X30883)),
    inference(variable_rename,[status(thm)],[fact_Domain__Un__eq]) ).

fof(i_0_8060,plain,
    ! [X28267,X28268,X28269,X28270] : hAPP(c_Relation_ORange(X28270,X28269),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28270,X28269),tc_HOL_Obool)),X28268),X28267)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X28269,tc_HOL_Obool)),hAPP(c_Relation_ORange(X28270,X28269),X28268)),hAPP(c_Relation_ORange(X28270,X28269),X28267)),
    inference(variable_rename,[status(thm)],[fact_Range__Un__eq]) ).

fof(i_0_8061,plain,
    ! [X29713,X29714,X29715,X29716,X29717,X29718] : hAPP(hAPP(c_List_Omap(X29718,X29717),X29716),hAPP(hAPP(c_List_Olist__update(X29718,X29715),X29714),X29713)) = hAPP(hAPP(c_List_Olist__update(X29717,hAPP(hAPP(c_List_Omap(X29718,X29717),X29716),X29715)),X29714),hAPP(X29716,X29713)),
    inference(variable_rename,[status(thm)],[fact_map__update]) ).

fof(i_0_8062,plain,
    ! [X28858,X28859,X28860,X28861] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X28861),X28860),hAPP(c_List_Oset(X28861),hAPP(hAPP(c_List_Olist_OCons(X28861),X28859),X28858))))
      | X28860 = X28859
      | hBOOL(hAPP(hAPP(c_member(X28861),X28860),hAPP(c_List_Oset(X28861),X28858))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__ConsD])]) ).

fof(i_0_8063,plain,
    ! [X30404] :
      ( X30404 = 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,X30404)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Code__Numeral_Onat__of,X30404))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_code__numeral__decr])]) ).

fof(i_0_8064,plain,
    ! [X28831,X28832,X28833,X28834] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X28834),X28833),hAPP(c_List_Oset(X28834),hAPP(hAPP(c_List_Odrop(X28834),X28832),X28831))))
      | hBOOL(hAPP(hAPP(c_member(X28834),X28833),hAPP(c_List_Oset(X28834),X28831))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__set__dropD])]) ).

fof(i_0_8065,plain,
    ! [X28820,X28821,X28822,X28823] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X28823),X28822),hAPP(c_List_Oset(X28823),hAPP(hAPP(c_List_Otake(X28823),X28821),X28820))))
      | hBOOL(hAPP(hAPP(c_member(X28823),X28822),hAPP(c_List_Oset(X28823),X28820))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__set__takeD])]) ).

fof(i_0_8066,plain,
    ! [X20477,X20478,X20479] :
      ( ~ class_Rings_Olinordered__semidom(X20479)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20479),c_Groups_Ozero__class_Ozero(X20479)),X20478))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20479),X20478),c_Groups_Oone__class_Oone(X20479)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20479),hAPP(hAPP(c_Power_Opower__class_Opower(X20479),X20478),hAPP(c_Nat_OSuc,X20477))),c_Groups_Oone__class_Oone(X20479))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__Suc__less__one])]) ).

fof(i_0_8067,plain,
    ! [X33112,X33113,X33114] :
      ( ( hBOOL(hAPP(hAPP(c_member(X33114),X33113),esk499_3(X33112,X33113,X33114)))
        | ~ hBOOL(hAPP(hAPP(c_member(X33114),X33113),c_Complete__Lattice_OSup__class_OSup(tc_fun(X33114,tc_HOL_Obool),X33112))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_fun(X33114,tc_HOL_Obool)),esk499_3(X33112,X33113,X33114)),X33112))
        | ~ hBOOL(hAPP(hAPP(c_member(X33114),X33113),c_Complete__Lattice_OSup__class_OSup(tc_fun(X33114,tc_HOL_Obool),X33112))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5694])])])]) ).

fof(i_0_8068,plain,
    ! [X19682,X19683,X19684] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19684),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)),X19683))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19683),X19682))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19684),X19683)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19684),X19682))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono2__neg])]) ).

fof(i_0_8069,plain,
    ! [X25364,X25365,X25366] :
      ( ( hBOOL(hAPP(hAPP(c_member(X25366),esk166_3(X25364,X25365,X25366)),X25364))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X25366,X25366)),X25365),c_Relation_OId__on(X25366,X25364))) )
      & ( X25365 = hAPP(hAPP(c_Product__Type_OPair(X25366,X25366),esk166_3(X25364,X25365,X25366)),esk166_3(X25364,X25365,X25366))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X25366,X25366)),X25365),c_Relation_OId__on(X25366,X25364))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Id__onE])])])]) ).

fof(i_0_8070,plain,
    ! [X34040,X34041,X34042,X34043] :
      ( ~ c_Fun_Oinj__on(X34043,X34042,X34041,c_Orderings_Otop__class_Otop(tc_fun(X34043,tc_HOL_Obool)))
      | hAPP(c_Hilbert__Choice_Oinv__into(X34043,X34042,c_Orderings_Otop__class_Otop(tc_fun(X34043,tc_HOL_Obool)),X34041),hAPP(X34041,X34040)) = X34040 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__f__f])]) ).

fof(i_0_8071,plain,
    ! [X26767,X26768,X26769,X26770] :
      ( ~ c_Fun_Oinj__on(X26770,X26769,X26768,c_Orderings_Otop__class_Otop(tc_fun(X26770,tc_HOL_Obool)))
      | hAPP(c_Fun_Othe__inv__into(X26770,X26769,c_Orderings_Otop__class_Otop(tc_fun(X26770,tc_HOL_Obool)),X26768),hAPP(X26768,X26767)) = X26767 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_the__inv__f__f])]) ).

fof(i_0_8072,plain,
    ! [X32982,X32983,X32984,X32985,X32986,X32987] :
      ( ~ c_Finite__Set_Ofun__left__comm(X32987,X32986,X32985)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32987),X32984))
      | hAPP(hAPP(X32985,X32983),hAPP(hAPP(c_Finite__Set_Ofold(X32987,X32986,X32985),X32982),X32984)) = hAPP(hAPP(c_Finite__Set_Ofold(X32987,X32986,X32985),hAPP(hAPP(X32985,X32983),X32982)),X32984) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__fun__comm])]) ).

fof(i_0_8073,plain,
    ! [X34044,X34045,X34046,X34047,X34048] :
      ( ~ c_Fun_Oinj__on(X34048,X34047,X34046,c_Orderings_Otop__class_Otop(tc_fun(X34048,tc_HOL_Obool)))
      | hAPP(X34046,X34045) != X34044
      | hAPP(c_Hilbert__Choice_Oinv__into(X34048,X34047,c_Orderings_Otop__class_Otop(tc_fun(X34048,tc_HOL_Obool)),X34046),X34044) = X34045 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__f__eq])]) ).

fof(i_0_8074,plain,
    ! [X31977,X31978,X31979] :
      ( ~ c_Wellfounded_OwfP(X31979,X31978)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X31979,tc_fun(X31979,tc_HOL_Obool))),X31977),X31978))
      | c_Wellfounded_OwfP(X31979,X31977) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wfP__subset])]) ).

fof(i_0_8075,plain,
    ! [X22288,X22289,X22290] :
      ( ( hAPP(hAPP(c_COMBC(X22290,tc_fun(X22290,tc_HOL_Obool),tc_HOL_Obool),c_member(X22290)),X22289) != hAPP(hAPP(c_COMBC(X22290,tc_fun(X22290,tc_HOL_Obool),tc_HOL_Obool),c_member(X22290)),X22288)
        | X22289 = X22288 )
      & ( X22289 != X22288
        | hAPP(hAPP(c_COMBC(X22290,tc_fun(X22290,tc_HOL_Obool),tc_HOL_Obool),c_member(X22290)),X22289) = hAPP(hAPP(c_COMBC(X22290,tc_fun(X22290,tc_HOL_Obool),tc_HOL_Obool),c_member(X22290)),X22288) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__equals__eq])]) ).

fof(i_0_8076,plain,
    ! [X18859,X18860,X18861] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18861))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18861),X18860)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18861),X18859))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18860),X18859))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18861),X18860)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18861),X18859))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18861))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18860),X18859))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18861),X18860)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18861),X18859))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel1])])]) ).

fof(i_0_8077,plain,
    ! [X18856,X18857,X18858] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18857))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18858),X18857)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18856),X18857))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18858),X18856))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18858),X18857)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18856),X18857))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18857))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18858),X18856))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18858),X18857)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18856),X18857))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel2])])]) ).

fof(i_0_8078,plain,
    ! [X31888,X31889,X31890,X31891,X31892] :
      ( ~ class_Orderings_Olinorder(X31892)
      | c_List_Olinorder__class_Osort__key(X31891,X31892,X31890,hAPP(hAPP(c_List_Olist_OCons(X31891),X31889),X31888)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X31891,X31892,X31890),X31889),c_List_Olinorder__class_Osort__key(X31891,X31892,X31890,X31888)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sort__key__simps_I2_J])]) ).

fof(i_0_8079,plain,
    ! [X21305,X21306,X21307,X21308] :
      ( ~ class_Fields_Olinordered__field__inverse__zero(X21308)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21308),X21307),X21306))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21308),c_Groups_Ozero__class_Ozero(X21308)),X21305))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21308),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21308),X21307),X21305)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21308),X21306),X21305))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__right__mono])]) ).

fof(i_0_8080,plain,
    ! [X20550,X20551,X20552,X20553] :
      ( ~ class_Rings_Olinordered__semidom(X20553)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20553),X20552),X20551))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20553),c_Groups_Ozero__class_Ozero(X20553)),X20552))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20553),hAPP(hAPP(c_Power_Opower__class_Opower(X20553),X20552),X20550)),hAPP(hAPP(c_Power_Opower__class_Opower(X20553),X20551),X20550))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__mono])]) ).

fof(i_0_8081,plain,
    ! [X18786,X18787,X18788,X18789] :
      ( ~ class_Rings_Oordered__semiring(X18789)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18789),X18788),X18787))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18789),c_Groups_Ozero__class_Ozero(X18789)),X18786))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18789),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18789),X18788),X18786)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18789),X18787),X18786))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__mono])]) ).

fof(i_0_8082,plain,
    ! [X18794,X18795,X18796,X18797] :
      ( ~ class_Rings_Oordered__comm__semiring(X18797)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18797),X18796),X18795))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18797),c_Groups_Ozero__class_Ozero(X18797)),X18794))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18797),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18797),X18794),X18796)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18797),X18794),X18795))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__mult__left__mono])]) ).

fof(i_0_8083,plain,
    ! [X18790,X18791,X18792,X18793] :
      ( ~ class_Rings_Oordered__semiring(X18793)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18793),X18792),X18791))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18793),c_Groups_Ozero__class_Ozero(X18793)),X18790))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18793),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18793),X18790),X18792)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18793),X18790),X18791))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__mono])]) ).

fof(i_0_8084,plain,
    ! [X21317,X21318,X21319,X21320] :
      ( ~ class_Fields_Olinordered__field(X21320)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21320),X21319),X21318))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21320),c_Groups_Ozero__class_Ozero(X21320)),X21317))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21320),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21320),X21319),X21317)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21320),X21318),X21317))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__strict__right__mono])]) ).

fof(i_0_8085,plain,
    ! [X18367,X18368,X18369,X18370] :
      ( ~ class_Rings_Olinordered__semiring__strict(X18370)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18370),X18369),X18368))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18370),c_Groups_Ozero__class_Ozero(X18370)),X18367))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18370),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18370),X18369),X18367)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18370),X18368),X18367))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__right__mono])]) ).

fof(i_0_8086,plain,
    ! [X18375,X18376,X18377,X18378] :
      ( ~ class_Rings_Olinordered__comm__semiring__strict(X18378)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18378),X18377),X18376))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18378),c_Groups_Ozero__class_Ozero(X18378)),X18375))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18378),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18378),X18375),X18377)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18378),X18375),X18376))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__mult__strict__left__mono])]) ).

fof(i_0_8087,plain,
    ! [X18371,X18372,X18373,X18374] :
      ( ~ class_Rings_Olinordered__semiring__strict(X18374)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18374),X18373),X18372))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18374),c_Groups_Ozero__class_Ozero(X18374)),X18371))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18374),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18374),X18371),X18373)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18374),X18371),X18372))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__left__mono])]) ).

fof(i_0_8088,plain,
    ! [X29118,X29119,X29120,X29121,X29122,X29123] : hAPP(hAPP(c_List_Ozip(X29123,X29122),hAPP(hAPP(c_List_Olist_OCons(X29123),X29121),X29120)),hAPP(hAPP(c_List_Olist_OCons(X29122),X29119),X29118)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(X29123,X29122)),hAPP(hAPP(c_Product__Type_OPair(X29123,X29122),X29121),X29119)),hAPP(hAPP(c_List_Ozip(X29123,X29122),X29120),X29118)),
    inference(variable_rename,[status(thm)],[fact_zip__Cons__Cons]) ).

fof(i_0_8089,plain,
    ! [X21302,X21303,X21304] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21304),X21303),c_Groups_Ozero__class_Ozero(X21304)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21304),c_Groups_Ozero__class_Ozero(X21304)),X21303))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21304),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21304),X21303),X21302)),c_Groups_Ozero__class_Ozero(X21304)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21304) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21304),c_Groups_Ozero__class_Ozero(X21304)),X21302))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21304),c_Groups_Ozero__class_Ozero(X21304)),X21303))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21304),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21304),X21303),X21302)),c_Groups_Ozero__class_Ozero(X21304)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21304) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21304),X21303),c_Groups_Ozero__class_Ozero(X21304)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21304),X21302),c_Groups_Ozero__class_Ozero(X21304)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21304),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21304),X21303),X21302)),c_Groups_Ozero__class_Ozero(X21304)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21304) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21304),c_Groups_Ozero__class_Ozero(X21304)),X21302))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21304),X21302),c_Groups_Ozero__class_Ozero(X21304)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21304),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21304),X21303),X21302)),c_Groups_Ozero__class_Ozero(X21304)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21304) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21304),c_Groups_Ozero__class_Ozero(X21304)),X21303))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21304),X21302),c_Groups_Ozero__class_Ozero(X21304)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21304),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21304),X21303),X21302)),c_Groups_Ozero__class_Ozero(X21304)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21304) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21304),X21303),c_Groups_Ozero__class_Ozero(X21304)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21304),c_Groups_Ozero__class_Ozero(X21304)),X21302))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21304),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21304),X21303),X21302)),c_Groups_Ozero__class_Ozero(X21304)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21304) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__le__0__iff])])]) ).

fof(i_0_8090,plain,
    ! [X18768,X18769,X18770] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18770),X18769),c_Groups_Ozero__class_Ozero(X18770)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18770),c_Groups_Ozero__class_Ozero(X18770)),X18769))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18770),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18770),X18769),X18768)),c_Groups_Ozero__class_Ozero(X18770)))
        | ~ class_Rings_Olinordered__ring__strict(X18770) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18770),c_Groups_Ozero__class_Ozero(X18770)),X18768))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18770),c_Groups_Ozero__class_Ozero(X18770)),X18769))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18770),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18770),X18769),X18768)),c_Groups_Ozero__class_Ozero(X18770)))
        | ~ class_Rings_Olinordered__ring__strict(X18770) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18770),X18769),c_Groups_Ozero__class_Ozero(X18770)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18770),X18768),c_Groups_Ozero__class_Ozero(X18770)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18770),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18770),X18769),X18768)),c_Groups_Ozero__class_Ozero(X18770)))
        | ~ class_Rings_Olinordered__ring__strict(X18770) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18770),c_Groups_Ozero__class_Ozero(X18770)),X18768))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18770),X18768),c_Groups_Ozero__class_Ozero(X18770)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18770),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18770),X18769),X18768)),c_Groups_Ozero__class_Ozero(X18770)))
        | ~ class_Rings_Olinordered__ring__strict(X18770) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18770),c_Groups_Ozero__class_Ozero(X18770)),X18769))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18770),X18768),c_Groups_Ozero__class_Ozero(X18770)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18770),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18770),X18769),X18768)),c_Groups_Ozero__class_Ozero(X18770)))
        | ~ class_Rings_Olinordered__ring__strict(X18770) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18770),X18769),c_Groups_Ozero__class_Ozero(X18770)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18770),c_Groups_Ozero__class_Ozero(X18770)),X18768))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18770),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18770),X18769),X18768)),c_Groups_Ozero__class_Ozero(X18770)))
        | ~ class_Rings_Olinordered__ring__strict(X18770) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__0__iff])])]) ).

fof(i_0_8091,plain,
    ! [X21333,X21334,X21335] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21335),X21334),c_Groups_Ozero__class_Ozero(X21335)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21335),c_Groups_Ozero__class_Ozero(X21335)),X21334))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21335),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21335),X21334),X21333)),c_Groups_Ozero__class_Ozero(X21335)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21335) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21335),c_Groups_Ozero__class_Ozero(X21335)),X21333))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21335),c_Groups_Ozero__class_Ozero(X21335)),X21334))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21335),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21335),X21334),X21333)),c_Groups_Ozero__class_Ozero(X21335)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21335) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21335),X21334),c_Groups_Ozero__class_Ozero(X21335)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21335),X21333),c_Groups_Ozero__class_Ozero(X21335)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21335),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21335),X21334),X21333)),c_Groups_Ozero__class_Ozero(X21335)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21335) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21335),c_Groups_Ozero__class_Ozero(X21335)),X21333))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21335),X21333),c_Groups_Ozero__class_Ozero(X21335)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21335),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21335),X21334),X21333)),c_Groups_Ozero__class_Ozero(X21335)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21335) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21335),c_Groups_Ozero__class_Ozero(X21335)),X21334))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21335),X21333),c_Groups_Ozero__class_Ozero(X21335)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21335),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21335),X21334),X21333)),c_Groups_Ozero__class_Ozero(X21335)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21335) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21335),X21334),c_Groups_Ozero__class_Ozero(X21335)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21335),c_Groups_Ozero__class_Ozero(X21335)),X21333))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21335),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21335),X21334),X21333)),c_Groups_Ozero__class_Ozero(X21335)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21335) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__less__0__iff])])]) ).

fof(i_0_8092,plain,
    ! [X23438,X23439] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X23439),X23438))
        | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,X23439)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X23438)))
        | ~ c_Nat__Transfer_Onat__set(X23438)
        | ~ c_Nat__Transfer_Ois__nat(X23439) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,X23439)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X23438)))
        | hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X23439),X23438))
        | ~ c_Nat__Transfer_Onat__set(X23438)
        | ~ c_Nat__Transfer_Ois__nat(X23439) ) ),
    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_8093,plain,
    ! [X32703,X32704,X32705] :
      ( ( hBOOL(hAPP(hAPP(c_member(X32705),esk474_3(X32703,X32704,X32705)),X32704))
        | ~ hBOOL(hAPP(hAPP(c_member(X32705),X32703),X32704))
        | c_Big__Operators_Olinorder__class_OMax(X32705,X32704) = X32703
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32705),X32704))
        | ~ class_Orderings_Olinorder(X32705) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X32705),esk474_3(X32703,X32704,X32705)),X32703))
        | ~ hBOOL(hAPP(hAPP(c_member(X32705),X32703),X32704))
        | c_Big__Operators_Olinorder__class_OMax(X32705,X32704) = X32703
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32705),X32704))
        | ~ class_Orderings_Olinorder(X32705) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max__eqI])])])]) ).

fof(i_0_8094,plain,
    ! [X33157,X33158,X33159,X33160,X33161,X33162,X33163] :
      ( ( ~ c_List_Olist__all(X33159,X33158,X33157)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33160),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33159)),X33157)))
        | hBOOL(hAPP(X33158,hAPP(hAPP(c_List_Onth(X33159),X33157),X33160))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk506_3(X33161,X33162,X33163)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33163)),X33161)))
        | c_List_Olist__all(X33163,X33162,X33161) )
      & ( ~ hBOOL(hAPP(X33162,hAPP(hAPP(c_List_Onth(X33163),X33161),esk506_3(X33161,X33162,X33163))))
        | c_List_Olist__all(X33163,X33162,X33161) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all__length])])])])])]) ).

fof(i_0_8095,plain,
    ! [X22144] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X22144)),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),X22144)) = 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),X22144))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__pos__neg__1__number__of])]) ).

fof(i_0_8096,plain,
    ! [X25672,X25673,X25674,X25675,X25676] :
      ( ~ c_Fun_Oinj__on(X25676,X25675,X25674,X25673)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25676,tc_HOL_Obool)),X25672),X25673))
      | c_Fun_Oinj__on(X25676,X25675,X25674,X25672) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__inj__on])]) ).

fof(i_0_8097,plain,
    ! [X31146,X31147,X31148] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31148)),hAPP(c_List_Ofilter(X31148,X31147),X31146))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31148)),X31146))),
    inference(variable_rename,[status(thm)],[fact_length__filter__le]) ).

fof(i_0_8098,plain,
    ! [X32137,X32138,X32139] : hBOOL(hAPP(hAPP(c_member(tc_prod(X32139,X32139)),hAPP(hAPP(c_Product__Type_OPair(X32139,X32139),X32138),X32138)),c_Transitive__Closure_Ortrancl(X32139,X32137))),
    inference(variable_rename,[status(thm)],[fact_rtrancl_Ortrancl__refl]) ).

cnf(i_0_8099,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_8100,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_8101,plain,
    ! [X19148,X19149,X19150] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19150),X19149)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19150),X19148)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19149),X19148)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19149),X19148))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19150),X19149)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19150),X19148))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__le])]) ).

cnf(i_0_8102,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_5697]) ).

cnf(i_0_8103,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_5698]) ).

fof(i_0_8104,plain,
    ! [X17443,X17444,X17445] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17445),X17444)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17445),X17443)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17444),X17443)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17444),X17443))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17445),X17444)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17445),X17443))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__less])]) ).

fof(i_0_8105,plain,
    ! [X34035,X34036,X34037,X34038,X34039] :
      ( ~ c_Fun_Oinj__on(X34039,X34038,X34037,X34036)
      | ~ hBOOL(hAPP(hAPP(c_member(X34039),X34035),X34036))
      | hAPP(c_Hilbert__Choice_Oinv__into(X34039,X34038,X34036,X34037),hAPP(X34037,X34035)) = X34035 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__f__f])]) ).

fof(i_0_8106,plain,
    ! [X26039,X26040,X26041,X26042,X26043] :
      ( ~ c_Fun_Oinj__on(X26043,X26042,X26041,X26040)
      | ~ hBOOL(hAPP(hAPP(c_member(X26043),X26039),X26040))
      | hAPP(c_Fun_Othe__inv__into(X26043,X26042,X26040,X26041),hAPP(X26041,X26039)) = X26039 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_the__inv__into__f__f])]) ).

cnf(i_0_8107,plain,
    hAPP(c_List_OremoveAll(X1,X2),c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
    inference(split_conjunct,[status(thm)],[i_0_5699]) ).

fof(i_0_8108,plain,
    ! [X22197] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X22197)),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),X22197)) = 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),X22197))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__pos__neg__1__number__of])]) ).

fof(i_0_8109,plain,
    ! [X34029,X34030,X34031,X34032,X34033,X34034] :
      ( ~ c_Fun_Oinj__on(X34034,X34033,X34032,X34031)
      | ~ hBOOL(hAPP(hAPP(c_member(X34034),X34030),X34031))
      | hAPP(X34032,X34030) != X34029
      | hAPP(c_Hilbert__Choice_Oinv__into(X34034,X34033,X34031,X34032),X34029) = X34030 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__f__eq])]) ).

fof(i_0_8110,plain,
    ! [X26044,X26045,X26046,X26047,X26048,X26049] :
      ( ~ c_Fun_Oinj__on(X26049,X26048,X26047,X26046)
      | hAPP(X26047,X26045) != X26044
      | ~ hBOOL(hAPP(hAPP(c_member(X26049),X26045),X26046))
      | hAPP(c_Fun_Othe__inv__into(X26049,X26048,X26046,X26047),X26044) = X26045 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_the__inv__into__f__eq])]) ).

fof(i_0_8111,plain,
    ! [X29682,X29683,X29684,X29685,X29686] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X29685),X29686),X29684))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29683),hAPP(X29682,X29686)))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X29683),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29685,tc_fun(X29683,tc_HOL_Obool)),X29684),X29682))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__INT])])]) ).

fof(i_0_8112,plain,
    ! [X20622,X20623,X20624,X20625] :
      ( ~ class_Rings_Olinordered__semidom(X20625)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20624),X20623))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20625),c_Groups_Oone__class_Oone(X20625)),X20622))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20625),hAPP(hAPP(c_Power_Opower__class_Opower(X20625),X20622),X20624)),hAPP(hAPP(c_Power_Opower__class_Opower(X20625),X20622),X20623))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__increasing])]) ).

fof(i_0_8113,plain,
    ! [X20607,X20608,X20609,X20610] :
      ( ~ class_Rings_Olinordered__semidom(X20610)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20609),X20608))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20610),c_Groups_Oone__class_Oone(X20610)),X20607))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20610),hAPP(hAPP(c_Power_Opower__class_Opower(X20610),X20607),X20609)),hAPP(hAPP(c_Power_Opower__class_Opower(X20610),X20607),X20608))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__strict__increasing])]) ).

fof(i_0_8114,plain,
    ! [X21309,X21310,X21311,X21312] :
      ( ~ class_Fields_Olinordered__field__inverse__zero(X21312)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21312),X21311),X21310))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21312),X21309),c_Groups_Ozero__class_Ozero(X21312)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21312),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21312),X21310),X21309)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21312),X21311),X21309))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__right__mono__neg])]) ).

fof(i_0_8115,plain,
    ! [X18798,X18799,X18800,X18801] :
      ( ~ class_Rings_Oordered__ring(X18801)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18801),X18800),X18799))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18801),X18798),c_Groups_Ozero__class_Ozero(X18801)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18801),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18801),X18799),X18798)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18801),X18800),X18798))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__mono__neg])]) ).

fof(i_0_8116,plain,
    ! [X18802,X18803,X18804,X18805] :
      ( ~ class_Rings_Oordered__ring(X18805)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18805),X18804),X18803))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18805),X18802),c_Groups_Ozero__class_Ozero(X18805)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18805),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18805),X18802),X18803)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18805),X18802),X18804))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__mono__neg])]) ).

fof(i_0_8117,plain,
    ! [X21313,X21314,X21315,X21316] :
      ( ~ class_Fields_Olinordered__field(X21316)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21316),X21315),X21314))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21316),X21313),c_Groups_Ozero__class_Ozero(X21316)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21316),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21316),X21314),X21313)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21316),X21315),X21313))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__strict__right__mono__neg])]) ).

fof(i_0_8118,plain,
    ! [X18379,X18380,X18381,X18382] :
      ( ~ class_Rings_Olinordered__ring__strict(X18382)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18382),X18381),X18380))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18382),X18379),c_Groups_Ozero__class_Ozero(X18382)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18382),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18382),X18380),X18379)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18382),X18381),X18379))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__right__mono__neg])]) ).

fof(i_0_8119,plain,
    ! [X18383,X18384,X18385,X18386] :
      ( ~ class_Rings_Olinordered__ring__strict(X18386)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18386),X18385),X18384))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18386),X18383),c_Groups_Ozero__class_Ozero(X18386)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18386),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18386),X18383),X18384)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18386),X18383),X18385))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__left__mono__neg])]) ).

cnf(i_0_8120,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_8121,plain,
    ! [X24518,X24519,X24520] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24520),X24519))
      | ~ hBOOL(hAPP(hAPP(c_member(X24520),X24518),X24519))
      | hAPP(c_Finite__Set_Ocard(X24520),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24520,tc_HOL_Obool)),X24519),hAPP(hAPP(c_Set_Oinsert(X24520),X24518),c_Orderings_Obot__class_Obot(tc_fun(X24520,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X24520),X24519)),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_8122,plain,
    ! [X24515,X24516,X24517] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X24517),X24515),X24516))
        | hAPP(c_Finite__Set_Ocard(X24517),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24517,tc_HOL_Obool)),X24516),hAPP(hAPP(c_Set_Oinsert(X24517),X24515),c_Orderings_Obot__class_Obot(tc_fun(X24517,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X24517),X24516)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24517),X24516)) )
      & ( hBOOL(hAPP(hAPP(c_member(X24517),X24515),X24516))
        | hAPP(c_Finite__Set_Ocard(X24517),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24517,tc_HOL_Obool)),X24516),hAPP(hAPP(c_Set_Oinsert(X24517),X24515),c_Orderings_Obot__class_Obot(tc_fun(X24517,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(X24517),X24516)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24517),X24516)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5700])])]) ).

fof(i_0_8123,plain,
    ! [X23558,X23559,X23560] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23560),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23560,tc_HOL_Obool)),X23558),X23559)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X23560),X23558))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23560),X23559)) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23560),X23558))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X23560),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23560,tc_HOL_Obool)),X23558),X23559)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23560),X23559)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Diff2])])]) ).

cnf(i_0_8124,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_5701]) ).

fof(i_0_8125,plain,
    ! [X20325,X20326,X20327] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20327),hAPP(c_Int_Onumber__class_Onumber__of(X20327),X20326)),hAPP(c_Int_Onumber__class_Onumber__of(X20327),X20325)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20327),hAPP(c_Int_Onumber__class_Onumber__of(X20327),X20325)),hAPP(c_Int_Onumber__class_Onumber__of(X20327),X20326)))
        | ~ class_Int_Onumber(X20327)
        | ~ class_Orderings_Olinorder(X20327) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20327),hAPP(c_Int_Onumber__class_Onumber__of(X20327),X20325)),hAPP(c_Int_Onumber__class_Onumber__of(X20327),X20326)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20327),hAPP(c_Int_Onumber__class_Onumber__of(X20327),X20326)),hAPP(c_Int_Onumber__class_Onumber__of(X20327),X20325)))
        | ~ class_Int_Onumber(X20327)
        | ~ class_Orderings_Olinorder(X20327) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5702])])]) ).

fof(i_0_8126,plain,
    ! [X22202,X22203,X22204,X22205] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X22205,tc_fun(X22204,tc_HOL_Obool))),X22203),X22202)),
    inference(variable_rename,[status(thm)],[i_0_5703]) ).

fof(i_0_8127,plain,
    ! [X29580,X29581,X29582] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29582),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),X29581)))
      | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat,X29581),X29582),X29580)) = 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),X29581)),X29580)),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),X29581),X29582)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__update__nat])]) ).

fof(i_0_8128,plain,
    ! [X21700,X21701,X21702,X21703,X21704,X21705] : hAPP(hAPP(c_Fun_Ocomp(X21705,X21704,X21703,X21702),X21701),X21700) = hAPP(X21702,hAPP(X21701,X21700)),
    inference(variable_rename,[status(thm)],[fact_o__def]) ).

fof(i_0_8129,plain,
    ! [X18045,X18046,X18047,X18048,X18049,X18050] : hAPP(hAPP(c_Fun_Ocomp(X18050,X18049,X18048,X18047),X18046),X18045) = hAPP(X18047,hAPP(X18046,X18045)),
    inference(variable_rename,[status(thm)],[fact_o__apply]) ).

fof(i_0_8130,plain,
    ! [X23781,X23782,X23783,X23784,X23785] :
      ( ~ class_Lattices_Osemilattice__inf(X23785)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23785),X23784),X23783))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23785),X23782),X23781))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23785),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23785),X23784),X23782)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23785),X23783),X23781))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__mono])]) ).

fof(i_0_8131,plain,
    ! [X22885,X22886,X22887,X22888,X22889] :
      ( ~ class_Lattices_Osemilattice__sup(X22889)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22889),X22888),X22887))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22889),X22886),X22885))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22889),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X22889),X22888),X22886)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X22889),X22887),X22885))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__mono])]) ).

fof(i_0_8132,plain,
    ! [X22597,X22598,X22599,X22600,X22601] :
      ( ~ class_Orderings_Olinorder(X22601)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22601),X22600),X22599))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22601),X22598),X22597))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22601),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22601),X22600),X22598)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22601),X22599),X22597))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__mono])]) ).

fof(i_0_8133,plain,
    ! [X22453,X22454,X22455,X22456,X22457] :
      ( ~ class_Orderings_Olinorder(X22457)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22457),X22456),X22455))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22457),X22454),X22453))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22457),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22457),X22456),X22454)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22457),X22455),X22453))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__mono])]) ).

fof(i_0_8134,plain,
    ! [X18646,X18647,X18648,X18649,X18650] :
      ( ~ class_Groups_Oordered__ab__semigroup__add(X18650)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18650),X18649),X18648))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18650),X18647),X18646))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18650),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18650),X18649),X18647)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18650),X18648),X18646))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__mono])]) ).

fof(i_0_8135,plain,
    ! [X18822,X18823,X18824,X18825,X18826] :
      ( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X18826)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18826),X18825),X18824))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18826),X18823),X18822))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18826),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18826),X18825),X18823)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18826),X18824),X18822))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__le__mono])]) ).

fof(i_0_8136,plain,
    ! [X18827,X18828,X18829,X18830,X18831] :
      ( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X18831)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18831),X18830),X18829))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18831),X18828),X18827))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18831),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18831),X18830),X18828)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18831),X18829),X18827))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__less__mono])]) ).

fof(i_0_8137,plain,
    ! [X17292,X17293,X17294,X17295,X17296] :
      ( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X17296)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17296),X17295),X17294))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17296),X17293),X17292))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17296),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17296),X17295),X17293)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17296),X17294),X17292))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__mono])]) ).

fof(i_0_8138,plain,
    ! [X20349,X20350,X20351,X20352] :
      ( ~ class_Int_Onumber(X20352)
      | ~ class_Rings_Oring(X20352)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20352),hAPP(c_Int_Onumber__class_Onumber__of(X20352),X20351)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20352),X20350),X20349)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20352),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20352),hAPP(c_Int_Onumber__class_Onumber__of(X20352),X20351)),X20350)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20352),hAPP(c_Int_Onumber__class_Onumber__of(X20352),X20351)),X20349)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__diff__distrib__number__of])]) ).

fof(i_0_8139,plain,
    ! [X20328,X20329,X20330,X20331] :
      ( ~ class_Int_Onumber(X20331)
      | ~ class_Rings_Osemiring(X20331)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20331),hAPP(c_Int_Onumber__class_Onumber__of(X20331),X20330)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20331),X20329),X20328)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20331),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20331),hAPP(c_Int_Onumber__class_Onumber__of(X20331),X20330)),X20329)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20331),hAPP(c_Int_Onumber__class_Onumber__of(X20331),X20330)),X20328)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__distrib__number__of])]) ).

fof(i_0_8140,plain,
    ! [X32819,X32820,X32821,X32822] :
      ( ~ class_Lattices_Osemilattice__inf(X32822)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32822),X32821))
      | hAPP(hAPP(c_Finite__Set_Ofold(X32822,X32822,c_Lattices_Osemilattice__inf__class_Oinf(X32822)),X32820),hAPP(hAPP(c_Set_Oinsert(X32822),X32819),X32821)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X32822),X32819),hAPP(hAPP(c_Finite__Set_Ofold(X32822,X32822,c_Lattices_Osemilattice__inf__class_Oinf(X32822)),X32820),X32821)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__inf__insert])]) ).

fof(i_0_8141,plain,
    ! [X32823,X32824,X32825,X32826] :
      ( ~ class_Lattices_Osemilattice__sup(X32826)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32826),X32825))
      | hAPP(hAPP(c_Finite__Set_Ofold(X32826,X32826,c_Lattices_Osemilattice__sup__class_Osup(X32826)),X32824),hAPP(hAPP(c_Set_Oinsert(X32826),X32823),X32825)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X32826),X32823),hAPP(hAPP(c_Finite__Set_Ofold(X32826,X32826,c_Lattices_Osemilattice__sup__class_Osup(X32826)),X32824),X32825)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__sup__insert])]) ).

fof(i_0_8142,plain,
    ! [X32830,X32831,X32832,X32833] :
      ( ~ class_Orderings_Olinorder(X32833)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32833),X32832))
      | hAPP(hAPP(c_Finite__Set_Ofold(X32833,X32833,c_Orderings_Oord__class_Omax(X32833)),X32831),hAPP(hAPP(c_Set_Oinsert(X32833),X32830),X32832)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X32833),X32830),hAPP(hAPP(c_Finite__Set_Ofold(X32833,X32833,c_Orderings_Oord__class_Omax(X32833)),X32831),X32832)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ofold__sup__insert])]) ).

fof(i_0_8143,plain,
    ! [X32834,X32835,X32836,X32837] :
      ( ~ class_Orderings_Olinorder(X32837)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32837),X32836))
      | hAPP(hAPP(c_Finite__Set_Ofold(X32837,X32837,c_Orderings_Oord__class_Omin(X32837)),X32835),hAPP(hAPP(c_Set_Oinsert(X32837),X32834),X32836)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X32837),X32834),hAPP(hAPP(c_Finite__Set_Ofold(X32837,X32837,c_Orderings_Oord__class_Omin(X32837)),X32835),X32836)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ofold__inf__insert])]) ).

fof(i_0_8144,plain,
    ! [X27208,X27209,X27210,X27211] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27211),X27210))
      | ~ c_Fun_Oinj__on(X27209,X27211,X27208,c_Orderings_Otop__class_Otop(tc_fun(X27209,tc_HOL_Obool)))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X27209),hAPP(c_Set_Ovimage(X27209,X27211,X27208),X27210))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__vimageI])]) ).

fof(i_0_8145,plain,
    ! [X30192,X30193,X30194,X30195,X30196] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X30196)
      | ~ hBOOL(hAPP(hAPP(c_member(X30195),X30194),X30193))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X30196),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30195,X30196),X30193),X30192)),hAPP(X30192,X30194))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF__leI])]) ).

fof(i_0_8146,plain,
    ! [X20450,X20451,X20452,X20453] :
      ( ~ class_Int_Onumber__ring(X20453)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20453),hAPP(c_Int_Onumber__class_Onumber__of(X20453),X20452)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20453),X20451),hAPP(c_Int_Onumber__class_Onumber__of(X20453),X20450))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20453),hAPP(c_Int_Onumber__class_Onumber__of(X20453),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20452),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X20450)))),X20451) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__number__of__diff2])]) ).

fof(i_0_8147,plain,
    ! [X21717,X21718] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21718)),X21717))
        | hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21718),X21717)) )
      & ( ~ hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21718),X21717))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21718)),X21717)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__nat_Osimps_I2_J])]) ).

fof(i_0_8148,plain,
    ! [X24820,X24821,X24822,X24823,X24824,X24825] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X24825),X24824),X24823))
      | ~ hBOOL(hAPP(hAPP(X24822,X24824),X24821))
      | hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24825,tc_fun(X24820,tc_HOL_Obool)),X24823),X24822),X24821)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUP1__I])]) ).

fof(i_0_8149,plain,
    ! [X30843,X30844,X30845,X30846] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X30845),c_Complete__Lattice_OSup__class_OSup(X30845,X30844)),X30843))
        | ~ hBOOL(hAPP(hAPP(c_member(X30845),X30846),X30844))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X30845),X30846),X30843))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X30845) )
      & ( hBOOL(hAPP(hAPP(c_member(X30845),esk368_3(X30843,X30844,X30845)),X30844))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X30845),c_Complete__Lattice_OSup__class_OSup(X30845,X30844)),X30843))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X30845) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X30845),esk368_3(X30843,X30844,X30845)),X30843))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X30845),c_Complete__Lattice_OSup__class_OSup(X30845,X30844)),X30843))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X30845) ) ),
    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_8150,plain,
    ! [X32838,X32839,X32840,X32841,X32842,X32843] :
      ( ~ c_Finite__Set_Ofun__left__comm__idem(X32843,X32842,X32841)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32843),X32840))
      | hAPP(hAPP(c_Finite__Set_Ofold(X32843,X32842,X32841),X32839),hAPP(hAPP(c_Set_Oinsert(X32843),X32838),X32840)) = hAPP(hAPP(X32841,X32838),hAPP(hAPP(c_Finite__Set_Ofold(X32843,X32842,X32841),X32839),X32840)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofold__insert__idem])]) ).

fof(i_0_8151,plain,
    ! [X29398,X29399,X29400,X29401,X29402] :
      ( ( X29399 = 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),X29399),X29398) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X29400),hAPP(c_List_Oset(tc_Nat_Onat),X29398)))
        | X29400 = 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),X29399),X29398) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk341_2(X29401,X29402)),hAPP(c_List_Oset(tc_Nat_Onat),X29401)))
        | X29402 != 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),X29402),X29401) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( esk341_2(X29401,X29402) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X29402 != 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),X29402),X29401) = 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_8152,plain,
    ! [X17695,X17696,X17697,X17698,X17699,X17700] :
      ( ( ~ hBOOL(hAPP(X17700,X17697))
        | hBOOL(hAPP(X17700,X17697))
        | ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X17700,X17699,X17698),X17697,X17696,X17695) )
      & ( c_Natural_Oevaln(X17698,X17697,X17696,X17695)
        | hBOOL(hAPP(X17700,X17697))
        | ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X17700,X17699,X17698),X17697,X17696,X17695) )
      & ( ~ hBOOL(hAPP(X17700,X17697))
        | c_Natural_Oevaln(X17699,X17697,X17696,X17695)
        | ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X17700,X17699,X17698),X17697,X17696,X17695) )
      & ( c_Natural_Oevaln(X17698,X17697,X17696,X17695)
        | c_Natural_Oevaln(X17699,X17697,X17696,X17695)
        | ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X17700,X17699,X17698),X17697,X17696,X17695) )
      & ( ~ hBOOL(hAPP(X17700,X17697))
        | ~ c_Natural_Oevaln(X17699,X17697,X17696,X17695)
        | c_Natural_Oevaln(c_Com_Ocom_OCond(X17700,X17699,X17698),X17697,X17696,X17695) )
      & ( hBOOL(hAPP(X17700,X17697))
        | ~ c_Natural_Oevaln(X17698,X17697,X17696,X17695)
        | c_Natural_Oevaln(c_Com_Ocom_OCond(X17700,X17699,X17698),X17697,X17696,X17695) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5704])])]) ).

fof(i_0_8153,plain,
    ! [X17689,X17690,X17691,X17692,X17693,X17694] :
      ( ( ~ hBOOL(hAPP(X17694,X17691))
        | hBOOL(hAPP(X17694,X17691))
        | ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X17694,X17693,X17692),X17691,X17690,X17689) )
      & ( c_Natural_Oevaln(X17692,X17691,X17690,X17689)
        | hBOOL(hAPP(X17694,X17691))
        | ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X17694,X17693,X17692),X17691,X17690,X17689) )
      & ( ~ hBOOL(hAPP(X17694,X17691))
        | c_Natural_Oevaln(X17693,X17691,X17690,X17689)
        | ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X17694,X17693,X17692),X17691,X17690,X17689) )
      & ( c_Natural_Oevaln(X17692,X17691,X17690,X17689)
        | c_Natural_Oevaln(X17693,X17691,X17690,X17689)
        | ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X17694,X17693,X17692),X17691,X17690,X17689) )
      & ( ~ hBOOL(hAPP(X17694,X17691))
        | ~ c_Natural_Oevaln(X17693,X17691,X17690,X17689)
        | c_Natural_Oevaln(c_Com_Ocom_OCond(X17694,X17693,X17692),X17691,X17690,X17689) )
      & ( hBOOL(hAPP(X17694,X17691))
        | ~ c_Natural_Oevaln(X17692,X17691,X17690,X17689)
        | c_Natural_Oevaln(c_Com_Ocom_OCond(X17694,X17693,X17692),X17691,X17690,X17689) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5705])])]) ).

fof(i_0_8154,plain,
    ! [X17642,X17643,X17644,X17645,X17646,X17647] :
      ( ( ~ hBOOL(hAPP(X17647,X17644))
        | hBOOL(hAPP(X17647,X17644))
        | ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X17647,X17646,X17645),X17644,X17643,X17642) )
      & ( c_Natural_Oevaln(X17645,X17644,X17643,X17642)
        | hBOOL(hAPP(X17647,X17644))
        | ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X17647,X17646,X17645),X17644,X17643,X17642) )
      & ( ~ hBOOL(hAPP(X17647,X17644))
        | c_Natural_Oevaln(X17646,X17644,X17643,X17642)
        | ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X17647,X17646,X17645),X17644,X17643,X17642) )
      & ( c_Natural_Oevaln(X17645,X17644,X17643,X17642)
        | c_Natural_Oevaln(X17646,X17644,X17643,X17642)
        | ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X17647,X17646,X17645),X17644,X17643,X17642) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5706])])]) ).

fof(i_0_8155,plain,
    ! [X17162,X17163,X17164,X17165,X17166,X17167] :
      ( ~ c_Natural_Oevaln(X17167,X17166,X17165,X17164)
      | ~ c_Natural_Oevaln(X17163,X17164,X17165,X17162)
      | c_Natural_Oevaln(c_Com_Ocom_OSemi(X17167,X17163),X17166,X17165,X17162) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evaln_OSemi])]) ).

fof(i_0_8156,plain,
    ! [X19253,X19254] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X19254))
        | ~ 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),X19254),X19253))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X19253))
        | ~ 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),X19254),X19253))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X19254))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X19253))
        | 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),X19254),X19253))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__le__mult__iff])])]) ).

fof(i_0_8157,plain,
    ! [X19009,X19010] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X19010))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X19009))
      | 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),X19009),X19010))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__less__mult])]) ).

fof(i_0_8158,plain,
    ! [X19711,X19712,X19713] : 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),X19713),X19712)),X19711)),X19712) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X19711),X19712),
    inference(variable_rename,[status(thm)],[fact_mod__mult__self4]) ).

fof(i_0_8159,plain,
    ! [X31033,X31034,X31035] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X31035,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X31035,tc_HOL_Obool),tc_HOL_Obool)),X31034),X31033)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31035,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X31035,tc_HOL_Obool),X31034)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X31035,tc_HOL_Obool),X31033)),
    inference(variable_rename,[status(thm)],[fact_Inter__Un__distrib]) ).

fof(i_0_8160,plain,
    ! [X30880,X30881,X30882] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X30882,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X30882,tc_HOL_Obool),tc_HOL_Obool)),X30881),X30880)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X30882,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X30882,tc_HOL_Obool),X30881)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X30882,tc_HOL_Obool),X30880)),
    inference(variable_rename,[status(thm)],[fact_Union__Un__distrib]) ).

fof(i_0_8161,plain,
    ! [X19766,X19767,X19768,X19769,X19770,X19771,X19772,X19773] :
      ( ( X19766 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(X19768,X19767))
        | ~ hBOOL(hAPP(X19768,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19767,X19766))) )
      & ( X19766 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19770),X19766))
        | X19767 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19766),X19769)),X19770)
        | hBOOL(hAPP(X19768,X19770))
        | ~ hBOOL(hAPP(X19768,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19767,X19766))) )
      & ( X19771 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X19771 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(X19773,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19772,X19771))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk61_3(X19771,X19772,X19773)),X19771))
        | X19771 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(X19773,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19772,X19771))) )
      & ( X19772 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19771),esk60_3(X19771,X19772,X19773))),esk61_3(X19771,X19772,X19773))
        | X19771 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(X19773,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19772,X19771))) )
      & ( ~ hBOOL(hAPP(X19773,esk61_3(X19771,X19772,X19773)))
        | X19771 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(X19773,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19772,X19771))) )
      & ( X19771 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(X19773,X19772))
        | hBOOL(hAPP(X19773,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19772,X19771))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk61_3(X19771,X19772,X19773)),X19771))
        | ~ hBOOL(hAPP(X19773,X19772))
        | hBOOL(hAPP(X19773,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19772,X19771))) )
      & ( X19772 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19771),esk60_3(X19771,X19772,X19773))),esk61_3(X19771,X19772,X19773))
        | ~ hBOOL(hAPP(X19773,X19772))
        | hBOOL(hAPP(X19773,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19772,X19771))) )
      & ( ~ hBOOL(hAPP(X19773,esk61_3(X19771,X19772,X19773)))
        | ~ hBOOL(hAPP(X19773,X19772))
        | hBOOL(hAPP(X19773,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19772,X19771))) ) ),
    inference(distribute,[status(thm)],[inference(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_8162,plain,
    ! [X28938,X28939,X28940,X28941,X28942,X28943,X28944] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X28940)),X28939),c_List_Olists(X28940,X28938)))
        | ~ hBOOL(hAPP(hAPP(c_member(X28940),X28941),hAPP(c_List_Oset(X28940),X28939)))
        | hBOOL(hAPP(hAPP(c_member(X28940),X28941),X28938)) )
      & ( hBOOL(hAPP(hAPP(c_member(X28944),esk325_3(X28942,X28943,X28944)),hAPP(c_List_Oset(X28944),X28943)))
        | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X28944)),X28943),c_List_Olists(X28944,X28942))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X28944),esk325_3(X28942,X28943,X28944)),X28942))
        | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X28944)),X28943),c_List_Olists(X28944,X28942))) ) ),
    inference(distribute,[status(thm)],[inference(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_8163,plain,
    ! [X28639,X28640,X28641,X28642] : c_List_Olist_Olist__size(X28642,X28641,hAPP(hAPP(c_List_Olist_OCons(X28642),X28640),X28639)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X28641,X28640)),c_List_Olist_Olist__size(X28642,X28641,X28639))),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_8164,plain,
    ! [X28496,X28497,X28498] : c_Random_Oselect__weight(X28498,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X28498)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X28498),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),X28497)),X28496)) = c_Random_Oselect__weight(X28498,X28496),
    inference(variable_rename,[status(thm)],[fact_select__weight__cons__zero]) ).

fof(i_0_8165,plain,
    ! [X19289,X19290,X19291,X19292] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19291))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19291))
        | X19291 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,X19292,X19291) = X19289
        | X19292 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19291),X19290)),X19289) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19291),X19289))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19289),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)),X19291))
        | X19291 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,X19292,X19291) = X19289
        | X19292 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19291),X19290)),X19289) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19291))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19289))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19289),X19291))
        | X19291 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,X19292,X19291) = X19289
        | X19292 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19291),X19290)),X19289) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19291),X19289))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19289),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)),X19289))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19289),X19291))
        | X19291 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,X19292,X19291) = X19289
        | X19292 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19291),X19290)),X19289) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5707])])]) ).

fof(i_0_8166,plain,
    ! [X31304,X31305] :
      ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(X31305)),c_List_Otranspose__rel(X31305)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X31305)),c_List_Olist_ONil(X31305)),X31304)))
      | c_List_Otranspose(X31305,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X31305)),c_List_Olist_ONil(X31305)),X31304)) = c_List_Otranspose(X31305,X31304) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transpose_Opsimps_I2_J])]) ).

cnf(i_0_8167,plain,
    c_List_Ofoldr(X1,X2,X3,c_List_Olist_ONil(X1),X4) = X4,
    inference(split_conjunct,[status(thm)],[i_0_5708]) ).

fof(i_0_8168,plain,
    ! [X24104,X24105,X24106] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24106,tc_HOL_Obool)),X24105),X24104) != c_Orderings_Obot__class_Obot(tc_fun(X24106,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24106,tc_HOL_Obool)),X24105),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X24106,tc_HOL_Obool)),X24104))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24106,tc_HOL_Obool)),X24105),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X24106,tc_HOL_Obool)),X24104)))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24106,tc_HOL_Obool)),X24105),X24104) = c_Orderings_Obot__class_Obot(tc_fun(X24106,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_disjoint__eq__subset__Compl])]) ).

cnf(i_0_8169,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_5709]) ).

cnf(i_0_8170,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_5710]) ).

fof(i_0_8171,plain,
    ! [X24539,X24540,X24541] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24541),X24540))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24541,tc_HOL_Obool)),X24539),X24540))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X24541),X24540)),hAPP(c_Finite__Set_Ocard(X24541),X24539)))
      | X24539 = X24540 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__seteq])]) ).

fof(i_0_8172,plain,
    ! [X31024,X31025,X31026] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X31026,tc_HOL_Obool)),X31025),X31024))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X31026,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X31026,tc_HOL_Obool),X31024)),X31025)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inter__lower])]) ).

fof(i_0_8173,plain,
    ! [X32459,X32460,X32461,X32462,X32463] : hAPP(c_Relation_Oconverse(X32463,X32462),hAPP(hAPP(c_Relation_Orel__comp(X32463,X32461,X32462),X32460),X32459)) = hAPP(hAPP(c_Relation_Orel__comp(X32462,X32461,X32463),hAPP(c_Relation_Oconverse(X32461,X32462),X32459)),hAPP(c_Relation_Oconverse(X32463,X32461),X32460)),
    inference(variable_rename,[status(thm)],[fact_converse__rel__comp]) ).

fof(i_0_8174,plain,
    ! [X19540,X19541,X19542,X19543] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19542))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19542))
        | X19542 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19543),X19542) = X19541
        | X19543 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19542),X19541)),X19540) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19542),X19540))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19540),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)),X19542))
        | X19542 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19543),X19542) = X19541
        | X19543 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19542),X19541)),X19540) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19542))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19540))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19540),X19542))
        | X19542 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19543),X19542) = X19541
        | X19543 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19542),X19541)),X19540) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19542),X19540))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19540),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)),X19540))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19540),X19542))
        | X19542 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19543),X19542) = X19541
        | X19543 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19542),X19541)),X19540) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5711])])]) ).

fof(i_0_8175,plain,
    ! [X22493,X22494,X22495,X22496] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22496),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22496),X22495),X22494)),X22493))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22496),X22495),X22493))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22496),X22494),X22493))
        | ~ class_Orderings_Olinorder(X22496) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22496),X22495),X22493))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22496),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22496),X22495),X22494)),X22493))
        | ~ class_Orderings_Olinorder(X22496) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22496),X22494),X22493))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22496),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22496),X22495),X22494)),X22493))
        | ~ class_Orderings_Olinorder(X22496) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__le__iff__disj])])]) ).

fof(i_0_8176,plain,
    ! [X22435,X22436,X22437,X22438] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22438),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22438),X22437),X22436)),X22435))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22438),X22437),X22435))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22438),X22436),X22435))
        | ~ class_Orderings_Olinorder(X22438) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22438),X22437),X22435))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22438),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22438),X22437),X22436)),X22435))
        | ~ class_Orderings_Olinorder(X22438) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22438),X22436),X22435))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22438),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22438),X22437),X22436)),X22435))
        | ~ class_Orderings_Olinorder(X22438) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__less__iff__disj])])]) ).

fof(i_0_8177,plain,
    ! [X19756,X19757,X19758,X19759,X19760,X19761,X19762,X19763] :
      ( ( X19756 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(X19758,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(X19758,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19757),X19756))) )
      & ( X19756 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19760),X19756))
        | X19757 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19756),X19759)),X19760)
        | hBOOL(hAPP(X19758,X19759))
        | ~ hBOOL(hAPP(X19758,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19757),X19756))) )
      & ( X19761 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X19761 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(X19763,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19762),X19761))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk59_3(X19761,X19762,X19763)),X19761))
        | X19761 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(X19763,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19762),X19761))) )
      & ( X19762 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19761),esk58_3(X19761,X19762,X19763))),esk59_3(X19761,X19762,X19763))
        | X19761 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(X19763,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19762),X19761))) )
      & ( ~ hBOOL(hAPP(X19763,esk58_3(X19761,X19762,X19763)))
        | X19761 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(X19763,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19762),X19761))) )
      & ( X19761 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(X19763,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | hBOOL(hAPP(X19763,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19762),X19761))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk59_3(X19761,X19762,X19763)),X19761))
        | ~ hBOOL(hAPP(X19763,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | hBOOL(hAPP(X19763,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19762),X19761))) )
      & ( X19762 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19761),esk58_3(X19761,X19762,X19763))),esk59_3(X19761,X19762,X19763))
        | ~ hBOOL(hAPP(X19763,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | hBOOL(hAPP(X19763,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19762),X19761))) )
      & ( ~ hBOOL(hAPP(X19763,esk58_3(X19761,X19762,X19763)))
        | ~ hBOOL(hAPP(X19763,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | hBOOL(hAPP(X19763,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19762),X19761))) ) ),
    inference(distribute,[status(thm)],[inference(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_8178,plain,
    ! [X24434,X24435,X24436] :
      ( ~ class_Orderings_Olinorder(X24436)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24436),X24435))
      | X24434 = c_Orderings_Obot__class_Obot(tc_fun(X24436,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24436,tc_HOL_Obool)),X24434),X24435))
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X24436),c_Big__Operators_Olattice_OSup__fin(X24436,c_Orderings_Oord__class_Omax(X24436),X24434)),c_Big__Operators_Olattice_OSup__fin(X24436,c_Orderings_Oord__class_Omax(X24436),X24435)) = c_Big__Operators_Olattice_OSup__fin(X24436,c_Orderings_Oord__class_Omax(X24436),X24435) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Osubset__idem])]) ).

fof(i_0_8179,plain,
    ! [X24490,X24491,X24492] :
      ( ~ class_Orderings_Olinorder(X24492)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24492),X24491))
      | X24490 = c_Orderings_Obot__class_Obot(tc_fun(X24492,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24492,tc_HOL_Obool)),X24490),X24491))
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X24492),c_Big__Operators_Olattice_OInf__fin(X24492,c_Orderings_Oord__class_Omin(X24492),X24490)),c_Big__Operators_Olattice_OInf__fin(X24492,c_Orderings_Oord__class_Omin(X24492),X24491)) = c_Big__Operators_Olattice_OInf__fin(X24492,c_Orderings_Oord__class_Omin(X24492),X24491) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Osubset__idem])]) ).

cnf(i_0_8180,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_5712]) ).

fof(i_0_8181,plain,
    ! [X32999,X33000,X33001,X33002,X33003,X33004] :
      ( ~ c_Finite__Set_Ofun__left__comm(X33004,X33003,X33002)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33004),X33001))
      | hBOOL(hAPP(hAPP(c_member(X33004),X33000),X33001))
      | hAPP(hAPP(c_Finite__Set_Ofold(X33004,X33003,X33002),X32999),hAPP(hAPP(c_Set_Oinsert(X33004),X33000),X33001)) = hAPP(hAPP(c_Finite__Set_Ofold(X33004,X33003,X33002),hAPP(hAPP(X33002,X33000),X32999)),X33001) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5713])]) ).

fof(i_0_8182,plain,
    ! [X17879,X17880,X17881,X17882,X17883] :
      ( ~ hBOOL(hAPP(X17883,X17882))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17881),X17882),X17880))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X17883,X17881)),X17880),X17879))
      | hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X17883,X17881)),X17882),X17879)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evalc_OWhileTrue])]) ).

cnf(i_0_8183,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_5714]) ).

fof(i_0_8184,plain,
    ! [X30849,X30850] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X30850,tc_HOL_Obool),tc_HOL_Obool)),X30849),hAPP(c_Set_OPow(X30850),c_Complete__Lattice_OSup__class_OSup(tc_fun(X30850,tc_HOL_Obool),X30849)))),
    inference(variable_rename,[status(thm)],[fact_subset__Pow__Union]) ).

fof(i_0_8185,plain,
    ! [X23724,X23725,X23726,X23727] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X23727),X23726),X23725))
      | ~ hBOOL(hAPP(hAPP(c_member(X23727),X23726),X23724))
      | hBOOL(hAPP(hAPP(c_member(X23727),X23726),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23727,tc_HOL_Obool)),X23725),X23724))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_IntI])]) ).

fof(i_0_8186,plain,
    ! [X26396,X26397,X26398,X26399] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X26398),X26397))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26399),X26396),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X26397),hAPP(c_Nat_OSuc,X26398))) = c_Groups_Ozero__class_Ozero(X26399)
        | ~ class_Groups_Ocomm__monoid__add(X26399) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X26398),X26397))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26399),X26396),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X26397),hAPP(c_Nat_OSuc,X26398))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26399),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26399),X26396),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X26397),X26398))),hAPP(X26396,X26398))
        | ~ class_Groups_Ocomm__monoid__add(X26399) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5715])])]) ).

fof(i_0_8187,plain,
    ! [X22329,X22330,X22331,X22332,X22333,X22334] :
      ( ( hBOOL(hAPP(X22334,hAPP(c_Product__Type_Ofst(X22330,X22329),hAPP(hAPP(c_Product__Type_OPair(X22330,X22329),X22333),X22331))))
        | ~ hBOOL(hAPP(X22332,X22331))
        | ~ hBOOL(hAPP(X22334,X22333)) )
      & ( hBOOL(hAPP(X22332,hAPP(c_Product__Type_Osnd(X22330,X22329),hAPP(hAPP(c_Product__Type_OPair(X22330,X22329),X22333),X22331))))
        | ~ hBOOL(hAPP(X22332,X22331))
        | ~ hBOOL(hAPP(X22334,X22333)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_conjI__realizer])])]) ).

fof(i_0_8188,plain,
    ! [X29990,X29991,X29992,X29993,X29994,X29995] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X29995)
      | hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29994,tc_fun(X29993,X29995)),X29992),X29991),X29990) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29994,X29995),X29992),hAPP(hAPP(c_COMBC(X29994,X29993,X29995),X29991),X29990)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INFI__apply])]) ).

fof(i_0_8189,plain,
    ! [X25149,X25150,X25151,X25152,X25153,X25154] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X25154)
      | hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25153,tc_fun(X25152,X25154)),X25151),X25150),X25149) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25153,X25154),X25151),hAPP(hAPP(c_COMBC(X25153,X25152,X25154),X25150),X25149)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUPR__apply])]) ).

fof(i_0_8190,plain,
    ! [X23555,X23556,X23557] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X23557),X23556))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23557),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23557,tc_HOL_Obool)),X23556),X23555))) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X23557),X23555))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23557),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23557,tc_HOL_Obool)),X23556),X23555))) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23557),X23556))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23557),X23555))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X23557),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23557,tc_HOL_Obool)),X23556),X23555))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Un])])]) ).

fof(i_0_8191,plain,
    ! [X22801,X22802,X22803,X22804] :
      ( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22804,tc_HOL_Obool)),X22803),X22802),X22801))
      | hBOOL(hAPP(X22803,X22801))
      | hBOOL(hAPP(X22802,X22801)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5716])]) ).

fof(i_0_8192,plain,
    ! [X24068,X24069,X24070] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24070,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24070,tc_HOL_Obool)),X24069),X24068)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24070,tc_HOL_Obool)),X24069),X24068)) = X24069,
    inference(variable_rename,[status(thm)],[fact_Un__Diff__Int]) ).

fof(i_0_8193,plain,
    ! [X30572,X30573,X30574] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X30574,tc_HOL_Obool)),X30573),X30572))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(X30574),tc_HOL_Obool)),c_List_Olistsp(X30574,X30573)),c_List_Olistsp(X30574,X30572))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsp__mono])]) ).

fof(i_0_8194,plain,
    ! [X28649,X28650,X28651] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28651,tc_HOL_Obool)),X28650),X28649))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(X28651),tc_HOL_Obool)),c_List_Olists(X28651,X28650)),c_List_Olists(X28651,X28649))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lists__mono])]) ).

fof(i_0_8195,plain,
    ! [X21548,X21549,X21550,X21551] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21551),X21549),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21551),X21548),X21550)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21551),X21548),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21551),X21549),X21550)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21551),X21550),c_Groups_Ozero__class_Ozero(X21551)))
        | ~ class_Fields_Olinordered__field(X21551) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21551),X21548),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21551),X21549),X21550)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21551),X21549),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21551),X21548),X21550)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21551),X21550),c_Groups_Ozero__class_Ozero(X21551)))
        | ~ class_Fields_Olinordered__field(X21551) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__le__divide__eq])])]) ).

fof(i_0_8196,plain,
    ! [X21440,X21441,X21442,X21443] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21443),X21441),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21443),X21440),X21442)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21443),X21440),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21443),X21441),X21442)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21443),X21442),c_Groups_Ozero__class_Ozero(X21443)))
        | ~ class_Fields_Olinordered__field(X21443) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21443),X21440),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21443),X21441),X21442)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21443),X21441),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21443),X21440),X21442)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21443),X21442),c_Groups_Ozero__class_Ozero(X21443)))
        | ~ class_Fields_Olinordered__field(X21443) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__less__divide__eq])])]) ).

fof(i_0_8197,plain,
    ! [X33941,X33942] :
      ( ( ~ c_Predicate_Osymp(X33942,X33941)
        | c_Relation_Osym(X33942,hAPP(c_Set_OCollect(tc_prod(X33942,X33942)),hAPP(c_Product__Type_Oprod_Oprod__case(X33942,X33942,tc_HOL_Obool),X33941))) )
      & ( ~ c_Relation_Osym(X33942,hAPP(c_Set_OCollect(tc_prod(X33942,X33942)),hAPP(c_Product__Type_Oprod_Oprod__case(X33942,X33942,tc_HOL_Obool),X33941)))
        | c_Predicate_Osymp(X33942,X33941) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_symp__def])]) ).

fof(i_0_8198,plain,
    ! [X33821,X33822] :
      ( ( ~ c_Predicate_Otransp(X33822,X33821)
        | c_Relation_Otrans(X33822,hAPP(c_Set_OCollect(tc_prod(X33822,X33822)),hAPP(c_Product__Type_Oprod_Oprod__case(X33822,X33822,tc_HOL_Obool),X33821))) )
      & ( ~ c_Relation_Otrans(X33822,hAPP(c_Set_OCollect(tc_prod(X33822,X33822)),hAPP(c_Product__Type_Oprod_Oprod__case(X33822,X33822,tc_HOL_Obool),X33821)))
        | c_Predicate_Otransp(X33822,X33821) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transp__def])]) ).

fof(i_0_8199,plain,
    ! [X31974,X31975] :
      ( ( ~ c_Wellfounded_OwfP(X31975,X31974)
        | c_Wellfounded_Owf(X31975,hAPP(c_Set_OCollect(tc_prod(X31975,X31975)),hAPP(c_Product__Type_Oprod_Oprod__case(X31975,X31975,tc_HOL_Obool),X31974))) )
      & ( ~ c_Wellfounded_Owf(X31975,hAPP(c_Set_OCollect(tc_prod(X31975,X31975)),hAPP(c_Product__Type_Oprod_Oprod__case(X31975,X31975,tc_HOL_Obool),X31974)))
        | c_Wellfounded_OwfP(X31975,X31974) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wfP__def])]) ).

fof(i_0_8200,plain,
    ! [X19617,X19618] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19617),X19618)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19617),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)),X19618)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19617),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),X19617),X19618)),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)),X19618)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__imp__zdiv__neg__iff])])]) ).

cnf(i_0_8201,plain,
    ( c_List_OdropWhile(X3,X1,X2) = c_List_Olist_ONil(X3)
    | ~ hBOOL(hAPP(X1,esk398_3(X2,X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_5660]) ).

fof(i_0_8202,plain,
    ! [X27257,X27258,X27259,X27260,X27261,X27262] :
      ( ( hAPP(hAPP(c_Product__Type_OSigma(X27259,X27262),X27258),hAPP(c_COMBK(tc_fun(X27262,tc_HOL_Obool),X27259),X27260)) != hAPP(hAPP(c_Product__Type_OSigma(X27259,X27262),X27257),hAPP(c_COMBK(tc_fun(X27262,tc_HOL_Obool),X27259),X27260))
        | X27258 = X27257
        | ~ hBOOL(hAPP(hAPP(c_member(X27262),X27261),X27260)) )
      & ( X27258 != X27257
        | hAPP(hAPP(c_Product__Type_OSigma(X27259,X27262),X27258),hAPP(c_COMBK(tc_fun(X27262,tc_HOL_Obool),X27259),X27260)) = hAPP(hAPP(c_Product__Type_OSigma(X27259,X27262),X27257),hAPP(c_COMBK(tc_fun(X27262,tc_HOL_Obool),X27259),X27260))
        | ~ hBOOL(hAPP(hAPP(c_member(X27262),X27261),X27260)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Times__eq__cancel2])])]) ).

fof(i_0_8203,plain,
    ! [X19491,X19492] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19492))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19492),X19491)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,X19492,X19491) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19492),X19491) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__pos__neg__trivial])]) ).

fof(i_0_8204,plain,
    ! [X32112,X32113] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X32113,tc_HOL_Obool)),esk436_2(X32112,X32113)),hAPP(c_Relation_OImage(X32113,X32113,X32112),esk436_2(X32112,X32113))))
        | c_Wellfounded_Owf(X32113,X32112) )
      & ( esk436_2(X32112,X32113) != c_Orderings_Obot__class_Obot(tc_fun(X32113,tc_HOL_Obool))
        | c_Wellfounded_Owf(X32113,X32112) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wfI__pf])])])]) ).

fof(i_0_8205,plain,
    ! [X21914,X21915,X21916,X21917,X21918] :
      ( ~ hBOOL(hAPP(hAPP(X21918,X21917),X21916))
      | hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X21915,X21914,tc_HOL_Obool),X21918),hAPP(hAPP(c_Product__Type_OPair(X21915,X21914),X21917),X21916))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_splitI])]) ).

fof(i_0_8206,plain,
    ! [X21909,X21910,X21911,X21912,X21913] :
      ( ~ hBOOL(hAPP(hAPP(X21913,X21912),X21911))
      | hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X21910,X21909,tc_HOL_Obool),X21913),hAPP(hAPP(c_Product__Type_OPair(X21910,X21909),X21912),X21911))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_prod__caseI])]) ).

fof(i_0_8207,plain,
    ! [X19615,X19616] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19615),X19616)),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)),X19615))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19616),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)),X19615))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19615),X19616)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19616),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_8208,plain,
    ! [X20040,X20041,X20042] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20042),X20041)),X20040))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20042),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20040),X20041))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20042),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20040),X20041)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20042),X20041)),X20040)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__diff__conv])]) ).

fof(i_0_8209,plain,
    ! [X20002,X20003,X20004] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20004),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20003),X20002)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20004),X20002)),X20003)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20004),X20002)),X20003))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20004),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20003),X20002))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__diff__conv])]) ).

fof(i_0_8210,plain,
    ! [X24563,X24564,X24565] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24565),X24564))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24565,tc_HOL_Obool)),X24564),X24563))
      | hAPP(c_Finite__Set_Ocard(X24565),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24565,tc_HOL_Obool)),X24563),X24564)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X24565),X24563)),hAPP(c_Finite__Set_Ocard(X24565),X24564)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Diff__subset])]) ).

fof(i_0_8211,plain,
    ! [X24421,X24422,X24423,X24424,X24425] :
      ( ~ c_Finite__Set_Ofolding__idem(X24425,X24424,X24423,X24422)
      | hAPP(c_Fun_Ocomp(X24424,X24424,X24424,hAPP(X24423,X24421)),hAPP(X24423,X24421)) = hAPP(X24423,X24421) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__idem_Oidem__comp])]) ).

cnf(i_0_8212,plain,
    c_Int_Opred(c_Int_OBit1(X1)) = c_Int_OBit0(X1),
    inference(split_conjunct,[status(thm)],[i_0_5717]) ).

fof(i_0_8213,plain,
    ! [X20683,X20684,X20685] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20685)))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20685)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20684)),X20683)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20684)),X20683) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20684)))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20685)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20684)),X20683)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20685)),X20683)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20685))) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20684)))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20685)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20684)),X20683)) = 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),X20685),X20684))),X20683)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20685))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5718])])]) ).

cnf(i_0_8214,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_5719]) ).

cnf(i_0_8215,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_5720]) ).

cnf(i_0_8216,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_5721]) ).

fof(i_0_8217,plain,
    ! [X23290,X23291,X23292] : hAPP(c_Relation_OField(X23292),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X23292,X23292),tc_HOL_Obool)),X23291),X23290)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23292,tc_HOL_Obool)),hAPP(c_Relation_OField(X23292),X23291)),hAPP(c_Relation_OField(X23292),X23290)),
    inference(variable_rename,[status(thm)],[fact_Field__Un]) ).

fof(i_0_8218,plain,
    ! [X30732,X30733,X30734,X30735] : hAPP(c_List_Oset(tc_prod(X30735,X30734)),c_Enum_Oproduct(X30735,X30734,X30733,X30732)) = hAPP(hAPP(c_Product__Type_OSigma(X30735,X30734),hAPP(c_List_Oset(X30735),X30733)),hAPP(c_COMBK(tc_fun(X30734,tc_HOL_Obool),X30735),hAPP(c_List_Oset(X30734),X30732))),
    inference(variable_rename,[status(thm)],[fact_product__list__set]) ).

fof(i_0_8219,plain,
    ! [X30296,X30297,X30298,X30299,X30300] :
      ( ( hAPP(hAPP(c_List_Omap(tc_prod(X30300,X30298),X30300),c_Product__Type_Ofst(X30300,X30298)),X30296) = X30299
        | hAPP(hAPP(c_List_Ozip(X30300,X30298),X30299),X30297) != X30296
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30300)),X30299) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30298)),X30297) )
      & ( hAPP(hAPP(c_List_Omap(tc_prod(X30300,X30298),X30298),c_Product__Type_Osnd(X30300,X30298)),X30296) = X30297
        | hAPP(hAPP(c_List_Ozip(X30300,X30298),X30299),X30297) != X30296
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30300)),X30299) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30298)),X30297) )
      & ( hAPP(hAPP(c_List_Omap(tc_prod(X30300,X30298),X30300),c_Product__Type_Ofst(X30300,X30298)),X30296) != X30299
        | hAPP(hAPP(c_List_Omap(tc_prod(X30300,X30298),X30298),c_Product__Type_Osnd(X30300,X30298)),X30296) != X30297
        | hAPP(hAPP(c_List_Ozip(X30300,X30298),X30299),X30297) = X30296
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30300)),X30299) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30298)),X30297) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zip__eq__conv])])]) ).

fof(i_0_8220,plain,
    ! [X23716,X23717,X23718,X23719] :
      ( ( hBOOL(hAPP(X23718,X23716))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23719,tc_HOL_Obool)),X23718),X23717),X23716)) )
      & ( hBOOL(hAPP(X23717,X23716))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23719,tc_HOL_Obool)),X23718),X23717),X23716)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5722])])]) ).

fof(i_0_8221,plain,
    ! [X23930,X23931,X23932,X23933] :
      ( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23933,tc_HOL_Obool)),X23932),X23931),X23930))
      | hBOOL(hAPP(X23932,X23930)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf1D1])]) ).

fof(i_0_8222,plain,
    ! [X23926,X23927,X23928,X23929] :
      ( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23929,tc_HOL_Obool)),X23928),X23927),X23926))
      | hBOOL(hAPP(X23927,X23926)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf1D2])]) ).

cnf(i_0_8223,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_5723]) ).

fof(i_0_8224,plain,
    ! [X28628,X28629,X28630,X28631,X28632,X28633] :
      ( ( hBOOL(hAPP(hAPP(X28632,X28631),X28629))
        | ~ c_List_Olistrelp(X28633,X28632,hAPP(hAPP(c_List_Olist_OCons(X28633),X28631),X28630),hAPP(hAPP(c_List_Olist_OCons(X28633),X28629),X28628)) )
      & ( c_List_Olistrelp(X28633,X28632,X28630,X28628)
        | ~ c_List_Olistrelp(X28633,X28632,hAPP(hAPP(c_List_Olist_OCons(X28633),X28631),X28630),hAPP(hAPP(c_List_Olist_OCons(X28633),X28629),X28628)) )
      & ( ~ hBOOL(hAPP(hAPP(X28632,X28631),X28629))
        | ~ c_List_Olistrelp(X28633,X28632,X28630,X28628)
        | c_List_Olistrelp(X28633,X28632,hAPP(hAPP(c_List_Olist_OCons(X28633),X28631),X28630),hAPP(hAPP(c_List_Olist_OCons(X28633),X28629),X28628)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrelp_Oequations_I2_J])])]) ).

fof(i_0_8225,plain,
    ! [X28622,X28623,X28624,X28625,X28626,X28627] :
      ( ~ hBOOL(hAPP(hAPP(X28627,X28626),X28625))
      | ~ c_List_Olistrelp(X28624,X28627,X28623,X28622)
      | c_List_Olistrelp(X28624,X28627,hAPP(hAPP(c_List_Olist_OCons(X28624),X28626),X28623),hAPP(hAPP(c_List_Olist_OCons(X28624),X28625),X28622)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrelp_OCons])]) ).

cnf(i_0_8226,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_5724]) ).

fof(i_0_8227,plain,
    ! [X27610] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X27610),c_Int_OInteg))
      | X27610 = hAPP(c_Int_ORep__Integ,esk286_1(X27610)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Rep__Integ__cases])])]) ).

fof(i_0_8228,plain,
    ! [X32688,X32689,X32690] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_fun(X32690,tc_HOL_Obool)),esk471_3(X32688,X32689,X32690)),X32689))
        | hBOOL(hAPP(hAPP(c_member(X32690),X32688),c_Complete__Lattice_OInf__class_OInf(tc_fun(X32690,tc_HOL_Obool),X32689))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X32690),X32688),esk471_3(X32688,X32689,X32690)))
        | hBOOL(hAPP(hAPP(c_member(X32690),X32688),c_Complete__Lattice_OInf__class_OInf(tc_fun(X32690,tc_HOL_Obool),X32689))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_InterI])])])]) ).

fof(i_0_8229,plain,
    ! [X29555,X29556,X29557,X29560,X29561,X29562,X29563,X29564] :
      ( ( X29556 = hAPP(hAPP(c_List_Olist_OCons(X29557),esk346_3(X29555,X29556,X29557)),esk347_3(X29555,X29556,X29557))
        | X29556 = c_List_Olist_ONil(X29557)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X29557)),X29556),c_List_Olists(X29557,X29555))) )
      & ( hBOOL(hAPP(hAPP(c_member(X29557),esk346_3(X29555,X29556,X29557)),X29555))
        | X29556 = c_List_Olist_ONil(X29557)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X29557)),X29556),c_List_Olists(X29557,X29555))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X29557)),esk347_3(X29555,X29556,X29557)),c_List_Olists(X29557,X29555)))
        | X29556 = c_List_Olist_ONil(X29557)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X29557)),X29556),c_List_Olists(X29557,X29555))) )
      & ( X29561 != c_List_Olist_ONil(X29562)
        | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X29562)),X29561),c_List_Olists(X29562,X29560))) )
      & ( X29561 != hAPP(hAPP(c_List_Olist_OCons(X29562),X29563),X29564)
        | ~ hBOOL(hAPP(hAPP(c_member(X29562),X29563),X29560))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X29562)),X29564),c_List_Olists(X29562,X29560)))
        | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X29562)),X29561),c_List_Olists(X29562,X29560))) ) ),
    inference(distribute,[status(thm)],[inference(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_8230,plain,
    ! [X33483,X33484,X33485,X33486] :
      ( ( X33485 = X33483
        | ~ hBOOL(hAPP(hAPP(c_member(X33486),X33485),hAPP(c_List_Oset(X33486),c_List_Oreplicate(X33486,X33484,X33483)))) )
      & ( X33484 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(X33486),X33485),hAPP(c_List_Oset(X33486),c_List_Oreplicate(X33486,X33484,X33483)))) )
      & ( X33485 != X33483
        | X33484 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_member(X33486),X33485),hAPP(c_List_Oset(X33486),c_List_Oreplicate(X33486,X33484,X33483)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__set__replicate])])]) ).

fof(i_0_8231,plain,
    ! [X24132,X24133,X24134,X24135,X24136] :
      ( ~ c_Finite__Set_Ofolding__one(X24136,X24135,X24134)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24136),X24133))
      | X24133 = c_Orderings_Obot__class_Obot(tc_fun(X24136,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24136),X24132))
      | X24132 = c_Orderings_Obot__class_Obot(tc_fun(X24136,tc_HOL_Obool))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24136,tc_HOL_Obool)),X24133),X24132) != c_Orderings_Obot__class_Obot(tc_fun(X24136,tc_HOL_Obool))
      | hAPP(X24134,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24136,tc_HOL_Obool)),X24133),X24132)) = hAPP(hAPP(X24135,hAPP(X24134,X24133)),hAPP(X24134,X24132)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one_Ounion__disjoint])]) ).

fof(i_0_8232,plain,
    ! [X19869,X19870,X19871,X19872] :
      ( ~ class_Divides_Oring__div(X19872)
      | c_Divides_Odiv__class_Omod(X19872,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19872),X19871),X19870),X19869) = c_Divides_Odiv__class_Omod(X19872,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19872),c_Divides_Odiv__class_Omod(X19872,X19871,X19869)),c_Divides_Odiv__class_Omod(X19872,X19870,X19869)),X19869) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__diff__eq])]) ).

fof(i_0_8233,plain,
    ! [X19376,X19377,X19378,X19379] :
      ( ~ class_Divides_Osemiring__div(X19379)
      | c_Divides_Odiv__class_Omod(X19379,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19379),X19378),X19377),X19376) = c_Divides_Odiv__class_Omod(X19379,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19379),c_Divides_Odiv__class_Omod(X19379,X19378,X19376)),c_Divides_Odiv__class_Omod(X19379,X19377,X19376)),X19376) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__eq])]) ).

fof(i_0_8234,plain,
    ! [X19350,X19351,X19352,X19353] :
      ( ~ class_Divides_Osemiring__div(X19353)
      | c_Divides_Odiv__class_Omod(X19353,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19353),X19352),X19351),X19350) = c_Divides_Odiv__class_Omod(X19353,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19353),c_Divides_Odiv__class_Omod(X19353,X19352,X19350)),c_Divides_Odiv__class_Omod(X19353,X19351,X19350)),X19350) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__eq])]) ).

fof(i_0_8235,plain,
    ! [X20599,X20600,X20601] :
      ( ~ class_Rings_Olinordered__semidom(X20601)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20601),c_Groups_Oone__class_Oone(X20601)),X20600))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20601),c_Groups_Oone__class_Oone(X20601)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20601),X20600),hAPP(hAPP(c_Power_Opower__class_Opower(X20601),X20600),X20599)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__gt1__lemma])]) ).

fof(i_0_8236,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_8237,plain,
    ! [X17600,X17601] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17601),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17601),X17600),X17600)),c_Groups_Ozero__class_Ozero(X17601)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17601),X17600),c_Groups_Ozero__class_Ozero(X17601)))
        | ~ class_Rings_Olinordered__idom(X17601) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17601),X17600),c_Groups_Ozero__class_Ozero(X17601)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17601),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17601),X17600),X17600)),c_Groups_Ozero__class_Ozero(X17601)))
        | ~ class_Rings_Olinordered__idom(X17601) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_even__less__0__iff])])]) ).

fof(i_0_8238,plain,
    ! [X17473,X17474] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17474),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17474),X17473),X17473)),c_Groups_Ozero__class_Ozero(X17474)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17474),X17473),c_Groups_Ozero__class_Ozero(X17474)))
        | ~ class_Groups_Olinordered__ab__group__add(X17474) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17474),X17473),c_Groups_Ozero__class_Ozero(X17474)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17474),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17474),X17473),X17473)),c_Groups_Ozero__class_Ozero(X17474)))
        | ~ class_Groups_Olinordered__ab__group__add(X17474) ) ),
    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_8239,plain,
    ! [X32052,X32053] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk422_2(X32052,X32053)),X32053))
        | 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)),X32052),X32053) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X32052),esk422_2(X32052,X32053)))
        | 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)),X32052),X32053) ) ),
    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_8240,plain,
    ! [X31001,X31002,X31003,X31004] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X31004),X31003),c_Complete__Lattice_OInf__class_OInf(tc_fun(X31004,tc_HOL_Obool),X31002)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X31004,tc_HOL_Obool)),X31001),X31002))
      | hBOOL(hAPP(hAPP(c_member(X31004),X31003),X31001)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_InterE])]) ).

fof(i_0_8241,plain,
    ! [X30997,X30998,X30999,X31000] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X31000),X30999),c_Complete__Lattice_OInf__class_OInf(tc_fun(X31000,tc_HOL_Obool),X30998)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X31000,tc_HOL_Obool)),X30997),X30998))
      | hBOOL(hAPP(hAPP(c_member(X31000),X30999),X30997)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_InterD])]) ).

fof(i_0_8242,plain,
    ! [X20689,X20690] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20690))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20690),X20689)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20690),X20689) = 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_8243,plain,
    ! [X26771,X26772] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X26772,X26771)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X26772,X26771),tc_HOL_Obool))))
      | hAPP(c_Finite__Set_Ocard(X26771),c_Orderings_Otop__class_Otop(tc_fun(X26771,tc_HOL_Obool))) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X26772),c_Orderings_Otop__class_Otop(tc_fun(X26772,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__fun__UNIVD1])]) ).

fof(i_0_8244,plain,
    ! [X24496,X24497,X24498] :
      ( ~ class_Orderings_Olinorder(X24498)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24498),X24497))
      | X24497 = c_Orderings_Obot__class_Obot(tc_fun(X24498,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24498),X24496))
      | X24496 = c_Orderings_Obot__class_Obot(tc_fun(X24498,tc_HOL_Obool))
      | c_Big__Operators_Olattice_OInf__fin(X24498,c_Orderings_Oord__class_Omin(X24498),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24498,tc_HOL_Obool)),X24497),X24496)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X24498),c_Big__Operators_Olattice_OInf__fin(X24498,c_Orderings_Oord__class_Omin(X24498),X24497)),c_Big__Operators_Olattice_OInf__fin(X24498,c_Orderings_Oord__class_Omin(X24498),X24496)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Ounion__idem])]) ).

fof(i_0_8245,plain,
    ! [X24440,X24441,X24442] :
      ( ~ class_Orderings_Olinorder(X24442)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24442),X24441))
      | X24441 = c_Orderings_Obot__class_Obot(tc_fun(X24442,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24442),X24440))
      | X24440 = c_Orderings_Obot__class_Obot(tc_fun(X24442,tc_HOL_Obool))
      | c_Big__Operators_Olattice_OSup__fin(X24442,c_Orderings_Oord__class_Omax(X24442),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24442,tc_HOL_Obool)),X24441),X24440)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X24442),c_Big__Operators_Olattice_OSup__fin(X24442,c_Orderings_Oord__class_Omax(X24442),X24441)),c_Big__Operators_Olattice_OSup__fin(X24442,c_Orderings_Oord__class_Omax(X24442),X24440)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Ounion__idem])]) ).

fof(i_0_8246,plain,
    ! [X20730,X20731,X20732,X20733] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X20733),X20732),X20731))
      | hBOOL(hAPP(hAPP(c_member(X20733),X20732),X20730))
      | hBOOL(hAPP(hAPP(c_member(X20733),X20732),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20733,tc_HOL_Obool)),X20731),X20730))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5725])]) ).

fof(i_0_8247,plain,
    ! [X19677,X19678,X19679] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19679),X19678))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19677))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19679),X19677)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19678),X19677))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono1])]) ).

fof(i_0_8248,plain,
    ! [X19662,X19663,X19664] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19664))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19664),X19663))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19662),X19663)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19662),X19664))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__le__mono2])]) ).

fof(i_0_8249,plain,
    ! [X18401,X18402,X18403] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18403),X18402))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18401))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X18401),X18403)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X18401),X18402))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult__zless__mono2])]) ).

fof(i_0_8250,plain,
    ! [X18853,X18854,X18855] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18855),X18854))
      | ~ 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_Otimes__class_Otimes(tc_Nat_Onat),X18855),X18853)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18854),X18853))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__mono1])]) ).

fof(i_0_8251,plain,
    ! [X18850,X18851,X18852] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18852),X18851))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18850))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18850),X18852)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18850),X18851))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__mono2])]) ).

fof(i_0_8252,plain,
    ! [X30179,X30180,X30181] :
      ( ~ c_Fun_Oinj__on(tc_List_Olist(X30181),tc_List_Olist(X30180),hAPP(c_List_Omap(X30181,X30180),X30179),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X30181),tc_HOL_Obool)))
      | c_Fun_Oinj__on(X30181,X30180,X30179,c_Orderings_Otop__class_Otop(tc_fun(X30181,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__mapD])]) ).

fof(i_0_8253,plain,
    ! [X30176,X30177,X30178] :
      ( ( ~ c_Fun_Oinj__on(tc_List_Olist(X30178),tc_List_Olist(X30177),hAPP(c_List_Omap(X30178,X30177),X30176),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X30178),tc_HOL_Obool)))
        | c_Fun_Oinj__on(X30178,X30177,X30176,c_Orderings_Otop__class_Otop(tc_fun(X30178,tc_HOL_Obool))) )
      & ( ~ c_Fun_Oinj__on(X30178,X30177,X30176,c_Orderings_Otop__class_Otop(tc_fun(X30178,tc_HOL_Obool)))
        | c_Fun_Oinj__on(tc_List_Olist(X30178),tc_List_Olist(X30177),hAPP(c_List_Omap(X30178,X30177),X30176),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X30178),tc_HOL_Obool))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__map])]) ).

fof(i_0_8254,plain,
    ! [X19094,X19095,X19096,X19097] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19097,tc_HOL_Obool)),X19096),X19095))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19097,tc_HOL_Obool)),X19096),hAPP(hAPP(c_Set_Oinsert(X19097),X19094),X19095))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__insertI2])]) ).

fof(i_0_8255,plain,
    ! [X33476,X33477,X33478,X33479] : hAPP(hAPP(c_List_Oappend(X33479),c_List_Oreplicate(X33479,X33478,X33477)),hAPP(hAPP(c_List_Olist_OCons(X33479),X33477),X33476)) = hAPP(hAPP(c_List_Olist_OCons(X33479),X33477),hAPP(hAPP(c_List_Oappend(X33479),c_List_Oreplicate(X33479,X33478,X33477)),X33476)),
    inference(variable_rename,[status(thm)],[fact_replicate__app__Cons__same]) ).

fof(i_0_8256,plain,
    ! [X29930,X29931,X29932,X29933,X29934] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29934,tc_fun(X29933,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X29934),X29932),X29931)),X29930) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29933,tc_HOL_Obool)),hAPP(X29930,X29932)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29934,tc_fun(X29933,tc_HOL_Obool)),X29931),X29930)),
    inference(variable_rename,[status(thm)],[fact_INT__insert]) ).

fof(i_0_8257,plain,
    ! [X25223,X25224,X25225,X25226,X25227] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25227,tc_fun(X25226,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X25227),X25225),X25224)),X25223) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25226,tc_HOL_Obool)),hAPP(X25223,X25225)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25227,tc_fun(X25226,tc_HOL_Obool)),X25224),X25223)),
    inference(variable_rename,[status(thm)],[fact_UN__insert]) ).

fof(i_0_8258,plain,
    ! [X27072,X27073,X27074,X27075] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27074),X27072),hAPP(c_Finite__Set_Ofold1(X27074,c_Orderings_Oord__class_Omin(X27074)),X27073)))
        | ~ hBOOL(hAPP(hAPP(c_member(X27074),X27075),X27073))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27074),X27072),X27075))
        | X27073 = c_Orderings_Obot__class_Obot(tc_fun(X27074,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27074),X27073))
        | ~ class_Orderings_Olinorder(X27074) )
      & ( hBOOL(hAPP(hAPP(c_member(X27074),esk266_3(X27072,X27073,X27074)),X27073))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27074),X27072),hAPP(c_Finite__Set_Ofold1(X27074,c_Orderings_Oord__class_Omin(X27074)),X27073)))
        | X27073 = c_Orderings_Obot__class_Obot(tc_fun(X27074,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27074),X27073))
        | ~ class_Orderings_Olinorder(X27074) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27074),X27072),esk266_3(X27072,X27073,X27074)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27074),X27072),hAPP(c_Finite__Set_Ofold1(X27074,c_Orderings_Oord__class_Omin(X27074)),X27073)))
        | X27073 = c_Orderings_Obot__class_Obot(tc_fun(X27074,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27074),X27073))
        | ~ class_Orderings_Olinorder(X27074) ) ),
    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_8259,plain,
    ! [X27059,X27060,X27061,X27062] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27061),X27059),hAPP(c_Finite__Set_Ofold1(X27061,c_Orderings_Oord__class_Omin(X27061)),X27060)))
        | ~ hBOOL(hAPP(hAPP(c_member(X27061),X27062),X27060))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27061),X27059),X27062))
        | X27060 = c_Orderings_Obot__class_Obot(tc_fun(X27061,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27061),X27060))
        | ~ class_Orderings_Olinorder(X27061) )
      & ( hBOOL(hAPP(hAPP(c_member(X27061),esk264_3(X27059,X27060,X27061)),X27060))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27061),X27059),hAPP(c_Finite__Set_Ofold1(X27061,c_Orderings_Oord__class_Omin(X27061)),X27060)))
        | X27060 = c_Orderings_Obot__class_Obot(tc_fun(X27061,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27061),X27060))
        | ~ class_Orderings_Olinorder(X27061) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27061),X27059),esk264_3(X27059,X27060,X27061)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27061),X27059),hAPP(c_Finite__Set_Ofold1(X27061,c_Orderings_Oord__class_Omin(X27061)),X27060)))
        | X27060 = c_Orderings_Obot__class_Obot(tc_fun(X27061,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27061),X27060))
        | ~ class_Orderings_Olinorder(X27061) ) ),
    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_8260,plain,
    ! [X27043,X27044,X27045,X27046] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27045),X27043),hAPP(c_Finite__Set_Ofold1(X27045,c_Lattices_Osemilattice__inf__class_Oinf(X27045)),X27044)))
        | ~ hBOOL(hAPP(hAPP(c_member(X27045),X27046),X27044))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27045),X27043),X27046))
        | X27044 = c_Orderings_Obot__class_Obot(tc_fun(X27045,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27045),X27044))
        | ~ class_Lattices_Osemilattice__inf(X27045) )
      & ( hBOOL(hAPP(hAPP(c_member(X27045),esk262_3(X27043,X27044,X27045)),X27044))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27045),X27043),hAPP(c_Finite__Set_Ofold1(X27045,c_Lattices_Osemilattice__inf__class_Oinf(X27045)),X27044)))
        | X27044 = c_Orderings_Obot__class_Obot(tc_fun(X27045,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27045),X27044))
        | ~ class_Lattices_Osemilattice__inf(X27045) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27045),X27043),esk262_3(X27043,X27044,X27045)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27045),X27043),hAPP(c_Finite__Set_Ofold1(X27045,c_Lattices_Osemilattice__inf__class_Oinf(X27045)),X27044)))
        | X27044 = c_Orderings_Obot__class_Obot(tc_fun(X27045,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27045),X27044))
        | ~ class_Lattices_Osemilattice__inf(X27045) ) ),
    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_8261,plain,
    ! [X31920,X31921,X31922,X31923,X31924] : c_List_Omaps(X31924,X31923,X31922,hAPP(hAPP(c_List_Olist_OCons(X31924),X31921),X31920)) = hAPP(hAPP(c_List_Oappend(X31923),hAPP(X31922,X31921)),c_List_Omaps(X31924,X31923,X31922,X31920)),
    inference(variable_rename,[status(thm)],[fact_maps__simps_I1_J]) ).

cnf(i_0_8262,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk385_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_8263,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk386_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_8264,plain,
    ! [X19956,X19957,X19958] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19958),X19957),X19956))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19958),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19958),X19957),X19956)),c_Groups_Ozero__class_Ozero(X19958)))
        | ~ class_Groups_Oordered__ab__group__add(X19958) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19958),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19958),X19957),X19956)),c_Groups_Ozero__class_Ozero(X19958)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19958),X19957),X19956))
        | ~ class_Groups_Oordered__ab__group__add(X19958) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__iff__diff__le__0])])]) ).

fof(i_0_8265,plain,
    ! [X19959,X19960,X19961] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19961),X19960),X19959))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19961),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19961),X19960),X19959)),c_Groups_Ozero__class_Ozero(X19961)))
        | ~ class_Groups_Oordered__ab__group__add(X19961) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19961),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19961),X19960),X19959)),c_Groups_Ozero__class_Ozero(X19961)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19961),X19960),X19959))
        | ~ class_Groups_Oordered__ab__group__add(X19961) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__iff__diff__less__0])])]) ).

fof(i_0_8266,plain,
    ! [X19674,X19675,X19676] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19676),X19675))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19674),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),X19675),X19674)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19676),X19674))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono1__neg])]) ).

cnf(i_0_8267,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_5726]) ).

cnf(i_0_8268,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_5727]) ).

fof(i_0_8269,plain,
    ! [X28949,X28950,X28951] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X28951),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28950)),X28949)))
      | hBOOL(hAPP(hAPP(c_member(X28950),hAPP(hAPP(c_List_Onth(X28950),X28949),X28951)),hAPP(c_List_Oset(X28950),X28949))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__mem])]) ).

fof(i_0_8270,plain,
    ! [X19007,X19008] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X19008))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X19007))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19008),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19008),X19007))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_n__less__n__mult__m])]) ).

fof(i_0_8271,plain,
    ! [X19005,X19006] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X19006))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X19005))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19006),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19005),X19006))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_n__less__m__mult__n])]) ).

fof(i_0_8272,plain,
    ! [X24915,X24916] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24916),X24915))
        | hAPP(c_Finite__Set_Ocard(X24916),X24915) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,X24916,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,X24916),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X24915) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X24916),X24915))
        | hAPP(c_Finite__Set_Ocard(X24916),X24915) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5728])]) ).

fof(i_0_8273,plain,
    ! [X24913,X24914] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24914),X24913))
      | hAPP(c_Finite__Set_Ocard(X24914),X24913) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,X24914,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,X24914),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X24913) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card_Oeq__fold__g])]) ).

fof(i_0_8274,plain,
    ! [X21495,X21496,X21497,X21498] :
      ( ~ class_Fields_Ofield(X21498)
      | X21497 = c_Groups_Ozero__class_Ozero(X21498)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21498),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21498),X21496),X21497)),X21495) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21498),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21498),X21496),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21498),X21497),X21495))),X21497) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__diff__eq__iff])]) ).

fof(i_0_8275,plain,
    ! [X21474,X21475,X21476,X21477] :
      ( ~ class_Fields_Ofield(X21477)
      | X21476 = c_Groups_Ozero__class_Ozero(X21477)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21477),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21477),X21475),X21476)),X21474) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21477),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21477),X21475),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21477),X21476),X21474))),X21476) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__add__eq__iff])]) ).

fof(i_0_8276,plain,
    ! [X21478,X21479,X21480,X21481] :
      ( ~ class_Fields_Ofield__inverse__zero(X21481)
      | X21480 = c_Groups_Ozero__class_Ozero(X21481)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21481),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21481),X21479),X21480)),X21478) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21481),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21481),X21479),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21481),X21478),X21480))),X21480) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__frac__num])]) ).

fof(i_0_8277,plain,
    ! [X28952,X28953,X28954,X28956,X28957,X28958,X28959] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk326_3(X28952,X28953,X28954)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28954)),X28952)))
        | ~ hBOOL(hAPP(hAPP(c_member(X28954),X28953),hAPP(c_List_Oset(X28954),X28952))) )
      & ( hAPP(hAPP(c_List_Onth(X28954),X28952),esk326_3(X28952,X28953,X28954)) = X28953
        | ~ hBOOL(hAPP(hAPP(c_member(X28954),X28953),hAPP(c_List_Oset(X28954),X28952))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X28959),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28958)),X28956)))
        | hAPP(hAPP(c_List_Onth(X28958),X28956),X28959) != X28957
        | hBOOL(hAPP(hAPP(c_member(X28958),X28957),hAPP(c_List_Oset(X28958),X28956))) ) ),
    inference(distribute,[status(thm)],[inference(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_8278,plain,
    ! [X19175,X19176,X19177,X19178] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19178),X19177))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19176),X19175))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19178),X19176)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19177),X19175))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__mono])]) ).

fof(i_0_8279,plain,
    ! [X19135,X19136,X19137,X19138] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19138),X19137))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19136),X19135))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19138),X19136)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19137),X19135))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__mono])]) ).

fof(i_0_8280,plain,
    ! [X18903,X18904,X18905,X18906] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18906),X18905))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X18904),X18903))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18906),X18904)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18905),X18903))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zadd__zless__mono])]) ).

fof(i_0_8281,plain,
    ! [X20012,X20013,X20014] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20014),X20013))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20012),X20014))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20014),X20012)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20013),X20012))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__less__mono])]) ).

fof(i_0_8282,plain,
    ! [X19892,X19893,X19894] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19894),X19893))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19894),X19892))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19892),X19893)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19892),X19894))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__less__mono2])]) ).

fof(i_0_8283,plain,
    ! [X17423,X17424,X17425,X17426] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17426),X17425))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17424),X17423))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17426),X17424)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17425),X17423))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__mono])]) ).

fof(i_0_8284,plain,
    ! [X18134,X18135,X18136,X18137,X18138] :
      ( ~ class_Rings_Ocomm__semiring__1(X18138)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18138),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18138),X18137),X18136)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18138),X18135),X18134)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18138),X18135),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18138),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18138),X18137),X18136)),X18134)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J])]) ).

fof(i_0_8285,plain,
    ! [X25884,X25885,X25886] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25886,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X25886),X25885)),hAPP(c_SetInterval_Oord__class_OatMost(X25886),X25884)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25886),X25885),X25884))
        | ~ class_Orderings_Oorder(X25886) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25886),X25885),X25884))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25886,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X25886),X25885)),hAPP(c_SetInterval_Oord__class_OatMost(X25886),X25884)))
        | ~ class_Orderings_Oorder(X25886) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atMost__subset__iff])])]) ).

fof(i_0_8286,plain,
    ! [X26117,X26118,X26119] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26119,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X26119),X26118)),hAPP(c_SetInterval_Oord__class_OlessThan(X26119),X26117)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26119),X26118),X26117))
        | ~ class_Orderings_Olinorder(X26119) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26119),X26118),X26117))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26119,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X26119),X26118)),hAPP(c_SetInterval_Oord__class_OlessThan(X26119),X26117)))
        | ~ class_Orderings_Olinorder(X26119) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lessThan__subset__iff])])]) ).

fof(i_0_8287,plain,
    ! [X26304,X26305,X26306] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26306,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X26306),X26305)),hAPP(c_SetInterval_Oord__class_OatLeast(X26306),X26304)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26306),X26304),X26305))
        | ~ class_Orderings_Oorder(X26306) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26306),X26304),X26305))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26306,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X26306),X26305)),hAPP(c_SetInterval_Oord__class_OatLeast(X26306),X26304)))
        | ~ class_Orderings_Oorder(X26306) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeast__subset__iff])])]) ).

fof(i_0_8288,plain,
    ! [X26539,X26540,X26541] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26541,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X26541),X26540)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X26541),X26539)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26541),X26539),X26540))
        | ~ class_Orderings_Olinorder(X26541) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26541),X26539),X26540))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26541,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X26541),X26540)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X26541),X26539)))
        | ~ class_Orderings_Olinorder(X26541) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_greaterThan__subset__iff])])]) ).

fof(i_0_8289,plain,
    ! [X26120,X26121,X26122] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X26122,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X26122),X26121)),hAPP(c_SetInterval_Oord__class_OlessThan(X26122),X26120)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26122),X26121),X26120))
        | ~ class_Orderings_Olinorder(X26122) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26122),X26121),X26120))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X26122,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X26122),X26121)),hAPP(c_SetInterval_Oord__class_OlessThan(X26122),X26120)))
        | ~ class_Orderings_Olinorder(X26122) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lessThan__strict__subset__iff])])]) ).

cnf(i_0_8290,plain,
    hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X2),c_Relation_OId(X1)),X3) = X3,
    inference(split_conjunct,[status(thm)],[i_0_5729]) ).

fof(i_0_8291,plain,
    ! [X21404,X21405,X21406] :
      ( ~ class_Fields_Olinordered__field(X21406)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21406),X21405),c_Groups_Ozero__class_Ozero(X21406)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21406),c_Groups_Ozero__class_Ozero(X21406)),X21404))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21406),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21406),X21405),X21404)),c_Groups_Ozero__class_Ozero(X21406))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__nonpos__pos])]) ).

fof(i_0_8292,plain,
    ! [X21422,X21423,X21424] :
      ( ~ class_Fields_Olinordered__field(X21424)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21424),c_Groups_Ozero__class_Ozero(X21424)),X21423))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21424),X21422),c_Groups_Ozero__class_Ozero(X21424)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21424),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21424),X21423),X21422)),c_Groups_Ozero__class_Ozero(X21424))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__nonneg__neg])]) ).

fof(i_0_8293,plain,
    ! [X18819,X18820,X18821] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18821),c_Groups_Ozero__class_Ozero(X18821)),X18820))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18821),X18819),c_Groups_Ozero__class_Ozero(X18821)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18821),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18821),X18820),X18819)),c_Groups_Ozero__class_Ozero(X18821)))
        | ~ class_Rings_Oordered__cancel__semiring(X18821) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18821),X18820),c_Groups_Ozero__class_Ozero(X18821)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18821),c_Groups_Ozero__class_Ozero(X18821)),X18819))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18821),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18821),X18820),X18819)),c_Groups_Ozero__class_Ozero(X18821)))
        | ~ class_Rings_Oordered__cancel__semiring(X18821) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__mult__neg__le])])]) ).

fof(i_0_8294,plain,
    ! [X18780,X18781,X18782] :
      ( ~ class_Rings_Oordered__cancel__semiring(X18782)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18782),X18781),c_Groups_Ozero__class_Ozero(X18782)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18782),c_Groups_Ozero__class_Ozero(X18782)),X18780))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18782),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18782),X18781),X18780)),c_Groups_Ozero__class_Ozero(X18782))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonpos__nonneg])]) ).

fof(i_0_8295,plain,
    ! [X18774,X18775,X18776] :
      ( ~ class_Rings_Oordered__cancel__semiring(X18776)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18776),c_Groups_Ozero__class_Ozero(X18776)),X18775))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18776),X18774),c_Groups_Ozero__class_Ozero(X18776)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18776),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18776),X18775),X18774)),c_Groups_Ozero__class_Ozero(X18776))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonpos])]) ).

fof(i_0_8296,plain,
    ! [X18777,X18778,X18779] :
      ( ~ class_Rings_Oordered__cancel__semiring(X18779)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18779),c_Groups_Ozero__class_Ozero(X18779)),X18778))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18779),X18777),c_Groups_Ozero__class_Ozero(X18779)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18779),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18779),X18777),X18778)),c_Groups_Ozero__class_Ozero(X18779))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonpos2])]) ).

fof(i_0_8297,plain,
    ! [X21324,X21325,X21326] :
      ( ~ class_Fields_Olinordered__field(X21326)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21326),X21325),c_Groups_Ozero__class_Ozero(X21326)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21326),c_Groups_Ozero__class_Ozero(X21326)),X21324))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21326),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21326),X21325),X21324)),c_Groups_Ozero__class_Ozero(X21326))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__neg__pos])]) ).

fof(i_0_8298,plain,
    ! [X21327,X21328,X21329] :
      ( ~ class_Fields_Olinordered__field(X21329)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21329),c_Groups_Ozero__class_Ozero(X21329)),X21328))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21329),X21327),c_Groups_Ozero__class_Ozero(X21329)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21329),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21329),X21328),X21327)),c_Groups_Ozero__class_Ozero(X21329))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__pos__neg])]) ).

fof(i_0_8299,plain,
    ! [X18361,X18362,X18363] :
      ( ~ class_Rings_Olinordered__semiring__strict(X18363)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18363),X18362),c_Groups_Ozero__class_Ozero(X18363)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18363),c_Groups_Ozero__class_Ozero(X18363)),X18361))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18363),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18363),X18362),X18361)),c_Groups_Ozero__class_Ozero(X18363))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__neg__pos])]) ).

fof(i_0_8300,plain,
    ! [X18345,X18346,X18347] :
      ( ~ class_Rings_Olinordered__semiring__strict(X18347)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18347),c_Groups_Ozero__class_Ozero(X18347)),X18346))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18347),X18345),c_Groups_Ozero__class_Ozero(X18347)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18347),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18347),X18346),X18345)),c_Groups_Ozero__class_Ozero(X18347))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__pos__neg])]) ).

fof(i_0_8301,plain,
    ! [X18348,X18349,X18350] :
      ( ~ class_Rings_Olinordered__semiring__strict(X18350)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18350),c_Groups_Ozero__class_Ozero(X18350)),X18349))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18350),X18348),c_Groups_Ozero__class_Ozero(X18350)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18350),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18350),X18348),X18349)),c_Groups_Ozero__class_Ozero(X18350))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__pos__neg2])]) ).

fof(i_0_8302,plain,
    ! [X28865,X28866,X28867] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28867,tc_HOL_Obool)),hAPP(c_List_Oset(X28867),X28866)),hAPP(c_List_Oset(X28867),hAPP(hAPP(c_List_Olist_OCons(X28867),X28865),X28866)))),
    inference(variable_rename,[status(thm)],[fact_set__subset__Cons]) ).

fof(i_0_8303,plain,
    ! [X31310,X31311,X31312,X31313] : c_List_Otranspose(X31313,hAPP(hAPP(c_List_Omap(tc_List_Olist(X31312),tc_List_Olist(X31313)),hAPP(c_List_Omap(X31312,X31313),X31311)),X31310)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(X31312),tc_List_Olist(X31313)),hAPP(c_List_Omap(X31312,X31313),X31311)),c_List_Otranspose(X31312,X31310)),
    inference(variable_rename,[status(thm)],[fact_transpose__map__map]) ).

cnf(i_0_8304,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_5730]) ).

cnf(i_0_8305,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_5731]) ).

fof(i_0_8306,plain,
    ! [X22890,X22891,X22892,X22893] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22893),X22892),X22890))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22893),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X22893),X22892),X22891)),X22890))
        | ~ class_Lattices_Osemilattice__sup(X22893) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22893),X22891),X22890))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22893),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X22893),X22892),X22891)),X22890))
        | ~ class_Lattices_Osemilattice__sup(X22893) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5732])])]) ).

fof(i_0_8307,plain,
    ! [X22859,X22860,X22861,X22862] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22862),X22861),X22859))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22862),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X22862),X22861),X22860)),X22859))
        | ~ class_Lattices_Osemilattice__sup(X22862) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22862),X22860),X22859))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22862),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X22862),X22861),X22860)),X22859))
        | ~ class_Lattices_Osemilattice__sup(X22862) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22862),X22861),X22859))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22862),X22860),X22859))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22862),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X22862),X22861),X22860)),X22859))
        | ~ class_Lattices_Osemilattice__sup(X22862) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__sup__iff])])]) ).

fof(i_0_8308,plain,
    ! [X22602,X22603,X22604,X22605] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22605),X22604),X22602))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22605),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22605),X22604),X22603)),X22602))
        | ~ class_Orderings_Olinorder(X22605) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22605),X22603),X22602))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22605),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22605),X22604),X22603)),X22602))
        | ~ class_Orderings_Olinorder(X22605) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5733])])]) ).

fof(i_0_8309,plain,
    ! [X22571,X22572,X22573,X22574] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22574),X22573),X22571))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22574),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22574),X22573),X22572)),X22571))
        | ~ class_Orderings_Olinorder(X22574) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22574),X22572),X22571))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22574),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22574),X22573),X22572)),X22571))
        | ~ class_Orderings_Olinorder(X22574) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22574),X22573),X22571))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22574),X22572),X22571))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22574),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22574),X22573),X22572)),X22571))
        | ~ class_Orderings_Olinorder(X22574) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__sup__iff])])]) ).

fof(i_0_8310,plain,
    ! [X22618,X22619,X22620,X22621] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22621),X22620),X22618))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22621),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22621),X22620),X22619)),X22618))
        | ~ class_Orderings_Olinorder(X22621) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22621),X22619),X22618))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22621),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22621),X22620),X22619)),X22618))
        | ~ class_Orderings_Olinorder(X22621) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22621),X22620),X22618))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22621),X22619),X22618))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22621),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22621),X22620),X22619)),X22618))
        | ~ class_Orderings_Olinorder(X22621) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__less__iff__conj])])]) ).

fof(i_0_8311,plain,
    ! [X29372,X29373,X29374,X29375] :
      ( ( hAPP(hAPP(c_List_Onth(X29375),X29374),X29373) != hAPP(hAPP(c_List_Onth(X29375),X29374),X29372)
        | X29373 = X29372
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29372),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29375)),X29374)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29373),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29375)),X29374)))
        | ~ hBOOL(hAPP(c_List_Odistinct(X29375),X29374)) )
      & ( X29373 != X29372
        | hAPP(hAPP(c_List_Onth(X29375),X29374),X29373) = hAPP(hAPP(c_List_Onth(X29375),X29374),X29372)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29372),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29375)),X29374)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29373),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29375)),X29374)))
        | ~ hBOOL(hAPP(c_List_Odistinct(X29375),X29374)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__eq__iff__index__eq])])]) ).

fof(i_0_8312,plain,
    ! [X29364,X29365,X29366,X29367,X29368,X29369] :
      ( ( ~ hBOOL(hAPP(c_List_Odistinct(X29365),X29364))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29366),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29365)),X29364)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29367),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29365)),X29364)))
        | X29366 = X29367
        | hAPP(hAPP(c_List_Onth(X29365),X29364),X29366) != hAPP(hAPP(c_List_Onth(X29365),X29364),X29367) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk339_2(X29368,X29369)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29369)),X29368)))
        | hBOOL(hAPP(c_List_Odistinct(X29369),X29368)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk340_2(X29368,X29369)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29369)),X29368)))
        | hBOOL(hAPP(c_List_Odistinct(X29369),X29368)) )
      & ( esk339_2(X29368,X29369) != esk340_2(X29368,X29369)
        | hBOOL(hAPP(c_List_Odistinct(X29369),X29368)) )
      & ( hAPP(hAPP(c_List_Onth(X29369),X29368),esk339_2(X29368,X29369)) = hAPP(hAPP(c_List_Onth(X29369),X29368),esk340_2(X29368,X29369))
        | hBOOL(hAPP(c_List_Odistinct(X29369),X29368)) ) ),
    inference(distribute,[status(thm)],[inference(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_8313,plain,
    ! [X30137,X30138,X30139,X30140] :
      ( ( hBOOL(hAPP(c_List_Odistinct(X30139),X30137))
        | ~ hBOOL(hAPP(c_List_Odistinct(X30140),hAPP(hAPP(c_List_Omap(X30139,X30140),X30138),X30137))) )
      & ( c_Fun_Oinj__on(X30139,X30140,X30138,hAPP(c_List_Oset(X30139),X30137))
        | ~ hBOOL(hAPP(c_List_Odistinct(X30140),hAPP(hAPP(c_List_Omap(X30139,X30140),X30138),X30137))) )
      & ( ~ hBOOL(hAPP(c_List_Odistinct(X30139),X30137))
        | ~ c_Fun_Oinj__on(X30139,X30140,X30138,hAPP(c_List_Oset(X30139),X30137))
        | hBOOL(hAPP(c_List_Odistinct(X30140),hAPP(hAPP(c_List_Omap(X30139,X30140),X30138),X30137))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__map])])]) ).

fof(i_0_8314,plain,
    ! [X24471,X24472] :
      ( ~ class_Orderings_Olinorder(X24472)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24472),X24471))
      | X24471 = c_Orderings_Obot__class_Obot(tc_fun(X24472,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24472),c_Big__Operators_Olattice_OInf__fin(X24472,c_Orderings_Oord__class_Omin(X24472),X24471)),c_Big__Operators_Olattice_OSup__fin(X24472,c_Orderings_Oord__class_Omax(X24472),X24471))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__le__Sup])]) ).

fof(i_0_8315,plain,
    ! [X25715,X25716,X25717,X25718,X25719] :
      ( ~ c_Fun_Oinj__on(X25719,X25718,X25717,X25716)
      | c_Fun_Oinj__on(X25719,X25718,X25717,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25719,tc_HOL_Obool)),X25716),X25715)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__diff])]) ).

fof(i_0_8316,plain,
    ! [X33531,X33532,X33533,X33534] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X33534,X33533),c_Lazy__Sequence_Olazy__sequence_OInsert(X33534,X33532,X33531)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X33533,X33532)),hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X33534,X33533),X33531))),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_8317,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_5734]) ).

cnf(i_0_8318,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_5735]) ).

cnf(i_0_8319,plain,
    c_List_Omember(X1) = c_List_Oset(X1),
    inference(split_conjunct,[status(thm)],[i_0_5736]) ).

fof(i_0_8320,plain,
    ! [X32844,X32845,X32846,X32847,X32848,X32849] :
      ( ~ c_Finite__Set_Ofun__left__comm__idem(X32849,X32848,X32847)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32849),X32846))
      | hAPP(hAPP(c_Finite__Set_Ofold(X32849,X32848,X32847),X32845),hAPP(hAPP(c_Set_Oinsert(X32849),X32844),X32846)) = hAPP(hAPP(c_Finite__Set_Ofold(X32849,X32848,X32847),hAPP(hAPP(X32847,X32844),X32845)),X32846) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofold__insert__idem2])]) ).

fof(i_0_8321,plain,
    ! [X20863,X20864,X20865] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X20865),X20864),X20863))
      | hAPP(hAPP(c_Set_Oinsert(X20865),X20864),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20865,tc_HOL_Obool)),X20863),hAPP(hAPP(c_Set_Oinsert(X20865),X20864),c_Orderings_Obot__class_Obot(tc_fun(X20865,tc_HOL_Obool))))) = X20863 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__Diff])]) ).

fof(i_0_8322,plain,
    ! [X26680,X26681] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X26681),c_Orderings_Otop__class_Otop(tc_fun(X26681,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X26681,X26680)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X26681,X26680),tc_HOL_Obool)))) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X26680),c_Orderings_Otop__class_Otop(tc_fun(X26680,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X26681,X26680)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X26681,X26680),tc_HOL_Obool)))) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26681),c_Orderings_Otop__class_Otop(tc_fun(X26681,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26680),c_Orderings_Otop__class_Otop(tc_fun(X26680,tc_HOL_Obool))))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X26681,X26680)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X26681,X26680),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_8323,plain,
    ! [X26684,X26685] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26685),c_Orderings_Otop__class_Otop(tc_fun(X26685,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26684),c_Orderings_Otop__class_Otop(tc_fun(X26684,tc_HOL_Obool))))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X26685,X26684)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X26685,X26684),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Prod__UNIV])]) ).

fof(i_0_8324,plain,
    ! [X26358,X26359,X26360,X26361] :
      ( ~ class_Groups_Ocomm__monoid__add(X26361)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X26360),X26359))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26361),X26358),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X26360,X26359)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26361),hAPP(X26358,X26360)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26361),X26358),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X26360),X26359))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__head__Suc])]) ).

fof(i_0_8325,plain,
    ! [X27162,X27163,X27164,X27165,X27166] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X27166),hAPP(X27165,X27164)),X27163))
      | hBOOL(hAPP(hAPP(c_member(X27162),X27164),hAPP(c_Set_Ovimage(X27162,X27166,X27165),X27163))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vimageI2])]) ).

cnf(i_0_8326,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_5737]) ).

fof(i_0_8327,plain,
    ! [X31542,X31543,X31544] :
      ( ( ~ c_List_Olinorder__class_Osorted(X31544,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X31544,X31544,c_COMBI(X31544)),X31543),X31542))
        | c_List_Olinorder__class_Osorted(X31544,X31542)
        | ~ class_Orderings_Olinorder(X31544) )
      & ( ~ c_List_Olinorder__class_Osorted(X31544,X31542)
        | c_List_Olinorder__class_Osorted(X31544,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X31544,X31544,c_COMBI(X31544)),X31543),X31542))
        | ~ class_Orderings_Olinorder(X31544) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__insort])])]) ).

fof(i_0_8328,plain,
    ! [X26354,X26355,X26356,X26357] :
      ( ~ class_Groups_Ocomm__monoid__add(X26357)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X26356),X26355))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26357),X26354),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X26356),X26355)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26357),hAPP(X26354,X26356)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26357),X26354),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X26356)),X26355))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__head__upt__Suc])]) ).

fof(i_0_8329,plain,
    ! [X19304,X19305,X19306] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19304,tc_HOL_Obool)),X19306),X19305))
        | X19306 != X19305 )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19304,tc_HOL_Obool)),X19305),X19306))
        | X19306 != X19305 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19304,tc_HOL_Obool)),X19306),X19305))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19304,tc_HOL_Obool)),X19305),X19306))
        | X19306 = X19305 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__eq__subset])])]) ).

fof(i_0_8330,plain,
    ! [X19293,X19294,X19295] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19295,tc_HOL_Obool)),X19294),X19293))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19295,tc_HOL_Obool)),X19293),X19294))
      | X19294 = X19293 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equalityI])]) ).

fof(i_0_8331,plain,
    ! [X31694,X31695,X31696] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31696),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31695)),X31694)))
      | hAPP(hAPP(c_List_Onth(X31695),hAPP(c_List_Orev(X31695),X31694)),X31696) = hAPP(hAPP(c_List_Onth(X31695),X31694),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31695)),X31694)),hAPP(c_Nat_OSuc,X31696))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__nth])]) ).

fof(i_0_8332,plain,
    ! [X30027,X30028,X30029,X30030,X30031] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X30031),X30030),X30029))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X30028,tc_HOL_Obool)),hAPP(X30027,X30030)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30031,tc_fun(X30028,tc_HOL_Obool)),X30029),X30027)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30031,tc_fun(X30028,tc_HOL_Obool)),X30029),X30027) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__absorb])]) ).

fof(i_0_8333,plain,
    ! [X25186,X25187,X25188,X25189,X25190] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X25190),X25189),X25188))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25187,tc_HOL_Obool)),hAPP(X25186,X25189)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25190,tc_fun(X25187,tc_HOL_Obool)),X25188),X25186)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25190,tc_fun(X25187,tc_HOL_Obool)),X25188),X25186) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__absorb])]) ).

fof(i_0_8334,plain,
    ! [X29077,X29078,X29079,X29080,X29081] : hAPP(hAPP(c_List_Olist__update(X29081,hAPP(hAPP(c_List_Olist__update(X29081,X29080),X29079),X29078)),X29079),X29077) = hAPP(hAPP(c_List_Olist__update(X29081,X29080),X29079),X29077),
    inference(variable_rename,[status(thm)],[fact_list__update__overwrite]) ).

fof(i_0_8335,plain,
    ! [X18117,X18118] : 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,X18118)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18117))),
    inference(variable_rename,[status(thm)],[fact_negative__zless]) ).

fof(i_0_8336,plain,
    ! [X20910,X20911,X20912] :
      ( ~ class_Rings_Oring__1(X20912)
      | ~ hBOOL(hAPP(hAPP(c_member(X20912),X20911),c_Int_Oring__1__class_OInts(X20912)))
      | ~ hBOOL(hAPP(hAPP(c_member(X20912),X20910),c_Int_Oring__1__class_OInts(X20912)))
      | hBOOL(hAPP(hAPP(c_member(X20912),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20912),X20911),X20910)),c_Int_Oring__1__class_OInts(X20912))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__diff])]) ).

fof(i_0_8337,plain,
    ! [X21005,X21006,X21007] :
      ( ~ class_Rings_Osemiring__1(X21007)
      | ~ hBOOL(hAPP(hAPP(c_member(X21007),X21006),c_Nat_Osemiring__1__class_ONats(X21007)))
      | ~ hBOOL(hAPP(hAPP(c_member(X21007),X21005),c_Nat_Osemiring__1__class_ONats(X21007)))
      | hBOOL(hAPP(hAPP(c_member(X21007),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21007),X21006),X21005)),c_Nat_Osemiring__1__class_ONats(X21007))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nats__mult])]) ).

fof(i_0_8338,plain,
    ! [X20907,X20908,X20909] :
      ( ~ class_Rings_Oring__1(X20909)
      | ~ hBOOL(hAPP(hAPP(c_member(X20909),X20908),c_Int_Oring__1__class_OInts(X20909)))
      | ~ hBOOL(hAPP(hAPP(c_member(X20909),X20907),c_Int_Oring__1__class_OInts(X20909)))
      | hBOOL(hAPP(hAPP(c_member(X20909),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20909),X20908),X20907)),c_Int_Oring__1__class_OInts(X20909))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__mult])]) ).

fof(i_0_8339,plain,
    ! [X21002,X21003,X21004] :
      ( ~ class_Rings_Osemiring__1(X21004)
      | ~ hBOOL(hAPP(hAPP(c_member(X21004),X21003),c_Nat_Osemiring__1__class_ONats(X21004)))
      | ~ hBOOL(hAPP(hAPP(c_member(X21004),X21002),c_Nat_Osemiring__1__class_ONats(X21004)))
      | hBOOL(hAPP(hAPP(c_member(X21004),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21004),X21003),X21002)),c_Nat_Osemiring__1__class_ONats(X21004))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nats__add])]) ).

fof(i_0_8340,plain,
    ! [X20904,X20905,X20906] :
      ( ~ class_Rings_Oring__1(X20906)
      | ~ hBOOL(hAPP(hAPP(c_member(X20906),X20905),c_Int_Oring__1__class_OInts(X20906)))
      | ~ hBOOL(hAPP(hAPP(c_member(X20906),X20904),c_Int_Oring__1__class_OInts(X20906)))
      | hBOOL(hAPP(hAPP(c_member(X20906),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20906),X20905),X20904)),c_Int_Oring__1__class_OInts(X20906))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__add])]) ).

fof(i_0_8341,plain,
    ! [X18760,X18761,X18762] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X18762)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18762),X18761),c_Groups_Ozero__class_Ozero(X18762)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18762),X18760),c_Groups_Ozero__class_Ozero(X18762)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18762),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18762),X18761),X18760)),c_Groups_Ozero__class_Ozero(X18762))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonpos__nonpos])]) ).

fof(i_0_8342,plain,
    ! [X18928,X18929,X18930] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X18930)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18930),X18929),c_Groups_Ozero__class_Ozero(X18930)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18930),X18928),c_Groups_Ozero__class_Ozero(X18930)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18930),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18930),X18929),X18928)),c_Groups_Ozero__class_Ozero(X18930))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__neg__nonpos])]) ).

fof(i_0_8343,plain,
    ! [X18925,X18926,X18927] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X18927)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18927),X18926),c_Groups_Ozero__class_Ozero(X18927)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18927),X18925),c_Groups_Ozero__class_Ozero(X18927)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18927),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18927),X18926),X18925)),c_Groups_Ozero__class_Ozero(X18927))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonpos__neg])]) ).

fof(i_0_8344,plain,
    ! [X17467,X17468,X17469] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X17469)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17469),X17468),c_Groups_Ozero__class_Ozero(X17469)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17469),X17467),c_Groups_Ozero__class_Ozero(X17469)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17469),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17469),X17468),X17467)),c_Groups_Ozero__class_Ozero(X17469))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__neg__neg])]) ).

fof(i_0_8345,plain,
    ! [X30301,X30302,X30303] : c_List_Olist_Olist__size(X30303,X30302,X30301) = 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(X30303,tc_Nat_Onat),X30302),X30301))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30303)),X30301)),
    inference(variable_rename,[status(thm)],[fact_list__size__conv__listsum]) ).

fof(i_0_8346,plain,
    ! [X26799,X26800] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26800),c_Orderings_Otop__class_Otop(tc_fun(X26800,tc_HOL_Obool))))
      | ~ c_Fun_Oinj__on(X26800,X26800,X26799,c_Orderings_Otop__class_Otop(tc_fun(X26800,tc_HOL_Obool)))
      | hAPP(c_Set_Oimage(X26800,X26800,X26799),c_Orderings_Otop__class_Otop(tc_fun(X26800,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X26800,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV__inj__surj])]) ).

fof(i_0_8347,plain,
    ! [X30206,X30207,X30208,X30209] :
      ( ~ class_Rings_Osemiring__1(X30209)
      | hAPP(c_List_Omonoid__add__class_Olistsum(X30209),hAPP(hAPP(c_List_Omap(X30208,X30209),hAPP(c_COMBK(X30209,X30208),X30207)),X30206)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X30209),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X30209),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30208)),X30206))),X30207) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__triv])]) ).

fof(i_0_8348,plain,
    ! [X20626,X20627,X20628] :
      ( ~ class_Rings_Oring__1(X20628)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X20628),hAPP(c_Groups_Ouminus__class_Ouminus(X20628),X20627)),X20626) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20628),hAPP(hAPP(c_Power_Opower__class_Opower(X20628),hAPP(c_Groups_Ouminus__class_Ouminus(X20628),c_Groups_Oone__class_Oone(X20628))),X20626)),hAPP(hAPP(c_Power_Opower__class_Opower(X20628),X20627),X20626)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__minus])]) ).

fof(i_0_8349,plain,
    ! [X26718,X26719,X26720,X26721] : hBOOL(hAPP(hAPP(c_member(X26721),hAPP(X26720,X26719)),hAPP(c_Set_Oimage(X26718,X26721,X26720),c_Orderings_Otop__class_Otop(tc_fun(X26718,tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[fact_rangeI]) ).

fof(i_0_8350,plain,
    ! [X20345,X20346,X20347,X20348] :
      ( ~ class_Int_Onumber(X20348)
      | ~ class_Rings_Oring(X20348)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20348),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20348),X20347),X20346)),hAPP(c_Int_Onumber__class_Onumber__of(X20348),X20345)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20348),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20348),X20347),hAPP(c_Int_Onumber__class_Onumber__of(X20348),X20345))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20348),X20346),hAPP(c_Int_Onumber__class_Onumber__of(X20348),X20345))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_left__diff__distrib__number__of])]) ).

fof(i_0_8351,plain,
    ! [X20332,X20333,X20334,X20335] :
      ( ~ class_Int_Onumber(X20335)
      | ~ class_Rings_Osemiring(X20335)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20335),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20335),X20334),X20333)),hAPP(c_Int_Onumber__class_Onumber__of(X20335),X20332)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20335),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20335),X20334),hAPP(c_Int_Onumber__class_Onumber__of(X20335),X20332))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20335),X20333),hAPP(c_Int_Onumber__class_Onumber__of(X20335),X20332))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_left__distrib__number__of])]) ).

fof(i_0_8352,plain,
    ! [X24388,X24389,X24390] :
      ( ~ class_Orderings_Olinorder(X24390)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24390),X24389))
      | X24389 = c_Orderings_Obot__class_Obot(tc_fun(X24390,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24390),X24388))
      | X24388 = c_Orderings_Obot__class_Obot(tc_fun(X24390,tc_HOL_Obool))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24390,tc_HOL_Obool)),X24389),X24388) != c_Orderings_Obot__class_Obot(tc_fun(X24390,tc_HOL_Obool))
      | c_Big__Operators_Olinorder__class_OMin(X24390,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24390,tc_HOL_Obool)),X24389),X24388)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X24390),c_Big__Operators_Olinorder__class_OMin(X24390,X24389)),c_Big__Operators_Olinorder__class_OMin(X24390,X24388)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Ounion__disjoint])]) ).

fof(i_0_8353,plain,
    ! [X24339,X24340,X24341] :
      ( ~ class_Orderings_Olinorder(X24341)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24341),X24340))
      | X24340 = c_Orderings_Obot__class_Obot(tc_fun(X24341,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24341),X24339))
      | X24339 = c_Orderings_Obot__class_Obot(tc_fun(X24341,tc_HOL_Obool))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24341,tc_HOL_Obool)),X24340),X24339) != c_Orderings_Obot__class_Obot(tc_fun(X24341,tc_HOL_Obool))
      | c_Big__Operators_Olinorder__class_OMax(X24341,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24341,tc_HOL_Obool)),X24340),X24339)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X24341),c_Big__Operators_Olinorder__class_OMax(X24341,X24340)),c_Big__Operators_Olinorder__class_OMax(X24341,X24339)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Ounion__disjoint])]) ).

fof(i_0_8354,plain,
    ! [X24321,X24322,X24323] :
      ( ~ class_Lattices_Olattice(X24323)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24323),X24322))
      | X24322 = c_Orderings_Obot__class_Obot(tc_fun(X24323,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24323),X24321))
      | X24321 = c_Orderings_Obot__class_Obot(tc_fun(X24323,tc_HOL_Obool))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24323,tc_HOL_Obool)),X24322),X24321) != c_Orderings_Obot__class_Obot(tc_fun(X24323,tc_HOL_Obool))
      | c_Big__Operators_Olattice__class_OSup__fin(X24323,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24323,tc_HOL_Obool)),X24322),X24321)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24323),c_Big__Operators_Olattice__class_OSup__fin(X24323,X24322)),c_Big__Operators_Olattice__class_OSup__fin(X24323,X24321)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Ounion__disjoint])]) ).

fof(i_0_8355,plain,
    ! [X24333,X24334,X24335] :
      ( ~ class_Lattices_Olattice(X24335)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24335),X24334))
      | X24334 = c_Orderings_Obot__class_Obot(tc_fun(X24335,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24335),X24333))
      | X24333 = c_Orderings_Obot__class_Obot(tc_fun(X24335,tc_HOL_Obool))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24335,tc_HOL_Obool)),X24334),X24333) != c_Orderings_Obot__class_Obot(tc_fun(X24335,tc_HOL_Obool))
      | c_Big__Operators_Olattice__class_OInf__fin(X24335,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24335,tc_HOL_Obool)),X24334),X24333)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24335),c_Big__Operators_Olattice__class_OInf__fin(X24335,X24334)),c_Big__Operators_Olattice__class_OInf__fin(X24335,X24333)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Ounion__disjoint])]) ).

fof(i_0_8356,plain,
    ! [X18638,X18639,X18640,X18641] :
      ( ~ class_Groups_Oordered__ab__semigroup__add(X18641)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18641),X18640),X18639))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18641),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18641),X18640),X18638)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18641),X18639),X18638))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__mono])]) ).

fof(i_0_8357,plain,
    ! [X18642,X18643,X18644,X18645] :
      ( ~ class_Groups_Oordered__ab__semigroup__add(X18645)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18645),X18644),X18643))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18645),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18645),X18642),X18644)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18645),X18642),X18643))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__mono])]) ).

fof(i_0_8358,plain,
    ! [X17301,X17302,X17303,X17304] :
      ( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X17304)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17304),X17303),X17302))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17304),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17304),X17303),X17301)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17304),X17302),X17301))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__right__mono])]) ).

fof(i_0_8359,plain,
    ! [X17297,X17298,X17299,X17300] :
      ( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X17300)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17300),X17299),X17298))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17300),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17300),X17297),X17299)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17300),X17297),X17298))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__left__mono])]) ).

fof(i_0_8360,plain,
    ! [X27064,X27065,X27066] :
      ( ~ class_Lattices_Oab__semigroup__idem__mult(X27066)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27066),X27065))
      | X27065 = c_Orderings_Obot__class_Obot(tc_fun(X27066,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27066),X27064))
      | X27064 = c_Orderings_Obot__class_Obot(tc_fun(X27066,tc_HOL_Obool))
      | hAPP(c_Finite__Set_Ofold1(X27066,c_Groups_Otimes__class_Otimes(X27066)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27066,tc_HOL_Obool)),X27065),X27064)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27066),hAPP(c_Finite__Set_Ofold1(X27066,c_Groups_Otimes__class_Otimes(X27066)),X27065)),hAPP(c_Finite__Set_Ofold1(X27066,c_Groups_Otimes__class_Otimes(X27066)),X27064)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1__Un2])]) ).

fof(i_0_8361,plain,
    ! [X31688,X31689,X31690] : hAPP(c_List_Orev(X31690),hAPP(hAPP(c_List_Odrop(X31690),X31689),X31688)) = hAPP(hAPP(c_List_Otake(X31690),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31690)),X31688)),X31689)),hAPP(c_List_Orev(X31690),X31688)),
    inference(variable_rename,[status(thm)],[fact_rev__drop]) ).

fof(i_0_8362,plain,
    ! [X31685,X31686,X31687] : hAPP(c_List_Orev(X31687),hAPP(hAPP(c_List_Otake(X31687),X31686),X31685)) = hAPP(hAPP(c_List_Odrop(X31687),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31687)),X31685)),X31686)),hAPP(c_List_Orev(X31687),X31685)),
    inference(variable_rename,[status(thm)],[fact_rev__take]) ).

fof(i_0_8363,plain,
    ! [X25549,X25550,X25551] :
      ( ~ class_Orderings_Olinorder(X25551)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25551),X25550),X25549))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25551,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X25551),X25550),c_Orderings_Obot__class_Obot(tc_fun(X25551,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(X25551,X25550,X25549)) = c_SetInterval_Oord__class_OatLeastAtMost(X25551,X25550,X25549) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I5_J])]) ).

fof(i_0_8364,plain,
    ! [X19086,X19087] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19087,tc_HOL_Obool)),X19086),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X19087,tc_HOL_Obool)),X19086)))
        | X19086 = c_Orderings_Obot__class_Obot(tc_fun(X19087,tc_HOL_Obool)) )
      & ( X19086 != c_Orderings_Obot__class_Obot(tc_fun(X19087,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19087,tc_HOL_Obool)),X19086),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X19087,tc_HOL_Obool)),X19086))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__Compl__self__eq])]) ).

fof(i_0_8365,plain,
    ! [X20946,X20947,X20948] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20948),c_Int_OPls))
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20948)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20947)),X20946)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20948),c_Int_OPls))
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20948)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20947)),X20946)) = 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),X20948),X20947))),X20946) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5738])]) ).

fof(i_0_8366,plain,
    ! [X21898,X21899] : c_Divides_Opdivmod(X21899,X21898) = 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),X21899)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X21898))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X21899),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X21898))),
    inference(variable_rename,[status(thm)],[fact_pdivmod__def]) ).

fof(i_0_8367,plain,
    ! [X30840,X30841,X30842] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X30842,tc_HOL_Obool)),X30841),X30840))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X30842,tc_HOL_Obool)),X30841),c_Complete__Lattice_OSup__class_OSup(tc_fun(X30842,tc_HOL_Obool),X30840))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Union__upper])]) ).

fof(i_0_8368,plain,
    ! [X32811,X32812,X32813,X32814] : hAPP(c_Finite__Set_Ofold__image(X32814,X32813,X32812),X32811) = c_Finite__Set_Ofold(X32813,X32814,hAPP(hAPP(c_COMBB(X32814,tc_fun(X32814,X32814),X32813),X32812),X32811)),
    inference(variable_rename,[status(thm)],[fact_fold__image__def]) ).

fof(i_0_8369,plain,
    ! [X22721,X22722] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X22722)),X22721) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,X22722),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),X22722)),X22721),
    inference(variable_rename,[status(thm)],[fact_max__Suc1]) ).

fof(i_0_8370,plain,
    ! [X30787,X30788] : hAPP(c_Relation_OField(X30788),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X30788,X30788),tc_HOL_Obool),X30787)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(X30788,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(X30788,X30788),tc_HOL_Obool),tc_fun(X30788,tc_HOL_Obool),c_Relation_OField(X30788)),X30787)),
    inference(variable_rename,[status(thm)],[fact_Field__Union]) ).

fof(i_0_8371,plain,
    ! [X23065,X23066,X23067] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23067,tc_HOL_Obool)),X23066),X23065))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23067,tc_HOL_Obool)),X23066),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23067,tc_HOL_Obool)),X23065),X23066)) = X23065 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Diff__partition])]) ).

fof(i_0_8372,plain,
    ! [X29687,X29688,X29689] :
      ( ~ c_Fun_Oinj__on(X29689,X29688,X29687,c_Orderings_Otop__class_Otop(tc_fun(X29689,tc_HOL_Obool)))
      | c_Fun_Oinj__on(tc_List_Olist(X29689),tc_List_Olist(X29688),hAPP(c_List_Omap(X29689,X29688),X29687),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X29689),tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__mapI])]) ).

fof(i_0_8373,plain,
    ! [X24093,X24094,X24095] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X24095,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24095,tc_HOL_Obool)),X24094),X24093)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24095,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X24095,tc_HOL_Obool)),X24094)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X24095,tc_HOL_Obool)),X24093)),
    inference(variable_rename,[status(thm)],[fact_Compl__Int]) ).

fof(i_0_8374,plain,
    ! [X24090,X24091,X24092] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X24092,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24092,tc_HOL_Obool)),X24091),X24090)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24092,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X24092,tc_HOL_Obool)),X24091)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X24092,tc_HOL_Obool)),X24090)),
    inference(variable_rename,[status(thm)],[fact_Compl__Un]) ).

fof(i_0_8375,plain,
    ! [X21726,X21727,X21728,X21729,X21730] :
      ( ( hBOOL(hAPP(hAPP(X21729,X21727),X21726))
        | ~ hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(X21730,X21729,X21728),X21727),X21726)) )
      & ( hBOOL(hAPP(X21728,X21726))
        | ~ hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(X21730,X21729,X21728),X21727),X21726)) )
      & ( ~ hBOOL(hAPP(hAPP(X21729,X21727),X21726))
        | ~ hBOOL(hAPP(X21728,X21726))
        | hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(X21730,X21729,X21728),X21727),X21726)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_peek__and__def])])]) ).

fof(i_0_8376,plain,
    ! [X33367,X33368,X33369,X33370,X33371] :
      ( ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X33371,X33370,X33369),X33368),X33367))
      | hBOOL(hAPP(hAPP(X33369,X33367),X33368)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_conversepD])]) ).

fof(i_0_8377,plain,
    ! [X33357,X33358,X33359,X33360,X33361] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X33361,X33360,X33359),X33358),X33357))
        | hBOOL(hAPP(hAPP(X33359,X33357),X33358)) )
      & ( ~ hBOOL(hAPP(hAPP(X33359,X33357),X33358))
        | hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X33361,X33360,X33359),X33358),X33357)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_conversep_Oequations])]) ).

fof(i_0_8378,plain,
    ! [X33352,X33353,X33354,X33355,X33356] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X33356,X33355,X33354),X33353),X33352))
        | hBOOL(hAPP(hAPP(X33354,X33352),X33353)) )
      & ( ~ hBOOL(hAPP(hAPP(X33354,X33352),X33353))
        | hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X33356,X33355,X33354),X33353),X33352)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_conversep__iff])]) ).

fof(i_0_8379,plain,
    ! [X27143,X27144,X27145,X27146,X27147] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Set_Ovimage(X27147,X27146,X27145),X27144),X27143))
        | hBOOL(hAPP(X27144,hAPP(X27145,X27143))) )
      & ( ~ hBOOL(hAPP(X27144,hAPP(X27145,X27143)))
        | hBOOL(hAPP(hAPP(c_Set_Ovimage(X27147,X27146,X27145),X27144),X27143)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vimage__code])]) ).

fof(i_0_8380,plain,
    ! [X29269,X29270,X29271,X29273] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X29271)),esk335_3(X29269,X29270,X29271)),X29270))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X29271)),X29273),X29270))
        | c_Hoare__Mirabelle_Otriple__valid(X29271,X29269,X29273) )
      & ( ~ c_Hoare__Mirabelle_Otriple__valid(X29271,hAPP(c_Nat_OSuc,X29269),esk335_3(X29269,X29270,X29271))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X29271)),X29273),X29270))
        | c_Hoare__Mirabelle_Otriple__valid(X29271,X29269,X29273) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_triples__valid__Suc])])])])]) ).

fof(i_0_8381,plain,
    ! [X31019,X31020,X31021,X31023] :
      ( ( hBOOL(hAPP(hAPP(c_member(X31021),esk377_3(X31019,X31020,X31021)),X31020))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X31021),c_Complete__Lattice_OInf__class_OInf(X31021,X31020)),X31019))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X31021)
        | ~ class_Orderings_Olinorder(X31021) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X31021),esk377_3(X31019,X31020,X31021)),X31019))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X31021),c_Complete__Lattice_OInf__class_OInf(X31021,X31020)),X31019))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X31021)
        | ~ class_Orderings_Olinorder(X31021) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X31021),X31023),X31020))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X31021),X31023),X31019))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X31021),c_Complete__Lattice_OInf__class_OInf(X31021,X31020)),X31019))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X31021)
        | ~ class_Orderings_Olinorder(X31021) ) ),
    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_8382,plain,
    ! [X20388,X20389,X20390,X20391] :
      ( ~ class_Int_Onumber__ring(X20391)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20391),hAPP(c_Int_Onumber__class_Onumber__of(X20391),X20390)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20391),hAPP(c_Int_Onumber__class_Onumber__of(X20391),X20389)),X20388)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20391),hAPP(c_Int_Onumber__class_Onumber__of(X20391),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20390),X20389))),X20388) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__number__of__left])]) ).

fof(i_0_8383,plain,
    ! [X20437,X20438,X20439,X20440] :
      ( ~ class_Int_Onumber__ring(X20440)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20440),hAPP(c_Int_Onumber__class_Onumber__of(X20440),X20439)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20440),hAPP(c_Int_Onumber__class_Onumber__of(X20440),X20438)),X20437)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20440),hAPP(c_Int_Onumber__class_Onumber__of(X20440),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20439),X20438))),X20437) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__number__of__diff1])]) ).

fof(i_0_8384,plain,
    ! [X20371,X20372,X20373,X20374] :
      ( ~ class_Int_Onumber__ring(X20374)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20374),hAPP(c_Int_Onumber__class_Onumber__of(X20374),X20373)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20374),hAPP(c_Int_Onumber__class_Onumber__of(X20374),X20372)),X20371)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20374),hAPP(c_Int_Onumber__class_Onumber__of(X20374),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20373),X20372))),X20371) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__number__of__left])]) ).

fof(i_0_8385,plain,
    ! [X25992,X25993,X25994] :
      ( ~ class_Orderings_Olinorder(X25994)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25994),X25993),X25992))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25994,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X25994),X25993),c_Orderings_Obot__class_Obot(tc_fun(X25994,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(X25994,X25993,X25992)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X25994,X25993),X25992) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I3_J])]) ).

fof(i_0_8386,plain,
    ! [X30126,X30127,X30128,X30129,X30130] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30130),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30129)),X30128)))
      | hAPP(hAPP(c_List_Onth(X30127),hAPP(hAPP(c_List_Omap(X30129,X30127),X30126),X30128)),X30130) = hAPP(X30126,hAPP(hAPP(c_List_Onth(X30129),X30128),X30130)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__map])]) ).

fof(i_0_8387,plain,
    ! [X22186,X22187] :
      ( ( X22186 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Nitpick_Onat__gcd(X22187,X22186) = X22187
        | ~ 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),X22187),X22186))) )
      & ( X22186 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Nitpick_Onat__gcd(X22187,X22186) = c_Nitpick_Onat__gcd(X22186,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X22187,X22186))
        | ~ 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),X22187),X22186))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__gcd_Opsimps])])]) ).

fof(i_0_8388,plain,
    ! [X30778,X30779,X30780,X30781] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X30781,tc_HOL_Obool)),X30780),X30779))
      | ~ hBOOL(hAPP(hAPP(c_member(X30781),X30778),X30780))
      | hBOOL(hAPP(hAPP(c_member(X30781),X30778),c_Complete__Lattice_OSup__class_OSup(tc_fun(X30781,tc_HOL_Obool),X30779))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UnionI])]) ).

fof(i_0_8389,plain,
    ! [X18354,X18355,X18356] :
      ( ~ class_Rings_Olinordered__semiring__strict(X18356)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18356),c_Groups_Ozero__class_Ozero(X18356)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18356),X18355),X18354)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18356),c_Groups_Ozero__class_Ozero(X18356)),X18354))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18356),c_Groups_Ozero__class_Ozero(X18356)),X18355)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__mult__pos2])]) ).

fof(i_0_8390,plain,
    ! [X18351,X18352,X18353] :
      ( ~ class_Rings_Olinordered__semiring__strict(X18353)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18353),c_Groups_Ozero__class_Ozero(X18353)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18353),X18352),X18351)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18353),c_Groups_Ozero__class_Ozero(X18353)),X18352))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18353),c_Groups_Ozero__class_Ozero(X18353)),X18351)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__mult__pos])]) ).

fof(i_0_8391,plain,
    ! [X32781,X32782,X32783,X32786,X32787,X32788,X32789,X32790] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X32783),X32782),hAPP(c_List_Oset(X32783),X32781)))
        | X32781 = hAPP(hAPP(c_List_Oappend(X32783),esk485_3(X32781,X32782,X32783)),hAPP(hAPP(c_List_Olist_OCons(X32783),X32782),esk486_3(X32781,X32782,X32783))) )
      & ( X32786 != hAPP(hAPP(c_List_Oappend(X32788),X32789),hAPP(hAPP(c_List_Olist_OCons(X32788),X32787),X32790))
        | hBOOL(hAPP(hAPP(c_member(X32788),X32787),hAPP(c_List_Oset(X32788),X32786))) ) ),
    inference(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_8392,plain,
    ! [X33930,X33931] : c_Relation_Osym(X33931,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X33931,X33931),tc_HOL_Obool)),X33930),hAPP(c_Relation_Oconverse(X33931,X33931),X33930))),
    inference(variable_rename,[status(thm)],[fact_sym__Int__converse]) ).

fof(i_0_8393,plain,
    ! [X33886,X33887] : c_Relation_Osym(X33887,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X33887,X33887),tc_HOL_Obool)),X33886),hAPP(c_Relation_Oconverse(X33887,X33887),X33886))),
    inference(variable_rename,[status(thm)],[fact_sym__Un__converse]) ).

fof(i_0_8394,plain,
    ! [X24578,X24579,X24580] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24580),X24579))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24580),X24578))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24580,tc_HOL_Obool)),X24579),X24578) != c_Orderings_Obot__class_Obot(tc_fun(X24580,tc_HOL_Obool))
      | hAPP(c_Finite__Set_Ocard(X24580),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24580,tc_HOL_Obool)),X24579),X24578)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X24580),X24579)),hAPP(c_Finite__Set_Ocard(X24580),X24578)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Un__disjoint])]) ).

fof(i_0_8395,plain,
    ! [X22507,X22508] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X22508)),X22507) = 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),X22508)),X22507),
    inference(variable_rename,[status(thm)],[fact_min__Suc1]) ).

fof(i_0_8396,plain,
    ! [X30469,X30470,X30471] :
      ( ~ class_Orderings_Olinorder(X30471)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30471),X30470))
      | c_List_Olinorder__class_Osorted__list__of__set(X30471,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X30471,tc_HOL_Obool)),X30470),hAPP(hAPP(c_Set_Oinsert(X30471),X30469),c_Orderings_Obot__class_Obot(tc_fun(X30471,tc_HOL_Obool))))) = c_List_Oremove1(X30471,X30469,c_List_Olinorder__class_Osorted__list__of__set(X30471,X30470)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__list__of__set__remove])]) ).

fof(i_0_8397,plain,
    ! [X26682,X26683] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X26683,X26682)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X26683,X26682),tc_HOL_Obool))))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X26682),c_Orderings_Otop__class_Otop(tc_fun(X26682,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__fun__UNIVD2])]) ).

fof(i_0_8398,plain,
    ! [X31871,X31872,X31873,X31874,X31875] :
      ( ~ class_Orderings_Olinorder(X31875)
      | hAPP(c_List_Ofilter(X31874,X31873),c_List_Olinorder__class_Osort__key(X31874,X31875,X31872,X31871)) = c_List_Olinorder__class_Osort__key(X31874,X31875,X31872,hAPP(c_List_Ofilter(X31874,X31873),X31871)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_filter__sort])]) ).

fof(i_0_8399,plain,
    ! [X25501,X25502,X25503] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X25503,tc_HOL_Obool)),X25502),hAPP(c_Set_OPow(X25503),X25501)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25503,tc_HOL_Obool)),X25502),X25501)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_PowD])]) ).

fof(i_0_8400,plain,
    ! [X25498,X25499,X25500] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X25500,tc_HOL_Obool)),X25499),hAPP(c_Set_OPow(X25500),X25498)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25500,tc_HOL_Obool)),X25499),X25498)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25500,tc_HOL_Obool)),X25499),X25498))
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X25500,tc_HOL_Obool)),X25499),hAPP(c_Set_OPow(X25500),X25498))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pow__iff])]) ).

fof(i_0_8401,plain,
    ! [X20280,X20281] :
      ( ( ~ 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),X20281)),X20280)))
        | X20281 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | X20280 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X20281 = 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),X20281)),X20280))) )
      & ( X20280 != 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),X20281)),X20280))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__zpower__abs__iff])])]) ).

fof(i_0_8402,plain,
    ! [X25524,X25525,X25526,X25527] :
      ( ~ class_Orderings_Olinorder(X25527)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25527),X25526),X25525))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25527),X25525),X25524))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25527,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X25527,X25526,X25525)),c_SetInterval_Oord__class_OgreaterThanAtMost(X25527,X25525,X25524)) = c_SetInterval_Oord__class_OatLeastAtMost(X25527,X25526,X25524) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I22_J])]) ).

fof(i_0_8403,plain,
    ! [X25320,X25321,X25322,X25323] :
      ( ~ class_Orderings_Olinorder(X25323)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25323),X25322),X25321))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25323),X25321),X25320))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25323,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X25323,X25322,X25321)),c_SetInterval_Oord__class_OgreaterThanAtMost(X25323,X25321,X25320)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X25323,X25322,X25320) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I20_J])]) ).

fof(i_0_8404,plain,
    ! [X25360,X25361,X25362,X25363] :
      ( ~ class_Orderings_Olinorder(X25363)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25363),X25362),X25361))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25363),X25361),X25360))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25363,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X25363,X25362,X25361)),c_SetInterval_Oord__class_OgreaterThanLessThan(X25363,X25361,X25360)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X25363,X25362,X25360) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I16_J])]) ).

fof(i_0_8405,plain,
    ! [X25417,X25418,X25419,X25420] :
      ( ~ class_Orderings_Olinorder(X25420)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25420),X25419),X25418))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25420),X25418),X25417))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25420,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X25420,X25419,X25418)),c_SetInterval_Oord__class_OatLeastAtMost(X25420,X25418,X25417)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X25420,X25419,X25417) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I19_J])]) ).

fof(i_0_8406,plain,
    ! [X22923,X22924,X22925] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22925,tc_HOL_Obool)),X22924),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22925,tc_HOL_Obool)),X22924),X22923))),
    inference(variable_rename,[status(thm)],[fact_Un__upper1]) ).

fof(i_0_8407,plain,
    ! [X22920,X22921,X22922] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22922,tc_HOL_Obool)),X22921),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22922,tc_HOL_Obool)),X22920),X22921))),
    inference(variable_rename,[status(thm)],[fact_Un__upper2]) ).

fof(i_0_8408,plain,
    ! [X32134,X32135,X32136] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32136,X32136)),X32135),X32134))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X32136,X32136)),X32135),c_Transitive__Closure_Ortrancl(X32136,X32134))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_r__into__rtrancl])]) ).

fof(i_0_8409,plain,
    ! [X24770,X24771,X24772,X24773] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24773),X24772))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24771),X24770))
      | hAPP(c_Finite__Set_Ocard(tc_sum(X24773,X24771)),c_Sum__Type_OPlus(X24773,X24771,X24772,X24770)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X24773),X24772)),hAPP(c_Finite__Set_Ocard(X24771),X24770)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Plus])]) ).

fof(i_0_8410,plain,
    ! [X24618,X24619,X24620,X24621] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24621),X24620))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24619),X24618))
        | hAPP(c_Finite__Set_Ocard(tc_sum(X24621,X24619)),c_Sum__Type_OPlus(X24621,X24619,X24620,X24618)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X24621),X24620)),hAPP(c_Finite__Set_Ocard(X24619),X24618)) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X24621),X24620))
        | hAPP(c_Finite__Set_Ocard(tc_sum(X24621,X24619)),c_Sum__Type_OPlus(X24621,X24619,X24620,X24618)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X24619),X24618))
        | hAPP(c_Finite__Set_Ocard(tc_sum(X24621,X24619)),c_Sum__Type_OPlus(X24621,X24619,X24620,X24618)) = 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_8411,plain,
    ! [X22881,X22882,X22883,X22884] :
      ( ~ class_Lattices_Osemilattice__sup(X22884)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22884),X22883),X22882))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22884),X22881),X22882))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22884),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X22884),X22883),X22881)),X22882)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__least])]) ).

fof(i_0_8412,plain,
    ! [X22877,X22878,X22879,X22880] :
      ( ~ class_Lattices_Osemilattice__sup(X22880)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22880),X22879),X22878))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22880),X22877),X22878))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22880),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X22880),X22879),X22877)),X22878)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__supI])]) ).

fof(i_0_8413,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),X22593),X22594))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22596),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22596),X22595),X22593)),X22594)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__least])]) ).

fof(i_0_8414,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),X22589),X22590))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22592),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22592),X22591),X22589)),X22590)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__supI])]) ).

fof(i_0_8415,plain,
    ! [X23914,X23915,X23916,X23917] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23917,tc_HOL_Obool)),X23916),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23917,tc_HOL_Obool)),X23915),X23914)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23917,tc_HOL_Obool)),X23915),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23917,tc_HOL_Obool)),X23916),X23914)),
    inference(variable_rename,[status(thm)],[fact_Int__left__commute]) ).

fof(i_0_8416,plain,
    ! [X22942,X22943,X22944,X22945] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22945,tc_HOL_Obool)),X22944),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22945,tc_HOL_Obool)),X22943),X22942)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22945,tc_HOL_Obool)),X22943),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22945,tc_HOL_Obool)),X22944),X22942)),
    inference(variable_rename,[status(thm)],[fact_Un__left__commute]) ).

fof(i_0_8417,plain,
    ! [X22838,X22839,X22840] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22840,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X22840,tc_HOL_Obool)),X22839),X22838)),X22838) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22840,tc_HOL_Obool)),X22839),X22838),
    inference(variable_rename,[status(thm)],[fact_Un__Diff__cancel2]) ).

fof(i_0_8418,plain,
    ! [X20480,X20481,X20482] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20482,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20482,tc_HOL_Obool)),X20481),X20480)),X20480) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20482,tc_HOL_Obool)),X20481),X20480),
    inference(variable_rename,[status(thm)],[fact_Diff__idemp]) ).

cnf(i_0_8419,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_5739]) ).

fof(i_0_8420,plain,
    ! [X23205,X23206,X23207,X23208,X23209] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X23209),X23208),X23207))
      | hBOOL(hAPP(hAPP(c_member(X23206),hAPP(X23205,X23208)),hAPP(c_Set_Oimage(X23209,X23206,X23205),X23207))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_imageI])]) ).

fof(i_0_8421,plain,
    ! [X16969,X16970,X16971,X16972] :
      ( ~ c_Hoare__Mirabelle_Ohoare__derivs(X16972,X16971,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X16972)),X16970),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X16972),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(X16972,X16971,X16969)
      | c_Hoare__Mirabelle_Ohoare__derivs(X16972,X16971,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X16972)),X16970),X16969)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hoare__derivs_Oinsert])]) ).

fof(i_0_8422,plain,
    ! [X32962,X32963,X32964,X32965,X32966] :
      ( ~ c_Finite__Set_Ofun__left__comm(X32966,X32965,X32964)
      | c_Finite__Set_Ofun__left__comm(X32963,X32965,hAPP(hAPP(c_COMBB(X32966,tc_fun(X32965,X32965),X32963),X32964),X32962)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofun__left__comm__apply])]) ).

fof(i_0_8423,plain,
    ! [X27661,X27662,X27663,X27664,X27665] :
      ( ~ c_Finite__Set_Ofun__left__comm__idem(X27665,X27664,X27663)
      | c_Finite__Set_Ofun__left__comm__idem(X27662,X27664,hAPP(hAPP(c_COMBB(X27665,tc_fun(X27664,X27664),X27662),X27663),X27661)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofun__left__comm__idem__apply])]) ).

fof(i_0_8424,plain,
    ! [X24045,X24046,X24047,X24048] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X24048),X24047),X24046))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24048,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X24048),X24047),X24045)),X24046) = hAPP(hAPP(c_Set_Oinsert(X24048),X24047),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24048,tc_HOL_Obool)),X24045),X24046)) )
      & ( hBOOL(hAPP(hAPP(c_member(X24048),X24047),X24046))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24048,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X24048),X24047),X24045)),X24046) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24048,tc_HOL_Obool)),X24045),X24046) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5740])]) ).

fof(i_0_8425,plain,
    ! [X24029,X24030,X24031,X24032] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X24032),X24031),X24030))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24032,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X24032),X24031),X24029)),X24030) = hAPP(hAPP(c_Set_Oinsert(X24032),X24031),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24032,tc_HOL_Obool)),X24029),X24030)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__insert__left__if1])]) ).

fof(i_0_8426,plain,
    ! [X26731,X26732,X26733,X26734,X26735] :
      ( ( hAPP(c_Set_Oimage(X26735,X26734,X26733),X26732) != hAPP(c_Set_Oimage(X26735,X26734,X26733),X26731)
        | X26732 = X26731
        | ~ c_Fun_Oinj__on(X26735,X26734,X26733,c_Orderings_Otop__class_Otop(tc_fun(X26735,tc_HOL_Obool))) )
      & ( X26732 != X26731
        | hAPP(c_Set_Oimage(X26735,X26734,X26733),X26732) = hAPP(c_Set_Oimage(X26735,X26734,X26733),X26731)
        | ~ c_Fun_Oinj__on(X26735,X26734,X26733,c_Orderings_Otop__class_Otop(tc_fun(X26735,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_8427,plain,
    ! [X18051,X18052,X18053,X18054,X18055,X18056,X18057] :
      ( hAPP(c_Fun_Ocomp(X18057,X18056,X18055,X18054),X18053) != X18052
      | hAPP(X18054,hAPP(X18053,X18051)) = hAPP(X18052,X18051) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_o__eq__dest__lhs])]) ).

fof(i_0_8428,plain,
    ! [X18109] : 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,X18109)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[fact_negative__zless__0]) ).

fof(i_0_8429,plain,
    ! [X28977,X28978,X28979] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X28979),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28978)),X28977)))
      | hAPP(hAPP(c_List_Olist_OCons(X28978),hAPP(hAPP(c_List_Onth(X28978),X28977),X28979)),hAPP(hAPP(c_List_Odrop(X28978),hAPP(c_Nat_OSuc,X28979)),X28977)) = hAPP(hAPP(c_List_Odrop(X28978),X28979),X28977) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__drop_H])]) ).

fof(i_0_8430,plain,
    ! [X27204,X27205,X27206,X27207] : hAPP(c_Set_Oimage(X27207,X27206,X27205),hAPP(c_Set_Ovimage(X27207,X27206,X27205),X27204)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27206,tc_HOL_Obool)),X27204),hAPP(c_Set_Oimage(X27207,X27206,X27205),c_Orderings_Otop__class_Otop(tc_fun(X27207,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_image__vimage__eq]) ).

fof(i_0_8431,plain,
    ! [X18545,X18546] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18546),c_Groups_Oone__class_Oone(tc_Int_Oint))),X18545))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18546),X18545)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18546),X18545))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18546),c_Groups_Oone__class_Oone(tc_Int_Oint))),X18545)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add1__zle__eq])]) ).

fof(i_0_8432,plain,
    ! [X25995,X25996,X25997,X25998] :
      ( ~ class_Orderings_Olinorder(X25998)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25998),X25997),X25996))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25998),X25996),X25995))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25998,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X25998,X25997,X25996)),c_SetInterval_Oord__class_OgreaterThanLessThan(X25998,X25996,X25995)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X25998,X25997),X25995) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I18_J])]) ).

fof(i_0_8433,plain,
    ! [X23536] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X23536))
        | 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)),X23536))) )
      & ( ~ 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)),X23536)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X23536)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__relations_I1_J])]) ).

fof(i_0_8434,plain,
    ! [X24536,X24537,X24538] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24538),X24537))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24538,tc_HOL_Obool)),X24536),X24537))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X24538),X24536)),hAPP(c_Finite__Set_Ocard(X24538),X24537))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__mono])]) ).

fof(i_0_8435,plain,
    ! [X24546,X24547,X24548] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24548),X24547))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X24548,tc_HOL_Obool)),X24546),X24547))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X24548),X24546)),hAPP(c_Finite__Set_Ocard(X24548),X24547))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__card__mono])]) ).

fof(i_0_8436,plain,
    ! [X23046,X23047,X23048,X23049] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X23049),X23048),X23047))
      | hBOOL(hAPP(hAPP(c_member(X23049),X23048),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23049,tc_HOL_Obool)),X23047),X23046))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UnI1])]) ).

fof(i_0_8437,plain,
    ! [X22813,X22814,X22815,X22816] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X22816),X22815),X22814))
        | hBOOL(hAPP(hAPP(c_member(X22816),X22815),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22816,tc_HOL_Obool)),X22813),X22814))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X22816),X22815),X22813))
        | hBOOL(hAPP(hAPP(c_member(X22816),X22815),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22816,tc_HOL_Obool)),X22813),X22814))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5741])])]) ).

fof(i_0_8438,plain,
    ! [X23050,X23051,X23052,X23053] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X23053),X23052),X23051))
      | hBOOL(hAPP(hAPP(c_member(X23053),X23052),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23053,tc_HOL_Obool)),X23050),X23051))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UnI2])]) ).

fof(i_0_8439,plain,
    ! [X26797,X26798] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26798),c_Orderings_Otop__class_Otop(tc_fun(X26798,tc_HOL_Obool))))
      | hAPP(c_Set_Oimage(X26798,X26798,X26797),c_Orderings_Otop__class_Otop(tc_fun(X26798,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X26798,tc_HOL_Obool))
      | c_Fun_Oinj__on(X26798,X26798,X26797,c_Orderings_Otop__class_Otop(tc_fun(X26798,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV__surj__inj])]) ).

fof(i_0_8440,plain,
    ! [X20316,X20317,X20318] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X20318)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20318),X20317),X20316))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20318),hAPP(c_Groups_Ouminus__class_Ouminus(X20318),X20317)),X20316))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20318),hAPP(c_Groups_Oabs__class_Oabs(X20318),X20317)),X20316)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__leI])]) ).

fof(i_0_8441,plain,
    ! [X20313,X20314,X20315] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20315),X20314),X20313))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20315),hAPP(c_Groups_Oabs__class_Oabs(X20315),X20314)),X20313))
        | ~ class_Groups_Oordered__ab__group__add__abs(X20315) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20315),hAPP(c_Groups_Ouminus__class_Ouminus(X20315),X20314)),X20313))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20315),hAPP(c_Groups_Oabs__class_Oabs(X20315),X20314)),X20313))
        | ~ class_Groups_Oordered__ab__group__add__abs(X20315) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20315),X20314),X20313))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20315),hAPP(c_Groups_Ouminus__class_Ouminus(X20315),X20314)),X20313))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20315),hAPP(c_Groups_Oabs__class_Oabs(X20315),X20314)),X20313))
        | ~ class_Groups_Oordered__ab__group__add__abs(X20315) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__le__iff])])]) ).

fof(i_0_8442,plain,
    ! [X20322,X20323,X20324] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20324),X20323),X20322))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20324),hAPP(c_Groups_Oabs__class_Oabs(X20324),X20323)),X20322))
        | ~ class_Rings_Olinordered__idom(X20324) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20324),hAPP(c_Groups_Ouminus__class_Ouminus(X20324),X20323)),X20322))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20324),hAPP(c_Groups_Oabs__class_Oabs(X20324),X20323)),X20322))
        | ~ class_Rings_Olinordered__idom(X20324) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20324),X20323),X20322))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20324),hAPP(c_Groups_Ouminus__class_Ouminus(X20324),X20323)),X20322))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20324),hAPP(c_Groups_Oabs__class_Oabs(X20324),X20323)),X20322))
        | ~ class_Rings_Olinordered__idom(X20324) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__less__iff])])]) ).

fof(i_0_8443,plain,
    ! [X28672,X28673,X28674] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X28674)),X28673),c_Wellfounded_Oacc(tc_List_Olist(X28674),c_List_Olistrel1(X28674,X28672))))
      | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X28674)),X28673),c_List_Olists(X28674,c_Wellfounded_Oacc(X28674,X28672)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lists__accI])]) ).

fof(i_0_8444,plain,
    ! [X18328,X18329] :
      ( ~ class_Rings_Olinordered__ring(X18329)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18329),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18329),X18328),X18328)),c_Groups_Ozero__class_Ozero(X18329))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5742])]) ).

fof(i_0_8445,plain,
    ! [X27212,X27213,X27214,X27215] :
      ( ~ c_Fun_Oinj__on(X27215,X27214,X27213,c_Orderings_Otop__class_Otop(tc_fun(X27215,tc_HOL_Obool)))
      | hAPP(c_Set_Ovimage(X27215,X27214,X27213),hAPP(c_Set_Oimage(X27215,X27214,X27213),X27212)) = X27212 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__vimage__image__eq])]) ).

fof(i_0_8446,plain,
    ! [X25978,X25979,X25980,X25981] :
      ( ~ class_Orderings_Olinorder(X25981)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25981),X25980),X25979))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25981),X25979),X25978))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25981,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X25981,X25980,X25979)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X25981,X25979),X25978)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X25981,X25980,X25978) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I15_J])]) ).

fof(i_0_8447,plain,
    ! [X19725,X19726,X19727,X19728] :
      ( ~ class_Divides_Osemiring__div(X19728)
      | X19727 = c_Groups_Ozero__class_Ozero(X19728)
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X19728),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19728),X19726),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19728),X19727),X19725))),X19727) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19728),X19725),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X19728),X19726),X19727)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__self2])]) ).

fof(i_0_8448,plain,
    ! [X19729,X19730,X19731,X19732] :
      ( ~ class_Divides_Osemiring__div(X19732)
      | X19731 = c_Groups_Ozero__class_Ozero(X19732)
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X19732),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19732),X19730),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19732),X19729),X19731))),X19731) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19732),X19729),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X19732),X19730),X19731)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__self1])]) ).

fof(i_0_8449,plain,
    ! [X21486,X21487,X21488,X21489] :
      ( ~ class_Fields_Ofield__inverse__zero(X21489)
      | X21488 = c_Groups_Ozero__class_Ozero(X21489)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21489),X21487),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21489),X21486),X21488)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21489),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21489),X21486),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21489),X21487),X21488))),X21488) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__num__frac])]) ).

fof(i_0_8450,plain,
    ! [X27962,X27963,X27964,X27965] :
      ( ~ class_Groups_Ocomm__monoid__add(X27965)
      | ~ c_Fun_Oinj__on(X27964,X27965,X27963,X27962)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27964,X27965),X27963),X27962) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27965,X27965),c_Fun_Oid(X27965)),hAPP(c_Set_Oimage(X27964,X27965,X27963),X27962)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__reindex__id])]) ).

fof(i_0_8451,plain,
    ! [X27966,X27967,X27968,X27969] :
      ( ~ class_Groups_Ocomm__monoid__mult(X27969)
      | ~ c_Fun_Oinj__on(X27968,X27969,X27967,X27966)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27968,X27969),X27967),X27966) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27969,X27969),c_Fun_Oid(X27969)),hAPP(c_Set_Oimage(X27968,X27969,X27967),X27966)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__reindex__id])]) ).

fof(i_0_8452,plain,
    ! [X28117,X28118] :
      ( ( ~ c_Wellfounded_Owf(X28118,X28117)
        | c_Wellfounded_Owf(X28118,hAPP(hAPP(c_Relation_Orel__comp(X28118,X28118,X28118),X28117),X28117)) )
      & ( ~ c_Wellfounded_Owf(X28118,hAPP(hAPP(c_Relation_Orel__comp(X28118,X28118,X28118),X28117),X28117))
        | c_Wellfounded_Owf(X28118,X28117) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__comp__self])]) ).

fof(i_0_8453,plain,
    ! [X22206,X22207,X22208] :
      ( X22208 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X22207,X22207),tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X22207,X22207),tc_HOL_Obool)),X22208),X22206)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__by__empty])]) ).

fof(i_0_8454,plain,
    ! [X29379,X29380,X29381] :
      ( ( hBOOL(hAPP(c_List_Odistinct(X29381),X29380))
        | ~ hBOOL(hAPP(c_List_Odistinct(X29381),hAPP(hAPP(c_List_Oappend(X29381),X29380),X29379))) )
      & ( hBOOL(hAPP(c_List_Odistinct(X29381),X29379))
        | ~ hBOOL(hAPP(c_List_Odistinct(X29381),hAPP(hAPP(c_List_Oappend(X29381),X29380),X29379))) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29381,tc_HOL_Obool)),hAPP(c_List_Oset(X29381),X29380)),hAPP(c_List_Oset(X29381),X29379)) = c_Orderings_Obot__class_Obot(tc_fun(X29381,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_List_Odistinct(X29381),hAPP(hAPP(c_List_Oappend(X29381),X29380),X29379))) )
      & ( ~ hBOOL(hAPP(c_List_Odistinct(X29381),X29380))
        | ~ hBOOL(hAPP(c_List_Odistinct(X29381),X29379))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29381,tc_HOL_Obool)),hAPP(c_List_Oset(X29381),X29380)),hAPP(c_List_Oset(X29381),X29379)) != c_Orderings_Obot__class_Obot(tc_fun(X29381,tc_HOL_Obool))
        | hBOOL(hAPP(c_List_Odistinct(X29381),hAPP(hAPP(c_List_Oappend(X29381),X29380),X29379))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__append])])]) ).

fof(i_0_8455,plain,
    ! [X29478,X29479,X29480] :
      ( ~ class_Orderings_Olinorder(X29480)
      | c_Big__Operators_Olattice_OInf__fin(X29480,c_Orderings_Oord__class_Omin(X29480),hAPP(c_List_Oset(X29480),hAPP(hAPP(c_List_Olist_OCons(X29480),X29479),X29478))) = hAPP(c_List_Ofoldl(X29480,X29480,c_Orderings_Oord__class_Omin(X29480),X29479),X29478) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin__set__fold])]) ).

fof(i_0_8456,plain,
    ! [X29481,X29482,X29483] :
      ( ~ class_Orderings_Olinorder(X29483)
      | c_Big__Operators_Olattice_OSup__fin(X29483,c_Orderings_Oord__class_Omax(X29483),hAPP(c_List_Oset(X29483),hAPP(hAPP(c_List_Olist_OCons(X29483),X29482),X29481))) = hAPP(c_List_Ofoldl(X29483,X29483,c_Orderings_Oord__class_Omax(X29483),X29482),X29481) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin__set__fold])]) ).

fof(i_0_8457,plain,
    ! [X26404,X26405,X26406,X26407] :
      ( ~ class_Groups_Ocomm__monoid__add(X26407)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X26406),X26405))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26407),X26404),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X26406,X26405)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26407),hAPP(X26404,X26406)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26407),X26404),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X26406,X26405))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__head])]) ).

fof(i_0_8458,plain,
    ! [X18123,X18124,X18125] : hAPP(hAPP(c_Nat_Ocompow(X18125,X18125),hAPP(c_Nat_OSuc,X18124)),X18123) = hAPP(c_Fun_Ocomp(X18125,X18125,X18125,X18123),hAPP(hAPP(c_Nat_Ocompow(X18125,X18125),X18124),X18123)),
    inference(variable_rename,[status(thm)],[fact_funpow_Osimps_I2_J]) ).

fof(i_0_8459,plain,
    ! [X28933,X28934,X28935,X28936,X28937] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X28937),X28936),hAPP(c_List_Oset(X28937),X28935)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X28934),hAPP(X28933,X28936)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X28934),c_List_Olist_Olist__size(X28937,X28933,X28935))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__size__estimation_H])]) ).

fof(i_0_8460,plain,
    ! [X28928,X28929,X28930,X28931,X28932] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X28932),X28931),hAPP(c_List_Oset(X28932),X28930)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X28929),hAPP(X28928,X28931)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X28929),c_List_Olist_Olist__size(X28932,X28928,X28930))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__size__estimation])]) ).

fof(i_0_8461,plain,
    ! [X29568,X29569] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29569),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),X29568)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),X29568),X29569)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X29568))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_elem__le__listsum__nat])]) ).

fof(i_0_8462,plain,
    ! [X19795,X19796] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19796))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19796),X19795))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19795),X19796) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19795),X19796)),X19796)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__div__geq])]) ).

fof(i_0_8463,plain,
    ! [X28669,X28670,X28671] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X28671)),X28670),c_List_Olists(X28671,c_Wellfounded_Oacc(X28671,X28669))))
      | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X28671)),X28670),c_Wellfounded_Oacc(tc_List_Olist(X28671),c_List_Olistrel1(X28671,X28669)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lists__accD])]) ).

cnf(i_0_8464,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_5743]) ).

cnf(i_0_8465,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_5744]) ).

fof(i_0_8466,plain,
    ! [X21754,X21755] :
      ( ~ class_Rings_Osemiring__1(X21755)
      | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X21755),X21754) = c_Nat_Osemiring__1__class_Oof__nat__aux(X21755,hAPP(hAPP(c_COMBC(X21755,X21755,X21755),c_Groups_Oplus__class_Oplus(X21755)),c_Groups_Oone__class_Oone(X21755)),X21754,c_Groups_Ozero__class_Ozero(X21755)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_semiring__1__class_Oof__nat__code])]) ).

fof(i_0_8467,plain,
    ! [X28377,X28378,X28379,X28380] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28380)),X28379)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28380)),X28378)))
      | X28379 != hAPP(hAPP(c_List_Olist_OCons(X28380),X28377),X28378) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_impossible__Cons])]) ).

fof(i_0_8468,plain,
    ! [X25425,X25426,X25427] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25427,tc_HOL_Obool)),X25426),X25425))
      | hBOOL(hAPP(hAPP(c_member(tc_fun(X25427,tc_HOL_Obool)),X25426),hAPP(c_Set_OPow(X25427),X25425))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_PowI])]) ).

fof(i_0_8469,plain,
    ! [X20669,X20670,X20671,X20672,X20673] : hAPP(hAPP(c_Power_Opower_Opower(X20673,X20672,X20671),X20670),hAPP(c_Nat_OSuc,X20669)) = hAPP(hAPP(X20671,X20670),hAPP(hAPP(c_Power_Opower_Opower(X20673,X20672,X20671),X20670),X20669)),
    inference(variable_rename,[status(thm)],[fact_power_Opower_Opower__Suc]) ).

fof(i_0_8470,plain,
    ! [X24367,X24368,X24369] :
      ( ~ class_Orderings_Olinorder(X24369)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24369,tc_HOL_Obool)),X24368),X24367))
      | X24368 = c_Orderings_Obot__class_Obot(tc_fun(X24369,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24369),X24367))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24369),c_Big__Operators_Olinorder__class_OMin(X24369,X24367)),c_Big__Operators_Olinorder__class_OMin(X24369,X24368))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min__antimono])]) ).

fof(i_0_8471,plain,
    ! [X24276,X24277,X24278] :
      ( ~ class_Orderings_Olinorder(X24278)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24278,tc_HOL_Obool)),X24277),X24276))
      | X24277 = c_Orderings_Obot__class_Obot(tc_fun(X24278,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24278),X24276))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24278),c_Big__Operators_Olinorder__class_OMax(X24278,X24277)),c_Big__Operators_Olinorder__class_OMax(X24278,X24276))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max__mono])]) ).

fof(i_0_8472,plain,
    ! [X19988,X19989] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19989),X19988))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X19989),X19988)),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),X19989),X19988)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19989),X19988)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__bin__lemma])]) ).

fof(i_0_8473,plain,
    ! [X20836,X20837,X20838] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X20838),X20837),hAPP(hAPP(c_Set_Oinsert(X20838),X20836),c_Orderings_Obot__class_Obot(tc_fun(X20838,tc_HOL_Obool)))))
      | X20837 = X20836 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_singletonE])]) ).

fof(i_0_8474,plain,
    ! [X20833,X20834,X20835] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X20835),X20834),hAPP(hAPP(c_Set_Oinsert(X20835),X20833),c_Orderings_Obot__class_Obot(tc_fun(X20835,tc_HOL_Obool)))))
        | X20834 = X20833 )
      & ( X20834 != X20833
        | hBOOL(hAPP(hAPP(c_member(X20835),X20834),hAPP(hAPP(c_Set_Oinsert(X20835),X20833),c_Orderings_Obot__class_Obot(tc_fun(X20835,tc_HOL_Obool))))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_singleton__iff])]) ).

fof(i_0_8475,plain,
    ! [X26713,X26714,X26715,X26716,X26717] :
      ( X26717 != hAPP(X26716,X26715)
      | hBOOL(hAPP(hAPP(c_member(X26714),X26717),hAPP(c_Set_Oimage(X26713,X26714,X26716),c_Orderings_Otop__class_Otop(tc_fun(X26713,tc_HOL_Obool))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_range__eqI])]) ).

fof(i_0_8476,plain,
    ! [X27407,X27408,X27409,X27410] :
      ( ( X27410 != c_Orderings_Obot__class_Obot(tc_fun(X27409,tc_HOL_Obool))
        | hAPP(c_Set_Oimage(tc_prod(X27409,X27408),X27408,c_Product__Type_Osnd(X27409,X27408)),hAPP(hAPP(c_Product__Type_OSigma(X27409,X27408),X27410),hAPP(c_COMBK(tc_fun(X27408,tc_HOL_Obool),X27409),X27407))) = c_Orderings_Obot__class_Obot(tc_fun(X27408,tc_HOL_Obool)) )
      & ( X27410 = c_Orderings_Obot__class_Obot(tc_fun(X27409,tc_HOL_Obool))
        | hAPP(c_Set_Oimage(tc_prod(X27409,X27408),X27408,c_Product__Type_Osnd(X27409,X27408)),hAPP(hAPP(c_Product__Type_OSigma(X27409,X27408),X27410),hAPP(c_COMBK(tc_fun(X27408,tc_HOL_Obool),X27409),X27407))) = X27407 ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_snd__image__times])]) ).

fof(i_0_8477,plain,
    ! [X27403,X27404,X27405,X27406] :
      ( ( X27406 != c_Orderings_Obot__class_Obot(tc_fun(X27405,tc_HOL_Obool))
        | hAPP(c_Set_Oimage(tc_prod(X27404,X27405),X27404,c_Product__Type_Ofst(X27404,X27405)),hAPP(hAPP(c_Product__Type_OSigma(X27404,X27405),X27403),hAPP(c_COMBK(tc_fun(X27405,tc_HOL_Obool),X27404),X27406))) = c_Orderings_Obot__class_Obot(tc_fun(X27404,tc_HOL_Obool)) )
      & ( X27406 = c_Orderings_Obot__class_Obot(tc_fun(X27405,tc_HOL_Obool))
        | hAPP(c_Set_Oimage(tc_prod(X27404,X27405),X27404,c_Product__Type_Ofst(X27404,X27405)),hAPP(hAPP(c_Product__Type_OSigma(X27404,X27405),X27403),hAPP(c_COMBK(tc_fun(X27405,tc_HOL_Obool),X27404),X27406))) = X27403 ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fst__image__times])]) ).

fof(i_0_8478,plain,
    ! [X16996,X16997,X16998,X16999,X17000] :
      ( ( X16999 = X16996
        | X16999 = X16997
        | hAPP(hAPP(c_Set_Oinsert(X17000),X16999),hAPP(hAPP(c_Set_Oinsert(X17000),X16998),c_Orderings_Obot__class_Obot(tc_fun(X17000,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(X17000),X16997),hAPP(hAPP(c_Set_Oinsert(X17000),X16996),c_Orderings_Obot__class_Obot(tc_fun(X17000,tc_HOL_Obool)))) )
      & ( X16998 = X16997
        | X16999 = X16997
        | hAPP(hAPP(c_Set_Oinsert(X17000),X16999),hAPP(hAPP(c_Set_Oinsert(X17000),X16998),c_Orderings_Obot__class_Obot(tc_fun(X17000,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(X17000),X16997),hAPP(hAPP(c_Set_Oinsert(X17000),X16996),c_Orderings_Obot__class_Obot(tc_fun(X17000,tc_HOL_Obool)))) )
      & ( X16999 = X16996
        | X16998 = X16996
        | hAPP(hAPP(c_Set_Oinsert(X17000),X16999),hAPP(hAPP(c_Set_Oinsert(X17000),X16998),c_Orderings_Obot__class_Obot(tc_fun(X17000,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(X17000),X16997),hAPP(hAPP(c_Set_Oinsert(X17000),X16996),c_Orderings_Obot__class_Obot(tc_fun(X17000,tc_HOL_Obool)))) )
      & ( X16998 = X16997
        | X16998 = X16996
        | hAPP(hAPP(c_Set_Oinsert(X17000),X16999),hAPP(hAPP(c_Set_Oinsert(X17000),X16998),c_Orderings_Obot__class_Obot(tc_fun(X17000,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(X17000),X16997),hAPP(hAPP(c_Set_Oinsert(X17000),X16996),c_Orderings_Obot__class_Obot(tc_fun(X17000,tc_HOL_Obool)))) )
      & ( X16999 != X16997
        | X16998 != X16996
        | hAPP(hAPP(c_Set_Oinsert(X17000),X16999),hAPP(hAPP(c_Set_Oinsert(X17000),X16998),c_Orderings_Obot__class_Obot(tc_fun(X17000,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(X17000),X16997),hAPP(hAPP(c_Set_Oinsert(X17000),X16996),c_Orderings_Obot__class_Obot(tc_fun(X17000,tc_HOL_Obool)))) )
      & ( X16999 != X16996
        | X16998 != X16997
        | hAPP(hAPP(c_Set_Oinsert(X17000),X16999),hAPP(hAPP(c_Set_Oinsert(X17000),X16998),c_Orderings_Obot__class_Obot(tc_fun(X17000,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(X17000),X16997),hAPP(hAPP(c_Set_Oinsert(X17000),X16996),c_Orderings_Obot__class_Obot(tc_fun(X17000,tc_HOL_Obool)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_doubleton__eq__iff])])]) ).

fof(i_0_8479,plain,
    ! [X29142,X29143,X29144,X29145,X29146] :
      ( ( X29146 != X29143
        | hAPP(hAPP(c_List_Onth(X29145),hAPP(hAPP(c_List_Olist__update(X29145,X29144),X29146),X29142)),X29143) = X29142
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29146),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29145)),X29144))) )
      & ( X29146 = X29143
        | hAPP(hAPP(c_List_Onth(X29145),hAPP(hAPP(c_List_Olist__update(X29145,X29144),X29146),X29142)),X29143) = hAPP(hAPP(c_List_Onth(X29145),X29144),X29143)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29146),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29145)),X29144))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__list__update])])]) ).

fof(i_0_8480,plain,
    ! [X19126,X19127,X19128] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19128),X19126))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19128),X19127)),X19126)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19127),X19126))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19128),X19127)),X19126)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5745])])]) ).

fof(i_0_8481,plain,
    ! [X19129,X19130,X19131] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19131),X19130)),X19129))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19131),X19129)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__leD1])]) ).

fof(i_0_8482,plain,
    ! [X19132,X19133,X19134] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19134),X19133)),X19132))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19133),X19132)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__leD2])]) ).

fof(i_0_8483,plain,
    ! [X17416,X17417,X17418] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17418),X17417)),X17416))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17418),X17416)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__lessD1])]) ).

fof(i_0_8484,plain,
    ! [X20088,X20089] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20089))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20089),hAPP(c_Nat_OSuc,X20088))),X20089)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__Suc__less])]) ).

fof(i_0_8485,plain,
    ! [X17111,X17112,X17113,X17114] :
      ( ( ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X17114),X17113,hAPP(c_Nat_OSuc,X17112),X17111)
        | c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X17114)),X17113,X17112,X17111) )
      & ( ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X17114)),X17113,X17112,X17111)
        | c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X17114),X17113,hAPP(c_Nat_OSuc,X17112),X17111) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evaln_Oequations_I9_J])]) ).

fof(i_0_8486,plain,
    ! [X17107,X17108,X17109,X17110] :
      ( ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X17110)),X17109,X17108,X17107)
      | c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X17110),X17109,hAPP(c_Nat_OSuc,X17108),X17107) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evaln_OBody])]) ).

fof(i_0_8487,plain,
    ! [X25898,X25899,X25900,X25901] :
      ( ~ class_Orderings_Olinorder(X25901)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25901),X25900),X25899))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25901),X25899),X25898))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25901,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X25901,X25900),X25899)),c_SetInterval_Oord__class_OatLeastAtMost(X25901,X25899,X25898)) = c_SetInterval_Oord__class_OatLeastAtMost(X25901,X25900,X25898) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I21_J])]) ).

fof(i_0_8488,plain,
    ! [X25907,X25908,X25909] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25909),X25908))
      | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X25909),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25908),X25907)) = 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,X25909),X25908)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X25908),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25908),X25907))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__add__Un])]) ).

fof(i_0_8489,plain,
    ! [X20377,X20378,X20379] : hAPP(hAPP(c_Set_Oinsert(X20379),X20378),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20379,tc_HOL_Obool)),X20377),hAPP(hAPP(c_Set_Oinsert(X20379),X20378),c_Orderings_Obot__class_Obot(tc_fun(X20379,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(X20379),X20378),X20377),
    inference(variable_rename,[status(thm)],[fact_insert__Diff__single]) ).

cnf(i_0_8490,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_5746]) ).

cnf(i_0_8491,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_5747]) ).

cnf(i_0_8492,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_5748]) ).

cnf(i_0_8493,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_5749]) ).

cnf(i_0_8494,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_5750]) ).

cnf(i_0_8495,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_5565]) ).

fof(i_0_8496,plain,
    ! [X24533,X24534,X24535] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24535),X24534))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X24535),X24534)),hAPP(c_Finite__Set_Ocard(X24535),hAPP(hAPP(c_Set_Oinsert(X24535),X24533),X24534)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__insert__le])]) ).

fof(i_0_8497,plain,
    ! [X17916,X17917,X17918] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X17918)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X17917)),X17916)) = 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),X17918),X17917))),X17916),
    inference(variable_rename,[status(thm)],[fact_zadd__int__left]) ).

fof(i_0_8498,plain,
    ! [X30833,X30834,X30835,X30837] :
      ( ( hBOOL(hAPP(hAPP(c_member(X30835),esk367_3(X30833,X30834,X30835)),X30833))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X30835),X30834),c_Complete__Lattice_OSup__class_OSup(X30835,X30833)))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X30835)
        | ~ class_Orderings_Olinorder(X30835) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X30835),X30834),esk367_3(X30833,X30834,X30835)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X30835),X30834),c_Complete__Lattice_OSup__class_OSup(X30835,X30833)))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X30835)
        | ~ class_Orderings_Olinorder(X30835) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X30835),X30837),X30833))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X30835),X30834),X30837))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X30835),X30834),c_Complete__Lattice_OSup__class_OSup(X30835,X30833)))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X30835)
        | ~ class_Orderings_Olinorder(X30835) ) ),
    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_8499,plain,
    ! [X23537] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),X23537))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X23537)))
        | ~ c_Nat__Transfer_Onat__set(X23537) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X23537)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),X23537))
        | ~ c_Nat__Transfer_Onat__set(X23537) ) ),
    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_8500,plain,
    hAPP(c_Relation_OImage(X1,X1,c_Relation_OId(X1)),X2) = X2,
    inference(split_conjunct,[status(thm)],[i_0_5751]) ).

fof(i_0_8501,plain,
    ! [X19261,X19262] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X19262)),hAPP(c_Int_Onat,X19261)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19262),X19261))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19261))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19262)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19262),X19261))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X19262)),hAPP(c_Int_Onat,X19261)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19261))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19262)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__relations_I3_J])])]) ).

fof(i_0_8502,plain,
    ! [X19025,X19026] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X19026)),hAPP(c_Int_Onat,X19025)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19026),X19025))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19025))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19026)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19026),X19025))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X19026)),hAPP(c_Int_Onat,X19025)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19025))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19026)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__relations_I2_J])])]) ).

fof(i_0_8503,plain,
    ! [X25286,X25287,X25288] :
      ( ~ class_Orderings_Olinorder(X25288)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25288),X25287),X25286))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25288,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X25288,X25287,X25286)),hAPP(hAPP(c_Set_Oinsert(X25288),X25286),c_Orderings_Obot__class_Obot(tc_fun(X25288,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(X25288,X25287,X25286) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I4_J])]) ).

fof(i_0_8504,plain,
    ! [X20851,X20852,X20853,X20854] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X20854),X20853),X20852))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20854,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X20854),X20853),X20851)),X20852) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20854,tc_HOL_Obool)),X20851),X20852) )
      & ( hBOOL(hAPP(hAPP(c_member(X20854),X20853),X20852))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20854,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X20854),X20853),X20851)),X20852) = hAPP(hAPP(c_Set_Oinsert(X20854),X20853),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20854,tc_HOL_Obool)),X20851),X20852)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5752])]) ).

fof(i_0_8505,plain,
    ! [X17636,X17637,X17638,X17639,X17640,X17641] :
      ( ~ hBOOL(hAPP(X17641,X17640))
      | ~ c_Natural_Oevaln(X17639,X17640,X17638,X17637)
      | c_Natural_Oevaln(c_Com_Ocom_OCond(X17641,X17639,X17636),X17640,X17638,X17637) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evaln_OIfTrue])]) ).

fof(i_0_8506,plain,
    ! [X32699,X32700,X32701] :
      ( ( hBOOL(hAPP(hAPP(c_member(X32701),esk473_3(X32699,X32700,X32701)),X32700))
        | ~ hBOOL(hAPP(hAPP(c_member(X32701),X32699),X32700))
        | c_Big__Operators_Olinorder__class_OMin(X32701,X32700) = X32699
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32701),X32700))
        | ~ class_Orderings_Olinorder(X32701) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X32701),X32699),esk473_3(X32699,X32700,X32701)))
        | ~ hBOOL(hAPP(hAPP(c_member(X32701),X32699),X32700))
        | c_Big__Operators_Olinorder__class_OMin(X32701,X32700) = X32699
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32701),X32700))
        | ~ class_Orderings_Olinorder(X32701) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min__eqI])])])]) ).

fof(i_0_8507,plain,
    ! [X30061,X30062,X30063,X30064,X30065] : hAPP(hAPP(c_List_Omap(X30065,X30064),X30063),hAPP(hAPP(c_List_Oappend(X30065),X30062),X30061)) = hAPP(hAPP(c_List_Oappend(X30064),hAPP(hAPP(c_List_Omap(X30065,X30064),X30063),X30062)),hAPP(hAPP(c_List_Omap(X30065,X30064),X30063),X30061)),
    inference(variable_rename,[status(thm)],[fact_map__append]) ).

fof(i_0_8508,plain,
    ! [X30962,X30963] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_fun(X30963,tc_HOL_Obool)),esk371_2(X30962,X30963)),X30962))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X30963),c_Complete__Lattice_OSup__class_OSup(tc_fun(X30963,tc_HOL_Obool),X30962)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X30963,tc_HOL_Obool)),X30962)) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30963),esk371_2(X30962,X30963)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X30963),c_Complete__Lattice_OSup__class_OSup(tc_fun(X30963,tc_HOL_Obool),X30962)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X30963,tc_HOL_Obool)),X30962)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Union])])])]) ).

fof(i_0_8509,plain,
    ! [X19706,X19707] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19707))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X19706))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19707),X19706)),X19707)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__div__less__self])]) ).

fof(i_0_8510,plain,
    ! [X19990,X19991] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19991))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19990))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19990),X19991)),X19990)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__less])]) ).

fof(i_0_8511,plain,
    ! [X19672,X19673] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X19673))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19672))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19672),X19673)),X19672)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__less__dividend])]) ).

cnf(i_0_8512,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_5753]) ).

cnf(i_0_8513,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_5754]) ).

fof(i_0_8514,plain,
    ! [X23849,X23850,X23851,X23852] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23852,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X23852),X23851),X23850)),hAPP(hAPP(c_Set_Oinsert(X23852),X23851),X23849)) = hAPP(hAPP(c_Set_Oinsert(X23852),X23851),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23852,tc_HOL_Obool)),X23850),X23849)),
    inference(variable_rename,[status(thm)],[fact_insert__inter__insert]) ).

fof(i_0_8515,plain,
    ! [X19685,X19686] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19686),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)),X19685))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19686),X19685)),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_8516,plain,
    ! [X19691,X19692] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19692))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19691),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),X19692),X19691)),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_8517,plain,
    ! [X19613,X19614] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19614),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)),X19613))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19614),X19613)),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_8518,plain,
    ! [X19189,X19190,X19191,X19192,X19193] :
      ( ~ c_Natural_Oevaln(X19193,X19192,X19191,X19190)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19191),X19189))
      | c_Natural_Oevaln(X19193,X19192,X19189,X19190) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evaln__nonstrict])]) ).

fof(i_0_8519,plain,
    ! [X19753,X19754,X19755] :
      ( ~ class_Divides_Osemiring__div(X19755)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19755),c_Divides_Odiv__class_Omod(X19755,X19754,X19753)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19755),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X19755),X19754),X19753)),X19753)) = X19754 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_semiring__div__class_Omod__div__equality_H])]) ).

fof(i_0_8520,plain,
    ! [X21299,X21300,X21301] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21301),X21300),c_Groups_Ozero__class_Ozero(X21301)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21301),c_Groups_Ozero__class_Ozero(X21301)),X21300))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21301),c_Groups_Ozero__class_Ozero(X21301)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21301),X21300),X21299)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21301) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21301),X21299),c_Groups_Ozero__class_Ozero(X21301)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21301),c_Groups_Ozero__class_Ozero(X21301)),X21300))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21301),c_Groups_Ozero__class_Ozero(X21301)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21301),X21300),X21299)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21301) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21301),X21300),c_Groups_Ozero__class_Ozero(X21301)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21301),c_Groups_Ozero__class_Ozero(X21301)),X21299))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21301),c_Groups_Ozero__class_Ozero(X21301)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21301),X21300),X21299)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21301) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21301),X21299),c_Groups_Ozero__class_Ozero(X21301)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21301),c_Groups_Ozero__class_Ozero(X21301)),X21299))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21301),c_Groups_Ozero__class_Ozero(X21301)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21301),X21300),X21299)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21301) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21301),c_Groups_Ozero__class_Ozero(X21301)),X21300))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21301),c_Groups_Ozero__class_Ozero(X21301)),X21299))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21301),c_Groups_Ozero__class_Ozero(X21301)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21301),X21300),X21299)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21301) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21301),X21300),c_Groups_Ozero__class_Ozero(X21301)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21301),X21299),c_Groups_Ozero__class_Ozero(X21301)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21301),c_Groups_Ozero__class_Ozero(X21301)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21301),X21300),X21299)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21301) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__divide__iff])])]) ).

fof(i_0_8521,plain,
    ! [X18765,X18766,X18767] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18767),X18766),c_Groups_Ozero__class_Ozero(X18767)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18767),c_Groups_Ozero__class_Ozero(X18767)),X18766))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18767),c_Groups_Ozero__class_Ozero(X18767)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18767),X18766),X18765)))
        | ~ class_Rings_Olinordered__ring__strict(X18767) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18767),X18765),c_Groups_Ozero__class_Ozero(X18767)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18767),c_Groups_Ozero__class_Ozero(X18767)),X18766))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18767),c_Groups_Ozero__class_Ozero(X18767)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18767),X18766),X18765)))
        | ~ class_Rings_Olinordered__ring__strict(X18767) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18767),X18766),c_Groups_Ozero__class_Ozero(X18767)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18767),c_Groups_Ozero__class_Ozero(X18767)),X18765))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18767),c_Groups_Ozero__class_Ozero(X18767)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18767),X18766),X18765)))
        | ~ class_Rings_Olinordered__ring__strict(X18767) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18767),X18765),c_Groups_Ozero__class_Ozero(X18767)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18767),c_Groups_Ozero__class_Ozero(X18767)),X18765))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18767),c_Groups_Ozero__class_Ozero(X18767)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18767),X18766),X18765)))
        | ~ class_Rings_Olinordered__ring__strict(X18767) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18767),c_Groups_Ozero__class_Ozero(X18767)),X18766))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18767),c_Groups_Ozero__class_Ozero(X18767)),X18765))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18767),c_Groups_Ozero__class_Ozero(X18767)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18767),X18766),X18765)))
        | ~ class_Rings_Olinordered__ring__strict(X18767) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18767),X18766),c_Groups_Ozero__class_Ozero(X18767)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18767),X18765),c_Groups_Ozero__class_Ozero(X18767)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18767),c_Groups_Ozero__class_Ozero(X18767)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18767),X18766),X18765)))
        | ~ class_Rings_Olinordered__ring__strict(X18767) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__mult__iff])])]) ).

fof(i_0_8522,plain,
    ! [X21336,X21337,X21338] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21338),X21337),c_Groups_Ozero__class_Ozero(X21338)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21338),c_Groups_Ozero__class_Ozero(X21338)),X21337))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21338),c_Groups_Ozero__class_Ozero(X21338)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21338),X21337),X21336)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21338) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21338),X21336),c_Groups_Ozero__class_Ozero(X21338)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21338),c_Groups_Ozero__class_Ozero(X21338)),X21337))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21338),c_Groups_Ozero__class_Ozero(X21338)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21338),X21337),X21336)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21338) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21338),X21337),c_Groups_Ozero__class_Ozero(X21338)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21338),c_Groups_Ozero__class_Ozero(X21338)),X21336))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21338),c_Groups_Ozero__class_Ozero(X21338)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21338),X21337),X21336)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21338) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21338),X21336),c_Groups_Ozero__class_Ozero(X21338)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21338),c_Groups_Ozero__class_Ozero(X21338)),X21336))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21338),c_Groups_Ozero__class_Ozero(X21338)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21338),X21337),X21336)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21338) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21338),c_Groups_Ozero__class_Ozero(X21338)),X21337))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21338),c_Groups_Ozero__class_Ozero(X21338)),X21336))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21338),c_Groups_Ozero__class_Ozero(X21338)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21338),X21337),X21336)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21338) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21338),X21337),c_Groups_Ozero__class_Ozero(X21338)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21338),X21336),c_Groups_Ozero__class_Ozero(X21338)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21338),c_Groups_Ozero__class_Ozero(X21338)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21338),X21337),X21336)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X21338) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__divide__iff])])]) ).

fof(i_0_8523,plain,
    ! [X33650,X33651,X33652,X33653,X33654,X33655,X33656] :
      ( ( ~ c_List_Oall__interval__int(X33652,X33651,X33650)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X33653),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X33651,X33650)))
        | hBOOL(hAPP(X33652,X33653)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk532_3(X33654,X33655,X33656)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X33655,X33654)))
        | c_List_Oall__interval__int(X33656,X33655,X33654) )
      & ( ~ hBOOL(hAPP(X33656,esk532_3(X33654,X33655,X33656)))
        | c_List_Oall__interval__int(X33656,X33655,X33654) ) ),
    inference(distribute,[status(thm)],[inference(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_8524,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_8525,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_8526,plain,
    ! [X18694,X18695,X18696] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X18696),X18695))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18694),X18696)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18694),X18695))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zadd__left__mono])]) ).

fof(i_0_8527,plain,
    ! [X19923,X19924,X19925] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19925),X19924))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19925),X19923)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19924),X19923))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__le__mono])]) ).

fof(i_0_8528,plain,
    ! [X19926,X19927,X19928] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19928),X19927))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19926),X19927)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19926),X19928))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__le__mono2])]) ).

fof(i_0_8529,plain,
    ! [X19565,X19566,X19567] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19567),X19566))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19567),X19565)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19566),X19565))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__le__mono])]) ).

fof(i_0_8530,plain,
    ! [X19169,X19170,X19171] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19171),X19170))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19171),X19169)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19170),X19169))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__mono1])]) ).

fof(i_0_8531,plain,
    ! [X19172,X19173,X19174] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19174),X19173))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19172),X19174)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19172),X19173))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__mono2])]) ).

fof(i_0_8532,plain,
    ! [X19139,X19140,X19141] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19141),X19140))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19141),X19139)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19140),X19139))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__mono1])]) ).

cnf(i_0_8533,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_5697]) ).

cnf(i_0_8534,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_5698]) ).

fof(i_0_8535,plain,
    ! [X18083,X18084,X18085] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18085),X18084))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18085),X18083)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18084),X18083))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zadd__strict__right__mono])]) ).

fof(i_0_8536,plain,
    ! [X17427,X17428,X17429] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17429),X17428))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17429),X17427)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17428),X17427))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__mono1])]) ).

fof(i_0_8537,plain,
    ! [X29472,X29473,X29474] :
      ( ~ class_Orderings_Olinorder(X29474)
      | c_Big__Operators_Olinorder__class_OMin(X29474,hAPP(c_List_Oset(X29474),hAPP(hAPP(c_List_Olist_OCons(X29474),X29473),X29472))) = hAPP(c_List_Ofoldl(X29474,X29474,c_Orderings_Oord__class_Omin(X29474),X29473),X29472) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min__fin__set__fold])]) ).

fof(i_0_8538,plain,
    ! [X29475,X29476,X29477] :
      ( ~ class_Orderings_Olinorder(X29477)
      | c_Big__Operators_Olinorder__class_OMax(X29477,hAPP(c_List_Oset(X29477),hAPP(hAPP(c_List_Olist_OCons(X29477),X29476),X29475))) = hAPP(c_List_Ofoldl(X29477,X29477,c_Orderings_Oord__class_Omax(X29477),X29476),X29475) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max__fin__set__fold])]) ).

fof(i_0_8539,plain,
    ! [X29466,X29467,X29468] :
      ( ~ class_Lattices_Olattice(X29468)
      | c_Big__Operators_Olattice__class_OSup__fin(X29468,hAPP(c_List_Oset(X29468),hAPP(hAPP(c_List_Olist_OCons(X29468),X29467),X29466))) = hAPP(c_List_Ofoldl(X29468,X29468,c_Lattices_Osemilattice__sup__class_Osup(X29468),X29467),X29466) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin__set__fold])]) ).

fof(i_0_8540,plain,
    ! [X29469,X29470,X29471] :
      ( ~ class_Lattices_Olattice(X29471)
      | c_Big__Operators_Olattice__class_OInf__fin(X29471,hAPP(c_List_Oset(X29471),hAPP(hAPP(c_List_Olist_OCons(X29471),X29470),X29469))) = hAPP(c_List_Ofoldl(X29471,X29471,c_Lattices_Osemilattice__inf__class_Oinf(X29471),X29470),X29469) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin__set__fold])]) ).

fof(i_0_8541,plain,
    ! [X20108,X20109,X20110] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20110),X20109))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20109),X20110))),X20108) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X20109)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20110),X20108)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__Suc__diff__eq2])]) ).

fof(i_0_8542,plain,
    ! [X19750,X19751,X19752] :
      ( ~ class_Divides_Osemiring__div(X19752)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19752),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19752),X19751),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X19752),X19750),X19751))),c_Divides_Odiv__class_Omod(X19752,X19750,X19751)) = X19750 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__div__equality2])]) ).

cnf(i_0_8543,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_5755]) ).

fof(i_0_8544,plain,
    ! [X29034,X29035,X29036,X29037,X29038] : hAPP(hAPP(c_List_Olist__update(X29038,hAPP(hAPP(c_List_Olist_OCons(X29038),X29037),X29036)),hAPP(c_Nat_OSuc,X29035)),X29034) = hAPP(hAPP(c_List_Olist_OCons(X29038),X29037),hAPP(hAPP(c_List_Olist__update(X29038,X29036),X29035),X29034)),
    inference(variable_rename,[status(thm)],[fact_list__update__code_I3_J]) ).

fof(i_0_8545,plain,
    ! [X21731,X21732,X21733,X21734,X21735,X21736] :
      ( ( X21734 = X21732
        | c_Nitpick_Opair__box_OPairBox(X21736,X21735,X21734,X21733) != c_Nitpick_Opair__box_OPairBox(X21736,X21735,X21732,X21731) )
      & ( X21733 = X21731
        | c_Nitpick_Opair__box_OPairBox(X21736,X21735,X21734,X21733) != c_Nitpick_Opair__box_OPairBox(X21736,X21735,X21732,X21731) )
      & ( X21734 != X21732
        | X21733 != X21731
        | c_Nitpick_Opair__box_OPairBox(X21736,X21735,X21734,X21733) = c_Nitpick_Opair__box_OPairBox(X21736,X21735,X21732,X21731) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pair__box_Oinject])])]) ).

fof(i_0_8546,plain,
    ! [X27107,X27108,X27109,X27110,X27111,X27112] :
      ( hAPP(X27112,X27111) != X27110
      | ~ hBOOL(hAPP(hAPP(c_member(X27109),X27110),X27108))
      | hBOOL(hAPP(hAPP(c_member(X27107),X27111),hAPP(c_Set_Ovimage(X27107,X27109,X27112),X27108))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vimageI])]) ).

fof(i_0_8547,plain,
    ! [X23137,X23138,X23139,X23140,X23141,X23142] :
      ( X23142 != hAPP(X23141,X23140)
      | ~ hBOOL(hAPP(hAPP(c_member(X23139),X23140),X23138))
      | hBOOL(hAPP(hAPP(c_member(X23137),X23142),hAPP(c_Set_Oimage(X23139,X23137,X23141),X23138))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__eqI])]) ).

fof(i_0_8548,plain,
    ! [X23199,X23200,X23201,X23202,X23203,X23204] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X23204),X23203),X23202))
      | X23201 != hAPP(X23200,X23203)
      | hBOOL(hAPP(hAPP(c_member(X23199),X23201),hAPP(c_Set_Oimage(X23204,X23199,X23200),X23202))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__image__eqI])]) ).

fof(i_0_8549,plain,
    ! [X17630,X17631,X17632,X17633,X17634,X17635] :
      ( hBOOL(hAPP(X17635,X17634))
      | ~ c_Natural_Oevaln(X17633,X17634,X17632,X17631)
      | c_Natural_Oevaln(c_Com_Ocom_OCond(X17635,X17630,X17633),X17634,X17632,X17631) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5756])]) ).

fof(i_0_8550,plain,
    ! [X25689,X25690,X25691,X25692,X25693,X25694] :
      ( ( hAPP(X25692,X25690) != hAPP(X25692,X25689)
        | X25690 = X25689
        | ~ hBOOL(hAPP(hAPP(c_member(X25694),X25689),X25691))
        | ~ hBOOL(hAPP(hAPP(c_member(X25694),X25690),X25691))
        | ~ c_Fun_Oinj__on(X25694,X25693,X25692,X25691) )
      & ( X25690 != X25689
        | hAPP(X25692,X25690) = hAPP(X25692,X25689)
        | ~ hBOOL(hAPP(hAPP(c_member(X25694),X25689),X25691))
        | ~ hBOOL(hAPP(hAPP(c_member(X25694),X25690),X25691))
        | ~ c_Fun_Oinj__on(X25694,X25693,X25692,X25691) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__iff])])]) ).

fof(i_0_8551,plain,
    ! [X25695,X25696,X25697,X25698,X25699,X25700] :
      ( ~ c_Fun_Oinj__on(X25700,X25699,X25698,X25697)
      | X25696 = X25695
      | ~ hBOOL(hAPP(hAPP(c_member(X25700),X25696),X25697))
      | ~ hBOOL(hAPP(hAPP(c_member(X25700),X25695),X25697))
      | hAPP(X25698,X25696) != hAPP(X25698,X25695) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__contraD])]) ).

fof(i_0_8552,plain,
    ! [X25683,X25684,X25685,X25686,X25687,X25688] :
      ( ~ c_Fun_Oinj__on(X25688,X25687,X25686,X25685)
      | hAPP(X25686,X25684) != hAPP(X25686,X25683)
      | ~ hBOOL(hAPP(hAPP(c_member(X25688),X25684),X25685))
      | ~ hBOOL(hAPP(hAPP(c_member(X25688),X25683),X25685))
      | X25684 = X25683 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__onD])]) ).

fof(i_0_8553,plain,
    ! [X20168,X20169] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20168),X20169))
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20168),X20169) = 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)),X20169)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20168),X20169))
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20168),X20169) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20168),X20169)),X20169))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20169)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5757])])]) ).

fof(i_0_8554,plain,
    ! [X20170,X20171] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20171))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20170),X20171))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20170),X20171) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20170),X20171)),X20171)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5758])]) ).

fof(i_0_8555,plain,
    ! [X19696,X19697] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19696),X19697))
        | ~ 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),X19697),X19696)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19697)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19696))
        | ~ 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),X19697),X19696)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19697)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19696),X19697))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19696))
        | 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),X19697),X19696)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19697)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonneg1__imp__zdiv__pos__iff])])]) ).

fof(i_0_8556,plain,
    ! [X32711,X32712,X32713,X32715,X32716,X32717,X32718] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk476_3(X32711,X32712,X32713)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32713)),X32711)))
        | ~ c_List_Olist__ex(X32713,X32712,X32711) )
      & ( hBOOL(hAPP(X32712,hAPP(hAPP(c_List_Onth(X32713),X32711),esk476_3(X32711,X32712,X32713))))
        | ~ c_List_Olist__ex(X32713,X32712,X32711) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32718),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32717)),X32715)))
        | ~ hBOOL(hAPP(X32716,hAPP(hAPP(c_List_Onth(X32717),X32715),X32718)))
        | c_List_Olist__ex(X32717,X32716,X32715) ) ),
    inference(distribute,[status(thm)],[inference(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_8557,plain,
    ! [X26150,X26151,X26152,X26153,X26154] :
      ( ~ c_Finite__Set_Ofolding__one__idem(X26154,X26153,X26152)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26154),X26151))
      | X26150 = c_Orderings_Obot__class_Obot(tc_fun(X26154,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26154,tc_HOL_Obool)),X26150),X26151))
      | hAPP(hAPP(X26153,hAPP(X26152,X26150)),hAPP(X26152,X26151)) = hAPP(X26152,X26151) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Osubset__idem])]) ).

fof(i_0_8558,plain,
    ! [X33906,X33907,X33909,X33910,X33911,X33912,X33913,X33914,X33917] :
      ( ( hBOOL(hAPP(hAPP(X33906,esk550_1(X33906)),esk550_1(X33906)))
        | ~ c_Equiv__Relations_Opart__equivp(X33907,X33906) )
      & ( hBOOL(hAPP(hAPP(X33906,X33909),X33909))
        | ~ hBOOL(hAPP(hAPP(X33906,X33909),X33910))
        | ~ c_Equiv__Relations_Opart__equivp(X33907,X33906) )
      & ( hBOOL(hAPP(hAPP(X33906,X33910),X33910))
        | ~ hBOOL(hAPP(hAPP(X33906,X33909),X33910))
        | ~ c_Equiv__Relations_Opart__equivp(X33907,X33906) )
      & ( hAPP(X33906,X33909) = hAPP(X33906,X33910)
        | ~ hBOOL(hAPP(hAPP(X33906,X33909),X33910))
        | ~ c_Equiv__Relations_Opart__equivp(X33907,X33906) )
      & ( ~ hBOOL(hAPP(hAPP(X33906,X33911),X33911))
        | ~ hBOOL(hAPP(hAPP(X33906,X33912),X33912))
        | hAPP(X33906,X33911) != hAPP(X33906,X33912)
        | hBOOL(hAPP(hAPP(X33906,X33911),X33912))
        | ~ c_Equiv__Relations_Opart__equivp(X33907,X33906) )
      & ( ~ hBOOL(hAPP(hAPP(X33913,esk551_1(X33913)),esk552_1(X33913)))
        | ~ hBOOL(hAPP(hAPP(X33913,esk551_1(X33913)),esk551_1(X33913)))
        | ~ hBOOL(hAPP(hAPP(X33913,esk552_1(X33913)),esk552_1(X33913)))
        | hAPP(X33913,esk551_1(X33913)) != hAPP(X33913,esk552_1(X33913))
        | ~ hBOOL(hAPP(hAPP(X33913,X33914),X33914))
        | c_Equiv__Relations_Opart__equivp(X33917,X33913) )
      & ( hBOOL(hAPP(hAPP(X33913,esk551_1(X33913)),esk551_1(X33913)))
        | hBOOL(hAPP(hAPP(X33913,esk551_1(X33913)),esk552_1(X33913)))
        | ~ hBOOL(hAPP(hAPP(X33913,X33914),X33914))
        | c_Equiv__Relations_Opart__equivp(X33917,X33913) )
      & ( hBOOL(hAPP(hAPP(X33913,esk552_1(X33913)),esk552_1(X33913)))
        | hBOOL(hAPP(hAPP(X33913,esk551_1(X33913)),esk552_1(X33913)))
        | ~ hBOOL(hAPP(hAPP(X33913,X33914),X33914))
        | c_Equiv__Relations_Opart__equivp(X33917,X33913) )
      & ( hAPP(X33913,esk551_1(X33913)) = hAPP(X33913,esk552_1(X33913))
        | hBOOL(hAPP(hAPP(X33913,esk551_1(X33913)),esk552_1(X33913)))
        | ~ hBOOL(hAPP(hAPP(X33913,X33914),X33914))
        | c_Equiv__Relations_Opart__equivp(X33917,X33913) ) ),
    inference(distribute,[status(thm)],[inference(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_8559,plain,
    ! [X32514,X32515,X32516] :
      ( hAPP(hAPP(c_Relation_Orel__comp(X32516,X32516,X32516),hAPP(c_Relation_Oconverse(X32516,X32516),X32515)),X32515) != X32515
      | hAPP(c_Relation_ODomain(X32516,X32516),X32515) != X32514
      | c_Equiv__Relations_Oequiv(X32516,X32514,X32515) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comp__equivI])]) ).

fof(i_0_8560,plain,
    ! [X33428,X33429,X33430,X33431,X33432,X33433] : hAPP(hAPP(c_List_Ozip(X33433,X33432),c_List_Oreplicate(X33433,X33431,X33430)),c_List_Oreplicate(X33432,X33429,X33428)) = c_List_Oreplicate(tc_prod(X33433,X33432),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X33431),X33429),hAPP(hAPP(c_Product__Type_OPair(X33433,X33432),X33430),X33428)),
    inference(variable_rename,[status(thm)],[fact_zip__replicate]) ).

fof(i_0_8561,plain,
    ! [X17624,X17625,X17626] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCond(X17626,X17625,X17624)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X17625)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X17624))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[fact_com_Osize_I13_J]) ).

fof(i_0_8562,plain,
    ! [X18508,X18509,X18510,X18511,X18512] :
      ( ~ class_Orderings_Oord(X18512)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18511,X18512)),X18510),X18509))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18512),hAPP(X18510,X18508)),hAPP(X18509,X18508))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__funE])]) ).

fof(i_0_8563,plain,
    ! [X18470,X18471,X18472,X18473,X18474] :
      ( ~ class_Orderings_Oord(X18474)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18473,X18474)),X18472),X18471))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18474),hAPP(X18472,X18470)),hAPP(X18471,X18470))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__funD])]) ).

fof(i_0_8564,plain,
    ! [X29871,X29872,X29873,X29874,X29875] :
      ( ( hAPP(hAPP(c_List_Omap(X29875,X29874),X29873),X29872) != hAPP(hAPP(c_List_Omap(X29875,X29874),X29873),X29871)
        | X29872 = X29871
        | ~ c_Fun_Oinj__on(X29875,X29874,X29873,c_Orderings_Otop__class_Otop(tc_fun(X29875,tc_HOL_Obool))) )
      & ( X29872 != X29871
        | hAPP(hAPP(c_List_Omap(X29875,X29874),X29873),X29872) = hAPP(hAPP(c_List_Omap(X29875,X29874),X29873),X29871)
        | ~ c_Fun_Oinj__on(X29875,X29874,X29873,c_Orderings_Otop__class_Otop(tc_fun(X29875,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_8565,plain,
    ! [X29866,X29867,X29868,X29869,X29870] :
      ( hAPP(hAPP(c_List_Omap(X29870,X29869),X29868),X29867) != hAPP(hAPP(c_List_Omap(X29870,X29869),X29868),X29866)
      | ~ c_Fun_Oinj__on(X29870,X29869,X29868,c_Orderings_Otop__class_Otop(tc_fun(X29870,tc_HOL_Obool)))
      | X29867 = X29866 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__injective])]) ).

fof(i_0_8566,plain,
    ! [X29134,X29135,X29136,X29137] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29137),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29136)),X29135)))
      | hAPP(hAPP(c_List_Onth(X29136),hAPP(hAPP(c_List_Olist__update(X29136,X29135),X29137),X29134)),X29137) = X29134 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__list__update__eq])]) ).

fof(i_0_8567,plain,
    ! [X26311,X26312,X26313] :
      ( ~ class_Groups_Ocomm__monoid__add(X26313)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26313),X26312),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,X26311))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26313),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26313),X26312),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X26311))),hAPP(X26312,hAPP(c_Nat_OSuc,X26311))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__atMost__Suc])]) ).

fof(i_0_8568,plain,
    ! [X33923,X33924,X33925] :
      ( ~ c_Relation_Osym(X33925,X33924)
      | ~ c_Relation_Osym(X33925,X33923)
      | c_Relation_Osym(X33925,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X33925,X33925),tc_HOL_Obool)),X33924),X33923)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sym__Int])]) ).

fof(i_0_8569,plain,
    ! [X33920,X33921,X33922] :
      ( ~ c_Relation_Osym(X33922,X33921)
      | ~ c_Relation_Osym(X33922,X33920)
      | c_Relation_Osym(X33922,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X33922,X33922),tc_HOL_Obool)),X33921),X33920)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sym__Un])]) ).

fof(i_0_8570,plain,
    ! [X33787,X33788,X33789] :
      ( ~ c_Relation_Otrans(X33789,X33788)
      | ~ c_Relation_Otrans(X33789,X33787)
      | c_Relation_Otrans(X33789,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X33789,X33789),tc_HOL_Obool)),X33788),X33787)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__Int])]) ).

fof(i_0_8571,plain,
    ! [X25811,X25812,X25813,X25814] :
      ( ~ class_Orderings_Olinorder(X25814)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25814),X25813),X25812))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25814),X25812),X25811))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25814,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X25814,X25813),X25812)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X25814,X25812),X25811)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X25814,X25813),X25811) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I17_J])]) ).

fof(i_0_8572,plain,
    ! [X29624,X29625] : c_List_Obutlast(X29625,X29624) = hAPP(hAPP(c_List_Otake(X29625),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29625)),X29624)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X29624),
    inference(variable_rename,[status(thm)],[fact_butlast__conv__take]) ).

fof(i_0_8573,plain,
    ! [X27040,X27041,X27042] :
      ( ~ class_Lattices_Osemilattice__inf(X27042)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27042),X27041))
      | ~ hBOOL(hAPP(hAPP(c_member(X27042),X27040),X27041))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27042),hAPP(c_Finite__Set_Ofold1(X27042,c_Lattices_Osemilattice__inf__class_Oinf(X27042)),X27041)),X27040)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1__belowI])]) ).

fof(i_0_8574,plain,
    ! [X27048,X27049,X27050] :
      ( ~ class_Orderings_Olinorder(X27050)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27050),X27049))
      | ~ hBOOL(hAPP(hAPP(c_member(X27050),X27048),X27049))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27050),hAPP(c_Finite__Set_Ofold1(X27050,c_Orderings_Oord__class_Omin(X27050)),X27049)),X27048)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ofold1__belowI])]) ).

fof(i_0_8575,plain,
    ! [X18439] : ~ 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,X18439))))),
    inference(variable_rename,[status(thm)],[i_0_5759]) ).

fof(i_0_8576,plain,
    ! [X32684,X32685,X32686] :
      ( ( hBOOL(hAPP(hAPP(c_member(X32686),esk470_3(X32684,X32685,X32686)),hAPP(c_List_Oset(X32686),X32685)))
        | ~ c_List_Olinorder__class_Osorted(X32686,X32685)
        | c_List_Olinorder__class_Osorted(X32686,hAPP(hAPP(c_List_Olist_OCons(X32686),X32684),X32685))
        | ~ class_Orderings_Olinorder(X32686) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X32686),X32684),esk470_3(X32684,X32685,X32686)))
        | ~ c_List_Olinorder__class_Osorted(X32686,X32685)
        | c_List_Olinorder__class_Osorted(X32686,hAPP(hAPP(c_List_Olist_OCons(X32686),X32684),X32685))
        | ~ class_Orderings_Olinorder(X32686) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted_OCons])])])]) ).

fof(i_0_8577,plain,
    ! [X31573,X31574,X31575,X31576] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X31575),X31576),hAPP(c_List_Oset(X31575),X31573)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31575),X31574),X31576))
        | ~ c_List_Olinorder__class_Osorted(X31575,hAPP(hAPP(c_List_Olist_OCons(X31575),X31574),X31573))
        | ~ class_Orderings_Olinorder(X31575) )
      & ( c_List_Olinorder__class_Osorted(X31575,X31573)
        | ~ c_List_Olinorder__class_Osorted(X31575,hAPP(hAPP(c_List_Olist_OCons(X31575),X31574),X31573))
        | ~ class_Orderings_Olinorder(X31575) )
      & ( hBOOL(hAPP(hAPP(c_member(X31575),esk394_3(X31573,X31574,X31575)),hAPP(c_List_Oset(X31575),X31573)))
        | ~ c_List_Olinorder__class_Osorted(X31575,X31573)
        | c_List_Olinorder__class_Osorted(X31575,hAPP(hAPP(c_List_Olist_OCons(X31575),X31574),X31573))
        | ~ class_Orderings_Olinorder(X31575) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31575),X31574),esk394_3(X31573,X31574,X31575)))
        | ~ c_List_Olinorder__class_Osorted(X31575,X31573)
        | c_List_Olinorder__class_Osorted(X31575,hAPP(hAPP(c_List_Olist_OCons(X31575),X31574),X31573))
        | ~ class_Orderings_Olinorder(X31575) ) ),
    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_8578,plain,
    ! [X31550,X31551,X31552,X31553] :
      ( ( c_List_Olinorder__class_Osorted(X31552,X31550)
        | ~ c_List_Olinorder__class_Osorted(X31552,hAPP(hAPP(c_List_Olist_OCons(X31552),X31551),X31550))
        | ~ class_Orderings_Olinorder(X31552) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X31552),X31553),hAPP(c_List_Oset(X31552),X31550)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31552),X31551),X31553))
        | ~ c_List_Olinorder__class_Osorted(X31552,hAPP(hAPP(c_List_Olist_OCons(X31552),X31551),X31550))
        | ~ class_Orderings_Olinorder(X31552) )
      & ( hBOOL(hAPP(hAPP(c_member(X31552),esk391_3(X31550,X31551,X31552)),hAPP(c_List_Oset(X31552),X31550)))
        | ~ c_List_Olinorder__class_Osorted(X31552,X31550)
        | c_List_Olinorder__class_Osorted(X31552,hAPP(hAPP(c_List_Olist_OCons(X31552),X31551),X31550))
        | ~ class_Orderings_Olinorder(X31552) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31552),X31551),esk391_3(X31550,X31551,X31552)))
        | ~ c_List_Olinorder__class_Osorted(X31552,X31550)
        | c_List_Olinorder__class_Osorted(X31552,hAPP(hAPP(c_List_Olist_OCons(X31552),X31551),X31550))
        | ~ class_Orderings_Olinorder(X31552) ) ),
    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_8579,plain,
    ! [X22504,X22505,X22506] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(X22506,X22505)),X22504),hAPP(hAPP(hAPP(c_Natural_Oupdate,X22504),X22506),hAPP(X22505,X22504)))),
    inference(variable_rename,[status(thm)],[fact_evalc_Oequations_I2_J]) ).

fof(i_0_8580,plain,
    ! [X22381,X22382,X22383] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(X22383,X22382)),X22381),hAPP(hAPP(hAPP(c_Natural_Oupdate,X22381),X22383),hAPP(X22382,X22381)))),
    inference(variable_rename,[status(thm)],[fact_evalc_OAssign]) ).

fof(i_0_8581,plain,
    ! [X20174,X20175] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20175))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20174))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X20174),X20175)),X20174) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X20174),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20175),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_8582,plain,
    ! [X21425,X21426,X21427] :
      ( ~ class_Fields_Olinordered__field(X21427)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21427),c_Groups_Ozero__class_Ozero(X21427)),X21426))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21427),c_Groups_Ozero__class_Ozero(X21427)),X21425))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21427),c_Groups_Ozero__class_Ozero(X21427)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21427),X21426),X21425))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__nonneg__pos])]) ).

fof(i_0_8583,plain,
    ! [X18816,X18817,X18818] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18818),c_Groups_Ozero__class_Ozero(X18818)),X18817))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18818),c_Groups_Ozero__class_Ozero(X18818)),X18816))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18818),c_Groups_Ozero__class_Ozero(X18818)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18818),X18817),X18816)))
        | ~ class_Rings_Oordered__ring(X18818) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18818),X18817),c_Groups_Ozero__class_Ozero(X18818)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18818),X18816),c_Groups_Ozero__class_Ozero(X18818)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18818),c_Groups_Ozero__class_Ozero(X18818)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18818),X18817),X18816)))
        | ~ class_Rings_Oordered__ring(X18818) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__mult__pos__le])])]) ).

fof(i_0_8584,plain,
    ! [X18771,X18772,X18773] :
      ( ~ class_Rings_Oordered__cancel__semiring(X18773)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18773),c_Groups_Ozero__class_Ozero(X18773)),X18772))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18773),c_Groups_Ozero__class_Ozero(X18773)),X18771))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18773),c_Groups_Ozero__class_Ozero(X18773)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18773),X18772),X18771))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonneg])]) ).

fof(i_0_8585,plain,
    ! [X18746,X18747,X18748] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X18748)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18748),c_Groups_Ozero__class_Ozero(X18748)),X18747))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18748),c_Groups_Ozero__class_Ozero(X18748)),X18746))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18748),c_Groups_Ozero__class_Ozero(X18748)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18748),X18747),X18746))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__nonneg])]) ).

fof(i_0_8586,plain,
    ! [X18731,X18732,X18733] :
      ( ~ class_Rings_Olinordered__semidom(X18733)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18733),c_Groups_Oone__class_Oone(X18733)),X18732))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18733),c_Groups_Oone__class_Oone(X18733)),X18731))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18733),c_Groups_Oone__class_Oone(X18733)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18733),X18732),X18731))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__1__mult])]) ).

fof(i_0_8587,plain,
    ! [X21330,X21331,X21332] :
      ( ~ class_Fields_Olinordered__field(X21332)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21332),c_Groups_Ozero__class_Ozero(X21332)),X21331))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21332),c_Groups_Ozero__class_Ozero(X21332)),X21330))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21332),c_Groups_Ozero__class_Ozero(X21332)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21332),X21331),X21330))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__pos__pos])]) ).

fof(i_0_8588,plain,
    ! [X18342,X18343,X18344] :
      ( ~ class_Rings_Olinordered__semiring__strict(X18344)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18344),c_Groups_Ozero__class_Ozero(X18344)),X18343))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18344),c_Groups_Ozero__class_Ozero(X18344)),X18342))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18344),c_Groups_Ozero__class_Ozero(X18344)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18344),X18343),X18342))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__pos__pos])]) ).

fof(i_0_8589,plain,
    ! [X18942,X18943,X18944] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X18944)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18944),c_Groups_Ozero__class_Ozero(X18944)),X18943))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18944),c_Groups_Ozero__class_Ozero(X18944)),X18942))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18944),c_Groups_Ozero__class_Ozero(X18944)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18944),X18943),X18942))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__pos__nonneg])]) ).

fof(i_0_8590,plain,
    ! [X18939,X18940,X18941] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X18941)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18941),c_Groups_Ozero__class_Ozero(X18941)),X18940))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18941),c_Groups_Ozero__class_Ozero(X18941)),X18939))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18941),c_Groups_Ozero__class_Ozero(X18941)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18941),X18940),X18939))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__pos])]) ).

fof(i_0_8591,plain,
    ! [X17470,X17471,X17472] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X17472)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17472),c_Groups_Ozero__class_Ozero(X17472)),X17471))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17472),c_Groups_Ozero__class_Ozero(X17472)),X17470))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17472),c_Groups_Ozero__class_Ozero(X17472)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17472),X17471),X17470))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__pos__pos])]) ).

fof(i_0_8592,plain,
    ! [X25845,X25846,X25847,X25848] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25848),X25847))
      | hAPP(c_Finite__Set_Ocard(X25846),hAPP(c_Set_Oimage(X25848,X25846,X25845),X25847)) != hAPP(c_Finite__Set_Ocard(X25848),X25847)
      | c_Fun_Oinj__on(X25848,X25846,X25845,X25847) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__card__imp__inj__on])]) ).

fof(i_0_8593,plain,
    ! [X25841,X25842,X25843,X25844] :
      ( ( ~ c_Fun_Oinj__on(X25844,X25842,X25841,X25843)
        | hAPP(c_Finite__Set_Ocard(X25842),hAPP(c_Set_Oimage(X25844,X25842,X25841),X25843)) = hAPP(c_Finite__Set_Ocard(X25844),X25843)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25844),X25843)) )
      & ( hAPP(c_Finite__Set_Ocard(X25842),hAPP(c_Set_Oimage(X25844,X25842,X25841),X25843)) != hAPP(c_Finite__Set_Ocard(X25844),X25843)
        | c_Fun_Oinj__on(X25844,X25842,X25841,X25843)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25844),X25843)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__iff__eq__card])])]) ).

fof(i_0_8594,plain,
    ! [X23068,X23069,X23070] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X23070,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23070,tc_HOL_Obool)),X23069),X23068)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23070,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X23070,tc_HOL_Obool)),X23069)),X23068),
    inference(variable_rename,[status(thm)],[fact_Compl__Diff__eq]) ).

cnf(i_0_8595,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_5760]) ).

fof(i_0_8596,plain,
    ! [X20632,X20633,X20634,X20635] :
      ( ~ class_Rings_Olinordered__semidom(X20635)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X20635),X20634),X20633) != hAPP(hAPP(c_Power_Opower__class_Opower(X20635),X20632),X20633)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20635),c_Groups_Ozero__class_Ozero(X20635)),X20634))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20635),c_Groups_Ozero__class_Ozero(X20635)),X20632))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20633))
      | X20634 = X20632 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__eq__imp__eq__base])]) ).

cnf(i_0_8597,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_5761]) ).

cnf(i_0_8598,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_5762]) ).

fof(i_0_8599,plain,
    ! [X27266,X27267,X27268,X27269] : hAPP(c_Finite__Set_Ocard(tc_prod(X27269,X27268)),hAPP(hAPP(c_Product__Type_OSigma(X27269,X27268),X27267),hAPP(c_COMBK(tc_fun(X27268,tc_HOL_Obool),X27269),X27266))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X27269),X27267)),hAPP(c_Finite__Set_Ocard(X27268),X27266)),
    inference(variable_rename,[status(thm)],[fact_card__cartesian__product]) ).

fof(i_0_8600,plain,
    ! [X24049,X24050,X24051,X24052] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X24052),X24051),X24050))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24052,tc_HOL_Obool)),X24050),hAPP(hAPP(c_Set_Oinsert(X24052),X24051),X24049)) = hAPP(hAPP(c_Set_Oinsert(X24052),X24051),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24052,tc_HOL_Obool)),X24050),X24049)) )
      & ( hBOOL(hAPP(hAPP(c_member(X24052),X24051),X24050))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24052,tc_HOL_Obool)),X24050),hAPP(hAPP(c_Set_Oinsert(X24052),X24051),X24049)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24052,tc_HOL_Obool)),X24050),X24049) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5763])]) ).

fof(i_0_8601,plain,
    ! [X24033,X24034,X24035,X24036] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X24036),X24035),X24034))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24036,tc_HOL_Obool)),X24034),hAPP(hAPP(c_Set_Oinsert(X24036),X24035),X24033)) = hAPP(hAPP(c_Set_Oinsert(X24036),X24035),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24036,tc_HOL_Obool)),X24034),X24033)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__insert__right__if1])]) ).

fof(i_0_8602,plain,
    ! [X28702,X28703,X28704,X28705,X28706,X28707,X28708] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28702)),X28704) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28702)),X28703)
        | X28704 != X28703 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X28705),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28702)),X28704)))
        | hAPP(hAPP(c_List_Onth(X28702),X28704),X28705) = hAPP(hAPP(c_List_Onth(X28702),X28703),X28705)
        | X28704 != X28703 )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk320_3(X28706,X28707,X28708)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28706)),X28708)))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28706)),X28708) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28706)),X28707)
        | X28708 = X28707 )
      & ( hAPP(hAPP(c_List_Onth(X28706),X28708),esk320_3(X28706,X28707,X28708)) != hAPP(hAPP(c_List_Onth(X28706),X28707),esk320_3(X28706,X28707,X28708))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28706)),X28708) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28706)),X28707)
        | X28708 = X28707 ) ),
    inference(distribute,[status(thm)],[inference(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_8603,plain,
    ! [X32805,X32806,X32807,X32808,X32809,X32810] :
      ( ~ c_Finite__Set_Ofolding(X32810,X32809,X32808,X32807)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32810),X32806))
      | hAPP(hAPP(X32807,X32806),X32805) = hAPP(hAPP(c_Finite__Set_Ofold(X32810,X32809,X32808),X32805),X32806) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Oeq__fold])]) ).

fof(i_0_8604,plain,
    ! [X19198,X19199,X19200,X19201] :
      ( ~ c_Hoare__Mirabelle_Ohoare__derivs(X19201,X19200,X19199)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X19201),tc_HOL_Obool)),X19198),X19199))
      | c_Hoare__Mirabelle_Ohoare__derivs(X19201,X19200,X19198) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_weaken])]) ).

fof(i_0_8605,plain,
    ! [X19194,X19195,X19196,X19197] :
      ( ~ c_Hoare__Mirabelle_Ohoare__derivs(X19197,X19196,X19195)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X19197),tc_HOL_Obool)),X19196),X19194))
      | c_Hoare__Mirabelle_Ohoare__derivs(X19197,X19194,X19195) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_thin])]) ).

fof(i_0_8606,plain,
    ! [X25170,X25171,X25172,X25173,X25174] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X25174)
      | ~ hBOOL(hAPP(hAPP(c_member(X25173),X25172),X25171))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25174),hAPP(X25170,X25172)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25173,X25174),X25171),X25170))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__SUPI])]) ).

fof(i_0_8607,plain,
    ! [X19388,X19389,X19390,X19391] :
      ( ~ class_Divides_Osemiring__div(X19391)
      | c_Divides_Odiv__class_Omod(X19391,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19391),c_Divides_Odiv__class_Omod(X19391,X19390,X19389)),X19388),X19389) = c_Divides_Odiv__class_Omod(X19391,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19391),X19390),X19388),X19389) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__simps_I4_J])]) ).

fof(i_0_8608,plain,
    ! [X19358,X19359,X19360,X19361] :
      ( ~ class_Divides_Osemiring__div(X19361)
      | c_Divides_Odiv__class_Omod(X19361,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19361),c_Divides_Odiv__class_Omod(X19361,X19360,X19359)),X19358),X19359) = c_Divides_Odiv__class_Omod(X19361,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19361),X19360),X19358),X19359) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__simps_I1_J])]) ).

fof(i_0_8609,plain,
    ! [X19865,X19866,X19867,X19868] :
      ( ~ class_Divides_Oring__div(X19868)
      | c_Divides_Odiv__class_Omod(X19868,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19868),X19867),X19866),X19865) = c_Divides_Odiv__class_Omod(X19868,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19868),c_Divides_Odiv__class_Omod(X19868,X19867,X19865)),X19866),X19865) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__diff__left__eq])]) ).

fof(i_0_8610,plain,
    ! [X19372,X19373,X19374,X19375] :
      ( ~ class_Divides_Osemiring__div(X19375)
      | c_Divides_Odiv__class_Omod(X19375,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19375),X19374),X19373),X19372) = c_Divides_Odiv__class_Omod(X19375,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19375),c_Divides_Odiv__class_Omod(X19375,X19374,X19372)),X19373),X19372) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__left__eq])]) ).

fof(i_0_8611,plain,
    ! [X19346,X19347,X19348,X19349] :
      ( ~ class_Divides_Osemiring__div(X19349)
      | c_Divides_Odiv__class_Omod(X19349,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19349),X19348),X19347),X19346) = c_Divides_Odiv__class_Omod(X19349,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19349),c_Divides_Odiv__class_Omod(X19349,X19348,X19346)),X19347),X19346) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__left__eq])]) ).

fof(i_0_8612,plain,
    ! [X19219,X19220,X19221] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19221,tc_HOL_Obool)),X19220),X19219))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X19221,tc_HOL_Obool)),X19220),X19219)) )
      & ( X19220 != X19219
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X19221,tc_HOL_Obool)),X19220),X19219)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19221,tc_HOL_Obool)),X19220),X19219))
        | X19220 = X19219
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X19221,tc_HOL_Obool)),X19220),X19219)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__eq])])]) ).

fof(i_0_8613,plain,
    ! [X19216,X19217,X19218] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19218,tc_HOL_Obool)),X19217),X19216))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X19218,tc_HOL_Obool)),X19217),X19216))
        | X19217 = X19216 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X19218,tc_HOL_Obool)),X19217),X19216))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19218,tc_HOL_Obool)),X19217),X19216)) )
      & ( X19217 != X19216
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19218,tc_HOL_Obool)),X19217),X19216)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__iff__psubset__eq])])]) ).

fof(i_0_8614,plain,
    ! [X23552,X23553,X23554] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23554),X23553))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23554),X23552))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X23554),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23554,tc_HOL_Obool)),X23553),X23552))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UnI])]) ).

fof(i_0_8615,plain,
    ! [X25456,X25457,X25458] : hAPP(c_Set_OPow(X25458),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25458,tc_HOL_Obool)),X25457),X25456)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X25458,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X25458),X25457)),hAPP(c_Set_OPow(X25458),X25456)),
    inference(variable_rename,[status(thm)],[fact_Pow__Int__eq]) ).

fof(i_0_8616,plain,
    ! [X33625,X33626,X33628] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X33626)),X33625))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X33626)),X33628),X33625))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33626)),X33628)),esk531_2(X33625,X33626))) ),
    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_8617,plain,
    ! [X26347,X26348,X26349,X26350] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26349),X26348))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26349,X26350),X26347),X26348) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X26350,X26349,c_Groups_Oplus__class_Oplus(X26350)),X26347),c_Groups_Ozero__class_Ozero(X26350)),X26348)
        | ~ class_Groups_Ocomm__monoid__add(X26350) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X26349),X26348))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26349,X26350),X26347),X26348) = c_Groups_Ozero__class_Ozero(X26350)
        | ~ class_Groups_Ocomm__monoid__add(X26350) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5764])])]) ).

fof(i_0_8618,plain,
    ! [X26343,X26344,X26345,X26346] :
      ( ~ class_Groups_Ocomm__monoid__add(X26346)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26345),X26344))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26345,X26346),X26343),X26344) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X26346,X26345,c_Groups_Oplus__class_Oplus(X26346)),X26343),c_Groups_Ozero__class_Ozero(X26346)),X26344) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum_Oeq__fold])]) ).

fof(i_0_8619,plain,
    ! [X24896,X24897,X24898,X24899] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24898),X24897))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24898,X24899),X24896),X24897) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X24899,X24898,c_Groups_Otimes__class_Otimes(X24899)),X24896),c_Groups_Oone__class_Oone(X24899)),X24897)
        | ~ class_Groups_Ocomm__monoid__mult(X24899) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X24898),X24897))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24898,X24899),X24896),X24897) = c_Groups_Oone__class_Oone(X24899)
        | ~ class_Groups_Ocomm__monoid__mult(X24899) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5765])])]) ).

fof(i_0_8620,plain,
    ! [X24900,X24901,X24902,X24903] :
      ( ~ class_Groups_Ocomm__monoid__mult(X24903)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24902),X24901))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24902,X24903),X24900),X24901) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X24903,X24902,c_Groups_Otimes__class_Otimes(X24903)),X24900),c_Groups_Oone__class_Oone(X24903)),X24901) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod_Oeq__fold])]) ).

fof(i_0_8621,plain,
    ! [X19213,X19214,X19215] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X19215,tc_HOL_Obool)),X19214),X19213))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19215,tc_HOL_Obool)),X19214),X19213)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__imp__subset])]) ).

fof(i_0_8622,plain,
    ! [X33468,X33469,X33470,X33471] : hAPP(hAPP(c_List_Oappend(X33471),c_List_Oreplicate(X33471,X33470,X33469)),c_List_Oreplicate(X33471,X33468,X33469)) = hAPP(hAPP(c_List_Oappend(X33471),c_List_Oreplicate(X33471,X33468,X33469)),c_List_Oreplicate(X33471,X33470,X33469)),
    inference(variable_rename,[status(thm)],[fact_append__replicate__commute]) ).

fof(i_0_8623,plain,
    ! [X22182,X22183] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22183))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22182),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,X22183,X22182) = 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),X22183),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22182)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__pos__neg])]) ).

fof(i_0_8624,plain,
    ! [X28729,X28730,X28731,X28732] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X28732),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28731)),X28730)))
        | hAPP(hAPP(c_List_Onth(X28731),hAPP(hAPP(c_List_Oappend(X28731),X28730),X28729)),X28732) = hAPP(hAPP(c_List_Onth(X28731),X28730),X28732) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X28732),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28731)),X28730)))
        | hAPP(hAPP(c_List_Onth(X28731),hAPP(hAPP(c_List_Oappend(X28731),X28730),X28729)),X28732) = hAPP(hAPP(c_List_Onth(X28731),X28729),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X28732),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28731)),X28730))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5766])]) ).

fof(i_0_8625,plain,
    ! [X20822,X20823,X20824] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X20824),X20823),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20824,tc_HOL_Obool)),X20822)))
      | ~ hBOOL(hAPP(hAPP(c_member(X20824),X20823),X20822)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5767])]) ).

fof(i_0_8626,plain,
    ! [X20819,X20820,X20821] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X20821),X20820),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20821,tc_HOL_Obool)),X20819)))
      | ~ hBOOL(hAPP(hAPP(c_member(X20821),X20820),X20819)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5768])]) ).

fof(i_0_8627,plain,
    ! [X20816,X20817,X20818] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X20818),X20817),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20818,tc_HOL_Obool)),X20816)))
        | ~ hBOOL(hAPP(hAPP(c_member(X20818),X20817),X20816)) )
      & ( hBOOL(hAPP(hAPP(c_member(X20818),X20817),X20816))
        | hBOOL(hAPP(hAPP(c_member(X20818),X20817),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20818,tc_HOL_Obool)),X20816))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5769])]) ).

fof(i_0_8628,plain,
    ! [X25576,X25577,X25578,X25580,X25581,X25582] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk189_2(X25576,X25577)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X25577)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25578),X25577))
        | ~ hBOOL(hAPP(X25576,X25578)) )
      & ( hBOOL(hAPP(X25576,esk189_2(X25576,X25577)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25578),X25577))
        | ~ hBOOL(hAPP(X25576,X25578)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk190_2(X25580,X25581)),X25581))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X25582),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X25581)))
        | ~ hBOOL(hAPP(X25580,X25582)) )
      & ( hBOOL(hAPP(X25580,esk190_2(X25580,X25581)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X25582),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X25581)))
        | ~ hBOOL(hAPP(X25580,X25582)) ) ),
    inference(distribute,[status(thm)],[inference(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_8629,plain,
    ! [X28980,X28981,X28982,X28983] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X28983) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Odrop(X28982),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X28983)),hAPP(hAPP(c_List_Olist_OCons(X28982),X28981),X28980)) = hAPP(hAPP(c_List_Olist_OCons(X28982),X28981),X28980) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X28983) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Odrop(X28982),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X28983)),hAPP(hAPP(c_List_Olist_OCons(X28982),X28981),X28980)) = hAPP(hAPP(c_List_Odrop(X28982),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X28983)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X28980) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_drop__Cons__number__of])]) ).

fof(i_0_8630,plain,
    ! [X32042,X32043] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),esk419_2(X32042,X32043)),c_Int_OInteg))
        | hBOOL(hAPP(X32043,X32042)) )
      & ( ~ hBOOL(hAPP(X32043,hAPP(c_Int_OAbs__Integ,esk419_2(X32042,X32043))))
        | hBOOL(hAPP(X32043,X32042)) ) ),
    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_8631,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_5770]) ).

fof(i_0_8632,plain,
    ! [X28122,X28123,X28124] :
      ( ~ c_Wellfounded_Owf(X28124,X28123)
      | c_Wellfounded_Owf(X28124,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X28124,X28124),tc_HOL_Obool)),X28123),X28122)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__Int1])]) ).

fof(i_0_8633,plain,
    ! [X28119,X28120,X28121] :
      ( ~ c_Wellfounded_Owf(X28121,X28120)
      | c_Wellfounded_Owf(X28121,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X28121,X28121),tc_HOL_Obool)),X28119),X28120)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__Int2])]) ).

fof(i_0_8634,plain,
    ! [X22306,X22307] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22307))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22306),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X22307),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),X22307),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22306)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__pos__neg])]) ).

fof(i_0_8635,plain,
    ! [X29390,X29391] :
      ( ~ class_Lattices_Oab__semigroup__idem__mult(X29391)
      | X29390 = c_List_Olist_ONil(X29391)
      | hAPP(c_Finite__Set_Ofold1(X29391,c_Groups_Otimes__class_Otimes(X29391)),hAPP(c_List_Oset(X29391),X29390)) = hAPP(c_List_Ofoldl(X29391,X29391,c_Groups_Otimes__class_Otimes(X29391),hAPP(c_List_Ohd(X29391),X29390)),hAPP(c_List_Otl(X29391),X29390)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1__set])]) ).

fof(i_0_8636,plain,
    ! [X29100,X29101,X29102,X29103,X29104] : hAPP(hAPP(c_List_Odrop(tc_prod(X29104,X29103)),X29102),hAPP(hAPP(c_List_Ozip(X29104,X29103),X29101),X29100)) = hAPP(hAPP(c_List_Ozip(X29104,X29103),hAPP(hAPP(c_List_Odrop(X29104),X29102),X29101)),hAPP(hAPP(c_List_Odrop(X29103),X29102),X29100)),
    inference(variable_rename,[status(thm)],[fact_drop__zip]) ).

fof(i_0_8637,plain,
    ! [X29039,X29040,X29041,X29042,X29043] : hAPP(hAPP(c_List_Otake(tc_prod(X29043,X29042)),X29041),hAPP(hAPP(c_List_Ozip(X29043,X29042),X29040),X29039)) = hAPP(hAPP(c_List_Ozip(X29043,X29042),hAPP(hAPP(c_List_Otake(X29043),X29041),X29040)),hAPP(hAPP(c_List_Otake(X29042),X29041),X29039)),
    inference(variable_rename,[status(thm)],[fact_take__zip]) ).

fof(i_0_8638,plain,
    ! [X25989,X25990,X25991] :
      ( ~ class_Orderings_Olinorder(X25991)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25991),X25990),X25989))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25991,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X25991,X25990),X25989)),hAPP(hAPP(c_Set_Oinsert(X25991),X25989),c_Orderings_Obot__class_Obot(tc_fun(X25991,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(X25991,X25990,X25989) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I6_J])]) ).

fof(i_0_8639,plain,
    ! [X22184,X22185] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22185),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22184),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,X22185,X22184) = 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),X22185),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22184)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__neg__neg])]) ).

fof(i_0_8640,plain,
    ! [X32542,X32543,X32544,X32545,X32546] :
      ( ~ c_Relation_Osingle__valued(X32546,X32545,X32544)
      | ~ c_Relation_Osingle__valued(X32545,X32543,X32542)
      | c_Relation_Osingle__valued(X32546,X32543,hAPP(hAPP(c_Relation_Orel__comp(X32546,X32545,X32543),X32544),X32542)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_single__valued__rel__comp])]) ).

fof(i_0_8641,plain,
    ! [X31681,X31682] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X31682),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X31682))),c_List_Otranspose(X31682,X31681)))),
    inference(variable_rename,[status(thm)],[fact_sorted__transpose]) ).

fof(i_0_8642,plain,
    ! [X25914,X25915,X25916,X25917,X25918] :
      ( ~ class_Orderings_Olinorder(X25918)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25918,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X25918,X25917),X25916)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X25918,X25915),X25914)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X25918,hAPP(hAPP(c_Orderings_Oord__class_Omax(X25918),X25917),X25915)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X25918),X25916),X25914)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__atLeastLessThan])]) ).

fof(i_0_8643,plain,
    ! [X25514,X25515,X25516,X25517,X25518] :
      ( ~ class_Orderings_Olinorder(X25518)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25518,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X25518,X25517,X25516)),c_SetInterval_Oord__class_OatLeastAtMost(X25518,X25515,X25514)) = c_SetInterval_Oord__class_OatLeastAtMost(X25518,hAPP(hAPP(c_Orderings_Oord__class_Omax(X25518),X25517),X25515),hAPP(hAPP(c_Orderings_Oord__class_Omin(X25518),X25516),X25514)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMost])]) ).

fof(i_0_8644,plain,
    ! [X25334,X25335,X25336,X25337,X25338] :
      ( ~ class_Orderings_Olinorder(X25338)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25338,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X25338,X25337,X25336)),c_SetInterval_Oord__class_OgreaterThanAtMost(X25338,X25335,X25334)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X25338,hAPP(hAPP(c_Orderings_Oord__class_Omax(X25338),X25337),X25335),hAPP(hAPP(c_Orderings_Oord__class_Omin(X25338),X25336),X25334)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__greaterThanAtMost])]) ).

fof(i_0_8645,plain,
    ! [X24891,X24892,X24893,X24894,X24895] :
      ( ~ class_Orderings_Olinorder(X24895)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24895,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X24895,X24894,X24893)),c_SetInterval_Oord__class_OgreaterThanLessThan(X24895,X24892,X24891)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X24895,hAPP(hAPP(c_Orderings_Oord__class_Omax(X24895),X24894),X24892),hAPP(hAPP(c_Orderings_Oord__class_Omin(X24895),X24893),X24891)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__greaterThanLessThan])]) ).

fof(i_0_8646,plain,
    ! [X20796,X20797,X20798,X20799] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X20799),X20798),X20797))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20799,tc_HOL_Obool)),X20797),X20796))
      | hBOOL(hAPP(hAPP(c_member(X20799),X20798),X20796)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__rev__mp])]) ).

fof(i_0_8647,plain,
    ! [X20800,X20801,X20802,X20803] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20803,tc_HOL_Obool)),X20802),X20801))
      | ~ hBOOL(hAPP(hAPP(c_member(X20803),X20800),X20802))
      | hBOOL(hAPP(hAPP(c_member(X20803),X20800),X20801)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__mp])]) ).

fof(i_0_8648,plain,
    ! [X20792,X20793,X20794,X20795] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20795,tc_HOL_Obool)),X20794),X20793))
      | ~ hBOOL(hAPP(hAPP(c_member(X20795),X20792),X20794))
      | hBOOL(hAPP(hAPP(c_member(X20795),X20792),X20793)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__mono])]) ).

fof(i_0_8649,plain,
    ! [X20726,X20727,X20728,X20729] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X20729,tc_HOL_Obool)),X20728),X20727))
      | ~ hBOOL(hAPP(hAPP(c_member(X20729),X20726),X20728))
      | hBOOL(hAPP(hAPP(c_member(X20729),X20726),X20727)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subsetD])]) ).

fof(i_0_8650,plain,
    ! [X20825,X20826,X20827,X20828] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X20828,tc_HOL_Obool)),X20827),X20826))
      | ~ hBOOL(hAPP(hAPP(c_member(X20828),X20825),X20827))
      | hBOOL(hAPP(hAPP(c_member(X20828),X20825),X20826)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubsetD])]) ).

fof(i_0_8651,plain,
    ! [X28721,X28722,X28723,X28724] : hAPP(hAPP(c_List_Onth(X28724),hAPP(hAPP(c_List_Oappend(X28724),X28723),hAPP(hAPP(c_List_Olist_OCons(X28724),X28722),X28721))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28724)),X28723)) = X28722,
    inference(variable_rename,[status(thm)],[fact_nth__append__length]) ).

fof(i_0_8652,plain,
    ! [X22693,X22694,X22695] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22695),hAPP(c_Int_Onumber__class_Onumber__of(X22695),X22694)),hAPP(c_Int_Onumber__class_Onumber__of(X22695),X22693)))
        | hAPP(hAPP(c_Orderings_Oord__class_Omax(X22695),hAPP(c_Int_Onumber__class_Onumber__of(X22695),X22694)),hAPP(c_Int_Onumber__class_Onumber__of(X22695),X22693)) = hAPP(c_Int_Onumber__class_Onumber__of(X22695),X22693)
        | ~ class_Int_Onumber(X22695)
        | ~ class_Orderings_Oord(X22695) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22695),hAPP(c_Int_Onumber__class_Onumber__of(X22695),X22694)),hAPP(c_Int_Onumber__class_Onumber__of(X22695),X22693)))
        | hAPP(hAPP(c_Orderings_Oord__class_Omax(X22695),hAPP(c_Int_Onumber__class_Onumber__of(X22695),X22694)),hAPP(c_Int_Onumber__class_Onumber__of(X22695),X22693)) = hAPP(c_Int_Onumber__class_Onumber__of(X22695),X22694)
        | ~ class_Int_Onumber(X22695)
        | ~ class_Orderings_Oord(X22695) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5771])])]) ).

fof(i_0_8653,plain,
    ! [X22497,X22498,X22499] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22499),hAPP(c_Int_Onumber__class_Onumber__of(X22499),X22498)),hAPP(c_Int_Onumber__class_Onumber__of(X22499),X22497)))
        | hAPP(hAPP(c_Orderings_Oord__class_Omin(X22499),hAPP(c_Int_Onumber__class_Onumber__of(X22499),X22498)),hAPP(c_Int_Onumber__class_Onumber__of(X22499),X22497)) = hAPP(c_Int_Onumber__class_Onumber__of(X22499),X22498)
        | ~ class_Int_Onumber(X22499)
        | ~ class_Orderings_Oord(X22499) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22499),hAPP(c_Int_Onumber__class_Onumber__of(X22499),X22498)),hAPP(c_Int_Onumber__class_Onumber__of(X22499),X22497)))
        | hAPP(hAPP(c_Orderings_Oord__class_Omin(X22499),hAPP(c_Int_Onumber__class_Onumber__of(X22499),X22498)),hAPP(c_Int_Onumber__class_Onumber__of(X22499),X22497)) = hAPP(c_Int_Onumber__class_Onumber__of(X22499),X22497)
        | ~ class_Int_Onumber(X22499)
        | ~ class_Orderings_Oord(X22499) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5772])])]) ).

fof(i_0_8654,plain,
    ! [X22308,X22309] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22309),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22308),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X22309),X22308) = 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),X22309),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22308)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__neg__neg])]) ).

fof(i_0_8655,plain,
    ! [X26025,X26026] : 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)),X26026),X26025),
    inference(variable_rename,[status(thm)],[fact_inj__on__add__nat]) ).

fof(i_0_8656,plain,
    ! [X19700,X19701] :
      ( ( ~ 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),X19700),X19701)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19700))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19701)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19700))
        | 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),X19700),X19701)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19701)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__imp__zdiv__nonneg__iff])])]) ).

fof(i_0_8657,plain,
    ! [X21257,X21258,X21259,X21260,X21261] :
      ( ~ class_Fields_Ofield__inverse__zero(X21261)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21261),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21261),X21260),X21259)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21261),X21258),X21257)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21261),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21261),X21260),X21258)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21261),X21259),X21257)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_times__divide__times__eq])]) ).

fof(i_0_8658,plain,
    ! [X18129,X18130,X18131,X18132,X18133] :
      ( ~ class_Rings_Ocomm__semiring__1(X18133)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18133),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18133),X18132),X18131)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18133),X18130),X18129)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18133),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18133),X18132),X18130)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18133),X18131),X18129)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J])]) ).

fof(i_0_8659,plain,
    ! [X17806,X17807,X17808,X17809,X17810] :
      ( ~ class_Rings_Ocomm__semiring__1(X17810)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17810),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17810),X17809),X17808)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17810),X17807),X17806)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17810),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17810),X17809),X17807)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17810),X17808),X17806)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J])]) ).

fof(i_0_8660,plain,
    ! [X18139,X18140,X18141,X18142,X18143] :
      ( ~ class_Rings_Ocomm__semiring__1(X18143)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18143),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18143),X18142),X18141)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18143),X18140),X18139)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18143),X18142),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18143),X18141),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18143),X18140),X18139))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J])]) ).

fof(i_0_8661,plain,
    ! [X31500,X31501,X31502,X31503,X31504] :
      ( ~ class_Orderings_Olinorder(X31504)
      | ~ c_List_Olinorder__class_Osorted(X31504,hAPP(hAPP(c_List_Omap(X31503,X31504),X31502),X31501))
      | c_List_Olinorder__class_Osorted(X31504,hAPP(hAPP(c_List_Omap(X31503,X31504),X31502),c_List_Oremove1(X31503,X31500,X31501))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__map__remove1])]) ).

fof(i_0_8662,plain,
    ! [X30821,X30822,X30823] : hAPP(c_Relation_ODomain(X30823,X30822),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X30823,X30822),tc_HOL_Obool),X30821)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(X30823,X30822),tc_HOL_Obool),tc_fun(X30823,tc_HOL_Obool)),X30821),c_Relation_ODomain(X30823,X30822)),
    inference(variable_rename,[status(thm)],[fact_Domain__Union]) ).

fof(i_0_8663,plain,
    ! [X30828,X30829,X30830] : hAPP(c_Relation_ORange(X30830,X30829),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X30830,X30829),tc_HOL_Obool),X30828)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(X30830,X30829),tc_HOL_Obool),tc_fun(X30829,tc_HOL_Obool)),X30828),c_Relation_ORange(X30830,X30829)),
    inference(variable_rename,[status(thm)],[fact_Range__Union]) ).

fof(i_0_8664,plain,
    ! [X25584,X25585,X25587,X25588,X25589,X25591] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk191_2(X25584,X25585)),X25585))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X25587),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X25585)))
        | hBOOL(hAPP(X25584,X25587)) )
      & ( ~ hBOOL(hAPP(X25584,esk191_2(X25584,X25585)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X25587),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X25585)))
        | hBOOL(hAPP(X25584,X25587)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk192_2(X25588,X25589)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X25589)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25591),X25589))
        | hBOOL(hAPP(X25588,X25591)) )
      & ( ~ hBOOL(hAPP(X25588,esk192_2(X25588,X25589)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25591),X25589))
        | hBOOL(hAPP(X25588,X25591)) ) ),
    inference(distribute,[status(thm)],[inference(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_8665,plain,
    ! [X20920,X20921,X20922] :
      ( ~ class_Rings_Oring__1(X20922)
      | ~ hBOOL(hAPP(hAPP(c_member(X20922),X20921),c_Int_Oring__1__class_OInts(X20922)))
      | hBOOL(hAPP(hAPP(c_member(X20922),hAPP(hAPP(c_Power_Opower__class_Opower(X20922),X20921),X20920)),c_Int_Oring__1__class_OInts(X20922))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__power])]) ).

fof(i_0_8666,plain,
    ! [X27704,X27705] : hAPP(c_Set_OCollect(X27705),hAPP(hAPP(c_COMBC(X27705,tc_fun(X27705,tc_HOL_Obool),tc_HOL_Obool),c_member(X27705)),X27704)) = X27704,
    inference(variable_rename,[status(thm)],[fact_Collect__mem__eq]) ).

fof(i_0_8667,plain,
    ! [X20502,X20503] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X20503))
      | 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),X20503),X20502))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__one__le__power])]) ).

fof(i_0_8668,plain,
    ! [X20458,X20459,X20460] :
      ( ~ class_Rings_Olinordered__semidom(X20460)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20460),c_Groups_Oone__class_Oone(X20460)),X20459))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20458))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20460),c_Groups_Oone__class_Oone(X20460)),hAPP(hAPP(c_Power_Opower__class_Opower(X20460),X20459),X20458))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__less__power])]) ).

fof(i_0_8669,plain,
    ! [X21401,X21402,X21403] :
      ( ~ class_Fields_Olinordered__field(X21403)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21403),X21402),c_Groups_Ozero__class_Ozero(X21403)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21403),X21401),c_Groups_Ozero__class_Ozero(X21403)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21403),c_Groups_Ozero__class_Ozero(X21403)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21403),X21402),X21401))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__nonpos__neg])]) ).

fof(i_0_8670,plain,
    ! [X18783,X18784,X18785] :
      ( ~ class_Rings_Oordered__ring(X18785)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18785),X18784),c_Groups_Ozero__class_Ozero(X18785)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18785),X18783),c_Groups_Ozero__class_Ozero(X18785)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18785),c_Groups_Ozero__class_Ozero(X18785)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18785),X18784),X18783))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonpos__nonpos])]) ).

fof(i_0_8671,plain,
    ! [X21321,X21322,X21323] :
      ( ~ class_Fields_Olinordered__field(X21323)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21323),X21322),c_Groups_Ozero__class_Ozero(X21323)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21323),X21321),c_Groups_Ozero__class_Ozero(X21323)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21323),c_Groups_Ozero__class_Ozero(X21323)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21323),X21322),X21321))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__neg__neg])]) ).

fof(i_0_8672,plain,
    ! [X18364,X18365,X18366] :
      ( ~ class_Rings_Olinordered__ring__strict(X18366)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18366),X18365),c_Groups_Ozero__class_Ozero(X18366)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18366),X18364),c_Groups_Ozero__class_Ozero(X18366)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18366),c_Groups_Ozero__class_Ozero(X18366)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18366),X18365),X18364))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__neg__neg])]) ).

fof(i_0_8673,plain,
    ! [X26254,X26255,X26256] :
      ( ~ class_Groups_Ocomm__monoid__add(X26256)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26256),X26255),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X26254))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26256),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26256),X26255),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X26254))),hAPP(X26255,X26254)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__lessThan__Suc])]) ).

fof(i_0_8674,plain,
    ! [X17464,X17465] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17465),X17464)),X17465)),
    inference(variable_rename,[status(thm)],[i_0_5773]) ).

fof(i_0_8675,plain,
    ! [X17462,X17463] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17463),X17462)),X17462)),
    inference(variable_rename,[status(thm)],[i_0_5774]) ).

fof(i_0_8676,plain,
    ! [X21819,X21820] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21820))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21819))
      | c_Divides_OposDivAlg(X21820,X21819) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X21820),X21819)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X21820,X21819)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_posDivAlg__div__mod])]) ).

fof(i_0_8677,plain,
    ! [X19698,X19699] :
      ( ( ~ 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),X19698),X19699)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19699),X19698))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19699)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19699),X19698))
        | 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),X19698),X19699)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19699)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__imp__zdiv__pos__iff])])]) ).

fof(i_0_8678,plain,
    ! [X28326,X28327] : c_List_Olex(X28327,X28326) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(X28327),tc_List_Olist(X28327)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(X28327,X28326)),
    inference(variable_rename,[status(thm)],[fact_lex__def]) ).

fof(i_0_8679,plain,
    ! [X30462,X30463,X30464,X30465] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X30465),X30464),hAPP(c_List_Oset(X30465),X30463)))
        | c_List_Oremove1(X30465,X30464,hAPP(hAPP(c_List_Oappend(X30465),X30463),X30462)) = hAPP(hAPP(c_List_Oappend(X30465),c_List_Oremove1(X30465,X30464,X30463)),X30462) )
      & ( hBOOL(hAPP(hAPP(c_member(X30465),X30464),hAPP(c_List_Oset(X30465),X30463)))
        | c_List_Oremove1(X30465,X30464,hAPP(hAPP(c_List_Oappend(X30465),X30463),X30462)) = hAPP(hAPP(c_List_Oappend(X30465),X30463),c_List_Oremove1(X30465,X30464,X30462)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5775])]) ).

cnf(i_0_8680,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_5776]) ).

fof(i_0_8681,plain,
    ! [X22558,X22559,X22560,X22561] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22561),X22560),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22561),X22559),X22558)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22561),X22560),X22559))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22561),X22560),X22558))
        | ~ class_Orderings_Olinorder(X22561) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22561),X22560),X22559))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22561),X22560),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22561),X22559),X22558)))
        | ~ class_Orderings_Olinorder(X22561) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22561),X22560),X22558))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22561),X22560),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22561),X22559),X22558)))
        | ~ class_Orderings_Olinorder(X22561) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__max__iff__disj])])]) ).

fof(i_0_8682,plain,
    ! [X22622,X22623,X22624,X22625] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22625),X22624),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22625),X22623),X22622)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22625),X22624),X22623))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22625),X22624),X22622))
        | ~ class_Orderings_Olinorder(X22625) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22625),X22624),X22623))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22625),X22624),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22625),X22623),X22622)))
        | ~ class_Orderings_Olinorder(X22625) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22625),X22624),X22622))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22625),X22624),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22625),X22623),X22622)))
        | ~ class_Orderings_Olinorder(X22625) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__max__iff__disj])])]) ).

fof(i_0_8683,plain,
    ! [X26863,X26864,X26865] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X26865,X26864,c_Orderings_Obot__class_Obot(tc_fun(X26865,tc_HOL_Obool))),X26863)),
    inference(variable_rename,[status(thm)],[i_0_5777]) ).

fof(i_0_8684,plain,
    ! [X19687,X19688] :
      ( ( ~ 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),X19687),X19688)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19687),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19688),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19687),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),X19687),X19688)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19688),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_8685,plain,
    ! [X29636,X29637] :
      ( X29637 = c_List_Olist_ONil(X29636)
      | c_Random_Oselect__weight(X29636,hAPP(hAPP(c_List_Omap(X29636,tc_prod(tc_Code__Numeral_Ocode__numeral,X29636)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X29636),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),X29637)) = c_Random_Oselect(X29636,X29637) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_select__weigth__select])]) ).

fof(i_0_8686,plain,
    ! [X30994,X30995,X30996] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X30995,tc_HOL_Obool)),X30996),X30994))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30995),X30996))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X30995),c_Complete__Lattice_OInf__class_OInf(tc_fun(X30995,tc_HOL_Obool),X30994))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Inter])])]) ).

fof(i_0_8687,plain,
    ! [X20417,X20418,X20419] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20419),c_Groups_Ozero__class_Ozero(X20419)),X20417))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20419),c_Groups_Ozero__class_Ozero(X20419)),X20418))
        | hAPP(c_Groups_Oabs__class_Oabs(X20419),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20419),X20418),X20417)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20419),hAPP(c_Groups_Oabs__class_Oabs(X20419),X20418)),hAPP(c_Groups_Oabs__class_Oabs(X20419),X20417))
        | ~ class_Rings_Oordered__ring__abs(X20419) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20419),X20417),c_Groups_Ozero__class_Ozero(X20419)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20419),c_Groups_Ozero__class_Ozero(X20419)),X20418))
        | hAPP(c_Groups_Oabs__class_Oabs(X20419),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20419),X20418),X20417)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20419),hAPP(c_Groups_Oabs__class_Oabs(X20419),X20418)),hAPP(c_Groups_Oabs__class_Oabs(X20419),X20417))
        | ~ class_Rings_Oordered__ring__abs(X20419) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20419),c_Groups_Ozero__class_Ozero(X20419)),X20417))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20419),X20418),c_Groups_Ozero__class_Ozero(X20419)))
        | hAPP(c_Groups_Oabs__class_Oabs(X20419),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20419),X20418),X20417)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20419),hAPP(c_Groups_Oabs__class_Oabs(X20419),X20418)),hAPP(c_Groups_Oabs__class_Oabs(X20419),X20417))
        | ~ class_Rings_Oordered__ring__abs(X20419) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20419),X20417),c_Groups_Ozero__class_Ozero(X20419)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20419),X20418),c_Groups_Ozero__class_Ozero(X20419)))
        | hAPP(c_Groups_Oabs__class_Oabs(X20419),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20419),X20418),X20417)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20419),hAPP(c_Groups_Oabs__class_Oabs(X20419),X20418)),hAPP(c_Groups_Oabs__class_Oabs(X20419),X20417))
        | ~ class_Rings_Oordered__ring__abs(X20419) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__eq__mult])])]) ).

cnf(i_0_8688,plain,
    ( X1 = X2
    | c_Int_OBit1(X1) != c_Int_OBit1(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5778]) ).

fof(i_0_8689,plain,
    ! [X29591,X29592,X29593] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X29593),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29592)),X29591)))
      | c_List_Obutlast(X29592,hAPP(hAPP(c_List_Otake(X29592),X29593),X29591)) = hAPP(hAPP(c_List_Otake(X29592),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X29593),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X29591) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_butlast__take])]) ).

fof(i_0_8690,plain,
    ! [X26128,X26129] :
      ( ~ class_Orderings_Oorder(X26129)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26129,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X26129),X26128),c_Orderings_Obot__class_Obot(tc_fun(X26129,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(X26129),X26128)) = hAPP(hAPP(c_Set_Oinsert(X26129),X26128),c_Orderings_Obot__class_Obot(tc_fun(X26129,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_single__Diff__lessThan])]) ).

fof(i_0_8691,plain,
    ! [X23823,X23824,X23825,X23826,X23827,X23828,X23829,X23830] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23825,tc_HOL_Obool)),X23824),X23823) != c_Orderings_Obot__class_Obot(tc_fun(X23825,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(X23825),X23826),X23824))
        | ~ hBOOL(hAPP(hAPP(c_member(X23825),X23827),X23823))
        | X23826 != X23827 )
      & ( hBOOL(hAPP(hAPP(c_member(X23830),esk121_3(X23828,X23829,X23830)),X23829))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23830,tc_HOL_Obool)),X23829),X23828) = c_Orderings_Obot__class_Obot(tc_fun(X23830,tc_HOL_Obool)) )
      & ( hBOOL(hAPP(hAPP(c_member(X23830),esk122_3(X23828,X23829,X23830)),X23828))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23830,tc_HOL_Obool)),X23829),X23828) = c_Orderings_Obot__class_Obot(tc_fun(X23830,tc_HOL_Obool)) )
      & ( esk121_3(X23828,X23829,X23830) = esk122_3(X23828,X23829,X23830)
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23830,tc_HOL_Obool)),X23829),X23828) = c_Orderings_Obot__class_Obot(tc_fun(X23830,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_8692,plain,
    ! [X31580,X31581,X31582] :
      ( ~ class_Orderings_Olinorder(X31582)
      | ~ hBOOL(hAPP(hAPP(c_member(X31582),X31581),hAPP(c_List_Oset(X31582),X31580)))
      | ~ c_List_Olinorder__class_Osorted(X31582,X31580)
      | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X31582,X31582,c_COMBI(X31582)),X31581),c_List_Oremove1(X31582,X31581,X31580)) = X31580 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insort__remove1])]) ).

fof(i_0_8693,plain,
    ! [X21751,X21752] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21752),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)),X21751))
      | c_Divides_OnegDivAlg(X21752,X21751) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X21752),X21751)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X21752,X21751)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_negDivAlg__div__mod])]) ).

fof(i_0_8694,plain,
    ! [X24291,X24292,X24293] :
      ( ~ class_Lattices_Olattice(X24293)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24293),X24292))
      | X24291 = c_Orderings_Obot__class_Obot(tc_fun(X24293,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24293,tc_HOL_Obool)),X24291),X24292))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24293),c_Big__Operators_Olattice__class_OInf__fin(X24293,X24291)),c_Big__Operators_Olattice__class_OInf__fin(X24293,X24292)) = c_Big__Operators_Olattice__class_OInf__fin(X24293,X24292) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Osubset__idem])]) ).

fof(i_0_8695,plain,
    ! [X24285,X24286,X24287] :
      ( ~ class_Lattices_Olattice(X24287)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24287),X24286))
      | X24285 = c_Orderings_Obot__class_Obot(tc_fun(X24287,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24287,tc_HOL_Obool)),X24285),X24286))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24287),c_Big__Operators_Olattice__class_OSup__fin(X24287,X24285)),c_Big__Operators_Olattice__class_OSup__fin(X24287,X24286)) = c_Big__Operators_Olattice__class_OSup__fin(X24287,X24286) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Osubset__idem])]) ).

fof(i_0_8696,plain,
    ! [X24297,X24298,X24299] :
      ( ~ class_Orderings_Olinorder(X24299)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24299),X24298))
      | X24297 = c_Orderings_Obot__class_Obot(tc_fun(X24299,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24299,tc_HOL_Obool)),X24297),X24298))
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X24299),c_Big__Operators_Olinorder__class_OMax(X24299,X24297)),c_Big__Operators_Olinorder__class_OMax(X24299,X24298)) = c_Big__Operators_Olinorder__class_OMax(X24299,X24298) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Osubset__idem])]) ).

fof(i_0_8697,plain,
    ! [X24373,X24374,X24375] :
      ( ~ class_Orderings_Olinorder(X24375)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24375),X24374))
      | X24373 = c_Orderings_Obot__class_Obot(tc_fun(X24375,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24375,tc_HOL_Obool)),X24373),X24374))
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X24375),c_Big__Operators_Olinorder__class_OMin(X24375,X24373)),c_Big__Operators_Olinorder__class_OMin(X24375,X24374)) = c_Big__Operators_Olinorder__class_OMin(X24375,X24374) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Osubset__idem])]) ).

fof(i_0_8698,plain,
    ! [X20271,X20272,X20273] : 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,X20273,X20272)),X20271),X20272) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X20273),X20271),X20272),
    inference(variable_rename,[status(thm)],[fact_zpower__zmod]) ).

fof(i_0_8699,plain,
    ! [X19948,X19949,X19950] : 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,X19950,X19949)),X19948),X19949) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X19950),X19948),X19949),
    inference(variable_rename,[status(thm)],[fact_zdiff__zmod__left]) ).

fof(i_0_8700,plain,
    ! [X31014,X31015,X31016,X31017] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31016),X31015),c_Complete__Lattice_OInf__class_OInf(X31016,X31014)))
        | ~ hBOOL(hAPP(hAPP(c_member(X31016),X31017),X31014))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31016),X31015),X31017))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X31016) )
      & ( hBOOL(hAPP(hAPP(c_member(X31016),esk376_3(X31014,X31015,X31016)),X31014))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31016),X31015),c_Complete__Lattice_OInf__class_OInf(X31016,X31014)))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X31016) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31016),X31015),esk376_3(X31014,X31015,X31016)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31016),X31015),c_Complete__Lattice_OInf__class_OInf(X31016,X31014)))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X31016) ) ),
    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_8701,plain,
    ! [X28797,X28798,X28799,X28800] :
      ( ( X28800 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Otake(X28799),X28800),hAPP(hAPP(c_List_Olist_OCons(X28799),X28798),X28797)) = c_List_Olist_ONil(X28799) )
      & ( X28800 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Otake(X28799),X28800),hAPP(hAPP(c_List_Olist_OCons(X28799),X28798),X28797)) = hAPP(hAPP(c_List_Olist_OCons(X28799),X28798),hAPP(hAPP(c_List_Otake(X28799),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X28800),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X28797)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__Cons_H])]) ).

fof(i_0_8702,plain,
    ! [X23720,X23721,X23722,X23723] :
      ( ~ hBOOL(hAPP(X23723,X23722))
      | ~ hBOOL(hAPP(X23721,X23722))
      | hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23720,tc_HOL_Obool)),X23723),X23721),X23722)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf1I])]) ).

fof(i_0_8703,plain,
    ! [X33694,X33695,X33696,X33698,X33699,X33700,X33701] :
      ( ( hBOOL(hAPP(hAPP(c_member(X33696),esk536_3(X33694,X33695,X33696)),hAPP(c_List_Oset(X33696),X33694)))
        | ~ c_List_Olist__ex(X33696,X33695,X33694) )
      & ( hBOOL(hAPP(X33695,esk536_3(X33694,X33695,X33696)))
        | ~ c_List_Olist__ex(X33696,X33695,X33694) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X33700),X33701),hAPP(c_List_Oset(X33700),X33698)))
        | ~ hBOOL(hAPP(X33699,X33701))
        | c_List_Olist__ex(X33700,X33699,X33698) ) ),
    inference(distribute,[status(thm)],[inference(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_8704,plain,
    ! [X33686,X33687,X33688,X33689,X33690,X33691,X33692] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X33688),X33689),hAPP(c_List_Oset(X33688),X33687)))
        | ~ hBOOL(hAPP(X33686,X33689))
        | c_List_Olist__ex(X33688,X33686,X33687) )
      & ( hBOOL(hAPP(hAPP(c_member(X33692),esk535_3(X33690,X33691,X33692)),hAPP(c_List_Oset(X33692),X33691)))
        | ~ c_List_Olist__ex(X33692,X33690,X33691) )
      & ( hBOOL(hAPP(X33690,esk535_3(X33690,X33691,X33692)))
        | ~ c_List_Olist__ex(X33692,X33690,X33691) ) ),
    inference(distribute,[status(thm)],[inference(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_8705,plain,
    ! [X32736,X32737,X32738,X32740,X32741,X32742,X32743] :
      ( ( hBOOL(hAPP(hAPP(c_member(X32738),esk478_3(X32736,X32737,X32738)),hAPP(c_List_Oset(X32738),X32736)))
        | ~ c_List_Olist__ex(X32738,X32737,X32736) )
      & ( hBOOL(hAPP(X32737,esk478_3(X32736,X32737,X32738)))
        | ~ c_List_Olist__ex(X32738,X32737,X32736) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X32742),X32743),hAPP(c_List_Oset(X32742),X32740)))
        | ~ hBOOL(hAPP(X32741,X32743))
        | c_List_Olist__ex(X32742,X32741,X32740) ) ),
    inference(distribute,[status(thm)],[inference(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_8706,plain,
    ! [X26903] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,X26903)),c_Int_OInteg)),
    inference(variable_rename,[status(thm)],[fact_Rep__Integ]) ).

fof(i_0_8707,plain,
    ! [X26097,X26098,X26099,X26100,X26101] :
      ( ~ c_Finite__Set_Ofolding__one__idem(X26101,X26100,X26099)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26101),X26098))
      | X26098 = c_Orderings_Obot__class_Obot(tc_fun(X26101,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26101),X26097))
      | X26097 = c_Orderings_Obot__class_Obot(tc_fun(X26101,tc_HOL_Obool))
      | hAPP(X26099,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26101,tc_HOL_Obool)),X26098),X26097)) = hAPP(hAPP(X26100,hAPP(X26099,X26098)),hAPP(X26099,X26097)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Ounion__idem])]) ).

fof(i_0_8708,plain,
    ! [X30520,X30521,X30522,X30523,X30524,X30525,X30526] :
      ( ( ~ hBOOL(hAPP(c_List_Olistsp(X30522,X30521),X30520))
        | ~ hBOOL(hAPP(hAPP(c_member(X30522),X30523),hAPP(c_List_Oset(X30522),X30520)))
        | hBOOL(hAPP(X30521,X30523)) )
      & ( hBOOL(hAPP(hAPP(c_member(X30526),esk363_3(X30524,X30525,X30526)),hAPP(c_List_Oset(X30526),X30524)))
        | hBOOL(hAPP(c_List_Olistsp(X30526,X30525),X30524)) )
      & ( ~ hBOOL(hAPP(X30525,esk363_3(X30524,X30525,X30526)))
        | hBOOL(hAPP(c_List_Olistsp(X30526,X30525),X30524)) ) ),
    inference(distribute,[status(thm)],[inference(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_8709,plain,
    ! [X18752,X18753,X18754,X18755] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X18755)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18755),c_Groups_Ozero__class_Ozero(X18755)),X18754))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18755),X18753),X18752))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18755),X18753),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18755),X18754),X18752))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__increasing])]) ).

fof(i_0_8710,plain,
    ! [X18756,X18757,X18758,X18759] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X18759)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18759),c_Groups_Ozero__class_Ozero(X18759)),X18758))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18759),X18757),X18756))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18759),X18757),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18759),X18756),X18758))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__increasing2])]) ).

fof(i_0_8711,plain,
    ! [X17602,X17603,X17604,X17605] :
      ( ~ class_Rings_Olinordered__semidom(X17605)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17605),c_Groups_Ozero__class_Ozero(X17605)),X17604))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17605),X17603),X17602))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17605),X17603),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17605),X17604),X17602))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__add__strict])]) ).

fof(i_0_8712,plain,
    ! [X18935,X18936,X18937,X18938] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X18938)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18938),c_Groups_Ozero__class_Ozero(X18938)),X18937))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18938),X18936),X18935))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18938),X18936),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18938),X18937),X18935))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__increasing])]) ).

fof(i_0_8713,plain,
    ! [X18931,X18932,X18933,X18934] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X18934)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18934),c_Groups_Ozero__class_Ozero(X18934)),X18933))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18934),X18932),X18931))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18934),X18932),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18934),X18933),X18931))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__increasing2])]) ).

fof(i_0_8714,plain,
    ! [X19723,X19724] : X19724 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19723),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19724),X19723))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19724,X19723)),
    inference(variable_rename,[status(thm)],[fact_zmod__zdiv__equality]) ).

cnf(i_0_8715,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_5779]) ).

fof(i_0_8716,plain,
    ! [X23759,X23760,X23761,X23762] :
      ( ~ class_Lattices_Osemilattice__inf(X23762)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23762),X23761),X23760))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23762),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23762),X23761),X23759)),X23760)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__infI1])]) ).

fof(i_0_8717,plain,
    ! [X23763,X23764,X23765,X23766] :
      ( ~ class_Lattices_Osemilattice__inf(X23766)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23766),X23765),X23764))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23766),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23766),X23763),X23765)),X23764)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__infI2])]) ).

fof(i_0_8718,plain,
    ! [X22476,X22477,X22478,X22479] :
      ( ~ class_Orderings_Olinorder(X22479)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22479),X22478),X22477))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22479),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22479),X22478),X22476)),X22477)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__infI1])]) ).

fof(i_0_8719,plain,
    ! [X22472,X22473,X22474,X22475] :
      ( ~ class_Orderings_Olinorder(X22475)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22475),X22474),X22473))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22475),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22475),X22472),X22474)),X22473)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__infI2])]) ).

fof(i_0_8720,plain,
    ! [X23794,X23795,X23796,X23797] :
      ( ~ class_Lattices_Osemilattice__inf(X23797)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23797),X23796),X23795))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23797),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23797),X23796),X23794)),X23795)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__infI1])]) ).

fof(i_0_8721,plain,
    ! [X23790,X23791,X23792,X23793] :
      ( ~ class_Lattices_Osemilattice__inf(X23793)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23793),X23792),X23791))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23793),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23793),X23790),X23792)),X23791)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__infI2])]) ).

fof(i_0_8722,plain,
    ! [X22423,X22424,X22425,X22426] :
      ( ~ class_Orderings_Olinorder(X22426)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22426),X22425),X22424))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22426),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22426),X22425),X22423)),X22424)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oless__infI1])]) ).

fof(i_0_8723,plain,
    ! [X22427,X22428,X22429,X22430] :
      ( ~ class_Orderings_Olinorder(X22430)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22430),X22429),X22428))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22430),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22430),X22427),X22429)),X22428)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oless__infI2])]) ).

fof(i_0_8724,plain,
    ! [X28586,X28587] : hAPP(c_Relation_OImage(tc_List_Olist(X28587),tc_List_Olist(X28587),c_List_Olistrel(X28587,X28586)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X28587)),c_List_Olist_ONil(X28587)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X28587),tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X28587)),c_List_Olist_ONil(X28587)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X28587),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_listrel__Nil]) ).

fof(i_0_8725,plain,
    ! [X26472,X26473,X26474,X26475] :
      ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26474,tc_Nat_Onat),X26472),X26473) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(X26474),X26475),X26473))
        | hAPP(X26472,X26475) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26474),X26473)) )
      & ( hBOOL(hAPP(hAPP(c_member(X26474),esk230_3(X26472,X26473,X26474)),X26473))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26474,tc_Nat_Onat),X26472),X26473) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26474),X26473)) )
      & ( hAPP(X26472,esk230_3(X26472,X26473,X26474)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26474,tc_Nat_Onat),X26472),X26473) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26474),X26473)) ) ),
    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_8726,plain,
    ! [X24682,X24683,X24684,X24685] :
      ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24684,tc_Nat_Onat),X24682),X24683) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(X24684),X24685),X24683))
        | hAPP(X24682,X24685) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24684),X24683)) )
      & ( hBOOL(hAPP(hAPP(c_member(X24684),esk142_3(X24682,X24683,X24684)),X24683))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24684,tc_Nat_Onat),X24682),X24683) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24684),X24683)) )
      & ( hAPP(X24682,esk142_3(X24682,X24683,X24684)) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24684,tc_Nat_Onat),X24682),X24683) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24684),X24683)) ) ),
    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_8727,plain,
    ! [X20098,X20099,X20100,X20101,X20102,X20103,X20104] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20099),X20098))
        | hBOOL(hAPP(X20100,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(X20100,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20099),X20098))) )
      & ( X20099 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20098),X20101)
        | hBOOL(hAPP(X20100,X20101))
        | ~ hBOOL(hAPP(X20100,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20099),X20098))) )
      & ( X20103 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20102),esk65_3(X20102,X20103,X20104))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20103),X20102))
        | hBOOL(hAPP(X20104,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20103),X20102))) )
      & ( ~ hBOOL(hAPP(X20104,esk65_3(X20102,X20103,X20104)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20103),X20102))
        | hBOOL(hAPP(X20104,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20103),X20102))) )
      & ( X20103 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20102),esk65_3(X20102,X20103,X20104))
        | ~ hBOOL(hAPP(X20104,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | hBOOL(hAPP(X20104,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20103),X20102))) )
      & ( ~ hBOOL(hAPP(X20104,esk65_3(X20102,X20103,X20104)))
        | ~ hBOOL(hAPP(X20104,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | hBOOL(hAPP(X20104,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20103),X20102))) ) ),
    inference(distribute,[status(thm)],[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_5780])])])])])]) ).

fof(i_0_8728,plain,
    ! [X20090,X20091,X20092,X20093,X20094,X20095,X20096] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20091),X20090))
        | hBOOL(hAPP(X20092,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(X20092,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20091),X20090))) )
      & ( X20091 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20090),X20093)
        | hBOOL(hAPP(X20092,X20093))
        | ~ hBOOL(hAPP(X20092,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20091),X20090))) )
      & ( X20095 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20094),esk64_3(X20094,X20095,X20096))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20095),X20094))
        | hBOOL(hAPP(X20096,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20095),X20094))) )
      & ( ~ hBOOL(hAPP(X20096,esk64_3(X20094,X20095,X20096)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20095),X20094))
        | hBOOL(hAPP(X20096,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20095),X20094))) )
      & ( X20095 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20094),esk64_3(X20094,X20095,X20096))
        | ~ hBOOL(hAPP(X20096,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | hBOOL(hAPP(X20096,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20095),X20094))) )
      & ( ~ hBOOL(hAPP(X20096,esk64_3(X20094,X20095,X20096)))
        | ~ hBOOL(hAPP(X20096,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | hBOOL(hAPP(X20096,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20095),X20094))) ) ),
    inference(distribute,[status(thm)],[inference(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_8729,plain,
    ! [X26743,X26744] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26744),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X26744,tc_HOL_Obool)),X26743)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X26744),c_Orderings_Otop__class_Otop(tc_fun(X26744,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26744),X26743)) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26744),c_Orderings_Otop__class_Otop(tc_fun(X26744,tc_HOL_Obool))))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X26744),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X26744,tc_HOL_Obool)),X26743)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26744),X26743)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__compl])])]) ).

fof(i_0_8730,plain,
    ! [X20927,X20928] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20928),X20927))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X20927))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20928)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20927))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20928),X20927))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20928)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20927))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20928),X20927))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20928),X20927))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20928)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20927))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X20927))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20928),X20927))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20928)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20927))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__nat__number__of])])]) ).

fof(i_0_8731,plain,
    ! [X23038,X23039,X23040,X23041] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23041,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X23041),X23040),X23039)),X23038) = hAPP(hAPP(c_Set_Oinsert(X23041),X23040),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23041,tc_HOL_Obool)),X23039),X23038)),
    inference(variable_rename,[status(thm)],[fact_Un__insert__left]) ).

fof(i_0_8732,plain,
    ! [X27670,X27671,X27672,X27673] :
      ( ~ c_Finite__Set_Ofun__left__comm__idem(X27673,X27672,X27671)
      | hAPP(c_Fun_Ocomp(X27672,X27672,X27672,hAPP(X27671,X27670)),hAPP(X27671,X27670)) = hAPP(X27671,X27670) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofun__comp__idem])]) ).

cnf(i_0_8733,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_5735]) ).

fof(i_0_8734,plain,
    ! [X17239,X17240] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSemi(X17240,X17239)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X17240)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X17239))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[fact_com_Osize_I12_J]) ).

fof(i_0_8735,plain,
    ! [X22094,X22095,X22096,X22097] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22097,X22096),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22095),X22094)))
      | X22096 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,X22097,X22096) = X22094 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__int__rel__mod])]) ).

fof(i_0_8736,plain,
    ! [X22169,X22170,X22171] : hAPP(c_Product__Type_Osnd(X22171,X22170),X22169) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X22171,X22170,X22170),hAPP(c_COMBK(tc_fun(X22170,X22170),X22171),c_COMBI(X22170))),X22169),
    inference(variable_rename,[status(thm)],[fact_snd__def]) ).

fof(i_0_8737,plain,
    ! [X20884,X20885] :
      ( ~ class_Int_Oring__char__0(X20885)
      | ~ hBOOL(hAPP(hAPP(c_member(X20885),X20884),c_Int_Oring__1__class_OInts(X20885)))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20885),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20885),c_Groups_Oone__class_Oone(X20885)),X20884)),X20884) != c_Groups_Ozero__class_Ozero(X20885) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__odd__nonzero])]) ).

fof(i_0_8738,plain,
    ! [X23732,X23733,X23734] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23734),X23733))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X23734),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23734,tc_HOL_Obool)),X23733),X23732))) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23734),X23732))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X23734),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23734,tc_HOL_Obool)),X23733),X23732))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Int])])]) ).

fof(i_0_8739,plain,
    ! [X23525,X23526,X23527] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23527),X23526))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X23527),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23527,tc_HOL_Obool)),X23526),X23525))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Diff])]) ).

fof(i_0_8740,plain,
    ! [X31463,X31464,X31465,X31466] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31466),X31465),X31464))
        | ~ c_List_Olinorder__class_Osorted(X31466,hAPP(hAPP(c_List_Olist_OCons(X31466),X31465),hAPP(hAPP(c_List_Olist_OCons(X31466),X31464),X31463)))
        | ~ class_Orderings_Olinorder(X31466) )
      & ( c_List_Olinorder__class_Osorted(X31466,hAPP(hAPP(c_List_Olist_OCons(X31466),X31464),X31463))
        | ~ c_List_Olinorder__class_Osorted(X31466,hAPP(hAPP(c_List_Olist_OCons(X31466),X31465),hAPP(hAPP(c_List_Olist_OCons(X31466),X31464),X31463)))
        | ~ class_Orderings_Olinorder(X31466) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31466),X31465),X31464))
        | ~ c_List_Olinorder__class_Osorted(X31466,hAPP(hAPP(c_List_Olist_OCons(X31466),X31464),X31463))
        | c_List_Olinorder__class_Osorted(X31466,hAPP(hAPP(c_List_Olist_OCons(X31466),X31465),hAPP(hAPP(c_List_Olist_OCons(X31466),X31464),X31463)))
        | ~ class_Orderings_Olinorder(X31466) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__many__eq])])]) ).

fof(i_0_8741,plain,
    ! [X31459,X31460,X31461,X31462] :
      ( ~ class_Orderings_Olinorder(X31462)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31462),X31461),X31460))
      | ~ c_List_Olinorder__class_Osorted(X31462,hAPP(hAPP(c_List_Olist_OCons(X31462),X31460),X31459))
      | c_List_Olinorder__class_Osorted(X31462,hAPP(hAPP(c_List_Olist_OCons(X31462),X31461),hAPP(hAPP(c_List_Olist_OCons(X31462),X31460),X31459))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__many])]) ).

fof(i_0_8742,plain,
    ! [X21879,X21880,X21881,X21882] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X21882,X21881),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X21880),X21879)))
      | c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21882,X21881) = X21879 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__eq])]) ).

fof(i_0_8743,plain,
    ! [X19441,X19442] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19442))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19442,X19441)),X19442)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__le__nonneg__dividend])]) ).

fof(i_0_8744,plain,
    ! [X19704,X19705] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19705))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19704,X19705)),X19705)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__le__divisor])]) ).

fof(i_0_8745,plain,
    ! [X19461,X19462] :
      ( ( 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,X19461,X19462)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19462)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19461,X19462)),X19462))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19462)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__mod__conj])])]) ).

fof(i_0_8746,plain,
    ! [X19445,X19446] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19446))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19445,X19446)),X19446)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__mod__bound])]) ).

fof(i_0_8747,plain,
    ! [X19611,X19612] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19612))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19611,X19612)),X19612)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__less__divisor])]) ).

fof(i_0_8748,plain,
    ! [X31455,X31456] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31456)),c_List_Oremdups(X31456,X31455))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31456)),X31455))),
    inference(variable_rename,[status(thm)],[fact_length__remdups__leq]) ).

fof(i_0_8749,plain,
    ! [X28898,X28899] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X28899),hAPP(c_List_Oset(X28899),X28898))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28899)),X28898))),
    inference(variable_rename,[status(thm)],[fact_card__length]) ).

fof(i_0_8750,plain,
    ! [X25443,X25444,X25445,X25446,X25447] :
      ( hAPP(c_Set_Oimage(X25447,X25446,X25445),X25444) != X25443
      | hAPP(c_Set_Oimage(tc_fun(X25447,tc_HOL_Obool),tc_fun(X25446,tc_HOL_Obool),c_Set_Oimage(X25447,X25446,X25445)),hAPP(c_Set_OPow(X25447),X25444)) = hAPP(c_Set_OPow(X25446),X25443) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__Pow__surj])]) ).

fof(i_0_8751,plain,
    ! [X29357,X29358,X29359] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X29359),X29358),hAPP(c_List_Oset(X29359),X29357)))
        | ~ hBOOL(hAPP(c_List_Odistinct(X29359),hAPP(hAPP(c_List_Olist_OCons(X29359),X29358),X29357))) )
      & ( hBOOL(hAPP(c_List_Odistinct(X29359),X29357))
        | ~ hBOOL(hAPP(c_List_Odistinct(X29359),hAPP(hAPP(c_List_Olist_OCons(X29359),X29358),X29357))) )
      & ( hBOOL(hAPP(hAPP(c_member(X29359),X29358),hAPP(c_List_Oset(X29359),X29357)))
        | ~ hBOOL(hAPP(c_List_Odistinct(X29359),X29357))
        | hBOOL(hAPP(c_List_Odistinct(X29359),hAPP(hAPP(c_List_Olist_OCons(X29359),X29358),X29357))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5781])])]) ).

fof(i_0_8752,plain,
    ! [X27181,X27182,X27183,X27184] :
      ( hAPP(c_Set_Oimage(X27184,X27183,X27182),c_Orderings_Otop__class_Otop(tc_fun(X27184,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X27183,tc_HOL_Obool))
      | hAPP(c_Set_Oimage(X27184,X27183,X27182),hAPP(c_Set_Ovimage(X27184,X27183,X27182),X27181)) = X27181 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_surj__image__vimage__eq])]) ).

cnf(i_0_8753,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_5714]) ).

fof(i_0_8754,plain,
    ! [X22098,X22099,X22100,X22101] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22101,X22100),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22099),X22098)))
      | X22100 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X22101),X22100) = X22099 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__int__rel__div])]) ).

fof(i_0_8755,plain,
    ! [X20319,X20320,X20321] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X20321)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20321),hAPP(c_Groups_Oabs__class_Oabs(X20321),X20320)),X20319))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20321),hAPP(c_Groups_Ouminus__class_Ouminus(X20321),X20320)),X20319)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__le__D2])]) ).

fof(i_0_8756,plain,
    ! [X18677,X18678,X18679] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18679),hAPP(c_Groups_Ouminus__class_Ouminus(X18679),X18678)),X18677))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18679),hAPP(c_Groups_Ouminus__class_Ouminus(X18679),X18677)),X18678))
        | ~ class_Groups_Oordered__ab__group__add(X18679) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18679),hAPP(c_Groups_Ouminus__class_Ouminus(X18679),X18677)),X18678))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18679),hAPP(c_Groups_Ouminus__class_Ouminus(X18679),X18678)),X18677))
        | ~ class_Groups_Oordered__ab__group__add(X18679) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__le__iff])])]) ).

fof(i_0_8757,plain,
    ! [X18232,X18233,X18234] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18234),hAPP(c_Groups_Ouminus__class_Ouminus(X18234),X18233)),X18232))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18234),hAPP(c_Groups_Ouminus__class_Ouminus(X18234),X18232)),X18233))
        | ~ class_Groups_Oordered__ab__group__add(X18234) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18234),hAPP(c_Groups_Ouminus__class_Ouminus(X18234),X18232)),X18233))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18234),hAPP(c_Groups_Ouminus__class_Ouminus(X18234),X18233)),X18232))
        | ~ class_Groups_Oordered__ab__group__add(X18234) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__less__iff])])]) ).

fof(i_0_8758,plain,
    ! [X19467,X19468] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19467,X19468)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19468),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19468),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19467,X19468)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19468),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_8759,plain,
    ! [X19465,X19466] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19466),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,X19465,X19466)),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_8760,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_5782]) ).

fof(i_0_8761,plain,
    ! [X27700,X27701,X27702,X27703] : hAPP(c_Set_Ovimage(X27703,X27702,X27701),hAPP(c_Set_OCollect(X27702),X27700)) = hAPP(c_Set_OCollect(X27703),hAPP(hAPP(c_COMBB(X27702,tc_HOL_Obool,X27703),X27700),X27701)),
    inference(variable_rename,[status(thm)],[fact_vimage__Collect__eq]) ).

fof(i_0_8762,plain,
    ! [X21883,X21884,X21885,X21886] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X21886,X21885),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X21884),X21883)))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X21886),X21885) = X21884 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__eq])]) ).

fof(i_0_8763,plain,
    ! [X25765,X25766,X25767,X25768] :
      ( ~ c_Fun_Oinj__on(X25768,X25767,X25766,X25765)
      | hAPP(c_Finite__Set_Ocard(X25767),hAPP(c_Set_Oimage(X25768,X25767,X25766),X25765)) = hAPP(c_Finite__Set_Ocard(X25768),X25765) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__image])]) ).

fof(i_0_8764,plain,
    ! [X28816,X28817,X28818,X28819] : hAPP(hAPP(c_List_Otake(X28819),X28818),hAPP(hAPP(c_List_Odrop(X28819),X28817),X28816)) = hAPP(hAPP(c_List_Odrop(X28819),X28817),hAPP(hAPP(c_List_Otake(X28819),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X28818),X28817)),X28816)),
    inference(variable_rename,[status(thm)],[fact_take__drop]) ).

fof(i_0_8765,plain,
    ! [X31486,X31487,X31488,X31489,X31490] :
      ( ~ class_Orderings_Olinorder(X31490)
      | ~ c_List_Olinorder__class_Osorted(X31490,hAPP(hAPP(c_List_Omap(X31489,X31490),X31488),X31487))
      | c_List_Olinorder__class_Osorted(X31490,hAPP(hAPP(c_List_Omap(X31489,X31490),X31488),hAPP(c_List_Ofilter(X31489,X31486),X31487))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__filter])]) ).

fof(i_0_8766,plain,
    ! [X20187,X20188,X20189] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20189,X20188) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20187,X20188)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20187),X20189))
      | X20189 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20187),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20188),esk67_3(X20187,X20188,X20189))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mod__eq__lemma])])]) ).

fof(i_0_8767,plain,
    ! [X31744,X31745,X31746,X31747,X31748,X31749,X31750] :
      ( ( c_List_OtakeWhile(X31746,X31745,X31744) != X31744
        | ~ hBOOL(hAPP(hAPP(c_member(X31746),X31747),hAPP(c_List_Oset(X31746),X31744)))
        | hBOOL(hAPP(X31745,X31747)) )
      & ( hBOOL(hAPP(hAPP(c_member(X31750),esk397_3(X31748,X31749,X31750)),hAPP(c_List_Oset(X31750),X31748)))
        | c_List_OtakeWhile(X31750,X31749,X31748) = X31748 )
      & ( ~ hBOOL(hAPP(X31749,esk397_3(X31748,X31749,X31750)))
        | c_List_OtakeWhile(X31750,X31749,X31748) = X31748 ) ),
    inference(distribute,[status(thm)],[inference(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_8768,plain,
    ! [X18742,X18743] :
      ( ( ~ 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),X18742)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18743),c_Groups_Ozero__class_Ozero(X18743)),X18742))
        | ~ class_Groups_Olinordered__ab__group__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)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18743),X18742),X18742)))
        | ~ class_Groups_Olinordered__ab__group__add(X18743) ) ),
    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_8769,plain,
    ! [X17475,X17476] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17476),c_Groups_Ozero__class_Ozero(X17476)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17476),X17475),X17475)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17476),c_Groups_Ozero__class_Ozero(X17476)),X17475))
        | ~ class_Groups_Olinordered__ab__group__add(X17476) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17476),c_Groups_Ozero__class_Ozero(X17476)),X17475))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17476),c_Groups_Ozero__class_Ozero(X17476)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17476),X17475),X17475)))
        | ~ class_Groups_Olinordered__ab__group__add(X17476) ) ),
    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_8770,plain,
    ! [X33186,X33187,X33188,X33190,X33191,X33192,X33193] :
      ( ( hBOOL(hAPP(hAPP(c_member(X33188),esk508_3(X33186,X33187,X33188)),hAPP(c_List_Oset(X33188),X33187)))
        | c_List_Olist__all(X33188,X33186,X33187) )
      & ( ~ hBOOL(hAPP(X33186,esk508_3(X33186,X33187,X33188)))
        | c_List_Olist__all(X33188,X33186,X33187) )
      & ( ~ c_List_Olist__all(X33192,X33190,X33191)
        | ~ hBOOL(hAPP(hAPP(c_member(X33192),X33193),hAPP(c_List_Oset(X33192),X33191)))
        | hBOOL(hAPP(X33190,X33193)) ) ),
    inference(distribute,[status(thm)],[inference(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_8771,plain,
    ! [X33194,X33195,X33196,X33197,X33198,X33199,X33200] :
      ( ( ~ c_List_Olist__all(X33196,X33195,X33194)
        | ~ hBOOL(hAPP(hAPP(c_member(X33196),X33197),hAPP(c_List_Oset(X33196),X33194)))
        | hBOOL(hAPP(X33195,X33197)) )
      & ( hBOOL(hAPP(hAPP(c_member(X33200),esk509_3(X33198,X33199,X33200)),hAPP(c_List_Oset(X33200),X33198)))
        | c_List_Olist__all(X33200,X33199,X33198) )
      & ( ~ hBOOL(hAPP(X33199,esk509_3(X33198,X33199,X33200)))
        | c_List_Olist__all(X33200,X33199,X33198) ) ),
    inference(distribute,[status(thm)],[inference(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_8772,plain,
    ! [X33173,X33174,X33175,X33176,X33177,X33178,X33179] :
      ( ( ~ c_List_Olist__all(X33175,X33174,X33173)
        | ~ hBOOL(hAPP(hAPP(c_member(X33175),X33176),hAPP(c_List_Oset(X33175),X33173)))
        | hBOOL(hAPP(X33174,X33176)) )
      & ( hBOOL(hAPP(hAPP(c_member(X33179),esk507_3(X33177,X33178,X33179)),hAPP(c_List_Oset(X33179),X33177)))
        | c_List_Olist__all(X33179,X33178,X33177) )
      & ( ~ hBOOL(hAPP(X33178,esk507_3(X33177,X33178,X33179)))
        | c_List_Olist__all(X33179,X33178,X33177) ) ),
    inference(distribute,[status(thm)],[inference(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_8773,plain,
    ! [X17477,X17478] :
      ( ( ~ 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),X17478),X17477)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17478))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17477)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17478))
        | 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),X17478),X17477))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17477))
        | 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),X17478),X17477))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__gr__0])])]) ).

fof(i_0_8774,plain,
    ! [X19202,X19203,X19204] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X19204),tc_HOL_Obool)),X19203),X19202))
      | c_Hoare__Mirabelle_Ohoare__derivs(X19204,X19202,X19203) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_asm])]) ).

cnf(i_0_8775,plain,
    c_List_OdropWhile(X1,X2,c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
    inference(split_conjunct,[status(thm)],[i_0_5783]) ).

fof(i_0_8776,plain,
    ! [X19873,X19874,X19875,X19876,X19877,X19878] :
      ( ~ class_Divides_Oring__div(X19878)
      | c_Divides_Odiv__class_Omod(X19878,X19877,X19876) != c_Divides_Odiv__class_Omod(X19878,X19875,X19876)
      | c_Divides_Odiv__class_Omod(X19878,X19874,X19876) != c_Divides_Odiv__class_Omod(X19878,X19873,X19876)
      | c_Divides_Odiv__class_Omod(X19878,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19878),X19877),X19874),X19876) = c_Divides_Odiv__class_Omod(X19878,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19878),X19875),X19873),X19876) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__diff__cong])]) ).

fof(i_0_8777,plain,
    ! [X19392,X19393,X19394,X19395,X19396,X19397] :
      ( ~ class_Divides_Osemiring__div(X19397)
      | c_Divides_Odiv__class_Omod(X19397,X19396,X19395) != c_Divides_Odiv__class_Omod(X19397,X19394,X19395)
      | c_Divides_Odiv__class_Omod(X19397,X19393,X19395) != c_Divides_Odiv__class_Omod(X19397,X19392,X19395)
      | c_Divides_Odiv__class_Omod(X19397,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19397),X19396),X19393),X19395) = c_Divides_Odiv__class_Omod(X19397,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19397),X19394),X19392),X19395) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__cong])]) ).

fof(i_0_8778,plain,
    ! [X19362,X19363,X19364,X19365,X19366,X19367] :
      ( ~ class_Divides_Osemiring__div(X19367)
      | c_Divides_Odiv__class_Omod(X19367,X19366,X19365) != c_Divides_Odiv__class_Omod(X19367,X19364,X19365)
      | c_Divides_Odiv__class_Omod(X19367,X19363,X19365) != c_Divides_Odiv__class_Omod(X19367,X19362,X19365)
      | c_Divides_Odiv__class_Omod(X19367,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19367),X19366),X19363),X19365) = c_Divides_Odiv__class_Omod(X19367,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19367),X19364),X19362),X19365) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__cong])]) ).

fof(i_0_8779,plain,
    ! [X21592,X21593,X21594,X21595] :
      ( ~ class_Fields_Ofield(X21595)
      | X21594 = c_Groups_Ozero__class_Ozero(X21595)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21593),X21592))
      | hAPP(hAPP(c_Power_Opower__class_Opower(X21595),X21594),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21592),X21593)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21595),hAPP(hAPP(c_Power_Opower__class_Opower(X21595),X21594),X21592)),hAPP(hAPP(c_Power_Opower__class_Opower(X21595),X21594),X21593)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__diff])]) ).

fof(i_0_8780,plain,
    ! [X20860,X20861,X20862] :
      ( hBOOL(hAPP(hAPP(c_member(X20862),X20861),X20860))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20862,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X20862),X20861),X20860)),hAPP(hAPP(c_Set_Oinsert(X20862),X20861),c_Orderings_Obot__class_Obot(tc_fun(X20862,tc_HOL_Obool)))) = X20860 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5784])]) ).

fof(i_0_8781,plain,
    ! [X26323,X26324,X26325,X26326,X26327] :
      ( ~ class_Groups_Ocomm__monoid__add(X26327)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26326),X26325))
      | hBOOL(hAPP(hAPP(c_member(X26326),X26324),X26325))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26326,X26327),X26323),hAPP(hAPP(c_Set_Oinsert(X26326),X26324),X26325)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26327),hAPP(X26323,X26324)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26326,X26327),X26323),X26325)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5785])]) ).

fof(i_0_8782,plain,
    ! [X26318,X26319,X26320,X26321,X26322] :
      ( ~ class_Groups_Ocomm__monoid__add(X26322)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26321),X26320))
      | hBOOL(hAPP(hAPP(c_member(X26321),X26319),X26320))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26321,X26322),X26318),hAPP(hAPP(c_Set_Oinsert(X26321),X26319),X26320)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X26322),hAPP(X26318,X26319)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26321,X26322),X26318),X26320)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5786])]) ).

fof(i_0_8783,plain,
    ! [X24740,X24741,X24742,X24743,X24744] :
      ( ~ class_Groups_Ocomm__monoid__mult(X24744)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24743),X24742))
      | hBOOL(hAPP(hAPP(c_member(X24743),X24741),X24742))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24743,X24744),X24740),hAPP(hAPP(c_Set_Oinsert(X24743),X24741),X24742)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24744),hAPP(X24740,X24741)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24743,X24744),X24740),X24742)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5787])]) ).

fof(i_0_8784,plain,
    ! [X24735,X24736,X24737,X24738,X24739] :
      ( ~ class_Groups_Ocomm__monoid__mult(X24739)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24738),X24737))
      | hBOOL(hAPP(hAPP(c_member(X24738),X24736),X24737))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24738,X24739),X24735),hAPP(hAPP(c_Set_Oinsert(X24738),X24736),X24737)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24739),hAPP(X24735,X24736)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24738,X24739),X24735),X24737)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5788])]) ).

fof(i_0_8785,plain,
    ! [X22086,X22087,X22088] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22088),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22087)),X22086))
      | hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22088,X22087),hAPP(c_Divides_OnegateSnd,X22086))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__int__rel__neg])]) ).

fof(i_0_8786,plain,
    ! [X17179,X17180,X17181,X17182] :
      ( ~ c_Natural_Oevaln(X17182,X17181,X17180,X17179)
      | c_Natural_Oevaln(X17182,X17181,hAPP(c_Nat_OSuc,X17180),X17179) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evaln__Suc])]) ).

fof(i_0_8787,plain,
    ! [X20847,X20848,X20849,X20850] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X20850),X20849),X20848))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20850,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X20850),X20849),X20847)),X20848) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20850,tc_HOL_Obool)),X20847),X20848) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__Diff1])]) ).

fof(i_0_8788,plain,
    ! [X19915,X19916,X19917] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19917),X19916))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19917),X19915))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19916),X19917)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19915),X19917)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19916),X19915) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat_Odiff__diff__eq])]) ).

fof(i_0_8789,plain,
    ! [X31734,X31735,X31736] : c_List_OtakeWhile(X31736,X31735,X31734) = hAPP(hAPP(c_List_Otake(X31736),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31736)),c_List_OtakeWhile(X31736,X31735,X31734))),X31734),
    inference(variable_rename,[status(thm)],[fact_takeWhile__eq__take]) ).

fof(i_0_8790,plain,
    ! [X25769,X25770,X25771,X25773,X25774,X25775] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk217_2(X25769,X25770)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25770)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25771),X25770))
        | ~ hBOOL(hAPP(X25769,X25771)) )
      & ( hBOOL(hAPP(X25769,esk217_2(X25769,X25770)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25771),X25770))
        | ~ hBOOL(hAPP(X25769,X25771)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk218_2(X25773,X25774)),X25774))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X25775),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25774)))
        | ~ hBOOL(hAPP(X25773,X25775)) )
      & ( hBOOL(hAPP(X25773,esk218_2(X25773,X25774)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X25775),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25774)))
        | ~ hBOOL(hAPP(X25773,X25775)) ) ),
    inference(distribute,[status(thm)],[inference(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_8791,plain,
    ! [X19884,X19885,X19886] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19886)),X19885)),hAPP(c_Nat_OSuc,X19884)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19886),X19885)),X19884),
    inference(variable_rename,[status(thm)],[fact_Suc__diff__diff]) ).

fof(i_0_8792,plain,
    ! [X20592,X20593,X20594,X20595] :
      ( ~ class_Rings_Olinordered__semidom(X20595)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X20595),X20594),hAPP(c_Nat_OSuc,X20593)) != hAPP(hAPP(c_Power_Opower__class_Opower(X20595),X20592),hAPP(c_Nat_OSuc,X20593))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20595),c_Groups_Ozero__class_Ozero(X20595)),X20594))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20595),c_Groups_Ozero__class_Ozero(X20595)),X20592))
      | X20594 = X20592 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__inject__base])]) ).

cnf(i_0_8793,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_5789]) ).

fof(i_0_8794,plain,
    ! [X19022,X19023] :
      ( ( X19023 = 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),X19023)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19022)))) )
      & ( X19022 = 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),X19023)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19022)))) )
      & ( X19023 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X19022 != 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),X19023)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19022)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__zle__neg])])]) ).

fof(i_0_8795,plain,
    ! [X28234] :
      ( ~ class_Orderings_Owellorder(X28234)
      | c_Wellfounded_Owf(X28234,hAPP(c_Set_OCollect(tc_prod(X28234,X28234)),hAPP(c_Product__Type_Oprod_Oprod__case(X28234,X28234,tc_HOL_Obool),c_Orderings_Oord__class_Oless(X28234)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf])]) ).

fof(i_0_8796,plain,
    ! [X31181,X31182,X31183,X31184,X31185,X31186,X31187] :
      ( ( hAPP(c_List_Ofilter(X31183,X31182),X31181) != c_List_Olist_ONil(X31183)
        | ~ hBOOL(hAPP(hAPP(c_member(X31183),X31184),hAPP(c_List_Oset(X31183),X31181)))
        | ~ hBOOL(hAPP(X31182,X31184)) )
      & ( hBOOL(hAPP(hAPP(c_member(X31187),esk383_3(X31185,X31186,X31187)),hAPP(c_List_Oset(X31187),X31185)))
        | hAPP(c_List_Ofilter(X31187,X31186),X31185) = c_List_Olist_ONil(X31187) )
      & ( hBOOL(hAPP(X31186,esk383_3(X31185,X31186,X31187)))
        | hAPP(c_List_Ofilter(X31187,X31186),X31185) = c_List_Olist_ONil(X31187) ) ),
    inference(distribute,[status(thm)],[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_5790])])])])])]) ).

fof(i_0_8797,plain,
    ! [X23777,X23778,X23779,X23780] :
      ( ~ class_Lattices_Osemilattice__inf(X23780)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23780),X23779),X23778))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23780),X23779),X23777))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23780),X23779),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23780),X23778),X23777))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__greatest])]) ).

fof(i_0_8798,plain,
    ! [X23773,X23774,X23775,X23776] :
      ( ~ class_Lattices_Osemilattice__inf(X23776)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23776),X23775),X23774))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23776),X23775),X23773))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23776),X23775),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23776),X23774),X23773))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__infI])]) ).

fof(i_0_8799,plain,
    ! [X23755,X23756,X23757,X23758] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23758),X23757),X23756))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23758),X23757),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23758),X23756),X23755)))
        | ~ class_Lattices_Osemilattice__inf(X23758) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23758),X23757),X23755))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23758),X23757),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23758),X23756),X23755)))
        | ~ class_Lattices_Osemilattice__inf(X23758) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23758),X23757),X23756))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23758),X23757),X23755))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23758),X23757),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23758),X23756),X23755)))
        | ~ class_Lattices_Osemilattice__inf(X23758) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__inf__iff])])]) ).

fof(i_0_8800,plain,
    ! [X22480,X22481,X22482,X22483] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22483),X22482),X22481))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22483),X22482),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22483),X22481),X22480)))
        | ~ class_Orderings_Olinorder(X22483) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22483),X22482),X22480))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22483),X22482),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22483),X22481),X22480)))
        | ~ class_Orderings_Olinorder(X22483) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22483),X22482),X22481))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22483),X22482),X22480))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22483),X22482),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22483),X22481),X22480)))
        | ~ class_Orderings_Olinorder(X22483) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__inf__iff])])]) ).

fof(i_0_8801,plain,
    ! [X22462,X22463,X22464,X22465] :
      ( ~ class_Orderings_Olinorder(X22465)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22465),X22464),X22463))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22465),X22464),X22462))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22465),X22464),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22465),X22463),X22462))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__infI])]) ).

fof(i_0_8802,plain,
    ! [X22458,X22459,X22460,X22461] :
      ( ~ class_Orderings_Olinorder(X22461)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22461),X22460),X22459))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22461),X22460),X22458))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22461),X22460),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22461),X22459),X22458))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__greatest])]) ).

fof(i_0_8803,plain,
    ! [X22431,X22432,X22433,X22434] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22434),X22433),X22432))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22434),X22433),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22434),X22432),X22431)))
        | ~ class_Orderings_Olinorder(X22434) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22434),X22433),X22431))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22434),X22433),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22434),X22432),X22431)))
        | ~ class_Orderings_Olinorder(X22434) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22434),X22433),X22432))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22434),X22433),X22431))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22434),X22433),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22434),X22432),X22431)))
        | ~ class_Orderings_Olinorder(X22434) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__less__iff__conj])])]) ).

fof(i_0_8804,plain,
    ! [X18399,X18400] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18400)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18399)))),
    inference(variable_rename,[status(thm)],[i_0_5791]) ).

fof(i_0_8805,plain,
    ! [X19031,X19032,X19033] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19033))
      | X19033 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19032),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19033),X19031))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19032))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19031),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_8806,plain,
    ! [X31202,X31203,X31204,X31205,X31206,X31207,X31208] :
      ( ( hAPP(c_List_Ofilter(X31204,X31203),X31202) != X31202
        | ~ hBOOL(hAPP(hAPP(c_member(X31204),X31205),hAPP(c_List_Oset(X31204),X31202)))
        | hBOOL(hAPP(X31203,X31205)) )
      & ( hBOOL(hAPP(hAPP(c_member(X31208),esk384_3(X31206,X31207,X31208)),hAPP(c_List_Oset(X31208),X31206)))
        | hAPP(c_List_Ofilter(X31208,X31207),X31206) = X31206 )
      & ( ~ hBOOL(hAPP(X31207,esk384_3(X31206,X31207,X31208)))
        | hAPP(c_List_Ofilter(X31208,X31207),X31206) = X31206 ) ),
    inference(distribute,[status(thm)],[inference(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_8807,plain,
    ! [X19443,X19444] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19444))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19443))
      | 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,X19444,X19443))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__nat__int__function__closures_I2_J])]) ).

fof(i_0_8808,plain,
    ! [X17078,X17079,X17080,X17081,X17082] :
      ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17082),X17081),X17080))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17079),X17080),X17078))
      | hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(X17082,X17079)),X17081),X17078)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evalc_OSemi])]) ).

fof(i_0_8809,plain,
    ! [X28725,X28726,X28727,X28728] : hAPP(hAPP(c_List_Onth(X28728),hAPP(hAPP(c_List_Oappend(X28728),X28727),X28726)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28728)),X28727)),X28725)) = hAPP(hAPP(c_List_Onth(X28728),X28726),X28725),
    inference(variable_rename,[status(thm)],[fact_nth__append__length__plus]) ).

cnf(i_0_8810,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_5792]) ).

fof(i_0_8811,plain,
    ! [X29274,X29275,X29276,X29277,X29278,X29279] : hAPP(c_List_Olist_Olist__case(X29279,X29278,X29277,X29276),hAPP(hAPP(c_List_Olist_OCons(X29278),X29275),X29274)) = hAPP(hAPP(X29276,X29275),X29274),
    inference(variable_rename,[status(thm)],[fact_list_Osimps_I5_J]) ).

fof(i_0_8812,plain,
    ! [X22894,X22895,X22896,X22897] :
      ( ~ hBOOL(hAPP(X22897,X22896))
      | hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22895,tc_HOL_Obool)),X22897),X22894),X22896)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup1I1])]) ).

fof(i_0_8813,plain,
    ! [X22805,X22806,X22807,X22808] :
      ( ( ~ hBOOL(hAPP(X22808,X22807))
        | hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22805,tc_HOL_Obool)),X22806),X22808),X22807)) )
      & ( ~ hBOOL(hAPP(X22806,X22807))
        | hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22805,tc_HOL_Obool)),X22806),X22808),X22807)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5793])])]) ).

fof(i_0_8814,plain,
    ! [X22898,X22899,X22900,X22901] :
      ( ~ hBOOL(hAPP(X22901,X22900))
      | hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22899,tc_HOL_Obool)),X22898),X22901),X22900)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup1I2])]) ).

fof(i_0_8815,plain,
    ! [X20619,X20620,X20621] :
      ( ~ class_Rings_Olinordered__idom(X20621)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20621),c_Groups_Ozero__class_Ozero(X20621)),hAPP(hAPP(c_Power_Opower__class_Opower(X20621),hAPP(c_Groups_Oabs__class_Oabs(X20621),X20620)),X20619))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__power__abs])]) ).

fof(i_0_8816,plain,
    ! [X20111,X20112,X20113] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20113),X20112))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20111),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20112),X20113))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20111),X20113)),hAPP(c_Nat_OSuc,X20112)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__Suc__diff__eq1])]) ).

fof(i_0_8817,plain,
    ! [X19084,X19085] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19085,tc_HOL_Obool)),X19084),c_Orderings_Obot__class_Obot(tc_fun(X19085,tc_HOL_Obool))))
        | X19084 = c_Orderings_Obot__class_Obot(tc_fun(X19085,tc_HOL_Obool)) )
      & ( X19084 != c_Orderings_Obot__class_Obot(tc_fun(X19085,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19085,tc_HOL_Obool)),X19084),c_Orderings_Obot__class_Obot(tc_fun(X19085,tc_HOL_Obool)))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__empty])]) ).

fof(i_0_8818,plain,
    ! [X31993,X31994] :
      ( ~ c_Wellfounded_OwfP(X31994,X31993)
      | c_Wellfounded_Oacyclic(X31994,hAPP(c_Set_OCollect(tc_prod(X31994,X31994)),hAPP(c_Product__Type_Oprod_Oprod__case(X31994,X31994,tc_HOL_Obool),X31993))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wfP__acyclicP])]) ).

fof(i_0_8819,plain,
    ! [X28028,X28029,X28030,X28031] : hAPP(hAPP(c_Relation_Orel__comp(X28031,X28030,X28029),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X28031,X28030),tc_HOL_Obool))),X28028) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X28031,X28029),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_rel__comp__empty1]) ).

fof(i_0_8820,plain,
    ! [X19793,X19794] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X19793,X19794) != 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),X19793)),X19794) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19793),X19794))
        | X19794 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X19793,X19794) = 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),X19793)),X19794) = 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),X19793),X19794))),c_Groups_Oone__class_Oone(tc_Int_Oint))
        | X19794 = 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_8821,plain,
    ! [X30478,X30479,X30480,X30481,X30482,X30483,X30484] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X30482),X30483),hAPP(c_List_Oset(X30482),X30479)))
        | hBOOL(hAPP(X30481,X30483))
        | c_List_Opartition(X30482,X30481,X30480) != hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30482),tc_List_Olist(X30482)),X30479),X30478) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X30482),X30484),hAPP(c_List_Oset(X30482),X30478)))
        | ~ hBOOL(hAPP(X30481,X30484))
        | c_List_Opartition(X30482,X30481,X30480) != hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30482),tc_List_Olist(X30482)),X30479),X30478) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5794])])])]) ).

fof(i_0_8822,plain,
    ! [X19272,X19273,X19274] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19274),hAPP(c_Groups_Ouminus__class_Ouminus(X19274),X19273)),hAPP(c_Groups_Ouminus__class_Ouminus(X19274),X19272)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19274),X19272),X19273))
        | ~ class_Lattices_Oboolean__algebra(X19274) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19274),X19272),X19273))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19274),hAPP(c_Groups_Ouminus__class_Ouminus(X19274),X19273)),hAPP(c_Groups_Ouminus__class_Ouminus(X19274),X19272)))
        | ~ class_Lattices_Oboolean__algebra(X19274) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__le__compl__iff])])]) ).

fof(i_0_8823,plain,
    ! [X18680,X18681,X18682] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18682),hAPP(c_Groups_Ouminus__class_Ouminus(X18682),X18681)),hAPP(c_Groups_Ouminus__class_Ouminus(X18682),X18680)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18682),X18680),X18681))
        | ~ class_Groups_Oordered__ab__group__add(X18682) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18682),X18680),X18681))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18682),hAPP(c_Groups_Ouminus__class_Ouminus(X18682),X18681)),hAPP(c_Groups_Ouminus__class_Ouminus(X18682),X18680)))
        | ~ class_Groups_Oordered__ab__group__add(X18682) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__le__iff__le])])]) ).

fof(i_0_8824,plain,
    ! [X18229,X18230,X18231] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18231),hAPP(c_Groups_Ouminus__class_Ouminus(X18231),X18230)),hAPP(c_Groups_Ouminus__class_Ouminus(X18231),X18229)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18231),X18229),X18230))
        | ~ class_Groups_Oordered__ab__group__add(X18231) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18231),X18229),X18230))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18231),hAPP(c_Groups_Ouminus__class_Ouminus(X18231),X18230)),hAPP(c_Groups_Ouminus__class_Ouminus(X18231),X18229)))
        | ~ class_Groups_Oordered__ab__group__add(X18231) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__less__iff__less])])]) ).

fof(i_0_8825,plain,
    ! [X25777,X25778,X25780,X25781,X25782,X25784] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk219_2(X25777,X25778)),X25778))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X25780),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25778)))
        | hBOOL(hAPP(X25777,X25780)) )
      & ( ~ hBOOL(hAPP(X25777,esk219_2(X25777,X25778)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X25780),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25778)))
        | hBOOL(hAPP(X25777,X25780)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk220_2(X25781,X25782)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25782)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25784),X25782))
        | hBOOL(hAPP(X25781,X25784)) )
      & ( ~ hBOOL(hAPP(X25781,esk220_2(X25781,X25782)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25784),X25782))
        | hBOOL(hAPP(X25781,X25784)) ) ),
    inference(distribute,[status(thm)],[inference(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_8826,plain,
    ! [X20604,X20605,X20606] :
      ( ~ class_Rings_Olinordered__semidom(X20606)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20606),c_Groups_Oone__class_Oone(X20606)),X20605))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20606),c_Groups_Oone__class_Oone(X20606)),hAPP(hAPP(c_Power_Opower__class_Opower(X20606),X20605),hAPP(c_Nat_OSuc,X20604)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__gt1])]) ).

fof(i_0_8827,plain,
    ! [X19034,X19035,X19036] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19036))
      | X19036 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19035),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19036),X19034))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19035),X19036))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X19034)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_self__quotient__aux1])]) ).

fof(i_0_8828,plain,
    ! [X33362,X33363,X33364,X33365,X33366] :
      ( ~ hBOOL(hAPP(hAPP(X33366,X33365),X33364))
      | hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X33363,X33362,X33366),X33364),X33365)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_conversep_Ointros])]) ).

cnf(i_0_8829,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_5795]) ).

cnf(i_0_8830,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_5796]) ).

fof(i_0_8831,plain,
    ! [X20929,X20930] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20930)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20929)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20930),X20929))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20930),c_Int_OPls)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20930),X20929))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20930)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20929))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20930),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),X20930)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20929))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5797])])]) ).

fof(i_0_8832,plain,
    ! [X20353,X20354,X20355] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20355),hAPP(c_Int_Onumber__class_Onumber__of(X20355),X20354)),hAPP(c_Int_Onumber__class_Onumber__of(X20355),X20353)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20354),X20353))
        | ~ class_Int_Onumber__ring(X20355)
        | ~ class_Rings_Olinordered__idom(X20355) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20354),X20353))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20355),hAPP(c_Int_Onumber__class_Onumber__of(X20355),X20354)),hAPP(c_Int_Onumber__class_Onumber__of(X20355),X20353)))
        | ~ class_Int_Onumber__ring(X20355)
        | ~ class_Rings_Olinordered__idom(X20355) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__number__of])])]) ).

fof(i_0_8833,plain,
    ! [X20362,X20363,X20364] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20364),hAPP(c_Int_Onumber__class_Onumber__of(X20364),X20363)),hAPP(c_Int_Onumber__class_Onumber__of(X20364),X20362)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20363),X20362))
        | ~ class_Int_Onumber__ring(X20364)
        | ~ class_Rings_Olinordered__idom(X20364) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20363),X20362))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20364),hAPP(c_Int_Onumber__class_Onumber__of(X20364),X20363)),hAPP(c_Int_Onumber__class_Onumber__of(X20364),X20362)))
        | ~ class_Int_Onumber__ring(X20364)
        | ~ class_Rings_Olinordered__idom(X20364) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__number__of])])]) ).

fof(i_0_8834,plain,
    ! [X29105,X29106,X29107,X29108] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29108)),X29107)),X29106))
      | hAPP(hAPP(c_List_Olist__update(X29108,X29107),X29106),X29105) = X29107 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__update__beyond])]) ).

fof(i_0_8835,plain,
    ! [X19168] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19168),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19168),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19168),X19168)))),
    inference(variable_rename,[status(thm)],[fact_le__cube]) ).

fof(i_0_8836,plain,
    ! [X29601,X29602,X29603] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X29603),X29602),hAPP(c_List_Oset(X29603),c_List_Obutlast(X29603,X29601))))
      | hBOOL(hAPP(hAPP(c_member(X29603),X29602),hAPP(c_List_Oset(X29603),X29601))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__set__butlastD])]) ).

fof(i_0_8837,plain,
    ! [X23238,X23239,X23240,X23241,X23242] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X23242),X23241),X23240))
      | hAPP(hAPP(c_Set_Oinsert(X23239),hAPP(X23238,X23241)),hAPP(c_Set_Oimage(X23242,X23239,X23238),X23240)) = hAPP(c_Set_Oimage(X23242,X23239,X23238),X23240) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__image])]) ).

cnf(i_0_8838,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_5798]) ).

cnf(i_0_8839,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_5799]) ).

fof(i_0_8840,plain,
    ! [X22091,X22092,X22093] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22093,X22093),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22092),X22091)))
      | X22093 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | X22092 = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_self__quotient])]) ).

fof(i_0_8841,plain,
    ! [X22082,X22083,X22084] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22084,X22084),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22083),X22082)))
      | X22084 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | X22082 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_self__remainder])]) ).

fof(i_0_8842,plain,
    ! [X32914,X32915,X32916,X32917,X32918] :
      ( ~ c_Finite__Set_Ofolding__one(X32918,X32917,X32916)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32918),X32915))
      | hBOOL(hAPP(hAPP(c_member(X32918),X32914),X32915))
      | hAPP(X32916,hAPP(hAPP(c_Set_Oinsert(X32918),X32914),X32915)) = hAPP(hAPP(c_Finite__Set_Ofold(X32918,X32918,X32917),X32914),X32915) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5800])]) ).

fof(i_0_8843,plain,
    ! [X28128,X28129,X28130] :
      ( ~ c_Wellfounded_Owf(X28130,hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28130,X28130),tc_HOL_Obool),X28129),X28128))
      | c_Wellfounded_Owf(X28130,X28128) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__exp])]) ).

fof(i_0_8844,plain,
    ! [X18532,X18533,X18534] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18534),hAPP(c_Int_Oring__1__class_Oof__int(X18534),X18533)),hAPP(c_Int_Oring__1__class_Oof__int(X18534),X18532)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X18533),X18532))
        | ~ class_Rings_Olinordered__idom(X18534) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X18533),X18532))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18534),hAPP(c_Int_Oring__1__class_Oof__int(X18534),X18533)),hAPP(c_Int_Oring__1__class_Oof__int(X18534),X18532)))
        | ~ class_Rings_Olinordered__idom(X18534) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__le__iff])])]) ).

fof(i_0_8845,plain,
    ! [X18529,X18530,X18531] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18531),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18531),X18530)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18531),X18529)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18530),X18529))
        | ~ class_Rings_Olinordered__semidom(X18531) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18530),X18529))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18531),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18531),X18530)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18531),X18529)))
        | ~ class_Rings_Olinordered__semidom(X18531) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__le__iff])])]) ).

fof(i_0_8846,plain,
    ! [X18409,X18410,X18411] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18411),hAPP(c_Int_Oring__1__class_Oof__int(X18411),X18410)),hAPP(c_Int_Oring__1__class_Oof__int(X18411),X18409)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18410),X18409))
        | ~ class_Rings_Olinordered__idom(X18411) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18410),X18409))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18411),hAPP(c_Int_Oring__1__class_Oof__int(X18411),X18410)),hAPP(c_Int_Oring__1__class_Oof__int(X18411),X18409)))
        | ~ class_Rings_Olinordered__idom(X18411) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__less__iff])])]) ).

fof(i_0_8847,plain,
    ! [X18032,X18033,X18034] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18034),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18034),X18033)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18034),X18032)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18033),X18032))
        | ~ class_Rings_Olinordered__semidom(X18034) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18033),X18032))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18034),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18034),X18033)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18034),X18032)))
        | ~ class_Rings_Olinordered__semidom(X18034) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__less__iff])])]) ).

fof(i_0_8848,plain,
    ! [X18026,X18027,X18028] :
      ( ~ class_Rings_Olinordered__semidom(X18028)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18028),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18028),X18027)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18028),X18026)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18027),X18026)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__less__imp__less])]) ).

fof(i_0_8849,plain,
    ! [X32045] :
      ( X32045 = hAPP(c_Int_OAbs__Integ,esk420_1(X32045))
      & hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),esk420_1(X32045)),c_Int_OInteg)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5801])])]) ).

cnf(i_0_8850,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_5802]) ).

cnf(i_0_8851,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_5803]) ).

fof(i_0_8852,plain,
    ! [X21389,X21390,X21391,X21392] :
      ( ~ class_Fields_Ofield(X21392)
      | X21391 = c_Groups_Ozero__class_Ozero(X21392)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X21392),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21392),X21390),X21391)),X21389) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21392),hAPP(hAPP(c_Power_Opower__class_Opower(X21392),X21390),X21389)),hAPP(hAPP(c_Power_Opower__class_Opower(X21392),X21391),X21389)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__power__divide])]) ).

fof(i_0_8853,plain,
    ! [X18547,X18548] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18548),X18547))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18548),c_Groups_Oone__class_Oone(tc_Int_Oint))),X18547)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__imp__add1__zle])]) ).

fof(i_0_8854,plain,
    ! [X24376,X24377,X24378] :
      ( ~ class_Orderings_Olinorder(X24378)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24378),X24377))
      | X24377 = c_Orderings_Obot__class_Obot(tc_fun(X24378,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24378),X24376))
      | X24376 = c_Orderings_Obot__class_Obot(tc_fun(X24378,tc_HOL_Obool))
      | c_Big__Operators_Olinorder__class_OMin(X24378,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24378,tc_HOL_Obool)),X24377),X24376)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X24378),c_Big__Operators_Olinorder__class_OMin(X24378,X24377)),c_Big__Operators_Olinorder__class_OMin(X24378,X24376)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min__Un])]) ).

fof(i_0_8855,plain,
    ! [X24303,X24304,X24305] :
      ( ~ class_Orderings_Olinorder(X24305)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24305),X24304))
      | X24304 = c_Orderings_Obot__class_Obot(tc_fun(X24305,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24305),X24303))
      | X24303 = c_Orderings_Obot__class_Obot(tc_fun(X24305,tc_HOL_Obool))
      | c_Big__Operators_Olinorder__class_OMax(X24305,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24305,tc_HOL_Obool)),X24304),X24303)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X24305),c_Big__Operators_Olinorder__class_OMax(X24305,X24304)),c_Big__Operators_Olinorder__class_OMax(X24305,X24303)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max__Un])]) ).

fof(i_0_8856,plain,
    ! [X24294,X24295,X24296] :
      ( ~ class_Lattices_Olattice(X24296)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24296),X24295))
      | X24295 = c_Orderings_Obot__class_Obot(tc_fun(X24296,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24296),X24294))
      | X24294 = c_Orderings_Obot__class_Obot(tc_fun(X24296,tc_HOL_Obool))
      | c_Big__Operators_Olattice__class_OSup__fin(X24296,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24296,tc_HOL_Obool)),X24295),X24294)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24296),c_Big__Operators_Olattice__class_OSup__fin(X24296,X24295)),c_Big__Operators_Olattice__class_OSup__fin(X24296,X24294)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Ounion__idem])]) ).

fof(i_0_8857,plain,
    ! [X24300,X24301,X24302] :
      ( ~ class_Lattices_Olattice(X24302)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24302),X24301))
      | X24301 = c_Orderings_Obot__class_Obot(tc_fun(X24302,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24302),X24300))
      | X24300 = c_Orderings_Obot__class_Obot(tc_fun(X24302,tc_HOL_Obool))
      | c_Big__Operators_Olattice__class_OInf__fin(X24302,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24302,tc_HOL_Obool)),X24301),X24300)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24302),c_Big__Operators_Olattice__class_OInf__fin(X24302,X24301)),c_Big__Operators_Olattice__class_OInf__fin(X24302,X24300)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Ounion__idem])]) ).

fof(i_0_8858,plain,
    ! [X33322,X33323,X33324,X33325,X33326] : c_List_Osplice(X33326,hAPP(hAPP(c_List_Olist_OCons(X33326),X33325),X33324),hAPP(hAPP(c_List_Olist_OCons(X33326),X33323),X33322)) = hAPP(hAPP(c_List_Olist_OCons(X33326),X33325),hAPP(hAPP(c_List_Olist_OCons(X33326),X33323),c_List_Osplice(X33326,X33324,X33322))),
    inference(variable_rename,[status(thm)],[fact_splice_Osimps_I3_J]) ).

fof(i_0_8859,plain,
    ! [X30274,X30275] :
      ( ( hAPP(c_Code__Numeral_Oof__nat,X30275) != hAPP(c_Code__Numeral_Oof__nat,X30274)
        | X30275 = X30274
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X30274),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X30275),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) )
      & ( X30275 != X30274
        | hAPP(c_Code__Numeral_Oof__nat,X30275) = hAPP(c_Code__Numeral_Oof__nat,X30274)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X30274),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X30275),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_8860,plain,
    ! [X19263,X19264] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X19264)),hAPP(c_Int_Onat,X19263)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19264),X19263))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19264)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19264),X19263))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X19264)),hAPP(c_Int_Onat,X19263)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19264)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X19264)),hAPP(c_Int_Onat,X19263)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19264),X19263))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19263)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19264),X19263))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X19264)),hAPP(c_Int_Onat,X19263)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19263)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__le__eq__zle])])]) ).

fof(i_0_8861,plain,
    ! [X19027,X19028] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X19028)),hAPP(c_Int_Onat,X19027)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19028),X19027))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19028)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19028),X19027))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X19028)),hAPP(c_Int_Onat,X19027)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19028)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__eq__zless])])]) ).

fof(i_0_8862,plain,
    ! [X18417,X18418] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X18417)),hAPP(c_Int_Onat,X18418)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18417),X18418))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18418)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18417),X18418))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X18417)),hAPP(c_Int_Onat,X18418)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18418)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mono__iff])])]) ).

fof(i_0_8863,plain,
    ! [X18206,X18207,X18208,X18209] : hAPP(X18209,hAPP(hAPP(hAPP(c_Nat_Ocompow(X18208,X18208),X18207),X18209),X18206)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(X18208,X18208),X18207),X18209),hAPP(X18209,X18206)),
    inference(variable_rename,[status(thm)],[fact_funpow__swap1]) ).

fof(i_0_8864,plain,
    ! [X31167,X31168,X31169,X31170,X31171,X31172] :
      ( ~ class_Orderings_Olinorder(X31172)
      | hBOOL(hAPP(X31171,X31170))
      | hAPP(c_List_Ofilter(X31169,X31171),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X31169,X31172,X31168),X31170),X31167)) = hAPP(c_List_Ofilter(X31169,X31171),X31167) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5804])]) ).

fof(i_0_8865,plain,
    ! [X18285,X18286,X18287,X18288] :
      ( ~ class_Rings_Ocomm__semiring__1(X18288)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18288),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18288),X18287),X18286)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18288),X18285),X18286)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18288),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18288),X18287),X18285)),X18286) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J])]) ).

fof(i_0_8866,plain,
    ! [X23988,X23989,X23990,X23991] :
      ( ~ class_Lattices_Odistrib__lattice(X23991)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23991),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23991),X23990),X23989)),X23988) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23991),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23991),X23990),X23988)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23991),X23989),X23988)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__distrib2])]) ).

fof(i_0_8867,plain,
    ! [X23992,X23993,X23994,X23995] :
      ( ~ class_Lattices_Odistrib__lattice(X23995)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23995),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23995),X23994),X23993)),X23992) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23995),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23995),X23994),X23992)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23995),X23993),X23992)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__inf__distrib2])]) ).

fof(i_0_8868,plain,
    ! [X22540,X22541,X22542,X22543] :
      ( ~ class_Orderings_Olinorder(X22543)
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X22543),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22543),X22542),X22541)),X22540) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X22543),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22543),X22542),X22540)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22543),X22541),X22540)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__inf__distrib2])]) ).

fof(i_0_8869,plain,
    ! [X22536,X22537,X22538,X22539] :
      ( ~ class_Orderings_Olinorder(X22539)
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X22539),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22539),X22538),X22537)),X22536) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X22539),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22539),X22538),X22536)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22539),X22537),X22536)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__sup__distrib2])]) ).

fof(i_0_8870,plain,
    ! [X21266,X21267,X21268,X21269] :
      ( ~ class_Rings_Odivision__ring(X21269)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21269),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21269),X21268),X21267)),X21266) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21269),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21269),X21268),X21266)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21269),X21267),X21266)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__divide__distrib])]) ).

fof(i_0_8871,plain,
    ! [X21253,X21254,X21255,X21256] :
      ( ~ class_Rings_Odivision__ring(X21256)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21256),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21256),X21255),X21254)),X21253) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21256),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21256),X21255),X21253)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21256),X21254),X21253)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__divide__distrib])]) ).

fof(i_0_8872,plain,
    ! [X21281,X21282,X21283,X21284] :
      ( ~ class_Fields_Ofield__inverse__zero(X21284)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X21284),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21284),X21283),X21282)),X21281) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21284),hAPP(hAPP(c_Power_Opower__class_Opower(X21284),X21283),X21281)),hAPP(hAPP(c_Power_Opower__class_Opower(X21284),X21282),X21281)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__divide])]) ).

fof(i_0_8873,plain,
    ! [X20528,X20529,X20530,X20531] :
      ( ~ class_Groups_Ocomm__monoid__mult(X20531)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X20531),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20531),X20530),X20529)),X20528) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20531),hAPP(hAPP(c_Power_Opower__class_Opower(X20531),X20530),X20528)),hAPP(hAPP(c_Power_Opower__class_Opower(X20531),X20529),X20528)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__mult__distrib])]) ).

fof(i_0_8874,plain,
    ! [X20237,X20238,X20239,X20240] :
      ( ~ class_Rings_Ocomm__semiring__1(X20240)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X20240),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20240),X20239),X20238)),X20237) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20240),hAPP(hAPP(c_Power_Opower__class_Opower(X20240),X20239),X20237)),hAPP(hAPP(c_Power_Opower__class_Opower(X20240),X20238),X20237)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J])]) ).

fof(i_0_8875,plain,
    ! [X22606,X22607,X22608,X22609] :
      ( ~ class_Groups_Oordered__ab__group__add(X22609)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X22609),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22609),X22608),X22607)),X22606) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X22609),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X22609),X22608),X22606)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X22609),X22607),X22606)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__diff__distrib__left])]) ).

fof(i_0_8876,plain,
    ! [X22445,X22446,X22447,X22448] :
      ( ~ class_Groups_Oordered__ab__group__add(X22448)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X22448),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22448),X22447),X22446)),X22445) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X22448),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X22448),X22447),X22445)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X22448),X22446),X22445)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__diff__distrib__left])]) ).

fof(i_0_8877,plain,
    ! [X18277,X18278,X18279,X18280] :
      ( ~ class_Rings_Ocomm__semiring(X18280)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18280),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18280),X18279),X18278)),X18277) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18280),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18280),X18279),X18277)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18280),X18278),X18277)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__class_Odistrib])]) ).

fof(i_0_8878,plain,
    ! [X18281,X18282,X18283,X18284] :
      ( ~ class_Rings_Ocomm__semiring__1(X18284)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18284),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18284),X18283),X18282)),X18281) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18284),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18284),X18283),X18281)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18284),X18282),X18281)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J])]) ).

fof(i_0_8879,plain,
    ! [X22614,X22615,X22616,X22617] :
      ( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X22617)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22617),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22617),X22616),X22615)),X22614) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X22617),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22617),X22616),X22614)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22617),X22615),X22614)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__add__distrib__left])]) ).

fof(i_0_8880,plain,
    ! [X22439,X22440,X22441,X22442] :
      ( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X22442)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22442),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22442),X22441),X22440)),X22439) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X22442),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22442),X22441),X22439)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22442),X22440),X22439)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__add__distrib__left])]) ).

fof(i_0_8881,plain,
    ! [X30506,X30507,X30508,X30509,X30510] :
      ( ~ class_Orderings_Olinorder(X30510)
      | hAPP(c_List_Oset(X30509),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30509,X30510,X30508),X30507),X30506)) = hAPP(hAPP(c_Set_Oinsert(X30509),X30507),hAPP(c_List_Oset(X30509),X30506)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__insort])]) ).

fof(i_0_8882,plain,
    ! [X19609,X19610] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19610))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19609))
      | 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),X19610),X19609))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__nat__int__function__closures_I1_J])]) ).

fof(i_0_8883,plain,
    ! [X18907,X18908] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18908))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18907))
      | 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),X18908),X18907))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J])]) ).

fof(i_0_8884,plain,
    ! [X18871,X18872] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18872))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18871))
      | 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),X18872),X18871))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J])]) ).

fof(i_0_8885,plain,
    ! [X18862,X18863] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18863))
        | ~ 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),X18863),X18862))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18862))
        | ~ 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),X18863),X18862))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18863))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18862))
        | 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),X18863),X18862))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__0__less__mult__iff])])]) ).

fof(i_0_8886,plain,
    ! [X32942,X32943,X32944] :
      ( ~ class_Orderings_Olinorder(X32944)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32944),X32943))
      | hBOOL(hAPP(hAPP(c_member(X32944),X32942),X32943))
      | c_Big__Operators_Olattice_OInf__fin(X32944,c_Orderings_Oord__class_Omin(X32944),hAPP(hAPP(c_Set_Oinsert(X32944),X32942),X32943)) = hAPP(hAPP(c_Finite__Set_Ofold(X32944,X32944,c_Orderings_Oord__class_Omin(X32944)),X32942),X32943) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5805])]) ).

fof(i_0_8887,plain,
    ! [X32791,X32792,X32793] :
      ( ~ class_Orderings_Olinorder(X32793)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32793),X32792))
      | hBOOL(hAPP(hAPP(c_member(X32793),X32791),X32792))
      | c_Big__Operators_Olattice_OSup__fin(X32793,c_Orderings_Oord__class_Omax(X32793),hAPP(hAPP(c_Set_Oinsert(X32793),X32791),X32792)) = hAPP(hAPP(c_Finite__Set_Ofold(X32793,X32793,c_Orderings_Oord__class_Omax(X32793)),X32791),X32792) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5806])]) ).

fof(i_0_8888,plain,
    ! [X26560,X26561] :
      ( ~ class_Orderings_Olinorder(X26561)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26561,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X26561),X26560),c_Orderings_Obot__class_Obot(tc_fun(X26561,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(X26561),X26560)) = hAPP(c_SetInterval_Oord__class_OatLeast(X26561),X26560) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I1_J])]) ).

fof(i_0_8889,plain,
    ! [X32441,X32442,X32443] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X32443,X32442)),hAPP(c_Relation_Oconverse(X32442,X32443),X32441)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X32442,X32443)),X32441)) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X32442,X32443)),X32441))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X32443,X32442)),hAPP(c_Relation_Oconverse(X32442,X32443),X32441))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__converse])]) ).

fof(i_0_8890,plain,
    ! [X26828] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26828),c_Orderings_Otop__class_Otop(tc_fun(X26828,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(X26828),c_Orderings_Otop__class_Otop(tc_fun(X26828,tc_HOL_Obool))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV__card__ge__0])]) ).

fof(i_0_8891,plain,
    ! [X30432,X30433,X30434] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X30434),X30433))
      | hAPP(c_List_Oset(X30434),c_List_Oremove1(X30434,X30432,X30433)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X30434,tc_HOL_Obool)),hAPP(c_List_Oset(X30434),X30433)),hAPP(hAPP(c_Set_Oinsert(X30434),X30432),c_Orderings_Obot__class_Obot(tc_fun(X30434,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__remove1__eq])]) ).

fof(i_0_8892,plain,
    ! [X30874,X30875,X30876] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X30876,tc_HOL_Obool)),X30875),c_Complete__Lattice_OSup__class_OSup(tc_fun(X30876,tc_HOL_Obool),X30874)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X30876,tc_HOL_Obool),tc_fun(X30876,tc_HOL_Obool)),X30874),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X30876,tc_HOL_Obool)),X30875)),
    inference(variable_rename,[status(thm)],[fact_Int__Union]) ).

fof(i_0_8893,plain,
    ! [X31051,X31052,X31053] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X31053,tc_HOL_Obool)),X31052),c_Complete__Lattice_OInf__class_OInf(tc_fun(X31053,tc_HOL_Obool),X31051)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X31053,tc_HOL_Obool),tc_fun(X31053,tc_HOL_Obool)),X31051),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X31053,tc_HOL_Obool)),X31052)),
    inference(variable_rename,[status(thm)],[fact_Un__Inter]) ).

fof(i_0_8894,plain,
    ! [X30511,X30512,X30513,X30514,X30515] :
      ( ~ class_Orderings_Olinorder(X30515)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30514)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30514,X30515,X30513),X30512),X30511)) = hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30514)),X30511)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_length__insort])]) ).

fof(i_0_8895,plain,
    ! [X18434,X18435] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X18435)),X18434))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18435),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18434)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18435)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18435),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18434)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X18435)),X18434))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18435)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__iff])])]) ).

cnf(i_0_8896,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_5743]) ).

fof(i_0_8897,plain,
    ! [X17687,X17688] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X17688,tc_HOL_Obool)),X17687),c_Orderings_Obot__class_Obot(tc_fun(X17688,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[i_0_5807]) ).

fof(i_0_8898,plain,
    ! [X30564,X30565,X30566] :
      ( ~ class_Orderings_Olinorder(X30566)
      | c_List_Oremove1(X30566,X30565,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30566,X30566,c_COMBI(X30566)),X30565),X30564)) = X30564 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_remove1__insort])]) ).

fof(i_0_8899,plain,
    ! [X29223,X29224,X29225,X29226,X29227,X29228,X29229] :
      ( ( ~ hBOOL(hAPP(c_Predicate_OPowp(X29225,X29224),X29223))
        | ~ hBOOL(hAPP(hAPP(c_member(X29225),X29226),X29223))
        | hBOOL(hAPP(X29224,X29226)) )
      & ( hBOOL(hAPP(hAPP(c_member(X29229),esk330_3(X29227,X29228,X29229)),X29227))
        | hBOOL(hAPP(c_Predicate_OPowp(X29229,X29228),X29227)) )
      & ( ~ hBOOL(hAPP(X29228,esk330_3(X29227,X29228,X29229)))
        | hBOOL(hAPP(c_Predicate_OPowp(X29229,X29228),X29227)) ) ),
    inference(distribute,[status(thm)],[inference(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_8900,plain,
    ! [X34145,X34146,X34147,X34148] : hAPP(c_Product__Type_Oprod_Oprod__case(X34148,X34147,X34146),c_Product__Type_Ocurry(X34148,X34147,X34146,X34145)) = X34145,
    inference(variable_rename,[status(thm)],[fact_split__curry]) ).

fof(i_0_8901,plain,
    ! [X20708,X20709,X20710] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(X20710),X20709) != hAPP(c_Int_Onumber__class_Onumber__of(X20710),X20708)
        | c_Int_Oiszero(X20710,hAPP(c_Int_Onumber__class_Onumber__of(X20710),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20709),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X20708))))
        | ~ class_Int_Onumber__ring(X20710) )
      & ( ~ c_Int_Oiszero(X20710,hAPP(c_Int_Onumber__class_Onumber__of(X20710),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20709),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X20708))))
        | hAPP(c_Int_Onumber__class_Onumber__of(X20710),X20709) = hAPP(c_Int_Onumber__class_Onumber__of(X20710),X20708)
        | ~ class_Int_Onumber__ring(X20710) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__number__of__eq])])]) ).

fof(i_0_8902,plain,
    ! [X28924,X28925,X28926,X28927] :
      ( ( X28926 = hAPP(hAPP(c_List_Otake(X28927),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28927)),X28926)),X28924)
        | hAPP(hAPP(c_List_Oappend(X28927),X28926),X28925) != X28924 )
      & ( X28925 = hAPP(hAPP(c_List_Odrop(X28927),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28927)),X28926)),X28924)
        | hAPP(hAPP(c_List_Oappend(X28927),X28926),X28925) != X28924 )
      & ( X28926 != hAPP(hAPP(c_List_Otake(X28927),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28927)),X28926)),X28924)
        | X28925 != hAPP(hAPP(c_List_Odrop(X28927),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28927)),X28926)),X28924)
        | hAPP(hAPP(c_List_Oappend(X28927),X28926),X28925) = X28924 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__eq__conv__conj])])]) ).

fof(i_0_8903,plain,
    ! [X32927,X32928,X32929] :
      ( ~ class_Groups_Oab__semigroup__mult(X32929)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32929),X32928))
      | hBOOL(hAPP(hAPP(c_member(X32929),X32927),X32928))
      | hAPP(c_Finite__Set_Ofold1(X32929,c_Groups_Otimes__class_Otimes(X32929)),hAPP(hAPP(c_Set_Oinsert(X32929),X32927),X32928)) = hAPP(hAPP(c_Finite__Set_Ofold(X32929,X32929,c_Groups_Otimes__class_Otimes(X32929)),X32927),X32928) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5808])]) ).

cnf(i_0_8904,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_5809]) ).

fof(i_0_8905,plain,
    ! [X19791,X19792] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X19791,X19792) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19791),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X19792)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19791),X19792))
        | X19792 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X19791,X19792) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19791),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X19792)) = 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),X19791),X19792))),c_Groups_Oone__class_Oone(tc_Int_Oint))
        | X19792 = 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_8906,plain,
    ! [X27761,X27762] : hAPP(c_Set_OCollect(X27762),hAPP(hAPP(c_COMBC(X27762,X27762,tc_HOL_Obool),c_fequal),X27761)) = hAPP(hAPP(c_Set_Oinsert(X27762),X27761),c_Orderings_Obot__class_Obot(tc_fun(X27762,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_singleton__conv]) ).

cnf(i_0_8907,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_5573]) ).

fof(i_0_8908,plain,
    ! [X23058,X23059,X23060] : hAPP(hAPP(c_Set_Oinsert(X23060),X23059),X23058) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23060,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X23060),X23059),c_Orderings_Obot__class_Obot(tc_fun(X23060,tc_HOL_Obool)))),X23058),
    inference(variable_rename,[status(thm)],[fact_insert__is__Un]) ).

fof(i_0_8909,plain,
    ! [X22384,X22385,X22386,X22387] :
      ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(X22387,X22386)),X22385),X22384))
      | X22384 = hAPP(hAPP(hAPP(c_Natural_Oupdate,X22385),X22387),hAPP(X22386,X22385)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evalc__elim__cases_I2_J])]) ).

fof(i_0_8910,plain,
    ! [X34083,X34084] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X34084),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(X34083,hAPP(c_Code__Numeral_Onat__of,esk561_2(X34083,X34084))))
      | hBOOL(hAPP(X34083,X34084)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__of__induct])])]) ).

cnf(i_0_8911,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_5810]) ).

fof(i_0_8912,plain,
    ! [X19889,X19890,X19891] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19891),X19890))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19891),X19889)),X19890)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__diff__less])]) ).

fof(i_0_8913,plain,
    ! [X23786,X23787,X23788,X23789] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23789),X23788),X23787))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23789),X23788),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23789),X23787),X23786)))
        | ~ class_Lattices_Osemilattice__inf(X23789) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23789),X23788),X23786))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23789),X23788),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23789),X23787),X23786)))
        | ~ class_Lattices_Osemilattice__inf(X23789) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5811])])]) ).

fof(i_0_8914,plain,
    ! [X22449,X22450,X22451,X22452] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22452),X22451),X22450))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22452),X22451),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22452),X22450),X22449)))
        | ~ class_Orderings_Olinorder(X22452) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22452),X22451),X22449))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22452),X22451),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22452),X22450),X22449)))
        | ~ class_Orderings_Olinorder(X22452) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5812])])]) ).

fof(i_0_8915,plain,
    ! [X30466,X30467,X30468] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X30468),X30467),hAPP(c_List_Oset(X30468),X30466)))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30468)),c_List_Oremove1(X30468,X30467,X30466)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30468)),X30466)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
      & ( hBOOL(hAPP(hAPP(c_member(X30468),X30467),hAPP(c_List_Oset(X30468),X30466)))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30468)),c_List_Oremove1(X30468,X30467,X30466)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30468)),X30466) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5813])]) ).

fof(i_0_8916,plain,
    ! [X20018,X20019,X20020] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20020),X20019))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20019),X20020)),X20018) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20019),X20018)),X20020) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__diff__assoc2])]) ).

fof(i_0_8917,plain,
    ! [X20015,X20016,X20017] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20017),X20016))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20016),X20015)),X20017) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20016),X20017)),X20015) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__add__assoc2])]) ).

fof(i_0_8918,plain,
    ! [X23810,X23811,X23812] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23812,tc_HOL_Obool)),X23811),X23810))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23812,tc_HOL_Obool)),X23811),X23810) = X23811 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__absorb2])]) ).

fof(i_0_8919,plain,
    ! [X23807,X23808,X23809] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23809,tc_HOL_Obool)),X23808),X23807))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23809,tc_HOL_Obool)),X23807),X23808) = X23808 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__absorb1])]) ).

fof(i_0_8920,plain,
    ! [X22917,X22918,X22919] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22919,tc_HOL_Obool)),X22918),X22917))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22919,tc_HOL_Obool)),X22918),X22917) = X22917 )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22919,tc_HOL_Obool)),X22918),X22917) != X22917
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22919,tc_HOL_Obool)),X22918),X22917)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__Un__eq])]) ).

fof(i_0_8921,plain,
    ! [X22914,X22915,X22916] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22916,tc_HOL_Obool)),X22915),X22914))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22916,tc_HOL_Obool)),X22915),X22914) = X22914 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Un__absorb1])]) ).

fof(i_0_8922,plain,
    ! [X22911,X22912,X22913] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22913,tc_HOL_Obool)),X22912),X22911))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22913,tc_HOL_Obool)),X22911),X22912) = X22911 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Un__absorb2])]) ).

fof(i_0_8923,plain,
    ! [X24037,X24038,X24039,X24040] :
      ( hBOOL(hAPP(hAPP(c_member(X24040),X24039),X24038))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24040,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X24040),X24039),X24037)),X24038) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24040,tc_HOL_Obool)),X24037),X24038) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5814])]) ).

fof(i_0_8924,plain,
    ! [X27698,X27699] : hAPP(c_Set_OCollect(X27699),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X27699),c_fNot),X27698)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X27699,tc_HOL_Obool)),hAPP(c_Set_OCollect(X27699),X27698)),
    inference(variable_rename,[status(thm)],[fact_Collect__neg__eq]) ).

fof(i_0_8925,plain,
    ! [X28917,X28918,X28919] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28919)),X28918)),X28917))
      | hAPP(hAPP(c_List_Odrop(X28919),X28917),X28918) = c_List_Olist_ONil(X28919) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_drop__all])]) ).

fof(i_0_8926,plain,
    ! [X28914,X28915,X28916] :
      ( ( hAPP(hAPP(c_List_Odrop(X28916),X28915),X28914) != c_List_Olist_ONil(X28916)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28916)),X28914)),X28915)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28916)),X28914)),X28915))
        | hAPP(hAPP(c_List_Odrop(X28916),X28915),X28914) = c_List_Olist_ONil(X28916) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_drop__eq__Nil])]) ).

fof(i_0_8927,plain,
    ! [X20777,X20778,X20779,X20780] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X20780),X20779),hAPP(hAPP(c_Set_Oinsert(X20780),X20778),X20777)))
        | X20779 = X20778
        | hBOOL(hAPP(hAPP(c_member(X20780),X20779),X20777)) )
      & ( X20779 != X20778
        | hBOOL(hAPP(hAPP(c_member(X20780),X20779),hAPP(hAPP(c_Set_Oinsert(X20780),X20778),X20777))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X20780),X20779),X20777))
        | hBOOL(hAPP(hAPP(c_member(X20780),X20779),hAPP(hAPP(c_Set_Oinsert(X20780),X20778),X20777))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__iff])])]) ).

fof(i_0_8928,plain,
    ! [X20718,X20719,X20720,X20721] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X20721),X20720),hAPP(hAPP(c_Set_Oinsert(X20721),X20719),X20718)))
      | X20720 = X20719
      | hBOOL(hAPP(hAPP(c_member(X20721),X20720),X20718)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insertE])]) ).

cnf(i_0_8929,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_5746]) ).

cnf(i_0_8930,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_5747]) ).

cnf(i_0_8931,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_5749]) ).

cnf(i_0_8932,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_5748]) ).

cnf(i_0_8933,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_5750]) ).

fof(i_0_8934,plain,
    ! [X28758,X28759,X28760] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28760)),X28759)),X28758))
      | hAPP(hAPP(c_List_Otake(X28760),X28758),X28759) = X28759 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__all])]) ).

cnf(i_0_8935,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_5815]) ).

cnf(i_0_8936,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_5816]) ).

cnf(i_0_8937,plain,
    ( c_Relation_Osym(X1,c_Transitive__Closure_Otrancl(X1,X2))
    | ~ c_Relation_Osym(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5817]) ).

cnf(i_0_8938,plain,
    ( c_Wellfounded_Owf(X1,c_Transitive__Closure_Otrancl(X1,X2))
    | ~ c_Wellfounded_Owf(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5818]) ).

fof(i_0_8939,plain,
    ! [X25815,X25816,X25817,X25818] :
      ( ~ class_Orderings_Olinorder(X25818)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25818),X25817),X25816))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25818,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X25818,X25817),X25815)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X25818,X25817),X25816)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X25818,X25816),X25815) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__diff])]) ).

fof(i_0_8940,plain,
    ! [X22052,X22053,X22054,X22055,X22056,X22057,X22058] :
      ( ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X22054,X22053),X22052))
        | ~ hBOOL(hAPP(hAPP(X22053,X22055),X22052))
        | hBOOL(hAPP(c_Wellfounded_Oaccp(X22054,X22053),X22055)) )
      & ( hBOOL(hAPP(hAPP(X22057,esk85_3(X22056,X22057,X22058)),X22056))
        | hBOOL(hAPP(c_Wellfounded_Oaccp(X22058,X22057),X22056)) )
      & ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X22058,X22057),esk85_3(X22056,X22057,X22058)))
        | hBOOL(hAPP(c_Wellfounded_Oaccp(X22058,X22057),X22056)) ) ),
    inference(distribute,[status(thm)],[inference(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_8941,plain,
    ! [X22044,X22045,X22046,X22047,X22048,X22049,X22050] :
      ( ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X22046,X22045),X22044))
        | ~ hBOOL(hAPP(hAPP(X22045,X22047),X22044))
        | hBOOL(hAPP(c_Wellfounded_Oaccp(X22046,X22045),X22047)) )
      & ( hBOOL(hAPP(hAPP(X22049,esk84_3(X22048,X22049,X22050)),X22048))
        | hBOOL(hAPP(c_Wellfounded_Oaccp(X22050,X22049),X22048)) )
      & ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X22050,X22049),esk84_3(X22048,X22049,X22050)))
        | hBOOL(hAPP(c_Wellfounded_Oaccp(X22050,X22049),X22048)) ) ),
    inference(distribute,[status(thm)],[inference(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_8942,plain,
    hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X2),X3),c_Relation_OId(X2)) = X3,
    inference(split_conjunct,[status(thm)],[i_0_5819]) ).

fof(i_0_8943,plain,
    ! [X27279,X27280,X27281,X27282] :
      ( ( hAPP(hAPP(c_Product__Type_OSigma(X27282,X27281),X27280),hAPP(c_COMBK(tc_fun(X27281,tc_HOL_Obool),X27282),X27279)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27282,X27281),tc_HOL_Obool))
        | X27280 = c_Orderings_Obot__class_Obot(tc_fun(X27282,tc_HOL_Obool))
        | X27279 = c_Orderings_Obot__class_Obot(tc_fun(X27281,tc_HOL_Obool)) )
      & ( X27280 != c_Orderings_Obot__class_Obot(tc_fun(X27282,tc_HOL_Obool))
        | hAPP(hAPP(c_Product__Type_OSigma(X27282,X27281),X27280),hAPP(c_COMBK(tc_fun(X27281,tc_HOL_Obool),X27282),X27279)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27282,X27281),tc_HOL_Obool)) )
      & ( X27279 != c_Orderings_Obot__class_Obot(tc_fun(X27281,tc_HOL_Obool))
        | hAPP(hAPP(c_Product__Type_OSigma(X27282,X27281),X27280),hAPP(c_COMBK(tc_fun(X27281,tc_HOL_Obool),X27282),X27279)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27282,X27281),tc_HOL_Obool)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Times__empty])])]) ).

cnf(i_0_8944,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_5753]) ).

fof(i_0_8945,plain,
    ! [X26562,X26563,X26564] :
      ( ~ class_Orderings_Olinorder(X26564)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26564),X26563),X26562))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26564,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X26564,X26563,X26562)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X26564),X26562)) = hAPP(c_SetInterval_Oord__class_OatLeast(X26564),X26563) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I13_J])]) ).

fof(i_0_8946,plain,
    ! [X26550,X26551,X26552] :
      ( ~ class_Orderings_Olinorder(X26552)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26552),X26551),X26550))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26552,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X26552,X26551,X26550)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X26552),X26550)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X26552),X26551) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I11_J])]) ).

fof(i_0_8947,plain,
    ! [X26565,X26566,X26567] :
      ( ~ class_Orderings_Olinorder(X26567)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26567),X26566),X26565))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26567,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X26567,X26566,X26565)),hAPP(c_SetInterval_Oord__class_OatLeast(X26567),X26565)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X26567),X26566) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I12_J])]) ).

fof(i_0_8948,plain,
    ! [X31070,X31071] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X31071)
      | c_Complete__Lattice_OInf__class_OInf(X31071,hAPP(c_List_Oset(X31071),X31070)) = hAPP(c_List_Ofoldl(X31071,X31071,c_Lattices_Osemilattice__inf__class_Oinf(X31071),c_Orderings_Otop__class_Otop(X31071)),X31070) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__set__fold])]) ).

fof(i_0_8949,plain,
    ! [X30956,X30957] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X30957)
      | c_Complete__Lattice_OSup__class_OSup(X30957,hAPP(c_List_Oset(X30957),X30956)) = hAPP(c_List_Ofoldl(X30957,X30957,c_Lattices_Osemilattice__sup__class_Osup(X30957),c_Orderings_Obot__class_Obot(X30957)),X30956) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__set__fold])]) ).

fof(i_0_8950,plain,
    ! [X25547,X25548] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X25548,X25547)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X25547),X25548)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[fact_card__atLeastAtMost__int]) ).

fof(i_0_8951,plain,
    ! [X23528,X23529,X23530,X23531] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23531),X23530))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X23529),hAPP(c_Set_Oimage(X23531,X23529,X23528),X23530))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__imageI])]) ).

cnf(i_0_8952,plain,
    ( c_List_Oconcat(X2,X1) = c_List_Olist_ONil(X2)
    | esk385_2(X1,X2) != c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5655]) ).

cnf(i_0_8953,plain,
    ( c_List_Olist_ONil(X2) = c_List_Oconcat(X2,X1)
    | esk386_2(X1,X2) != c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5656]) ).

fof(i_0_8954,plain,
    ! [X31065,X31066,X31067] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X31067)
      | c_Complete__Lattice_OInf__class_OInf(X31067,hAPP(hAPP(c_Set_Oinsert(X31067),X31066),hAPP(hAPP(c_Set_Oinsert(X31067),X31065),c_Orderings_Obot__class_Obot(tc_fun(X31067,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X31067),X31066),X31065) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__binary])]) ).

fof(i_0_8955,plain,
    ! [X30948,X30949,X30950] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X30950)
      | c_Complete__Lattice_OSup__class_OSup(X30950,hAPP(hAPP(c_Set_Oinsert(X30950),X30949),hAPP(hAPP(c_Set_Oinsert(X30950),X30948),c_Orderings_Obot__class_Obot(tc_fun(X30950,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X30950),X30949),X30948) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__binary])]) ).

fof(i_0_8956,plain,
    ! [X24174,X24175,X24176,X24177] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X24177),X24176),c_SetInterval_Oord_OlessThan(X24177,X24175,X24174)))
        | hBOOL(hAPP(hAPP(X24175,X24176),X24174)) )
      & ( ~ hBOOL(hAPP(hAPP(X24175,X24176),X24174))
        | hBOOL(hAPP(hAPP(c_member(X24177),X24176),c_SetInterval_Oord_OlessThan(X24177,X24175,X24174))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OlessThan__iff])]) ).

fof(i_0_8957,plain,
    ! [X24166,X24167,X24168,X24169] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X24169),X24168),c_SetInterval_Oord_OatMost(X24169,X24167,X24166)))
        | hBOOL(hAPP(hAPP(X24167,X24168),X24166)) )
      & ( ~ hBOOL(hAPP(hAPP(X24167,X24168),X24166))
        | hBOOL(hAPP(hAPP(c_member(X24169),X24168),c_SetInterval_Oord_OatMost(X24169,X24167,X24166))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OatMost__iff])]) ).

fof(i_0_8958,plain,
    ! [X24178,X24179,X24180,X24181] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X24181),X24180),c_SetInterval_Oord_OgreaterThan(X24181,X24179,X24178)))
        | hBOOL(hAPP(hAPP(X24179,X24178),X24180)) )
      & ( ~ hBOOL(hAPP(hAPP(X24179,X24178),X24180))
        | hBOOL(hAPP(hAPP(c_member(X24181),X24180),c_SetInterval_Oord_OgreaterThan(X24181,X24179,X24178))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OgreaterThan__iff])]) ).

fof(i_0_8959,plain,
    ! [X24170,X24171,X24172,X24173] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X24173),X24172),c_SetInterval_Oord_OatLeast(X24173,X24171,X24170)))
        | hBOOL(hAPP(hAPP(X24171,X24170),X24172)) )
      & ( ~ hBOOL(hAPP(hAPP(X24171,X24170),X24172))
        | hBOOL(hAPP(hAPP(c_member(X24173),X24172),c_SetInterval_Oord_OatLeast(X24173,X24171,X24170))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OatLeast__iff])]) ).

fof(i_0_8960,plain,
    ! [X30472,X30473,X30474,X30475,X30476] :
      ( c_List_Opartition(X30476,X30475,X30474) != hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30476),tc_List_Olist(X30476)),X30473),X30472)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X30476,tc_HOL_Obool)),hAPP(c_List_Oset(X30476),X30473)),hAPP(c_List_Oset(X30476),X30472)) = hAPP(c_List_Oset(X30476),X30474) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_partition__set])]) ).

fof(i_0_8961,plain,
    ! [X28737,X28738,X28739,X28740] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X28740) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Onth(X28739),hAPP(hAPP(c_List_Olist_OCons(X28739),X28738),X28737)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X28740)) = X28738 )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X28740) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Onth(X28739),hAPP(hAPP(c_List_Olist_OCons(X28739),X28738),X28737)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X28740)) = hAPP(hAPP(c_List_Onth(X28739),X28737),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X28740)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__Cons__number__of])]) ).

cnf(i_0_8962,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_5820]) ).

fof(i_0_8963,plain,
    ! [X32171,X32172] : hAPP(hAPP(c_Relation_Orel__comp(X32172,X32172,X32172),X32171),c_Transitive__Closure_Ortrancl(X32172,X32171)) = hAPP(hAPP(c_Relation_Orel__comp(X32172,X32172,X32172),c_Transitive__Closure_Ortrancl(X32172,X32171)),X32171),
    inference(variable_rename,[status(thm)],[fact_r__comp__rtrancl__eq]) ).

fof(i_0_8964,plain,
    ! [X34280,X34281,X34282,X34283,X34284,X34285] : hAPP(hAPP(hAPP(c_COMBS(X34285,X34284,X34283),X34282),X34281),X34280) = hAPP(hAPP(X34282,X34280),hAPP(X34281,X34280)),
    inference(variable_rename,[status(thm)],[help_c__COMBS__1]) ).

cnf(i_0_8965,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_5821]) ).

fof(i_0_8966,plain,
    ! [X20430,X20431] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X20431)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20431),hAPP(c_Groups_Ouminus__class_Ouminus(X20431),hAPP(c_Groups_Oabs__class_Oabs(X20431),X20430))),c_Groups_Ozero__class_Ozero(X20431))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__minus__le__zero])]) ).

fof(i_0_8967,plain,
    ! [X23034,X23035,X23036,X23037] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23037,tc_HOL_Obool)),X23036),hAPP(hAPP(c_Set_Oinsert(X23037),X23035),X23034)) = hAPP(hAPP(c_Set_Oinsert(X23037),X23035),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23037,tc_HOL_Obool)),X23036),X23034)),
    inference(variable_rename,[status(thm)],[fact_Un__insert__right]) ).

fof(i_0_8968,plain,
    ! [X18387,X18388,X18389] :
      ( ( X18388 = c_Groups_Ozero__class_Ozero(X18389)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18389),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18389),X18388),X18388)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18389),X18387),X18387)) != c_Groups_Ozero__class_Ozero(X18389)
        | ~ class_Rings_Olinordered__ring__strict(X18389) )
      & ( X18387 = c_Groups_Ozero__class_Ozero(X18389)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18389),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18389),X18388),X18388)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18389),X18387),X18387)) != c_Groups_Ozero__class_Ozero(X18389)
        | ~ class_Rings_Olinordered__ring__strict(X18389) )
      & ( X18388 != c_Groups_Ozero__class_Ozero(X18389)
        | X18387 != c_Groups_Ozero__class_Ozero(X18389)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18389),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18389),X18388),X18388)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18389),X18387),X18387)) = c_Groups_Ozero__class_Ozero(X18389)
        | ~ class_Rings_Olinordered__ring__strict(X18389) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__squares__eq__zero__iff])])]) ).

fof(i_0_8969,plain,
    ! [X32827,X32828,X32829] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32829),X32828))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X32829,tc_HOL_Obool)),X32828),X32827) = hAPP(hAPP(c_Finite__Set_Ofold(X32829,tc_fun(X32829,tc_HOL_Obool),c_Set_Oinsert(X32829)),X32827),X32828) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_union__fold__insert])]) ).

fof(i_0_8970,plain,
    ! [X20890,X20891] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(X20891),X20890) != c_Groups_Ozero__class_Ozero(X20891)
        | c_Int_Oiszero(X20891,hAPP(c_Int_Onumber__class_Onumber__of(X20891),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20890),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))
        | ~ class_Int_Onumber__ring(X20891) )
      & ( ~ c_Int_Oiszero(X20891,hAPP(c_Int_Onumber__class_Onumber__of(X20891),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20890),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))
        | hAPP(c_Int_Onumber__class_Onumber__of(X20891),X20890) = c_Groups_Ozero__class_Ozero(X20891)
        | ~ class_Int_Onumber__ring(X20891) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__special_I3_J])])]) ).

fof(i_0_8971,plain,
    ! [X20888,X20889] :
      ( ( c_Groups_Ozero__class_Ozero(X20889) != hAPP(c_Int_Onumber__class_Onumber__of(X20889),X20888)
        | c_Int_Oiszero(X20889,hAPP(c_Int_Onumber__class_Onumber__of(X20889),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X20888))))
        | ~ class_Int_Onumber__ring(X20889) )
      & ( ~ c_Int_Oiszero(X20889,hAPP(c_Int_Onumber__class_Onumber__of(X20889),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X20888))))
        | c_Groups_Ozero__class_Ozero(X20889) = hAPP(c_Int_Onumber__class_Onumber__of(X20889),X20888)
        | ~ class_Int_Onumber__ring(X20889) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__special_I1_J])])]) ).

fof(i_0_8972,plain,
    ! [X33775,X33776,X33777,X33778] :
      ( ~ c_Relation_Otrans(X33778,X33777)
      | ~ c_Relation_Otrans(X33776,X33775)
      | c_Relation_Otrans(tc_prod(X33778,X33776),c_Wellfounded_Olex__prod(X33778,X33776,X33777,X33775)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__lex__prod])]) ).

fof(i_0_8973,plain,
    ! [X28111,X28112,X28113,X28114] :
      ( ~ c_Wellfounded_Owf(X28114,X28113)
      | ~ c_Wellfounded_Owf(X28112,X28111)
      | c_Wellfounded_Owf(tc_prod(X28114,X28112),c_Wellfounded_Olex__prod(X28114,X28112,X28113,X28111)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__lex__prod])]) ).

cnf(i_0_8974,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_5822]) ).

fof(i_0_8975,plain,
    ! [X29340,X29341,X29342,X29343] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X29343),X29342))
      | hBOOL(hAPP(c_List_Odistinct(tc_prod(X29343,X29341)),hAPP(hAPP(c_List_Ozip(X29343,X29341),X29342),X29340))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__zipI1])]) ).

fof(i_0_8976,plain,
    ! [X29344,X29345,X29346,X29347] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X29347),X29346))
      | hBOOL(hAPP(c_List_Odistinct(tc_prod(X29345,X29347)),hAPP(hAPP(c_List_Ozip(X29345,X29347),X29344),X29346))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__zipI2])]) ).

fof(i_0_8977,plain,
    ! [X32936,X32937,X32938] :
      ( ~ class_Orderings_Olinorder(X32938)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32938),X32937))
      | hBOOL(hAPP(hAPP(c_member(X32938),X32936),X32937))
      | c_Big__Operators_Olinorder__class_OMin(X32938,hAPP(hAPP(c_Set_Oinsert(X32938),X32936),X32937)) = hAPP(hAPP(c_Finite__Set_Ofold(X32938,X32938,c_Orderings_Oord__class_Omin(X32938)),X32936),X32937) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5823])]) ).

fof(i_0_8978,plain,
    ! [X32939,X32940,X32941] :
      ( ~ class_Orderings_Olinorder(X32941)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32941),X32940))
      | hBOOL(hAPP(hAPP(c_member(X32941),X32939),X32940))
      | c_Big__Operators_Olinorder__class_OMax(X32941,hAPP(hAPP(c_Set_Oinsert(X32941),X32939),X32940)) = hAPP(hAPP(c_Finite__Set_Ofold(X32941,X32941,c_Orderings_Oord__class_Omax(X32941)),X32939),X32940) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5824])]) ).

fof(i_0_8979,plain,
    ! [X32930,X32931,X32932] :
      ( ~ class_Lattices_Olattice(X32932)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32932),X32931))
      | hBOOL(hAPP(hAPP(c_member(X32932),X32930),X32931))
      | c_Big__Operators_Olattice__class_OSup__fin(X32932,hAPP(hAPP(c_Set_Oinsert(X32932),X32930),X32931)) = hAPP(hAPP(c_Finite__Set_Ofold(X32932,X32932,c_Lattices_Osemilattice__sup__class_Osup(X32932)),X32930),X32931) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5825])]) ).

fof(i_0_8980,plain,
    ! [X32933,X32934,X32935] :
      ( ~ class_Lattices_Olattice(X32935)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32935),X32934))
      | hBOOL(hAPP(hAPP(c_member(X32935),X32933),X32934))
      | c_Big__Operators_Olattice__class_OInf__fin(X32935,hAPP(hAPP(c_Set_Oinsert(X32935),X32933),X32934)) = hAPP(hAPP(c_Finite__Set_Ofold(X32935,X32935,c_Lattices_Osemilattice__inf__class_Oinf(X32935)),X32933),X32934) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5826])]) ).

fof(i_0_8981,plain,
    ! [X30824,X30825,X30826,X30827] : hAPP(c_Set_Ovimage(X30827,X30826,X30825),c_Complete__Lattice_OSup__class_OSup(tc_fun(X30826,tc_HOL_Obool),X30824)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X30826,tc_HOL_Obool),tc_fun(X30827,tc_HOL_Obool)),X30824),c_Set_Ovimage(X30827,X30826,X30825)),
    inference(variable_rename,[status(thm)],[fact_vimage__Union]) ).

fof(i_0_8982,plain,
    ! [X30789,X30790,X30791,X30792] : hAPP(c_Set_Oimage(X30792,X30791,X30790),c_Complete__Lattice_OSup__class_OSup(tc_fun(X30792,tc_HOL_Obool),X30789)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X30792,tc_HOL_Obool),tc_fun(X30791,tc_HOL_Obool)),X30789),c_Set_Oimage(X30792,X30791,X30790)),
    inference(variable_rename,[status(thm)],[fact_image__Union]) ).

fof(i_0_8983,plain,
    ! [X25491,X25492] : hBOOL(hAPP(hAPP(c_member(tc_fun(X25492,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X25492,tc_HOL_Obool))),hAPP(c_Set_OPow(X25492),X25491))),
    inference(variable_rename,[status(thm)],[fact_Pow__bottom]) ).

fof(i_0_8984,plain,
    ! [X29695,X29696,X29697] :
      ( ~ class_Groups_Omonoid__add(X29697)
      | hAPP(c_List_Omonoid__add__class_Olistsum(X29697),hAPP(hAPP(c_List_Omap(X29696,X29697),hAPP(c_COMBK(X29697,X29696),c_Groups_Ozero__class_Ozero(X29697))),X29695)) = c_Groups_Ozero__class_Ozero(X29697) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__0])]) ).

fof(i_0_8985,plain,
    ! [X23918,X23919,X23920] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23920,tc_HOL_Obool)),X23919),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23920,tc_HOL_Obool)),X23919),X23918)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23920,tc_HOL_Obool)),X23919),X23918),
    inference(variable_rename,[status(thm)],[fact_Int__left__absorb]) ).

fof(i_0_8986,plain,
    ! [X22939,X22940,X22941] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22941,tc_HOL_Obool)),X22940),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22941,tc_HOL_Obool)),X22940),X22939)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22941,tc_HOL_Obool)),X22940),X22939),
    inference(variable_rename,[status(thm)],[fact_Un__left__absorb]) ).

fof(i_0_8987,plain,
    ! [X22841,X22842,X22843] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22843,tc_HOL_Obool)),X22842),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X22843,tc_HOL_Obool)),X22841),X22842)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22843,tc_HOL_Obool)),X22842),X22841),
    inference(variable_rename,[status(thm)],[fact_Un__Diff__cancel]) ).

fof(i_0_8988,plain,
    ! [X29308,X29309] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29309)),X29308)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
      | hAPP(c_List_Orotate1(X29309),X29308) = X29308 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rotate1__length01])]) ).

fof(i_0_8989,plain,
    ! [X24834,X24835,X24836,X24837,X24838] : hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X24838,X24837,X24836),X24835),X24834),c_Orderings_Obot__class_Obot(tc_fun(X24837,tc_HOL_Obool))) = X24834,
    inference(variable_rename,[status(thm)],[fact_fold__image__empty]) ).

cnf(i_0_8990,plain,
    c_Relation_Otrans(X1,c_Transitive__Closure_Otrancl(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_5827]) ).

fof(i_0_8991,plain,
    ! [X20172,X20173] :
      ( ( X20173 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20173),X20172) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X20173 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20173),X20172) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20172),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20173),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X20172)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__eq__if])]) ).

fof(i_0_8992,plain,
    ! [X30532,X30533,X30534] : c_List_Olistsp(X30534,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X30534,tc_HOL_Obool)),X30533),X30532)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X30534),tc_HOL_Obool)),c_List_Olistsp(X30534,X30533)),c_List_Olistsp(X30534,X30532)),
    inference(variable_rename,[status(thm)],[fact_listsp__inf__eq]) ).

fof(i_0_8993,plain,
    ! [X16984,X16985,X16986,X16987,X16988,X16989] : c_Hoare__Mirabelle_Otriple_Otriple__case(X16989,X16988,X16987,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X16989),X16986),X16985),X16984)) = hAPP(hAPP(hAPP(X16987,X16986),X16985),X16984),
    inference(variable_rename,[status(thm)],[fact_triple_Osimps_I2_J]) ).

fof(i_0_8994,plain,
    ! [X16978,X16979,X16980,X16981,X16982,X16983] : c_Hoare__Mirabelle_Otriple_Otriple__rec(X16983,X16982,X16981,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X16983),X16980),X16979),X16978)) = hAPP(hAPP(hAPP(X16981,X16980),X16979),X16978),
    inference(variable_rename,[status(thm)],[fact_triple_Orecs]) ).

fof(i_0_8995,plain,
    ! [X28314,X28315,X28316,X28317,X28319,X28320,X28321,X28322,X28323] :
      ( ( ~ hBOOL(hAPP(c_Predicate_ORangeP(X28317,X28316,X28315),X28314))
        | hBOOL(hAPP(hAPP(X28315,esk304_2(X28314,X28315)),X28314)) )
      & ( ~ hBOOL(hAPP(hAPP(X28320,X28321),X28319))
        | hBOOL(hAPP(c_Predicate_ORangeP(X28323,X28322,X28320),X28319)) ) ),
    inference(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_8996,plain,
    ! [X20681,X20682] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20682)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20681)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20682) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20681) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20681)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20682) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20682)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20682) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20681) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20681)))
        | X20682 = X20681
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20682)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20682) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20681) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20682)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20682)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20682) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20681) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20681)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20681)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20682)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20682) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20681) )
      & ( X20682 != X20681
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20681)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20682)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20682) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20681) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20681)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20682) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20682)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20682) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20681) )
      & ( X20682 != X20681
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20682) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20682)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20682) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20681) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20682)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20681)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20682) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20681) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20681)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20681)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20681)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20682) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20681) )
      & ( X20682 != X20681
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20681)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20681)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20682) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20681) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20681)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20682) != 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),X20681)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20682) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20681) )
      & ( X20682 != X20681
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20682) != 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),X20681)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20682) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20681) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5828])])]) ).

fof(i_0_8997,plain,
    ! [X18727,X18728] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X18728),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X18728),X18727)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X18728))),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X18727))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__distrib__neg])]) ).

fof(i_0_8998,plain,
    ! [X21756,X21757,X21758,X21759] : hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(X21759,X21758)),c_Nitpick_Opair__box_OPairBox(X21759,X21758,X21757,X21756)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_pair__box_Osize_I2_J]) ).

fof(i_0_8999,plain,
    ! [X29626,X29627,X29628,X29629] :
      ( ( X29629 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29628)),X29627)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | c_List_Obutlast(X29628,hAPP(hAPP(c_List_Olist__update(X29628,X29627),X29629),X29626)) = c_List_Obutlast(X29628,X29627) )
      & ( X29629 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29628)),X29627)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | c_List_Obutlast(X29628,hAPP(hAPP(c_List_Olist__update(X29628,X29627),X29629),X29626)) = hAPP(hAPP(c_List_Olist__update(X29628,c_List_Obutlast(X29628,X29627)),X29629),X29626) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_butlast__list__update])]) ).

fof(i_0_9000,plain,
    ! [X23222,X23223,X23224,X23225,X23226] : hAPP(c_Set_Oimage(X23226,X23225,X23224),hAPP(hAPP(c_Set_Oinsert(X23226),X23223),X23222)) = hAPP(hAPP(c_Set_Oinsert(X23225),hAPP(X23224,X23223)),hAPP(c_Set_Oimage(X23226,X23225,X23224),X23222)),
    inference(variable_rename,[status(thm)],[fact_image__insert]) ).

cnf(i_0_9001,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_5593]) ).

fof(i_0_9002,plain,
    ! [X23546,X23547,X23548] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23548,tc_HOL_Obool)),X23547),X23546))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23548),X23546))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X23548),X23547)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__subset])]) ).

fof(i_0_9003,plain,
    ! [X23549,X23550,X23551] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23551),X23550))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23551,tc_HOL_Obool)),X23549),X23550))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X23551),X23549)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__finite__subset])]) ).

fof(i_0_9004,plain,
    ! [X18840,X18841] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18841),hAPP(c_Groups_Ouminus__class_Ouminus(X18841),X18840)),c_Groups_Ozero__class_Ozero(X18841)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18841),c_Groups_Ozero__class_Ozero(X18841)),X18840))
        | ~ class_Groups_Oordered__ab__group__add(X18841) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18841),c_Groups_Ozero__class_Ozero(X18841)),X18840))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18841),hAPP(c_Groups_Ouminus__class_Ouminus(X18841),X18840)),c_Groups_Ozero__class_Ozero(X18841)))
        | ~ class_Groups_Oordered__ab__group__add(X18841) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__le__0__iff__le])])]) ).

fof(i_0_9005,plain,
    ! [X18310,X18311] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18311),hAPP(c_Groups_Ouminus__class_Ouminus(X18311),X18310)),c_Groups_Ozero__class_Ozero(X18311)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18311),c_Groups_Ozero__class_Ozero(X18311)),X18310))
        | ~ class_Groups_Oordered__ab__group__add(X18311) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18311),c_Groups_Ozero__class_Ozero(X18311)),X18310))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18311),hAPP(c_Groups_Ouminus__class_Ouminus(X18311),X18310)),c_Groups_Ozero__class_Ozero(X18311)))
        | ~ class_Groups_Oordered__ab__group__add(X18311) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__less__0__iff__less])])]) ).

fof(i_0_9006,plain,
    ! [X31880,X31881,X31882,X31883] :
      ( ~ class_Orderings_Olinorder(X31883)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31882)),c_List_Olinorder__class_Osort__key(X31882,X31883,X31881,X31880)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31882)),X31880) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_length__sort])]) ).

fof(i_0_9007,plain,
    ! [X31629,X31630,X31631,X31632] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31632)),X31631) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31630)),X31629)
      | hAPP(hAPP(c_List_Ozip(X31632,X31630),hAPP(c_List_Orev(X31632),X31631)),hAPP(c_List_Orev(X31630),X31629)) = hAPP(c_List_Orev(tc_prod(X31632,X31630)),hAPP(hAPP(c_List_Ozip(X31632,X31630),X31631),X31629)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zip__rev])]) ).

fof(i_0_9008,plain,
    ! [X20499,X20500] :
      ( ( ~ 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),X20500),X20499)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20500))
        | X20499 = 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)),X20500))
        | 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),X20500),X20499))) )
      & ( X20499 != 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),X20500),X20499))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__zero__less__power__iff])])]) ).

fof(i_0_9009,plain,
    ! [X26392,X26393,X26394,X26395] :
      ( ~ class_Orderings_Olinorder(X26395)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26395,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X26395,X26394,X26393)),hAPP(c_SetInterval_Oord__class_OatLeast(X26395),X26392)) = c_SetInterval_Oord__class_OatLeastAtMost(X26395,hAPP(hAPP(c_Orderings_Oord__class_Omax(X26395),X26394),X26392),X26393) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMostL2])]) ).

fof(i_0_9010,plain,
    ! [X25954,X25955,X25956,X25957] :
      ( ~ class_Orderings_Olinorder(X25957)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25957,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X25957,X25956,X25955)),hAPP(c_SetInterval_Oord__class_OatMost(X25957),X25954)) = c_SetInterval_Oord__class_OatLeastAtMost(X25957,X25956,hAPP(hAPP(c_Orderings_Oord__class_Omin(X25957),X25955),X25954)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMostL1])]) ).

fof(i_0_9011,plain,
    ! [X29030,X29031,X29032,X29033] : hAPP(hAPP(c_List_Olist__update(X29033,hAPP(hAPP(c_List_Olist_OCons(X29033),X29032),X29031)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29030) = hAPP(hAPP(c_List_Olist_OCons(X29033),X29030),X29031),
    inference(variable_rename,[status(thm)],[fact_list__update__code_I2_J]) ).

fof(i_0_9012,plain,
    ! [X34274,X34275,X34276,X34277,X34278,X34279] : hAPP(hAPP(hAPP(c_COMBC(X34279,X34278,X34277),X34276),X34275),X34274) = hAPP(hAPP(X34276,X34274),X34275),
    inference(variable_rename,[status(thm)],[help_c__COMBC__1]) ).

fof(i_0_9013,plain,
    ! [X34268,X34269,X34270,X34271,X34272,X34273] : hAPP(hAPP(hAPP(c_COMBB(X34273,X34272,X34271),X34270),X34269),X34268) = hAPP(X34270,hAPP(X34269,X34268)),
    inference(variable_rename,[status(thm)],[help_c__COMBB__1]) ).

fof(i_0_9014,plain,
    ! [X20278,X20279] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20279),hAPP(c_Int_Onumber__class_Onumber__of(X20279),X20278)),c_Groups_Ozero__class_Ozero(X20279)))
        | hAPP(c_Groups_Oabs__class_Oabs(X20279),hAPP(c_Int_Onumber__class_Onumber__of(X20279),X20278)) = hAPP(c_Groups_Ouminus__class_Ouminus(X20279),hAPP(c_Int_Onumber__class_Onumber__of(X20279),X20278))
        | ~ class_Int_Onumber__ring(X20279)
        | ~ class_Rings_Olinordered__idom(X20279) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20279),hAPP(c_Int_Onumber__class_Onumber__of(X20279),X20278)),c_Groups_Ozero__class_Ozero(X20279)))
        | hAPP(c_Groups_Oabs__class_Oabs(X20279),hAPP(c_Int_Onumber__class_Onumber__of(X20279),X20278)) = hAPP(c_Int_Onumber__class_Onumber__of(X20279),X20278)
        | ~ class_Int_Onumber__ring(X20279)
        | ~ class_Rings_Olinordered__idom(X20279) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5829])])]) ).

fof(i_0_9015,plain,
    ! [X27137,X27138,X27139,X27140] : hAPP(c_Set_Ovimage(X27140,X27139,X27138),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X27139,tc_HOL_Obool)),X27137)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X27140,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X27140,X27139,X27138),X27137)),
    inference(variable_rename,[status(thm)],[fact_vimage__Compl]) ).

fof(i_0_9016,plain,
    ! [X19629,X19630,X19631] : 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),X19631),X19630)),X19629),X19630) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19629,X19630),
    inference(variable_rename,[status(thm)],[fact_mod__mult__self3]) ).

fof(i_0_9017,plain,
    ! [X19598,X19599] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19599))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19598))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,X19599)),hAPP(c_Int_Onat,X19598)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19599),X19598)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__nat__int__functions_I1_J])]) ).

fof(i_0_9018,plain,
    ! [X18712,X18713] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18713))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18712))
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,X18713)),hAPP(c_Int_Onat,X18712)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X18713),X18712)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J])]) ).

fof(i_0_9019,plain,
    ! [X18442,X18443] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18443))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18442))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,X18443)),hAPP(c_Int_Onat,X18442)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18443),X18442)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J])]) ).

fof(i_0_9020,plain,
    ! [X18440,X18441] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18441))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18440))
      | hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18441),X18440)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,X18441)),hAPP(c_Int_Onat,X18440)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__distrib])]) ).

fof(i_0_9021,plain,
    ! [X29044,X29045,X29046,X29047] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(X29047,X29046))),hAPP(hAPP(c_List_Ozip(X29047,X29046),X29045),X29044)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29047)),X29045)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29046)),X29044)),
    inference(variable_rename,[status(thm)],[fact_length__zip]) ).

fof(i_0_9022,plain,
    ! [X31047,X31048,X31049,X31050] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X31050,tc_HOL_Obool),hAPP(c_Set_Oimage(X31049,tc_fun(X31050,tc_HOL_Obool),X31048),X31047)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31049,tc_fun(X31050,tc_HOL_Obool)),X31047),X31048),
    inference(variable_rename,[status(thm)],[fact_Inter__image__eq]) ).

fof(i_0_9023,plain,
    ! [X30892,X30893,X30894,X30895] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X30895,tc_HOL_Obool),hAPP(c_Set_Oimage(X30894,tc_fun(X30895,tc_HOL_Obool),X30893),X30892)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X30894,tc_fun(X30895,tc_HOL_Obool)),X30892),X30893),
    inference(variable_rename,[status(thm)],[fact_Union__image__eq]) ).

fof(i_0_9024,plain,
    ! [X31043,X31044,X31045,X31046] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X31046,tc_fun(X31045,tc_HOL_Obool)),X31044),X31043) = c_Complete__Lattice_OInf__class_OInf(tc_fun(X31045,tc_HOL_Obool),hAPP(c_Set_Oimage(X31046,tc_fun(X31045,tc_HOL_Obool),X31043),X31044)),
    inference(variable_rename,[status(thm)],[fact_INTER__eq__Inter__image]) ).

fof(i_0_9025,plain,
    ! [X30888,X30889,X30890,X30891] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X30891,tc_fun(X30890,tc_HOL_Obool)),X30889),X30888) = c_Complete__Lattice_OSup__class_OSup(tc_fun(X30890,tc_HOL_Obool),hAPP(c_Set_Oimage(X30891,tc_fun(X30890,tc_HOL_Obool),X30888),X30889)),
    inference(variable_rename,[status(thm)],[fact_UNION__eq__Union__image]) ).

fof(i_0_9026,plain,
    ! [X17228,X17229,X17230,X17231] :
      ( ~ class_Rings_Osemiring__1(X17231)
      | c_Nat_Osemiring__1__class_Oof__nat__aux(X17231,X17230,hAPP(c_Nat_OSuc,X17229),X17228) = c_Nat_Osemiring__1__class_Oof__nat__aux(X17231,X17230,X17229,hAPP(X17230,X17228)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__aux_Osimps_I2_J])]) ).

fof(i_0_9027,plain,
    ! [X19784,X19785] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19785))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19784))
      | c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,X19785),hAPP(c_Int_Onat,X19784)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,X19785,X19784)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__nat__int__functions_I2_J])]) ).

fof(i_0_9028,plain,
    ! [X19782,X19783] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19783))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19782))
      | hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,X19783,X19782)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,X19783),hAPP(c_Int_Onat,X19782)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mod__distrib])]) ).

fof(i_0_9029,plain,
    ! [X20148,X20149] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X20149,X20148) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20149),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20149),X20148)),X20148)),
    inference(variable_rename,[status(thm)],[fact_zmod__zdiv__equality_H]) ).

fof(i_0_9030,plain,
    ! [X20057,X20058] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20058,X20057) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20058),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20058),X20057)),X20057)),
    inference(variable_rename,[status(thm)],[fact_Divides_Omod__div__equality_H]) ).

fof(i_0_9031,plain,
    ! [X20560,X20561,X20562] :
      ( ~ class_Rings_Olinordered__semidom(X20562)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20562),c_Groups_Oone__class_Oone(X20562)),X20561))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20562),c_Groups_Oone__class_Oone(X20562)),hAPP(hAPP(c_Power_Opower__class_Opower(X20562),X20561),X20560))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__le__power])]) ).

fof(i_0_9032,plain,
    ! [X20547,X20548,X20549] :
      ( ~ class_Rings_Olinordered__semidom(X20549)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20549),c_Groups_Ozero__class_Ozero(X20549)),X20548))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20549),c_Groups_Ozero__class_Ozero(X20549)),hAPP(hAPP(c_Power_Opower__class_Opower(X20549),X20548),X20547))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__power])]) ).

fof(i_0_9033,plain,
    ! [X20554,X20555,X20556] :
      ( ~ class_Rings_Olinordered__semidom(X20556)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20556),c_Groups_Ozero__class_Ozero(X20556)),X20555))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20556),c_Groups_Ozero__class_Ozero(X20556)),hAPP(hAPP(c_Power_Opower__class_Opower(X20556),X20555),X20554))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__power])]) ).

fof(i_0_9034,plain,
    ! [X23281,X23282,X23283,X23284,X23285] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X23285),X23284),X23283))
      | hAPP(c_Set_Oimage(X23285,X23282,hAPP(c_COMBK(X23282,X23285),X23281)),X23283) = hAPP(hAPP(c_Set_Oinsert(X23282),X23281),c_Orderings_Obot__class_Obot(tc_fun(X23282,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__constant])]) ).

fof(i_0_9035,plain,
    ! [X18419,X18420] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18419))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X18420)),hAPP(c_Int_Onat,X18419))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18420),X18419))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X18420)),hAPP(c_Int_Onat,X18419))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18419))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18420),X18419))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X18420)),hAPP(c_Int_Onat,X18419))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__nat__conj])])]) ).

fof(i_0_9036,plain,
    ! [X27353,X27354] : hAPP(hAPP(c_Product__Type_OSigma(X27354,X27353),c_Orderings_Otop__class_Otop(tc_fun(X27354,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X27353,tc_HOL_Obool),X27354),c_Orderings_Otop__class_Otop(tc_fun(X27353,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X27354,X27353),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_UNIV__Times__UNIV]) ).

fof(i_0_9037,plain,
    ! [X18916,X18917] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18917),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18916),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18917),X18916))
        | X18917 = X18916 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18917),X18916))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18917),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18916),c_Groups_Oone__class_Oone(tc_Int_Oint)))) )
      & ( X18917 != X18916
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18917),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18916),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_9038,plain,
    hAPP(c_Relation_Oconverse(X1,X1),c_Relation_OId(X1)) = c_Relation_OId(X1),
    inference(split_conjunct,[status(thm)],[i_0_5830]) ).

fof(i_0_9039,plain,
    ! [X18842,X18843] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18843),hAPP(c_Groups_Ouminus__class_Ouminus(X18843),X18842)),X18842))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18843),c_Groups_Ozero__class_Ozero(X18843)),X18842))
        | ~ class_Groups_Olinordered__ab__group__add(X18843) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18843),c_Groups_Ozero__class_Ozero(X18843)),X18842))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18843),hAPP(c_Groups_Ouminus__class_Ouminus(X18843),X18842)),X18842))
        | ~ class_Groups_Olinordered__ab__group__add(X18843) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__le__self__iff])])]) ).

fof(i_0_9040,plain,
    ! [X18308,X18309] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18309),hAPP(c_Groups_Ouminus__class_Ouminus(X18309),X18308)),X18308))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18309),c_Groups_Ozero__class_Ozero(X18309)),X18308))
        | ~ class_Groups_Olinordered__ab__group__add(X18309) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18309),c_Groups_Ozero__class_Ozero(X18309)),X18308))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18309),hAPP(c_Groups_Ouminus__class_Ouminus(X18309),X18308)),X18308))
        | ~ class_Groups_Olinordered__ab__group__add(X18309) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__less__nonneg])])]) ).

fof(i_0_9041,plain,
    ! [X30549,X30550,X30551,X30552] :
      ( ( hBOOL(hAPP(c_List_Olistsp(X30552,X30551),X30550))
        | ~ hBOOL(hAPP(c_List_Olistsp(X30552,X30551),hAPP(hAPP(c_List_Oappend(X30552),X30550),X30549))) )
      & ( hBOOL(hAPP(c_List_Olistsp(X30552,X30551),X30549))
        | ~ hBOOL(hAPP(c_List_Olistsp(X30552,X30551),hAPP(hAPP(c_List_Oappend(X30552),X30550),X30549))) )
      & ( ~ hBOOL(hAPP(c_List_Olistsp(X30552,X30551),X30550))
        | ~ hBOOL(hAPP(c_List_Olistsp(X30552,X30551),X30549))
        | hBOOL(hAPP(c_List_Olistsp(X30552,X30551),hAPP(hAPP(c_List_Oappend(X30552),X30550),X30549))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__in__listsp__conv])])]) ).

fof(i_0_9042,plain,
    ! [X18699,X18700,X18701,X18702] : hAPP(hAPP(c_Nat_Ocompow(X18702,X18702),X18701),hAPP(hAPP(c_Nat_Ocompow(X18702,X18702),X18700),X18699)) = hAPP(hAPP(c_Nat_Ocompow(X18702,X18702),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18700),X18701)),X18699),
    inference(variable_rename,[status(thm)],[fact_funpow__mult]) ).

fof(i_0_9043,plain,
    ! [X20484,X20485] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20485)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20484)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20485),X20484)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20485),X20484))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20485)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20484))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__number__of__int__code])]) ).

fof(i_0_9044,plain,
    ! [X19251,X19252] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19252)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19251)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19252),X19251)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19252),X19251))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19252)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19251))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__int])]) ).

fof(i_0_9045,plain,
    ! [X19249,X19250] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19250)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19249)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19250),X19249)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19250),X19249))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19250)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19249))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__relations_I3_J])]) ).

fof(i_0_9046,plain,
    ! [X20486,X20487] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20487)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20486)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20487),X20486)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20487),X20486))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20487)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20486))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__number__of__int__code])]) ).

fof(i_0_9047,plain,
    ! [X18078,X18079] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18079)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18078)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18079),X18078)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18079),X18078))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18079)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18078))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__relations_I2_J])]) ).

fof(i_0_9048,plain,
    ! [X17914,X17915] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X17915)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X17914)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17915),X17914)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17915),X17914))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X17915)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X17914))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__int])]) ).

fof(i_0_9049,plain,
    ! [X19992,X19993] :
      ( ( ~ 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),X19993),X19992)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19992),X19993)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19992),X19993))
        | 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),X19993),X19992))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__diff])]) ).

fof(i_0_9050,plain,
    ! [X18543,X18544] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18544),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18543),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X18544),X18543)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X18544),X18543))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18544),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18543),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_9051,plain,
    ! [X20106,X20107] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20107),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20106),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20107),X20106)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20107),X20106))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20107),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20106),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_9052,plain,
    ! [X20442,X20443,X20444] :
      ( ~ class_Int_Onumber__ring(X20444)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20444),hAPP(c_Groups_Ouminus__class_Ouminus(X20444),hAPP(c_Int_Onumber__class_Onumber__of(X20444),X20443))),X20442) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20444),hAPP(c_Int_Onumber__class_Onumber__of(X20444),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X20443))),X20442) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__number__of__mult])]) ).

fof(i_0_9053,plain,
    ! [X18734,X18735,X18736] :
      ( ~ class_Rings_Ocomm__semiring__1(X18736)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18736),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18736),X18735),X18734)),X18734) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18736),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18736),X18735),c_Groups_Oone__class_Oone(X18736))),X18734) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J])]) ).

fof(i_0_9054,plain,
    ! [X29138,X29139,X29140,X29141] :
      ( ( hAPP(hAPP(c_List_Olist__update(X29140,X29139),X29141),X29138) != X29139
        | hAPP(hAPP(c_List_Onth(X29140),X29139),X29141) = X29138
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29141),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29140)),X29139))) )
      & ( hAPP(hAPP(c_List_Onth(X29140),X29139),X29141) != X29138
        | hAPP(hAPP(c_List_Olist__update(X29140,X29139),X29141),X29138) = X29139
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29141),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29140)),X29139))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__update__same__conv])])]) ).

fof(i_0_9055,plain,
    ! [X20640,X20641] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20641)))
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20641),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20640)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20640)))
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20641),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20640)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20641)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20641))) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20640)))
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20641),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20640)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20641),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20640)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20641))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5831])])]) ).

fof(i_0_9056,plain,
    ! [X24499,X24500,X24501] :
      ( ~ class_Orderings_Olinorder(X24501)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24501),X24500))
      | hBOOL(hAPP(hAPP(c_member(X24501),X24499),X24500))
      | X24500 = c_Orderings_Obot__class_Obot(tc_fun(X24501,tc_HOL_Obool))
      | c_Big__Operators_Olattice_OInf__fin(X24501,c_Orderings_Oord__class_Omin(X24501),hAPP(hAPP(c_Set_Oinsert(X24501),X24499),X24500)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X24501),X24499),c_Big__Operators_Olattice_OInf__fin(X24501,c_Orderings_Oord__class_Omin(X24501),X24500)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5832])]) ).

fof(i_0_9057,plain,
    ! [X24443,X24444,X24445] :
      ( ~ class_Orderings_Olinorder(X24445)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24445),X24444))
      | hBOOL(hAPP(hAPP(c_member(X24445),X24443),X24444))
      | X24444 = c_Orderings_Obot__class_Obot(tc_fun(X24445,tc_HOL_Obool))
      | c_Big__Operators_Olattice_OSup__fin(X24445,c_Orderings_Oord__class_Omax(X24445),hAPP(hAPP(c_Set_Oinsert(X24445),X24443),X24444)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X24445),X24443),c_Big__Operators_Olattice_OSup__fin(X24445,c_Orderings_Oord__class_Omax(X24445),X24444)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5833])]) ).

fof(i_0_9058,plain,
    ! [X22372,X22373,X22374,X22375,X22376] :
      ( ~ c_Natural_Oevaln(c_Com_Ocom_OAss(X22376,X22375),X22374,X22373,X22372)
      | X22372 = hAPP(hAPP(hAPP(c_Natural_Oupdate,X22374),X22376),hAPP(X22375,X22374)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evaln__elim__cases_I2_J])]) ).

fof(i_0_9059,plain,
    ! [X18448,X18449] : 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),X18449))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18448))),
    inference(variable_rename,[status(thm)],[fact_negative__zle]) ).

fof(i_0_9060,plain,
    ! [X20213,X20214] : 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),X20214)),X20213))),
    inference(variable_rename,[status(thm)],[fact_zero__le__zpower__abs]) ).

fof(i_0_9061,plain,
    ! [X22388,X22389,X22390] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22390),X22389)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22388),X22389)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X22390),X22388)),X22389),
    inference(variable_rename,[status(thm)],[fact_min__diff]) ).

fof(i_0_9062,plain,
    ! [X19936,X19937,X19938] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X19938),X19937)),X19936) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19938),X19936)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19937),X19936)),
    inference(variable_rename,[status(thm)],[fact_zdiff__zmult__distrib]) ).

cnf(i_0_9063,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_5834]) ).

fof(i_0_9064,plain,
    ! [X18304,X18305,X18306] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18306),X18305)),X18304) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X18306),X18304)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X18305),X18304)),
    inference(variable_rename,[status(thm)],[fact_zadd__zmult__distrib]) ).

fof(i_0_9065,plain,
    ! [X19939,X19940,X19941] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19941),X19940)),X19939) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19941),X19939)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19940),X19939)),
    inference(variable_rename,[status(thm)],[fact_diff__mult__distrib]) ).

fof(i_0_9066,plain,
    ! [X18689,X18690,X18691] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18691),X18690)),X18689) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18691),X18689)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18690),X18689)),
    inference(variable_rename,[status(thm)],[fact_add__mult__distrib]) ).

fof(i_0_9067,plain,
    ! [X28717,X28718,X28719,X28720] : hAPP(hAPP(c_List_Onth(X28720),hAPP(hAPP(c_List_Olist_OCons(X28720),X28719),X28718)),X28717) = c_Nat_Onat_Onat__case(X28720,X28719,hAPP(c_List_Onth(X28720),X28718),X28717),
    inference(variable_rename,[status(thm)],[fact_nth_Osimps]) ).

fof(i_0_9068,plain,
    ! [X33413,X33414,X33415] : c_List_Oreplicate(X33415,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33415)),hAPP(c_List_Ofilter(X33415,hAPP(c_fequal,X33414)),X33413)),X33414) = hAPP(c_List_Ofilter(X33415,hAPP(c_fequal,X33414)),X33413),
    inference(variable_rename,[status(thm)],[fact_replicate__length__filter]) ).

fof(i_0_9069,plain,
    ! [X24790,X24791,X24792,X24793] :
      ( ( X24791 = c_Orderings_Obot__class_Obot(tc_fun(X24793,tc_HOL_Obool))
        | c_Sum__Type_OPlus(X24793,X24792,X24791,X24790) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X24793,X24792),tc_HOL_Obool)) )
      & ( X24790 = c_Orderings_Obot__class_Obot(tc_fun(X24792,tc_HOL_Obool))
        | c_Sum__Type_OPlus(X24793,X24792,X24791,X24790) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X24793,X24792),tc_HOL_Obool)) )
      & ( X24791 != c_Orderings_Obot__class_Obot(tc_fun(X24793,tc_HOL_Obool))
        | X24790 != c_Orderings_Obot__class_Obot(tc_fun(X24792,tc_HOL_Obool))
        | c_Sum__Type_OPlus(X24793,X24792,X24791,X24790) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X24793,X24792),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_9070,plain,
    ! [X31876,X31877,X31878,X31879] :
      ( ~ class_Orderings_Olinorder(X31879)
      | hAPP(c_List_Oset(X31878),c_List_Olinorder__class_Osort__key(X31878,X31879,X31877,X31876)) = hAPP(c_List_Oset(X31878),X31876) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__sort])]) ).

fof(i_0_9071,plain,
    ! [X33487,X33488,X33489] : hAPP(hAPP(c_List_Oappend(X33489),c_List_Oreplicate(X33489,X33488,X33487)),hAPP(hAPP(c_List_Olist_OCons(X33489),X33487),c_List_Olist_ONil(X33489))) = hAPP(hAPP(c_List_Olist_OCons(X33489),X33487),c_List_Oreplicate(X33489,X33488,X33487)),
    inference(variable_rename,[status(thm)],[fact_replicate__append__same]) ).

fof(i_0_9072,plain,
    ! [X31005,X31006,X31007] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X31007,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X31007,tc_HOL_Obool)),X31006),X31005)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31007,tc_HOL_Obool)),X31006),c_Complete__Lattice_OInf__class_OInf(tc_fun(X31007,tc_HOL_Obool),X31005)),
    inference(variable_rename,[status(thm)],[fact_Inter__insert]) ).

fof(i_0_9073,plain,
    ! [X30801,X30802,X30803] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X30803,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X30803,tc_HOL_Obool)),X30802),X30801)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X30803,tc_HOL_Obool)),X30802),c_Complete__Lattice_OSup__class_OSup(tc_fun(X30803,tc_HOL_Obool),X30801)),
    inference(variable_rename,[status(thm)],[fact_Union__insert]) ).

fof(i_0_9074,plain,
    ! [X28215,X28216] :
      ( hAPP(hAPP(c_Relation_Orel__comp(X28216,X28216,X28216),X28215),X28215) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X28216,X28216),tc_HOL_Obool))
      | c_Wellfounded_Owf(X28216,X28215) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__no__loop])]) ).

fof(i_0_9075,plain,
    ! [X20166,X20167] :
      ( ( X20167 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20167),X20166) = X20166 )
      & ( X20167 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20167),X20166) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20167),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X20166)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__eq__if])]) ).

fof(i_0_9076,plain,
    ! [X26307,X26308,X26309,X26310] :
      ( ~ class_Rings_Osemiring__1(X26310)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26309,X26310),hAPP(c_COMBK(X26310,X26309),X26308)),X26307) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X26310),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X26310),hAPP(c_Finite__Set_Ocard(X26309),X26307))),X26308) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__constant])]) ).

fof(i_0_9077,plain,
    ! [X18716,X18717] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18717),hAPP(c_Int_Oring__1__class_Oof__int(X18717),X18716)),c_Groups_Ozero__class_Ozero(X18717)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X18716),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ class_Rings_Olinordered__idom(X18717) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X18716),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18717),hAPP(c_Int_Oring__1__class_Oof__int(X18717),X18716)),c_Groups_Ozero__class_Ozero(X18717)))
        | ~ class_Rings_Olinordered__idom(X18717) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__le__0__iff])])]) ).

fof(i_0_9078,plain,
    ! [X18102,X18103] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18103),hAPP(c_Int_Oring__1__class_Oof__int(X18103),X18102)),c_Groups_Ozero__class_Ozero(X18103)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18102),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ class_Rings_Olinordered__idom(X18103) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18102),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18103),hAPP(c_Int_Oring__1__class_Oof__int(X18103),X18102)),c_Groups_Ozero__class_Ozero(X18103)))
        | ~ class_Rings_Olinordered__idom(X18103) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__less__0__iff])])]) ).

fof(i_0_9079,plain,
    ! [X19354,X19355,X19356,X19357] :
      ( ~ class_Divides_Osemiring__div(X19357)
      | c_Divides_Odiv__class_Omod(X19357,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19357),X19356),c_Divides_Odiv__class_Omod(X19357,X19355,X19354)),X19354) = c_Divides_Odiv__class_Omod(X19357,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19357),X19356),X19355),X19354) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__simps_I2_J])]) ).

fof(i_0_9080,plain,
    ! [X19861,X19862,X19863,X19864] :
      ( ~ class_Divides_Oring__div(X19864)
      | c_Divides_Odiv__class_Omod(X19864,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19864),X19863),X19862),X19861) = c_Divides_Odiv__class_Omod(X19864,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19864),X19863),c_Divides_Odiv__class_Omod(X19864,X19862,X19861)),X19861) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__diff__right__eq])]) ).

fof(i_0_9081,plain,
    ! [X19368,X19369,X19370,X19371] :
      ( ~ class_Divides_Osemiring__div(X19371)
      | c_Divides_Odiv__class_Omod(X19371,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19371),X19370),X19369),X19368) = c_Divides_Odiv__class_Omod(X19371,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19371),X19370),c_Divides_Odiv__class_Omod(X19371,X19369,X19368)),X19368) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__right__eq])]) ).

fof(i_0_9082,plain,
    ! [X19342,X19343,X19344,X19345] :
      ( ~ class_Divides_Osemiring__div(X19345)
      | c_Divides_Odiv__class_Omod(X19345,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19345),X19344),X19343),X19342) = c_Divides_Odiv__class_Omod(X19345,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19345),X19344),c_Divides_Odiv__class_Omod(X19345,X19343,X19342)),X19342) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__right__eq])]) ).

fof(i_0_9083,plain,
    ! [X22282,X22283,X22284,X22285] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22285,tc_HOL_Obool)),X22284),X22283))
      | ~ hBOOL(hAPP(X22284,X22282))
      | hBOOL(hAPP(X22283,X22282)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_predicate1D])]) ).

fof(i_0_9084,plain,
    ! [X22278,X22279,X22280,X22281] :
      ( ~ hBOOL(hAPP(X22281,X22280))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22279,tc_HOL_Obool)),X22281),X22278))
      | hBOOL(hAPP(X22278,X22280)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__predicate1D])]) ).

fof(i_0_9085,plain,
    ! [X19951,X19952] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19952))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19952),X19951))
      | hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X19951),X19952)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X19951)),hAPP(c_Int_Onat,X19952)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__diff__distrib])]) ).

fof(i_0_9086,plain,
    ! [X30553,X30554,X30555,X30556] :
      ( ( hBOOL(hAPP(X30555,X30554))
        | ~ hBOOL(hAPP(c_List_Olistsp(X30556,X30555),hAPP(hAPP(c_List_Olist_OCons(X30556),X30554),X30553))) )
      & ( hBOOL(hAPP(c_List_Olistsp(X30556,X30555),X30553))
        | ~ hBOOL(hAPP(c_List_Olistsp(X30556,X30555),hAPP(hAPP(c_List_Olist_OCons(X30556),X30554),X30553))) )
      & ( ~ hBOOL(hAPP(X30555,X30554))
        | ~ hBOOL(hAPP(c_List_Olistsp(X30556,X30555),X30553))
        | hBOOL(hAPP(c_List_Olistsp(X30556,X30555),hAPP(hAPP(c_List_Olist_OCons(X30556),X30554),X30553))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsp_Oequations_I2_J])])]) ).

fof(i_0_9087,plain,
    ! [X26382,X26383,X26384] :
      ( ~ class_Orderings_Olinorder(X26384)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26384),X26383),X26382))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26384,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26384,X26383),X26382)),hAPP(c_SetInterval_Oord__class_OatLeast(X26384),X26382)) = hAPP(c_SetInterval_Oord__class_OatLeast(X26384),X26383) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I14_J])]) ).

fof(i_0_9088,plain,
    ! [X20933,X20934] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20934),hAPP(c_Int_Onumber__class_Onumber__of(X20934),X20933)),c_Groups_Ozero__class_Ozero(X20934)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20933),c_Int_OPls))
        | ~ class_Int_Onumber__ring(X20934)
        | ~ class_Rings_Olinordered__idom(X20934) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20933),c_Int_OPls))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20934),hAPP(c_Int_Onumber__class_Onumber__of(X20934),X20933)),c_Groups_Ozero__class_Ozero(X20934)))
        | ~ class_Int_Onumber__ring(X20934)
        | ~ class_Rings_Olinordered__idom(X20934) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__special_I3_J])])]) ).

fof(i_0_9089,plain,
    ! [X20937,X20938] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20938),hAPP(c_Int_Onumber__class_Onumber__of(X20938),X20937)),c_Groups_Ozero__class_Ozero(X20938)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20937),c_Int_OPls))
        | ~ class_Int_Onumber__ring(X20938)
        | ~ class_Rings_Olinordered__idom(X20938) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20937),c_Int_OPls))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20938),hAPP(c_Int_Onumber__class_Onumber__of(X20938),X20937)),c_Groups_Ozero__class_Ozero(X20938)))
        | ~ class_Int_Onumber__ring(X20938)
        | ~ class_Rings_Olinordered__idom(X20938) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__special_I3_J])])]) ).

fof(i_0_9090,plain,
    ! [X30276,X30277,X30278,X30279] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30279)),X30278) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30277)),X30276)
      | hAPP(hAPP(c_List_Omap(tc_prod(X30279,X30277),X30279),c_Product__Type_Ofst(X30279,X30277)),hAPP(hAPP(c_List_Ozip(X30279,X30277),X30278),X30276)) = X30278 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__fst__zip])]) ).

fof(i_0_9091,plain,
    ! [X30280,X30281,X30282,X30283] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30283)),X30282) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30281)),X30280)
      | hAPP(hAPP(c_List_Omap(tc_prod(X30283,X30281),X30281),c_Product__Type_Osnd(X30283,X30281)),hAPP(hAPP(c_List_Ozip(X30283,X30281),X30282),X30280)) = X30280 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__snd__zip])]) ).

fof(i_0_9092,plain,
    ! [X19736,X19737,X19738] :
      ( ~ class_Divides_Osemiring__div(X19738)
      | X19737 = c_Groups_Ozero__class_Ozero(X19738)
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X19738),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19738),X19737),X19736)),X19737) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19738),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X19738),X19736),X19737)),c_Groups_Oone__class_Oone(X19738)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__add__self1])]) ).

fof(i_0_9093,plain,
    ! [X19733,X19734,X19735] :
      ( ~ class_Divides_Osemiring__div(X19735)
      | X19734 = c_Groups_Ozero__class_Ozero(X19735)
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X19735),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19735),X19733),X19734)),X19734) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19735),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X19735),X19733),X19734)),c_Groups_Oone__class_Oone(X19735)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__add__self2])]) ).

fof(i_0_9094,plain,
    ! [X19384,X19385,X19386,X19387] :
      ( ~ class_Divides_Osemiring__div(X19387)
      | c_Divides_Odiv__class_Omod(X19387,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19387),X19386),X19385),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19387),X19384),X19385)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19387),c_Divides_Odiv__class_Omod(X19387,X19386,X19384)),X19385) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__mult2])]) ).

fof(i_0_9095,plain,
    ! [X20445,X20446] : hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20446),X20445))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X20446))),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X20445))),
    inference(variable_rename,[status(thm)],[fact_nat__abs__mult__distrib]) ).

fof(i_0_9096,plain,
    ! [X19669,X19670,X19671] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19671))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19671),X19670)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19671),X19669)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19670),X19669) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__div__cancel1])]) ).

fof(i_0_9097,plain,
    ! [X19708,X19709,X19710] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19710))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19709),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19708),X19710)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19709),X19708)),X19710) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__zmult2__eq])]) ).

fof(i_0_9098,plain,
    ! [X31766,X31767,X31768,X31769,X31770] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X31770),X31769),hAPP(c_List_Oset(X31770),X31768)))
      | hBOOL(hAPP(X31767,X31769))
      | c_List_OtakeWhile(X31770,X31767,hAPP(hAPP(c_List_Oappend(X31770),X31768),X31766)) = c_List_OtakeWhile(X31770,X31767,X31768) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5835])]) ).

fof(i_0_9099,plain,
    ! [X20642,X20643] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20643)))
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20643)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20642)) = 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),X20642)) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20643)))
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20643)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20642)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20643)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20642))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5836])]) ).

fof(i_0_9100,plain,
    ! [X20638,X20639] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20639)))
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20639)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20638)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20639)))
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20639)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20638)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20639)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20638))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5837])]) ).

fof(i_0_9101,plain,
    ! [X22270,X22271,X22272,X22273,X22274] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X22274,X22273,X22272),X22271),X22270) = hAPP(hAPP(X22271,hAPP(c_Product__Type_Ofst(X22274,X22273),X22270)),hAPP(c_Product__Type_Osnd(X22274,X22273),X22270)),
    inference(variable_rename,[status(thm)],[fact_split__def]) ).

fof(i_0_9102,plain,
    ! [X22265,X22266,X22267,X22268,X22269] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X22269,X22268,X22267),X22266),X22265) = hAPP(hAPP(X22266,hAPP(c_Product__Type_Ofst(X22269,X22268),X22265)),hAPP(c_Product__Type_Osnd(X22269,X22268),X22265)),
    inference(variable_rename,[status(thm)],[fact_split__beta]) ).

fof(i_0_9103,plain,
    ! [X22250,X22251,X22252,X22253,X22254] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X22254,X22253,X22252),X22251),X22250) = hAPP(hAPP(X22251,hAPP(c_Product__Type_Ofst(X22254,X22253),X22250)),hAPP(c_Product__Type_Osnd(X22254,X22253),X22250)),
    inference(variable_rename,[status(thm)],[fact_prod__case__beta]) ).

fof(i_0_9104,plain,
    ! [X31862,X31863] :
      ( ~ class_Orderings_Olinorder(X31863)
      | c_List_Olinorder__class_Osorted(X31863,c_List_Olinorder__class_Osort__key(X31863,X31863,c_COMBI(X31863),X31862)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__sort])]) ).

fof(i_0_9105,plain,
    ! [X28451,X28452,X28453,X28454,X28455] :
      ( ( X28454 = X28452
        | hAPP(hAPP(c_List_Oappend(X28455),X28454),hAPP(hAPP(c_List_Olist_OCons(X28455),X28453),c_List_Olist_ONil(X28455))) != hAPP(hAPP(c_List_Oappend(X28455),X28452),hAPP(hAPP(c_List_Olist_OCons(X28455),X28451),c_List_Olist_ONil(X28455))) )
      & ( X28453 = X28451
        | hAPP(hAPP(c_List_Oappend(X28455),X28454),hAPP(hAPP(c_List_Olist_OCons(X28455),X28453),c_List_Olist_ONil(X28455))) != hAPP(hAPP(c_List_Oappend(X28455),X28452),hAPP(hAPP(c_List_Olist_OCons(X28455),X28451),c_List_Olist_ONil(X28455))) )
      & ( X28454 != X28452
        | X28453 != X28451
        | hAPP(hAPP(c_List_Oappend(X28455),X28454),hAPP(hAPP(c_List_Olist_OCons(X28455),X28453),c_List_Olist_ONil(X28455))) = hAPP(hAPP(c_List_Oappend(X28455),X28452),hAPP(hAPP(c_List_Olist_OCons(X28455),X28451),c_List_Olist_ONil(X28455))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append1__eq__conv])])]) ).

fof(i_0_9106,plain,
    ! [X29013,X29014,X29015] :
      ( X29015 = c_List_Olist_ONil(X29014)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29013),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29014)),X29015)))
      | hAPP(c_List_Ohd(X29014),hAPP(hAPP(c_List_Odrop(X29014),X29013),X29015)) = hAPP(hAPP(c_List_Onth(X29014),X29015),X29013) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hd__drop__conv__nth])]) ).

fof(i_0_9107,plain,
    ! [X20223,X20224,X20225] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X20225)
      | hAPP(c_Groups_Oabs__class_Oabs(X20225),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20225),hAPP(c_Groups_Oabs__class_Oabs(X20225),X20224)),hAPP(c_Groups_Oabs__class_Oabs(X20225),X20223))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20225),hAPP(c_Groups_Oabs__class_Oabs(X20225),X20224)),hAPP(c_Groups_Oabs__class_Oabs(X20225),X20223)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__add__abs])]) ).

fof(i_0_9108,plain,
    ! [X32860,X32861,X32862,X32863,X32864] :
      ( ~ c_Finite__Set_Ofolding__one__idem(X32864,X32863,X32862)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32864),X32861))
      | hAPP(X32862,hAPP(hAPP(c_Set_Oinsert(X32864),X32860),X32861)) = hAPP(hAPP(c_Finite__Set_Ofold(X32864,X32864,X32863),X32860),X32861) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Oeq__fold__idem_H])]) ).

fof(i_0_9109,plain,
    ! [X23743,X23744,X23745] :
      ( ~ class_Lattices_Osemilattice__inf(X23745)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23745),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23745),X23744),X23743)),X23744)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__le1])]) ).

fof(i_0_9110,plain,
    ! [X23740,X23741,X23742] :
      ( ~ class_Lattices_Olattice(X23742)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23742),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23742),X23741),X23740)),X23741)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__ord_I1_J])]) ).

fof(i_0_9111,plain,
    ! [X23749,X23750,X23751] :
      ( ~ class_Lattices_Osemilattice__inf(X23751)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23751),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23751),X23750),X23749)),X23749)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__le2])]) ).

fof(i_0_9112,plain,
    ! [X23746,X23747,X23748] :
      ( ~ class_Lattices_Olattice(X23748)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23748),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23748),X23747),X23746)),X23746)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__ord_I2_J])]) ).

fof(i_0_9113,plain,
    ! [X22490,X22491,X22492] :
      ( ~ class_Orderings_Olinorder(X22492)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22492),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22492),X22491),X22490)),X22491)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__le1])]) ).

fof(i_0_9114,plain,
    ! [X22487,X22488,X22489] :
      ( ~ class_Orderings_Olinorder(X22489)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22489),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22489),X22488),X22487)),X22487)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__le2])]) ).

fof(i_0_9115,plain,
    ! [X20195] :
      ( ~ 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),X20195)))
      | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20195) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20195)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_expand__Suc])]) ).

fof(i_0_9116,plain,
    ! [X17235,X17236,X17237] :
      ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17237),X17236),X17235))
      | c_Natural_Oevaln(X17237,X17236,esk18_3(X17235,X17236,X17237),X17235) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evalc__evaln])])]) ).

fof(i_0_9117,plain,
    ! [X17183,X17184,X17185,X17187,X17188,X17189,X17190] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17185),X17184),X17183))
        | c_Natural_Oevaln(X17185,X17184,esk15_3(X17183,X17184,X17185),X17183) )
      & ( ~ c_Natural_Oevaln(X17189,X17188,X17190,X17187)
        | hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17189),X17188),X17187)) ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eval__eq])])])])]) ).

fof(i_0_9118,plain,
    ! [X26147,X26148,X26149] :
      ( ~ class_Orderings_Olinorder(X26149)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26149),X26148),X26147))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26149,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X26149),X26148)),c_SetInterval_Oord__class_OatLeastAtMost(X26149,X26148,X26147)) = hAPP(c_SetInterval_Oord__class_OatMost(X26149),X26147) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I10_J])]) ).

fof(i_0_9119,plain,
    ! [X25969,X25970,X25971] :
      ( ~ class_Orderings_Olinorder(X25971)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25971),X25970),X25969))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25971,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X25971),X25970)),c_SetInterval_Oord__class_OgreaterThanAtMost(X25971,X25970,X25969)) = hAPP(c_SetInterval_Oord__class_OatMost(X25971),X25969) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I9_J])]) ).

fof(i_0_9120,plain,
    ! [X26094,X26095,X26096] :
      ( ~ class_Orderings_Olinorder(X26096)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26096),X26095),X26094))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26096,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X26096),X26095)),c_SetInterval_Oord__class_OgreaterThanLessThan(X26096,X26095,X26094)) = hAPP(c_SetInterval_Oord__class_OlessThan(X26096),X26094) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I7_J])]) ).

fof(i_0_9121,plain,
    ! [X20215,X20216,X20217] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X20217)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20217),hAPP(c_Groups_Oabs__class_Oabs(X20217),X20216)),X20215))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20217),X20216),X20215)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__le__D1])]) ).

fof(i_0_9122,plain,
    ! [X23980,X23981,X23982,X23983] :
      ( ~ class_Lattices_Odistrib__lattice(X23983)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23983),X23982),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23983),X23981),X23980)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23983),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23983),X23982),X23981)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23983),X23982),X23980)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__distrib1])]) ).

fof(i_0_9123,plain,
    ! [X23984,X23985,X23986,X23987] :
      ( ~ class_Lattices_Odistrib__lattice(X23987)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23987),X23986),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23987),X23985),X23984)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23987),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23987),X23986),X23985)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23987),X23986),X23984)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__inf__distrib1])]) ).

fof(i_0_9124,plain,
    ! [X22548,X22549,X22550,X22551] :
      ( ~ class_Orderings_Olinorder(X22551)
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X22551),X22550),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22551),X22549),X22548)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X22551),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22551),X22550),X22549)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22551),X22550),X22548)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__inf__distrib1])]) ).

fof(i_0_9125,plain,
    ! [X22544,X22545,X22546,X22547] :
      ( ~ class_Orderings_Olinorder(X22547)
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X22547),X22546),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22547),X22545),X22544)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X22547),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22547),X22546),X22545)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22547),X22546),X22544)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__sup__distrib1])]) ).

fof(i_0_9126,plain,
    ! [X18268,X18269,X18270,X18271] :
      ( ~ class_Rings_Ocomm__semiring__1(X18271)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18271),X18270),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18271),X18269),X18268)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18271),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18271),X18270),X18269)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18271),X18270),X18268)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J])]) ).

fof(i_0_9127,plain,
    ! [X18144,X18145,X18146,X18147] :
      ( ~ class_Rings_Ocomm__semiring__1(X18147)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18147),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18147),X18146),X18145)),X18144) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18147),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18147),X18146),X18144)),X18145) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J])]) ).

fof(i_0_9128,plain,
    ! [X17811,X17812,X17813,X17814] :
      ( ~ class_Rings_Ocomm__semiring__1(X17814)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17814),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17814),X17813),X17812)),X17811) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17814),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17814),X17813),X17811)),X17812) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J])]) ).

fof(i_0_9129,plain,
    ! [X27910,X27911,X27912] : hAPP(c_Fun_Ocomp(X27912,X27912,X27911,c_Fun_Oid(X27912)),X27910) = X27910,
    inference(variable_rename,[status(thm)],[fact_id__o]) ).

fof(i_0_9130,plain,
    ! [X28946,X28947,X28948] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X28948),X28947),hAPP(c_List_Oset(X28948),X28946)))
      | 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(X28948)),X28946))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_length__pos__if__in__set])]) ).

cnf(i_0_9131,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_5735]) ).

fof(i_0_9132,plain,
    ! [X27080,X27081,X27082] :
      ( ~ class_Groups_Oab__semigroup__mult(X27082)
      | X27081 = c_Orderings_Obot__class_Obot(tc_fun(X27082,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27082),X27081))
      | hBOOL(hAPP(hAPP(c_member(X27082),X27080),X27081))
      | hAPP(c_Finite__Set_Ofold1(X27082,c_Groups_Otimes__class_Otimes(X27082)),hAPP(hAPP(c_Set_Oinsert(X27082),X27080),X27081)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27082),X27080),hAPP(c_Finite__Set_Ofold1(X27082,c_Groups_Otimes__class_Otimes(X27082)),X27081)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5838])]) ).

fof(i_0_9133,plain,
    ! [X32533,X32534,X32535] :
      ( ~ c_Relation_Osingle__valued(X32535,X32535,X32534)
      | c_Relation_Osingle__valued(X32535,X32535,hAPP(hAPP(c_Nat_Ocompow(tc_prod(X32535,X32535),tc_HOL_Obool),X32533),X32534)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_single__valued__rel__pow])]) ).

fof(i_0_9134,plain,
    ! [X33674,X33675,X33676,X33677] : hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(X33677),X33676),X33675),X33674) = 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(X33677)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_DSequence_Osingle(X33677),X33676)),
    inference(variable_rename,[status(thm)],[fact_Random__Sequence_Osingle__def]) ).

fof(i_0_9135,plain,
    ! [X30970,X30971,X30972,X30973,X30975,X30976,X30977,X30978,X30979] :
      ( ( ~ hBOOL(hAPP(c_Predicate_ODomainP(X30973,X30972,X30971),X30970))
        | hBOOL(hAPP(hAPP(X30971,X30970),esk372_2(X30970,X30971))) )
      & ( ~ hBOOL(hAPP(hAPP(X30976,X30975),X30977))
        | hBOOL(hAPP(c_Predicate_ODomainP(X30979,X30978,X30976),X30975)) ) ),
    inference(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_9136,plain,
    ! [X26644,X26645,X26646,X26647,X26648] :
      ( ( hAPP(X26646,X26645) != hAPP(X26646,X26644)
        | X26645 = X26644
        | ~ c_Fun_Oinj__on(X26648,X26647,X26646,c_Orderings_Otop__class_Otop(tc_fun(X26648,tc_HOL_Obool))) )
      & ( X26645 != X26644
        | hAPP(X26646,X26645) = hAPP(X26646,X26644)
        | ~ c_Fun_Oinj__on(X26648,X26647,X26646,c_Orderings_Otop__class_Otop(tc_fun(X26648,tc_HOL_Obool))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__eq])])]) ).

fof(i_0_9137,plain,
    ! [X26639,X26640,X26641,X26642,X26643] :
      ( ~ c_Fun_Oinj__on(X26643,X26642,X26641,c_Orderings_Otop__class_Otop(tc_fun(X26643,tc_HOL_Obool)))
      | hAPP(X26641,X26640) != hAPP(X26641,X26639)
      | X26640 = X26639 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_injD])]) ).

fof(i_0_9138,plain,
    ! [X33472,X33473,X33474,X33475] : c_List_Oreplicate(X33475,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33474),X33473),X33472) = hAPP(hAPP(c_List_Oappend(X33475),c_List_Oreplicate(X33475,X33474,X33472)),c_List_Oreplicate(X33475,X33473,X33472)),
    inference(variable_rename,[status(thm)],[fact_replicate__add]) ).

fof(i_0_9139,plain,
    ! [X32905,X32906,X32907] :
      ( ~ class_Orderings_Olinorder(X32907)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32907),X32906))
      | c_Big__Operators_Olattice_OInf__fin(X32907,c_Orderings_Oord__class_Omin(X32907),hAPP(hAPP(c_Set_Oinsert(X32907),X32905),X32906)) = hAPP(hAPP(c_Finite__Set_Ofold(X32907,X32907,c_Orderings_Oord__class_Omin(X32907)),X32905),X32906) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oeq__fold__idem_H])]) ).

fof(i_0_9140,plain,
    ! [X32908,X32909,X32910] :
      ( ~ class_Orderings_Olinorder(X32910)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32910),X32909))
      | c_Big__Operators_Olattice_OSup__fin(X32910,c_Orderings_Oord__class_Omax(X32910),hAPP(hAPP(c_Set_Oinsert(X32910),X32908),X32909)) = hAPP(hAPP(c_Finite__Set_Ofold(X32910,X32910,c_Orderings_Oord__class_Omax(X32910)),X32908),X32909) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oeq__fold__idem_H])]) ).

cnf(i_0_9141,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_9142,plain,
    ! [X19278,X19279,X19281] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk50_2(X19278,X19279)),X19278))
        | ~ hBOOL(hAPP(X19279,X19278))
        | hBOOL(hAPP(X19279,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19281),esk50_2(X19278,X19279)))
        | ~ hBOOL(hAPP(X19279,X19281))
        | ~ hBOOL(hAPP(X19279,X19278))
        | hBOOL(hAPP(X19279,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
      & ( hBOOL(hAPP(X19279,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk50_2(X19278,X19279)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | ~ hBOOL(hAPP(X19279,X19278))
        | hBOOL(hAPP(X19279,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_9143,plain,
    ! [X29425,X29426,X29427,X29428] : hAPP(c_List_Ofoldl(X29428,X29427,X29426,X29425),c_List_Olist_ONil(X29427)) = X29425,
    inference(variable_rename,[status(thm)],[fact_foldl__Nil]) ).

fof(i_0_9144,plain,
    ! [X29280,X29281,X29282,X29283] : hAPP(c_List_Olist_Olist__case(X29283,X29282,X29281,X29280),c_List_Olist_ONil(X29282)) = X29281,
    inference(variable_rename,[status(thm)],[fact_list_Osimps_I4_J]) ).

fof(i_0_9145,plain,
    ! [X27913,X27914,X27915] : hAPP(c_Fun_Ocomp(X27915,X27914,X27915,X27913),c_Fun_Oid(X27915)) = X27913,
    inference(variable_rename,[status(thm)],[fact_o__id]) ).

fof(i_0_9146,plain,
    ! [X18749,X18750,X18751] :
      ( ( X18750 = c_Groups_Ozero__class_Ozero(X18751)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18751),X18750),X18749) != c_Groups_Ozero__class_Ozero(X18751)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18751),c_Groups_Ozero__class_Ozero(X18751)),X18749))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18751),c_Groups_Ozero__class_Ozero(X18751)),X18750))
        | ~ class_Groups_Oordered__comm__monoid__add(X18751) )
      & ( X18749 = c_Groups_Ozero__class_Ozero(X18751)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18751),X18750),X18749) != c_Groups_Ozero__class_Ozero(X18751)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18751),c_Groups_Ozero__class_Ozero(X18751)),X18749))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18751),c_Groups_Ozero__class_Ozero(X18751)),X18750))
        | ~ class_Groups_Oordered__comm__monoid__add(X18751) )
      & ( X18750 != c_Groups_Ozero__class_Ozero(X18751)
        | X18749 != c_Groups_Ozero__class_Ozero(X18751)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18751),X18750),X18749) = c_Groups_Ozero__class_Ozero(X18751)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18751),c_Groups_Ozero__class_Ozero(X18751)),X18749))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18751),c_Groups_Ozero__class_Ozero(X18751)),X18750))
        | ~ class_Groups_Oordered__comm__monoid__add(X18751) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__eq__0__iff])])]) ).

cnf(i_0_9147,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_9148,plain,
    ! [X20021,X20022,X20023] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20023),X20022))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20021),X20022)),X20023) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20021),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20022),X20023)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__add__assoc])]) ).

fof(i_0_9149,plain,
    ! [X20043,X20044,X20045] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20045),X20044))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20043),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20044),X20045)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20043),X20045)),X20044) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__diff__right])]) ).

fof(i_0_9150,plain,
    ! [X20032,X20033,X20034] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20034),X20033))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20032),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20033),X20034)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20032),X20033)),X20034) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__diff__assoc])]) ).

fof(i_0_9151,plain,
    ! [X19275,X19276,X19277] :
      ( ~ class_Lattices_Oboolean__algebra(X19277)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19277),X19276),X19275))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19277),hAPP(c_Groups_Ouminus__class_Ouminus(X19277),X19275)),hAPP(c_Groups_Ouminus__class_Ouminus(X19277),X19276))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__mono])]) ).

fof(i_0_9152,plain,
    ! [X18683,X18684,X18685] :
      ( ~ class_Groups_Oordered__ab__group__add(X18685)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18685),X18684),X18683))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18685),hAPP(c_Groups_Ouminus__class_Ouminus(X18685),X18683)),hAPP(c_Groups_Ouminus__class_Ouminus(X18685),X18684))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__neg__le])]) ).

cnf(i_0_9153,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_5842]) ).

cnf(i_0_9154,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_5843]) ).

cnf(i_0_9155,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_5844]) ).

cnf(i_0_9156,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_5845]) ).

fof(i_0_9157,plain,
    ! [X18436] :
      ( ( ~ 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,X18436)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X18436)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X18436))
        | 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,X18436))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__less__nat__eq])]) ).

fof(i_0_9158,plain,
    ! [X19578,X19579] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19579,X19578)),X19579)),
    inference(variable_rename,[status(thm)],[fact_mod__less__eq__dividend]) ).

fof(i_0_9159,plain,
    ! [X26526] : hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X26526)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),X26526)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X26526)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_greaterThan__Suc]) ).

fof(i_0_9160,plain,
    ! [X20358,X20359,X20360,X20361] :
      ( ~ class_Rings_Ocomm__semiring__1(X20361)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20361),hAPP(hAPP(c_Power_Opower__class_Opower(X20361),X20360),X20359)),hAPP(hAPP(c_Power_Opower__class_Opower(X20361),X20360),X20358)) = hAPP(hAPP(c_Power_Opower__class_Opower(X20361),X20360),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20359),X20358)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J])]) ).

fof(i_0_9161,plain,
    ! [X20577,X20578,X20579,X20580] :
      ( ~ class_Groups_Omonoid__mult(X20580)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X20580),X20579),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20578),X20577)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20580),hAPP(hAPP(c_Power_Opower__class_Opower(X20580),X20579),X20578)),hAPP(hAPP(c_Power_Opower__class_Opower(X20580),X20579),X20577)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__add])]) ).

fof(i_0_9162,plain,
    ! [X32890,X32891,X32892] :
      ( ~ class_Lattices_Oab__semigroup__idem__mult(X32892)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32892),X32891))
      | hAPP(c_Finite__Set_Ofold1(X32892,c_Groups_Otimes__class_Otimes(X32892)),hAPP(hAPP(c_Set_Oinsert(X32892),X32890),X32891)) = hAPP(hAPP(c_Finite__Set_Ofold(X32892,X32892,c_Groups_Otimes__class_Otimes(X32892)),X32890),X32891) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1__eq__fold__idem])]) ).

fof(i_0_9163,plain,
    ! [X18390,X18391,X18392,X18393,X18394,X18395] :
      ( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X18395)
      | X18394 = c_Groups_Ozero__class_Ozero(X18395)
      | X18393 != X18392
      | X18391 = X18390
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18395),X18393),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18395),X18394),X18391)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18395),X18392),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18395),X18394),X18390)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__scale__eq__noteq])]) ).

fof(i_0_9164,plain,
    ! [X30264,X30265] : c_Hilbert__Choice_OEps(X30265,hAPP(hAPP(c_COMBC(X30265,X30265,tc_HOL_Obool),c_fequal),X30264)) = X30264,
    inference(variable_rename,[status(thm)],[fact_some__eq__trivial]) ).

fof(i_0_9165,plain,
    ! [X32035,X32036] : c_HOL_OThe(X32036,hAPP(hAPP(c_COMBC(X32036,X32036,tc_HOL_Obool),c_fequal),X32035)) = X32035,
    inference(variable_rename,[status(thm)],[fact_the__eq__trivial]) ).

fof(i_0_9166,plain,
    ! [X19994,X19995] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19995),X19994)),hAPP(c_Nat_OSuc,X19995))),
    inference(variable_rename,[status(thm)],[fact_diff__less__Suc]) ).

fof(i_0_9167,plain,
    ! [X17487,X17488] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17488),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17488),X17487)))),
    inference(variable_rename,[status(thm)],[fact_less__add__Suc1]) ).

fof(i_0_9168,plain,
    ! [X17485,X17486] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17486),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17485),X17486)))),
    inference(variable_rename,[status(thm)],[fact_less__add__Suc2]) ).

fof(i_0_9169,plain,
    ! [X25532,X25533,X25534,X25535] :
      ( ~ class_Orderings_Oorder(X25535)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25535,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X25535,X25534,X25533)),c_SetInterval_Oord__class_OgreaterThanAtMost(X25535,X25533,X25532)) = c_Orderings_Obot__class_Obot(tc_fun(X25535,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I16_J])]) ).

fof(i_0_9170,plain,
    ! [X25536,X25537,X25538,X25539] :
      ( ~ class_Orderings_Oorder(X25539)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25539,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X25539,X25538,X25537)),c_SetInterval_Oord__class_OgreaterThanLessThan(X25539,X25537,X25536)) = c_Orderings_Obot__class_Obot(tc_fun(X25539,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I12_J])]) ).

fof(i_0_9171,plain,
    ! [X25324,X25325,X25326,X25327] :
      ( ~ class_Orderings_Oorder(X25327)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25327,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X25327,X25326,X25325)),c_SetInterval_Oord__class_OgreaterThanAtMost(X25327,X25325,X25324)) = c_Orderings_Obot__class_Obot(tc_fun(X25327,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I14_J])]) ).

fof(i_0_9172,plain,
    ! [X25339,X25340,X25341,X25342] :
      ( ~ class_Orderings_Oorder(X25342)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25342,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X25342,X25341,X25340)),c_SetInterval_Oord__class_OgreaterThanLessThan(X25342,X25340,X25339)) = c_Orderings_Obot__class_Obot(tc_fun(X25342,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I10_J])]) ).

fof(i_0_9173,plain,
    ! [X25540,X25541,X25542,X25543] :
      ( ~ class_Orderings_Oorder(X25543)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25543,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X25543,X25542,X25541)),c_SetInterval_Oord__class_OatLeastAtMost(X25543,X25541,X25540)) = c_Orderings_Obot__class_Obot(tc_fun(X25543,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I13_J])]) ).

fof(i_0_9174,plain,
    ! [X19071,X19072] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19072,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X19072,tc_HOL_Obool))),X19071)),
    inference(variable_rename,[status(thm)],[fact_empty__subsetI]) ).

fof(i_0_9175,plain,
    ! [X32469,X32470,X32471] :
      ( ~ c_Equiv__Relations_Oequiv(X32471,X32470,X32469)
      | hAPP(hAPP(c_Relation_Orel__comp(X32471,X32471,X32471),hAPP(c_Relation_Oconverse(X32471,X32471),X32469)),X32469) = X32469 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__comp__eq])]) ).

fof(i_0_9176,plain,
    ! [X24041,X24042,X24043,X24044] :
      ( hBOOL(hAPP(hAPP(c_member(X24044),X24043),X24042))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24044,tc_HOL_Obool)),X24042),hAPP(hAPP(c_Set_Oinsert(X24044),X24043),X24041)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24044,tc_HOL_Obool)),X24042),X24041) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5846])]) ).

fof(i_0_9177,plain,
    ! [X17191,X17192,X17193,X17194] :
      ( ~ c_Natural_Oevaln(X17194,X17193,X17192,X17191)
      | hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17194),X17193),X17191)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evaln__evalc])]) ).

fof(i_0_9178,plain,
    ! [X22500,X22501,X22502,X22503] : c_Natural_Oevaln(c_Com_Ocom_OAss(X22503,X22502),X22501,X22500,hAPP(hAPP(hAPP(c_Natural_Oupdate,X22501),X22503),hAPP(X22502,X22501))),
    inference(variable_rename,[status(thm)],[fact_evaln_Oequations_I2_J]) ).

fof(i_0_9179,plain,
    ! [X22377,X22378,X22379,X22380] : c_Natural_Oevaln(c_Com_Ocom_OAss(X22380,X22379),X22378,X22377,hAPP(hAPP(hAPP(c_Natural_Oupdate,X22378),X22380),hAPP(X22379,X22378))),
    inference(variable_rename,[status(thm)],[fact_evaln_OAssign]) ).

fof(i_0_9180,plain,
    ! [X19535,X19536] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19536))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19535))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat__Transfer_Otsub(X19536,X19535))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J])]) ).

fof(i_0_9181,plain,
    ! [X19098,X19099,X19100] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19100,tc_HOL_Obool)),X19099),hAPP(hAPP(c_Set_Oinsert(X19100),X19098),X19099))),
    inference(variable_rename,[status(thm)],[fact_subset__insertI]) ).

fof(i_0_9182,plain,
    ! [X19945,X19946,X19947] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X19947),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19946,X19945)),X19945) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X19947),X19946),X19945),
    inference(variable_rename,[status(thm)],[fact_zdiff__zmod__right]) ).

fof(i_0_9183,plain,
    ! [X19407,X19408,X19409] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19409),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19408,X19407)),X19407) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19409),X19408),X19407),
    inference(variable_rename,[status(thm)],[fact_zmod__simps_I3_J]) ).

fof(i_0_9184,plain,
    ! [X19410,X19411,X19412] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19412),X19411),X19410) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19412),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19411,X19410)),X19410),
    inference(variable_rename,[status(thm)],[fact_zmod__zmult1__eq]) ).

fof(i_0_9185,plain,
    ! [X26130,X26131,X26132] :
      ( ~ class_Orderings_Olinorder(X26132)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26132),X26131),X26130))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26132,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X26132),X26131)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26132,X26131),X26130)) = hAPP(c_SetInterval_Oord__class_OlessThan(X26132),X26130) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I8_J])]) ).

cnf(i_0_9186,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_9187,plain,
    ! [X25510,X25511] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25511),hAPP(c_Nat_OSuc,X25510)))
      | c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X25511,hAPP(c_Nat_OSuc,X25510)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X25510)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X25511,X25510)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastAtMostSuc__conv])]) ).

cnf(i_0_9188,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_9189,plain,
    ! [X26679] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X26679)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X26679),tc_HOL_Obool))))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X26679),c_Orderings_Otop__class_Otop(tc_fun(X26679,tc_HOL_Obool)))) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26679),c_Orderings_Otop__class_Otop(tc_fun(X26679,tc_HOL_Obool))))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X26679)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X26679),tc_HOL_Obool)))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__option__UNIV])]) ).

fof(i_0_9190,plain,
    ! [X18029,X18030,X18031] :
      ( ~ class_Rings_Olinordered__semidom(X18031)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18030),X18029))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18031),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18031),X18030)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18031),X18029))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__of__nat__less])]) ).

fof(i_0_9191,plain,
    ! [X26388,X26389,X26390,X26391] :
      ( ~ class_Orderings_Olinorder(X26391)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26391,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X26391),X26390)),c_SetInterval_Oord__class_OatLeastAtMost(X26391,X26389,X26388)) = c_SetInterval_Oord__class_OatLeastAtMost(X26391,hAPP(hAPP(c_Orderings_Oord__class_Omax(X26391),X26390),X26389),X26388) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMostR2])]) ).

fof(i_0_9192,plain,
    ! [X25958,X25959,X25960,X25961] :
      ( ~ class_Orderings_Olinorder(X25961)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25961,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X25961),X25960)),c_SetInterval_Oord__class_OatLeastAtMost(X25961,X25959,X25958)) = c_SetInterval_Oord__class_OatLeastAtMost(X25961,X25959,hAPP(hAPP(c_Orderings_Oord__class_Omin(X25961),X25960),X25958)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMostR1])]) ).

fof(i_0_9193,plain,
    ! [X18421,X18422] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18422),hAPP(c_Int_Onat,X18421)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18422)),X18421)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18422)),X18421))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18422),hAPP(c_Int_Onat,X18421))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__nat__eq__int__zless])]) ).

fof(i_0_9194,plain,
    ! [X25545,X25546] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25546),X25545))
        | c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X25545,X25546) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25546),X25545))
        | c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X25545,X25546) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),X25545),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25545),c_Groups_Oone__class_Oone(tc_Int_Oint)),X25546)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5849])]) ).

fof(i_0_9195,plain,
    ! [X19800,X19801] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19801))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19800))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X19801)),hAPP(c_Int_Onat,X19800)) = hAPP(c_Int_Onat,c_Nat__Transfer_Otsub(X19801,X19800)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J])]) ).

fof(i_0_9196,plain,
    ! [X28880,X28881,X28882,X28883] : hAPP(hAPP(c_List_Odrop(X28883),X28882),hAPP(hAPP(c_List_Otake(X28883),X28881),X28880)) = hAPP(hAPP(c_List_Otake(X28883),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X28881),X28882)),hAPP(hAPP(c_List_Odrop(X28883),X28882),X28880)),
    inference(variable_rename,[status(thm)],[fact_drop__take]) ).

fof(i_0_9197,plain,
    ! [X28032,X28033,X28034,X28035] : hAPP(hAPP(c_Relation_Orel__comp(X28035,X28034,X28033),X28032),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X28034,X28033),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X28035,X28033),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_rel__comp__empty2]) ).

fof(i_0_9198,plain,
    ! [X34149,X34150,X34151,X34152] : c_Product__Type_Ocurry(X34152,X34151,X34150,hAPP(c_Product__Type_Oprod_Oprod__case(X34152,X34151,X34150),X34149)) = X34149,
    inference(variable_rename,[status(thm)],[fact_curry__split]) ).

fof(i_0_9199,plain,
    ! [X22181] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X22181)))
      | 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),X22181)) = 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),X22181))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__pos__pos__1__number__of])]) ).

fof(i_0_9200,plain,
    ! [X19580,X19581,X19582] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19582,X19581)),X19580) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19582),X19580),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19581),X19580)),
    inference(variable_rename,[status(thm)],[fact_mod__mult__distrib]) ).

fof(i_0_9201,plain,
    ! [X22863,X22864,X22865,X22866] :
      ( ~ class_Lattices_Osemilattice__sup(X22866)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22866),X22865),X22864))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22866),X22865),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X22866),X22864),X22863))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__supI1])]) ).

fof(i_0_9202,plain,
    ! [X22867,X22868,X22869,X22870] :
      ( ~ class_Lattices_Osemilattice__sup(X22870)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22870),X22869),X22868))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22870),X22869),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X22870),X22867),X22868))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__supI2])]) ).

fof(i_0_9203,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),X22577),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22578),X22576),X22575))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__supI1])]) ).

fof(i_0_9204,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),X22581),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22582),X22579),X22580))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__supI2])]) ).

fof(i_0_9205,plain,
    ! [X22930,X22931,X22932,X22933] :
      ( ~ class_Lattices_Osemilattice__sup(X22933)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22933),X22932),X22931))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22933),X22932),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X22933),X22931),X22930))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__supI1])]) ).

fof(i_0_9206,plain,
    ! [X22926,X22927,X22928,X22929] :
      ( ~ class_Lattices_Osemilattice__sup(X22929)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22929),X22928),X22927))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22929),X22928),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X22929),X22926),X22927))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__supI2])]) ).

fof(i_0_9207,plain,
    ! [X22630,X22631,X22632,X22633] :
      ( ~ class_Orderings_Olinorder(X22633)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22633),X22632),X22631))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22633),X22632),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22633),X22631),X22630))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oless__supI1])]) ).

fof(i_0_9208,plain,
    ! [X22626,X22627,X22628,X22629] :
      ( ~ class_Orderings_Olinorder(X22629)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22629),X22628),X22627))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22629),X22628),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22629),X22626),X22627))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oless__supI2])]) ).

cnf(i_0_9209,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_9210,plain,
    ! [X19024] : 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),X19024))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[fact_negative__zle__0]) ).

fof(i_0_9211,plain,
    ! [X31314,X31315,X31316,X31317,X31318] :
      ( ( c_List_Otranspose(X31315,X31314) != c_List_Olist_ONil(tc_List_Olist(X31315))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X31315)),X31316),hAPP(c_List_Oset(tc_List_Olist(X31315)),X31314)))
        | X31316 = c_List_Olist_ONil(X31315) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X31318)),esk389_2(X31317,X31318)),hAPP(c_List_Oset(tc_List_Olist(X31318)),X31317)))
        | c_List_Otranspose(X31318,X31317) = c_List_Olist_ONil(tc_List_Olist(X31318)) )
      & ( esk389_2(X31317,X31318) != c_List_Olist_ONil(X31318)
        | c_List_Otranspose(X31318,X31317) = c_List_Olist_ONil(tc_List_Olist(X31318)) ) ),
    inference(distribute,[status(thm)],[inference(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_9212,plain,
    ! [X26351,X26352,X26353] :
      ( ~ class_Groups_Ocomm__monoid__add(X26353)
      | hAPP(X26352,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(X26353)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26353),X26352),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X26351)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X26353),X26352),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X26351)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__shift__lb__Suc0__0__upt])]) ).

fof(i_0_9213,plain,
    ! [X25064,X25065,X25066] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25066,tc_fun(X25065,tc_HOL_Obool)),X25064),hAPP(c_COMBK(tc_fun(X25065,tc_HOL_Obool),X25066),c_Orderings_Obot__class_Obot(tc_fun(X25065,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X25065,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_UN__empty2]) ).

fof(i_0_9214,plain,
    ! [X17531,X17532,X17533] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17533),X17532))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17532),X17531))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X17533)),X17531)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__trans__Suc])]) ).

fof(i_0_9215,plain,
    ! [X22305] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X22305)))
      | 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),X22305)) = 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),X22305))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__pos__pos__1__number__of])]) ).

fof(i_0_9216,plain,
    ! [X19459,X19460] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19460))
      | 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,X19459,X19460))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__mod__sign])]) ).

fof(i_0_9217,plain,
    ! [X29491,X29492] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X29492,X29491) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X29492),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X29491),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(variable_rename,[status(thm)],[fact_greaterThanLessThan__upto]) ).

fof(i_0_9218,plain,
    ! [X30081,X30082,X30083,X30084,X30085] : hAPP(hAPP(c_List_Omap(X30085,X30084),X30083),hAPP(hAPP(c_List_Olist_OCons(X30085),X30082),X30081)) = hAPP(hAPP(c_List_Olist_OCons(X30084),hAPP(X30083,X30082)),hAPP(hAPP(c_List_Omap(X30085,X30084),X30083),X30081)),
    inference(variable_rename,[status(thm)],[fact_map_Osimps_I2_J]) ).

fof(i_0_9219,plain,
    ! [X21396,X21397,X21398] :
      ( ~ class_Fields_Ofield__inverse__zero(X21398)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21398),c_Groups_Oone__class_Oone(X21398)),hAPP(hAPP(c_Power_Opower__class_Opower(X21398),X21397),X21396)) = hAPP(hAPP(c_Power_Opower__class_Opower(X21398),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21398),c_Groups_Oone__class_Oone(X21398)),X21397)),X21396) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__one__over])]) ).

fof(i_0_9220,plain,
    ! [X18709] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18709))
      | 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)),X18709))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__0__less])]) ).

fof(i_0_9221,plain,
    ! [X20785,X20786,X20787,X20788] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X20788),X20787),X20786))
      | hBOOL(hAPP(hAPP(c_member(X20788),X20787),hAPP(hAPP(c_Set_Oinsert(X20788),X20785),X20786))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insertI2])]) ).

fof(i_0_9222,plain,
    ! [X20722,X20723,X20724,X20725] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X20725),X20724),X20723))
        | hBOOL(hAPP(hAPP(c_member(X20725),X20724),hAPP(hAPP(c_Set_Oinsert(X20725),X20722),X20723))) )
      & ( X20724 != X20722
        | hBOOL(hAPP(hAPP(c_member(X20725),X20724),hAPP(hAPP(c_Set_Oinsert(X20725),X20722),X20723))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5851])])]) ).

fof(i_0_9223,plain,
    ! [X18674,X18675,X18676] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18676),X18675),hAPP(c_Groups_Ouminus__class_Ouminus(X18676),X18674)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18676),X18674),hAPP(c_Groups_Ouminus__class_Ouminus(X18676),X18675)))
        | ~ class_Groups_Oordered__ab__group__add(X18676) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18676),X18674),hAPP(c_Groups_Ouminus__class_Ouminus(X18676),X18675)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18676),X18675),hAPP(c_Groups_Ouminus__class_Ouminus(X18676),X18674)))
        | ~ class_Groups_Oordered__ab__group__add(X18676) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__minus__iff])])]) ).

fof(i_0_9224,plain,
    ! [X18235,X18236,X18237] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18237),X18236),hAPP(c_Groups_Ouminus__class_Ouminus(X18237),X18235)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18237),X18235),hAPP(c_Groups_Ouminus__class_Ouminus(X18237),X18236)))
        | ~ class_Groups_Oordered__ab__group__add(X18237) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18237),X18235),hAPP(c_Groups_Ouminus__class_Ouminus(X18237),X18236)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18237),X18236),hAPP(c_Groups_Ouminus__class_Ouminus(X18237),X18235)))
        | ~ class_Groups_Oordered__ab__group__add(X18237) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__minus__iff])])]) ).

fof(i_0_9225,plain,
    ! [X29493,X29494,X29495,X29496] :
      ( ( X29494 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29495)),X29496)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | c_List_Olast(X29495,hAPP(hAPP(c_List_Olist__update(X29495,X29496),X29494),X29493)) = X29493
        | X29496 = c_List_Olist_ONil(X29495) )
      & ( X29494 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29495)),X29496)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | c_List_Olast(X29495,hAPP(hAPP(c_List_Olist__update(X29495,X29496),X29494),X29493)) = c_List_Olast(X29495,X29496)
        | X29496 = c_List_Olist_ONil(X29495) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__list__update])])]) ).

fof(i_0_9226,plain,
    ! [X19471,X19472] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19472),c_Groups_Osgn__class_Osgn(X19472,X19471)),c_Groups_Ozero__class_Ozero(X19472)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19472),X19471),c_Groups_Ozero__class_Ozero(X19472)))
        | ~ class_Rings_Olinordered__idom(X19472) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19472),X19471),c_Groups_Ozero__class_Ozero(X19472)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19472),c_Groups_Osgn__class_Osgn(X19472,X19471)),c_Groups_Ozero__class_Ozero(X19472)))
        | ~ class_Rings_Olinordered__idom(X19472) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__less])])]) ).

fof(i_0_9227,plain,
    ! [X29619,X29620,X29621] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29621),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29620)),X29619)))
      | hAPP(hAPP(c_List_Otake(X29620),X29621),c_List_Obutlast(X29620,X29619)) = hAPP(hAPP(c_List_Otake(X29620),X29621),X29619) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__butlast])]) ).

fof(i_0_9228,plain,
    ! [X29528,X29529,X29530] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29530),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29529)),X29528)))
      | c_List_Olast(X29529,hAPP(hAPP(c_List_Odrop(X29529),X29530),X29528)) = c_List_Olast(X29529,X29528) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__drop])]) ).

cnf(i_0_9229,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_9230,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_9231,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_9232,plain,
    ! [X21973,X21974,X21975,X21976,X21977,X21978] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X21978,X21977,X21976),X21975),hAPP(hAPP(c_Product__Type_OPair(X21978,X21977),X21974),X21973)) = hAPP(hAPP(X21975,X21974),X21973),
    inference(variable_rename,[status(thm)],[fact_prod_Osimps_I2_J]) ).

fof(i_0_9233,plain,
    ! [X21967,X21968,X21969,X21970,X21971,X21972] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X21972,X21971,X21970),X21969),hAPP(hAPP(c_Product__Type_OPair(X21972,X21971),X21968),X21967)) = hAPP(hAPP(X21969,X21968),X21967),
    inference(variable_rename,[status(thm)],[fact_split__conv]) ).

cnf(i_0_9234,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_9235,plain,
    ! [X24426,X24427,X24428] :
      ( ~ class_Orderings_Olinorder(X24428)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24428),X24427))
      | ~ hBOOL(hAPP(hAPP(c_member(X24428),X24426),X24427))
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X24428),X24426),c_Big__Operators_Olattice_OSup__fin(X24428,c_Orderings_Oord__class_Omax(X24428),X24427)) = c_Big__Operators_Olattice_OSup__fin(X24428,c_Orderings_Oord__class_Omax(X24428),X24427) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oin__idem])]) ).

fof(i_0_9236,plain,
    ! [X24482,X24483,X24484] :
      ( ~ class_Orderings_Olinorder(X24484)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24484),X24483))
      | ~ hBOOL(hAPP(hAPP(c_member(X24484),X24482),X24483))
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X24484),X24482),c_Big__Operators_Olattice_OInf__fin(X24484,c_Orderings_Oord__class_Omin(X24484),X24483)) = c_Big__Operators_Olattice_OInf__fin(X24484,c_Orderings_Oord__class_Omin(X24484),X24483) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oin__idem])]) ).

fof(i_0_9237,plain,
    ! [X20738,X20739,X20740] :
      ( hBOOL(hAPP(hAPP(c_member(X20740),X20739),X20738))
      | hBOOL(hAPP(hAPP(c_member(X20740),X20739),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X20740,tc_HOL_Obool)),X20738))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5856])]) ).

fof(i_0_9238,plain,
    ! [X27216,X27217,X27218,X27219] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X27219),X27218),X27217))
        | hAPP(c_Set_Ovimage(X27216,X27219,hAPP(c_COMBK(X27219,X27216),X27218)),X27217) = c_Orderings_Otop__class_Otop(tc_fun(X27216,tc_HOL_Obool)) )
      & ( hBOOL(hAPP(hAPP(c_member(X27219),X27218),X27217))
        | hAPP(c_Set_Ovimage(X27216,X27219,hAPP(c_COMBK(X27219,X27216),X27218)),X27217) = c_Orderings_Obot__class_Obot(tc_fun(X27216,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5857])]) ).

fof(i_0_9239,plain,
    ! [X25723,X25724,X25725,X25726,X25727] :
      ( ( X25726 = X25724
        | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X25727,X25726),X25725) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X25727,X25724),X25723)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25727),X25724),X25723))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25727),X25726),X25725))
        | ~ class_Orderings_Olinorder(X25727) )
      & ( X25725 = X25723
        | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X25727,X25726),X25725) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X25727,X25724),X25723)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25727),X25724),X25723))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25727),X25726),X25725))
        | ~ class_Orderings_Olinorder(X25727) )
      & ( X25726 != X25724
        | X25725 != X25723
        | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X25727,X25726),X25725) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X25727,X25724),X25723)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25727),X25724),X25723))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25727),X25726),X25725))
        | ~ class_Orderings_Olinorder(X25727) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__eq__iff])])]) ).

fof(i_0_9240,plain,
    ! [X25728,X25729,X25730,X25731,X25732] :
      ( ~ class_Orderings_Olinorder(X25732)
      | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X25732,X25731),X25730) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X25732,X25729),X25728)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25732),X25731),X25730))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25732),X25729),X25728))
      | X25731 = X25729 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__inj_I1_J])]) ).

fof(i_0_9241,plain,
    ! [X25733,X25734,X25735,X25736,X25737] :
      ( ~ class_Orderings_Olinorder(X25737)
      | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X25737,X25736),X25735) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X25737,X25734),X25733)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25737),X25736),X25735))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25737),X25734),X25733))
      | X25735 = X25733 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__inj_I2_J])]) ).

fof(i_0_9242,plain,
    ! [X23669,X23670,X23671,X23672,X23673] :
      ( ~ c_Finite__Set_Ofolding__one(X23673,X23672,X23671)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23673),X23670))
      | hBOOL(hAPP(hAPP(c_member(X23673),X23669),X23670))
      | X23670 = c_Orderings_Obot__class_Obot(tc_fun(X23673,tc_HOL_Obool))
      | hAPP(X23671,hAPP(hAPP(c_Set_Oinsert(X23673),X23669),X23670)) = hAPP(hAPP(X23672,X23669),hAPP(X23671,X23670)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5858])]) ).

cnf(i_0_9243,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_5776]) ).

fof(i_0_9244,plain,
    ! [X22106,X22107] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22107))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22106))
      | hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22107,X22106),c_Divides_OposDivAlg(X22107,X22106))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_posDivAlg__correct])]) ).

fof(i_0_9245,plain,
    ! [X29095,X29096,X29097,X29098,X29099] :
      ( X29099 = X29098
      | hAPP(hAPP(c_List_Onth(X29097),hAPP(hAPP(c_List_Olist__update(X29097,X29096),X29099),X29095)),X29098) = hAPP(hAPP(c_List_Onth(X29097),X29096),X29098) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__list__update__neq])]) ).

fof(i_0_9246,plain,
    ! [X25921,X25922,X25923,X25924] :
      ( ~ class_Orderings_Oorder(X25924)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25924,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X25924,X25923,X25922)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X25924,X25922),X25921)) = c_Orderings_Obot__class_Obot(tc_fun(X25924,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I9_J])]) ).

fof(i_0_9247,plain,
    ! [X32413,X32414,X32415,X32416] : hAPP(c_Relation_Oconverse(X32416,X32416),hAPP(hAPP(c_Relation_Oinv__image(X32415,X32416),X32414),X32413)) = hAPP(hAPP(c_Relation_Oinv__image(X32415,X32416),hAPP(c_Relation_Oconverse(X32415,X32415),X32414)),X32413),
    inference(variable_rename,[status(thm)],[fact_converse__inv__image]) ).

fof(i_0_9248,plain,
    ! [X32899,X32900,X32901] :
      ( ~ class_Orderings_Olinorder(X32901)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32901),X32900))
      | c_Big__Operators_Olinorder__class_OMin(X32901,hAPP(hAPP(c_Set_Oinsert(X32901),X32899),X32900)) = hAPP(hAPP(c_Finite__Set_Ofold(X32901,X32901,c_Orderings_Oord__class_Omin(X32901)),X32899),X32900) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Oeq__fold__idem_H])]) ).

fof(i_0_9249,plain,
    ! [X32902,X32903,X32904] :
      ( ~ class_Orderings_Olinorder(X32904)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32904),X32903))
      | c_Big__Operators_Olinorder__class_OMax(X32904,hAPP(hAPP(c_Set_Oinsert(X32904),X32902),X32903)) = hAPP(hAPP(c_Finite__Set_Ofold(X32904,X32904,c_Orderings_Oord__class_Omax(X32904)),X32902),X32903) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Oeq__fold__idem_H])]) ).

fof(i_0_9250,plain,
    ! [X32893,X32894,X32895] :
      ( ~ class_Lattices_Olattice(X32895)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32895),X32894))
      | c_Big__Operators_Olattice__class_OSup__fin(X32895,hAPP(hAPP(c_Set_Oinsert(X32895),X32893),X32894)) = hAPP(hAPP(c_Finite__Set_Ofold(X32895,X32895,c_Lattices_Osemilattice__sup__class_Osup(X32895)),X32893),X32894) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oeq__fold__idem_H])]) ).

fof(i_0_9251,plain,
    ! [X32896,X32897,X32898] :
      ( ~ class_Lattices_Olattice(X32898)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32898),X32897))
      | c_Big__Operators_Olattice__class_OInf__fin(X32898,hAPP(hAPP(c_Set_Oinsert(X32898),X32896),X32897)) = hAPP(hAPP(c_Finite__Set_Ofold(X32898,X32898,c_Lattices_Osemilattice__inf__class_Oinf(X32898)),X32896),X32897) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oeq__fold__idem_H])]) ).

fof(i_0_9252,plain,
    ! [X21619,X21620] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X21620),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))
        | c_Random_Olog(X21620,X21619) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X21619),X21620))
        | c_Random_Olog(X21620,X21619) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X21620),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X21619),X21620))
        | c_Random_Olog(X21620,X21619) = 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(X21620,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X21619),X21620))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_log_Osimps])])]) ).

fof(i_0_9253,plain,
    ! [X20916,X20917] :
      ( ~ class_Rings_Oring__1(X20917)
      | ~ hBOOL(hAPP(hAPP(c_member(X20917),X20916),c_Int_Oring__1__class_OInts(X20917)))
      | hBOOL(hAPP(hAPP(c_member(X20917),hAPP(c_Groups_Ouminus__class_Ouminus(X20917),X20916)),c_Int_Oring__1__class_OInts(X20917))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__minus])]) ).

fof(i_0_9254,plain,
    ! [X22310,X22311] :
      ( ( ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X22311,tc_HOL_Obool)),X22310))
        | hBOOL(hAPP(hAPP(c_member(X22311),X22310),c_Orderings_Obot__class_Obot(tc_fun(X22311,tc_HOL_Obool)))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X22311),X22310),c_Orderings_Obot__class_Obot(tc_fun(X22311,tc_HOL_Obool))))
        | hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X22311,tc_HOL_Obool)),X22310)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bot__empty__eq])]) ).

cnf(i_0_9255,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_5859]) ).

fof(i_0_9256,plain,
    ! [X21527,X21528,X21529] :
      ( ~ class_Fields_Olinordered__field__inverse__zero(X21529)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21529),c_Groups_Ozero__class_Ozero(X21529)),X21528))
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21529),hAPP(c_Groups_Oabs__class_Oabs(X21529),X21527)),X21528) = hAPP(c_Groups_Oabs__class_Oabs(X21529),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21529),X21527),X21528)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__div__pos])]) ).

fof(i_0_9257,plain,
    ! [X20414,X20415,X20416] :
      ( ~ class_Rings_Olinordered__idom(X20416)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20416),c_Groups_Ozero__class_Ozero(X20416)),X20415))
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20416),hAPP(c_Groups_Oabs__class_Oabs(X20416),X20414)),X20415) = hAPP(c_Groups_Oabs__class_Oabs(X20416),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20416),X20414),X20415)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__mult__pos])]) ).

fof(i_0_9258,plain,
    ! [X25544] : hAPP(c_Set_OPow(X25544),c_Orderings_Obot__class_Obot(tc_fun(X25544,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(X25544,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X25544,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X25544,tc_HOL_Obool),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_Pow__empty]) ).

fof(i_0_9259,plain,
    ! [X26496,X26497] :
      ( hAPP(X26497,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),X26497),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X26496)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X26497),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X26496)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__shift__lb__Suc0__0])]) ).

fof(i_0_9260,plain,
    ! [X23859,X23860,X23861,X23862,X23863] :
      ( ~ class_Lattices_Olattice(X23863)
      | hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23862,X23863)),X23861),X23860),X23859) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23863),hAPP(X23861,X23859)),hAPP(X23860,X23859)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__apply])]) ).

fof(i_0_9261,plain,
    ! [X23854,X23855,X23856,X23857,X23858] :
      ( ~ class_Lattices_Olattice(X23858)
      | hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23857,X23858)),X23856),X23855),X23854) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23858),hAPP(X23856,X23854)),hAPP(X23855,X23854)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__fun__def])]) ).

fof(i_0_9262,plain,
    ! [X23029,X23030,X23031,X23032,X23033] :
      ( ~ class_Lattices_Olattice(X23033)
      | hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23032,X23033)),X23031),X23030),X23029) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23033),hAPP(X23031,X23029)),hAPP(X23030,X23029)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__fun__def])]) ).

fof(i_0_9263,plain,
    ! [X23024,X23025,X23026,X23027,X23028] :
      ( ~ class_Lattices_Olattice(X23028)
      | hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23027,X23028)),X23026),X23025),X23024) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23028),hAPP(X23026,X23024)),hAPP(X23025,X23024)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__apply])]) ).

fof(i_0_9264,plain,
    ! [X21712,X21713,X21714,X21715,X21716] :
      ( ~ class_Groups_Ominus(X21716)
      | hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X21715,X21716)),X21714),X21713),X21712) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21716),hAPP(X21714,X21712)),hAPP(X21713,X21712)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__diff__def])]) ).

fof(i_0_9265,plain,
    ! [X19822,X19823,X19824,X19825,X19826] :
      ( ~ class_Groups_Ominus(X19826)
      | hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X19825,X19826)),X19824),X19823),X19822) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19826),hAPP(X19824,X19822)),hAPP(X19823,X19822)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__apply])]) ).

fof(i_0_9266,plain,
    ! [X22102,X22103] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22103),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)),X22102))
      | hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22103,X22102),c_Divides_OnegDivAlg(X22103,X22102))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_negDivAlg__correct])]) ).

fof(i_0_9267,plain,
    ! [X19447,X19448] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19448),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19448),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19447,X19448))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__mod__bound])]) ).

fof(i_0_9268,plain,
    ! [X27948,X27949,X27950,X27951] :
      ( ~ c_Finite__Set_Ofolding(X27951,X27950,X27949,X27948)
      | hAPP(X27948,c_Orderings_Obot__class_Obot(tc_fun(X27951,tc_HOL_Obool))) = c_Fun_Oid(X27950) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Oempty])]) ).

fof(i_0_9269,plain,
    ! [X21860,X21861] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21860))
        | c_Divides_Odivmod__int(X21861,X21860) = c_Divides_OposDivAlg(X21861,X21860)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21861)) )
      & ( X21861 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odivmod__int(X21861,X21860) = 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)),X21860))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21861)) )
      & ( X21861 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odivmod__int(X21861,X21860) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21861),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21860)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21860))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21861)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21860))
        | c_Divides_Odivmod__int(X21861,X21860) = c_Divides_OnegDivAlg(X21861,X21860)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21861)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21860))
        | c_Divides_Odivmod__int(X21861,X21860) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21861),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21860)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21861)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5860])])]) ).

fof(i_0_9270,plain,
    ! [X30387,X30388] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X30388),X30387))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X30388)),hAPP(c_Code__Numeral_Onat__of,X30387))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X30388)),hAPP(c_Code__Numeral_Onat__of,X30387)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X30388),X30387)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__code__numeral__def])]) ).

fof(i_0_9271,plain,
    ! [X30289,X30290] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X30290)),hAPP(c_Code__Numeral_Oof__nat,X30289)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X30290),X30289)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X30290),X30289))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X30290)),hAPP(c_Code__Numeral_Oof__nat,X30289))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__code__numeral__code])]) ).

fof(i_0_9272,plain,
    ! [X19106,X19107] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19107)),hAPP(c_Nat_OSuc,X19106)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19107),X19106)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19107),X19106))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19107)),hAPP(c_Nat_OSuc,X19106))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__mono])]) ).

fof(i_0_9273,plain,
    ! [X30383,X30384] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X30384),X30383))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X30384)),hAPP(c_Code__Numeral_Onat__of,X30383))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X30384)),hAPP(c_Code__Numeral_Onat__of,X30383)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X30384),X30383)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__code__numeral__def])]) ).

fof(i_0_9274,plain,
    ! [X30272,X30273] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X30273)),hAPP(c_Code__Numeral_Oof__nat,X30272)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30273),X30272)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30273),X30272))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X30273)),hAPP(c_Code__Numeral_Oof__nat,X30272))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__code__numeral__code])]) ).

fof(i_0_9275,plain,
    ! [X17538,X17539] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X17539)),hAPP(c_Nat_OSuc,X17538)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17539),X17538)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__less__SucD])]) ).

fof(i_0_9276,plain,
    ! [X17521,X17522] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X17522)),hAPP(c_Nat_OSuc,X17521)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17522),X17521)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17522),X17521))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X17522)),hAPP(c_Nat_OSuc,X17521))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__less__eq])]) ).

fof(i_0_9277,plain,
    ! [X28761,X28762,X28763,X28764] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X28764),X28763))
      | hAPP(hAPP(c_List_Onth(X28762),hAPP(hAPP(c_List_Otake(X28762),X28763),X28761)),X28764) = hAPP(hAPP(c_List_Onth(X28762),X28761),X28764) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__take])]) ).

fof(i_0_9278,plain,
    ! [X24058,X24059,X24060] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24060,tc_HOL_Obool)),X24059),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24060,tc_HOL_Obool)),X24058),X24059)) = c_Orderings_Obot__class_Obot(tc_fun(X24060,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Diff__disjoint]) ).

fof(i_0_9279,plain,
    ! [X31670,X31671,X31672,X31673] :
      ( ( hAPP(c_List_Orev(X31673),X31672) != hAPP(hAPP(c_List_Olist_OCons(X31673),X31671),X31670)
        | X31672 = hAPP(hAPP(c_List_Oappend(X31673),hAPP(c_List_Orev(X31673),X31670)),hAPP(hAPP(c_List_Olist_OCons(X31673),X31671),c_List_Olist_ONil(X31673))) )
      & ( X31672 != hAPP(hAPP(c_List_Oappend(X31673),hAPP(c_List_Orev(X31673),X31670)),hAPP(hAPP(c_List_Olist_OCons(X31673),X31671),c_List_Olist_ONil(X31673)))
        | hAPP(c_List_Orev(X31673),X31672) = hAPP(hAPP(c_List_Olist_OCons(X31673),X31671),X31670) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__eq__Cons__iff])]) ).

fof(i_0_9280,plain,
    ! [X20375,X20376] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20376))
      | 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),X20376),X20375))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J])]) ).

fof(i_0_9281,plain,
    ! [X19929,X19930] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19930),X19929)),X19930)),
    inference(variable_rename,[status(thm)],[fact_diff__le__self]) ).

fof(i_0_9282,plain,
    ! [X19568,X19569] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19569),X19568)),X19569)),
    inference(variable_rename,[status(thm)],[fact_div__le__dividend]) ).

fof(i_0_9283,plain,
    ! [X26140,X26141] :
      ( ~ class_Orderings_Olinorder(X26141)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26141,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X26141),X26140)),hAPP(hAPP(c_Set_Oinsert(X26141),X26140),c_Orderings_Obot__class_Obot(tc_fun(X26141,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(X26141),X26140) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I2_J])]) ).

fof(i_0_9284,plain,
    ! [X24359,X24360,X24361] :
      ( ~ class_Orderings_Olinorder(X24361)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24361),X24360))
      | ~ hBOOL(hAPP(hAPP(c_member(X24361),X24359),X24360))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24361),c_Big__Operators_Olinorder__class_OMin(X24361,X24360)),X24359)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min__le])]) ).

fof(i_0_9285,plain,
    ! [X20403,X20404,X20405] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X20405),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20404),X20403)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X20405),X20404)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X20405),X20403)),
    inference(variable_rename,[status(thm)],[fact_zpower__zadd__distrib]) ).

fof(i_0_9286,plain,
    ! [X19933,X19934,X19935] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19935),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X19934),X19933)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19935),X19934)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19935),X19933)),
    inference(variable_rename,[status(thm)],[fact_zdiff__zmult__distrib2]) ).

fof(i_0_9287,plain,
    ! [X18301,X18302,X18303] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X18303),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18302),X18301)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X18303),X18302)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X18303),X18301)),
    inference(variable_rename,[status(thm)],[fact_zadd__zmult__distrib2]) ).

fof(i_0_9288,plain,
    ! [X19942,X19943,X19944] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19944),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19943),X19942)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19944),X19943)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19944),X19942)),
    inference(variable_rename,[status(thm)],[fact_diff__mult__distrib2]) ).

fof(i_0_9289,plain,
    ! [X18686,X18687,X18688] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18688),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18687),X18686)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18688),X18687)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18688),X18686)),
    inference(variable_rename,[status(thm)],[fact_add__mult__distrib2]) ).

fof(i_0_9290,plain,
    ! [X19811,X19812,X19813] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19813),X19812)),X19811) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19813),X19811)),X19812),
    inference(variable_rename,[status(thm)],[fact_diff__commute]) ).

fof(i_0_9291,plain,
    ! [X18836,X18837] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18837),c_Groups_Ozero__class_Ozero(X18837)),hAPP(c_Groups_Ouminus__class_Ouminus(X18837),X18836)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18837),X18836),c_Groups_Ozero__class_Ozero(X18837)))
        | ~ class_Groups_Oordered__ab__group__add(X18837) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18837),X18836),c_Groups_Ozero__class_Ozero(X18837)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18837),c_Groups_Ozero__class_Ozero(X18837)),hAPP(c_Groups_Ouminus__class_Ouminus(X18837),X18836)))
        | ~ class_Groups_Oordered__ab__group__add(X18837) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__0__le__iff__le])])]) ).

fof(i_0_9292,plain,
    ! [X18312,X18313] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18313),c_Groups_Ozero__class_Ozero(X18313)),hAPP(c_Groups_Ouminus__class_Ouminus(X18313),X18312)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18313),X18312),c_Groups_Ozero__class_Ozero(X18313)))
        | ~ class_Groups_Oordered__ab__group__add(X18313) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18313),X18312),c_Groups_Ozero__class_Ozero(X18313)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18313),c_Groups_Ozero__class_Ozero(X18313)),hAPP(c_Groups_Ouminus__class_Ouminus(X18313),X18312)))
        | ~ class_Groups_Oordered__ab__group__add(X18313) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__0__less__iff__less])])]) ).

fof(i_0_9293,plain,
    ! [X18497,X18498,X18499,X18500] :
      ( ~ class_Orderings_Opreorder(X18500)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18500),X18499),X18498))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18500),X18498),X18497))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18500),X18499),X18497)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__trans])]) ).

fof(i_0_9294,plain,
    ! [X18504,X18505,X18506,X18507] :
      ( ~ class_Orderings_Oorder(X18507)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18507),X18506),X18505))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18507),X18504),X18506))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18507),X18504),X18505)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I6_J])]) ).

fof(i_0_9295,plain,
    ! [X18602,X18603,X18604,X18605] :
      ( ~ class_Orderings_Opreorder(X18605)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18605),X18604),X18603))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18605),X18603),X18602))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18605),X18604),X18602)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__le__trans])]) ).

fof(i_0_9296,plain,
    ! [X18610,X18611,X18612,X18613] :
      ( ~ class_Orderings_Opreorder(X18613)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18613),X18612),X18611))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18613),X18611),X18610))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18613),X18612),X18610)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__less__trans])]) ).

fof(i_0_9297,plain,
    ! [X17355,X17356,X17357,X17358] :
      ( ~ class_Orderings_Opreorder(X17358)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17358),X17357),X17356))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17358),X17356),X17355))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17358),X17357),X17355)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__trans])]) ).

fof(i_0_9298,plain,
    ! [X18606,X18607,X18608,X18609] :
      ( ~ class_Orderings_Oorder(X18609)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18609),X18608),X18607))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18609),X18606),X18608))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18609),X18606),X18607)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I7_J])]) ).

fof(i_0_9299,plain,
    ! [X18614,X18615,X18616,X18617] :
      ( ~ class_Orderings_Oorder(X18617)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18617),X18616),X18615))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18617),X18614),X18616))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18617),X18614),X18615)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I8_J])]) ).

fof(i_0_9300,plain,
    ! [X17351,X17352,X17353,X17354] :
      ( ~ class_Orderings_Oorder(X17354)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17354),X17353),X17352))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17354),X17351),X17353))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17354),X17351),X17352)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I10_J])]) ).

fof(i_0_9301,plain,
    ! [X22085] :
      ( X22085 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X22085),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_9302,plain,
    ! [X22179,X22180] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22180))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22179))
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,X22180,X22179) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(X22180,X22179)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__pos__pos])]) ).

fof(i_0_9303,plain,
    ! [X31727,X31728,X31729,X31730,X31731] :
      ( hBOOL(hAPP(X31731,X31730))
      | c_List_OtakeWhile(X31729,X31731,hAPP(hAPP(c_List_Oappend(X31729),X31728),hAPP(hAPP(c_List_Olist_OCons(X31729),X31730),X31727))) = c_List_OtakeWhile(X31729,X31731,X31728) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5861])]) ).

fof(i_0_9304,plain,
    ! [X19832,X19833,X19834,X19835,X19836] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19836),X19835),X19834))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19836),X19833),X19832))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19836),X19835),X19834) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19836),X19833),X19832)
        | ~ class_Groups_Oordered__ab__group__add(X19836) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19836),X19833),X19832))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19836),X19835),X19834))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19836),X19835),X19834) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19836),X19833),X19832)
        | ~ class_Groups_Oordered__ab__group__add(X19836) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__less__eq])])]) ).

fof(i_0_9305,plain,
    ! [X19847,X19848,X19849,X19850,X19851] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19851),X19850),X19849))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19851),X19848),X19847))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19851),X19850),X19849) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19851),X19848),X19847)
        | ~ class_Groups_Oordered__ab__group__add(X19851) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19851),X19848),X19847))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19851),X19850),X19849))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19851),X19850),X19849) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19851),X19848),X19847)
        | ~ class_Groups_Oordered__ab__group__add(X19851) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__less])])]) ).

fof(i_0_9306,plain,
    ! [X19918,X19919,X19920] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19919),X19920) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19918),X19920)
        | X19919 = X19918
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19920),X19918))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19920),X19919)) )
      & ( X19919 != X19918
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19919),X19920) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19918),X19920)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19920),X19918))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19920),X19919)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__diff__iff])])]) ).

fof(i_0_9307,plain,
    ! [X27276,X27277,X27278] : hAPP(hAPP(c_Product__Type_OSigma(X27278,X27277),X27276),hAPP(c_COMBK(tc_fun(X27277,tc_HOL_Obool),X27278),c_Orderings_Obot__class_Obot(tc_fun(X27277,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27278,X27277),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Sigma__empty2]) ).

cnf(i_0_9308,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_5862]) ).

cnf(i_0_9309,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_9310,plain,
    ! [X31491,X31492,X31493,X31494] : c_List_Oremdups(X31494,hAPP(hAPP(c_List_Omap(X31493,X31494),X31492),c_List_Oremdups(X31493,X31491))) = c_List_Oremdups(X31494,hAPP(hAPP(c_List_Omap(X31493,X31494),X31492),X31491)),
    inference(variable_rename,[status(thm)],[fact_remdups__map__remdups]) ).

fof(i_0_9311,plain,
    ! [X18737,X18738,X18739] :
      ( ~ class_Rings_Ocomm__semiring__1(X18739)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18739),X18738),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18739),X18737),X18738)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18739),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18739),X18737),c_Groups_Oone__class_Oone(X18739))),X18738) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J])]) ).

cnf(i_0_9312,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_5863]) ).

cnf(i_0_9313,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_5864]) ).

fof(i_0_9314,plain,
    ! [X22303,X22304] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22304))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22303))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X22304),X22303) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(X22304,X22303)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__pos__pos])]) ).

fof(i_0_9315,plain,
    ! [X19102,X19103] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19103),X19102))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19102)),X19103)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19102)),X19103))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19103),X19102)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5865])]) ).

fof(i_0_9316,plain,
    ! [X25910,X25911,X25912,X25913] :
      ( ~ class_Orderings_Oorder(X25913)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25913,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X25913,X25912),X25911)),c_SetInterval_Oord__class_OatLeastAtMost(X25913,X25911,X25910)) = c_Orderings_Obot__class_Obot(tc_fun(X25913,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I15_J])]) ).

fof(i_0_9317,plain,
    ! [X18714,X18715] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18715),c_Groups_Ozero__class_Ozero(X18715)),hAPP(c_Int_Oring__1__class_Oof__int(X18715),X18714)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18714))
        | ~ class_Rings_Olinordered__idom(X18715) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18714))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18715),c_Groups_Ozero__class_Ozero(X18715)),hAPP(c_Int_Oring__1__class_Oof__int(X18715),X18714)))
        | ~ class_Rings_Olinordered__idom(X18715) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__0__le__iff])])]) ).

fof(i_0_9318,plain,
    ! [X18104,X18105] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18105),c_Groups_Ozero__class_Ozero(X18105)),hAPP(c_Int_Oring__1__class_Oof__int(X18105),X18104)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18104))
        | ~ class_Rings_Olinordered__idom(X18105) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18104))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18105),c_Groups_Ozero__class_Ozero(X18105)),hAPP(c_Int_Oring__1__class_Oof__int(X18105),X18104)))
        | ~ class_Rings_Olinordered__idom(X18105) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__0__less__iff])])]) ).

fof(i_0_9319,plain,
    ! [X17838,X17839] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17839),c_Groups_Ozero__class_Ozero(X17839)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X17839),X17838)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17838))
        | ~ class_Rings_Olinordered__semidom(X17839) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17838))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17839),c_Groups_Ozero__class_Ozero(X17839)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X17839),X17838)))
        | ~ class_Rings_Olinordered__semidom(X17839) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__0__less__iff])])]) ).

fof(i_0_9320,plain,
    ! [X17621,X17622,X17623] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(X17623,X17622,X17621)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X17622)),c_Com_Ocom_Ocom__size(X17621))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[fact_com_Osize_I5_J]) ).

fof(i_0_9321,plain,
    ! [X20284,X20285] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20285),hAPP(c_Groups_Oabs__class_Oabs(X20285),X20284)),c_Groups_Ozero__class_Ozero(X20285)))
        | X20284 = c_Groups_Ozero__class_Ozero(X20285)
        | ~ class_Groups_Oordered__ab__group__add__abs(X20285) )
      & ( X20284 != c_Groups_Ozero__class_Ozero(X20285)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20285),hAPP(c_Groups_Oabs__class_Oabs(X20285),X20284)),c_Groups_Ozero__class_Ozero(X20285)))
        | ~ class_Groups_Oordered__ab__group__add__abs(X20285) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__le__zero__iff])])]) ).

fof(i_0_9322,plain,
    ! [X22177,X22178] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22178),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)),X22177))
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,X22178,X22177) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(X22178,X22177)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__neg__pos])]) ).

fof(i_0_9323,plain,
    ! [X24487,X24488,X24489] :
      ( ~ class_Orderings_Olinorder(X24489)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24489),X24488))
      | X24488 = c_Orderings_Obot__class_Obot(tc_fun(X24489,tc_HOL_Obool))
      | c_Big__Operators_Olattice_OInf__fin(X24489,c_Orderings_Oord__class_Omin(X24489),hAPP(hAPP(c_Set_Oinsert(X24489),X24487),X24488)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X24489),X24487),c_Big__Operators_Olattice_OInf__fin(X24489,c_Orderings_Oord__class_Omin(X24489),X24488)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oinsert__idem])]) ).

fof(i_0_9324,plain,
    ! [X24431,X24432,X24433] :
      ( ~ class_Orderings_Olinorder(X24433)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24433),X24432))
      | X24432 = c_Orderings_Obot__class_Obot(tc_fun(X24433,tc_HOL_Obool))
      | c_Big__Operators_Olattice_OSup__fin(X24433,c_Orderings_Oord__class_Omax(X24433),hAPP(hAPP(c_Set_Oinsert(X24433),X24431),X24432)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X24433),X24431),c_Big__Operators_Olattice_OSup__fin(X24433,c_Orderings_Oord__class_Omax(X24433),X24432)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oinsert__idem])]) ).

fof(i_0_9325,plain,
    ! [X20292,X20293] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X20293)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20293),hAPP(c_Groups_Oabs__class_Oabs(X20293),X20292)),c_Groups_Ozero__class_Ozero(X20293))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5866])]) ).

fof(i_0_9326,plain,
    ! [X18023,X18024] :
      ( ~ class_Rings_Olinordered__semidom(X18024)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18024),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18024),X18023)),c_Groups_Ozero__class_Ozero(X18024))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5867])]) ).

fof(i_0_9327,plain,
    ! [X19827,X19828,X19829] :
      ( ~ class_Rings_Oring__1(X19829)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19828),X19827))
      | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X19829),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19827),X19828)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19829),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X19829),X19827)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X19829),X19828)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__diff])]) ).

cnf(i_0_9328,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_5868]) ).

fof(i_0_9329,plain,
    ! [X20940,X20941] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20941),c_Int_OPls))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20941)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20940)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20940) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20940),c_Int_OPls))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20941)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20940)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20941)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20941),c_Int_OPls)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20940),c_Int_OPls))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20941)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20940)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20941),X20940))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20941),c_Int_OPls)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5869])])]) ).

fof(i_0_9330,plain,
    ! [X20644,X20645] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20645)))
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20645)),X20644) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20644) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20645)))
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20645)),X20644) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20645)),X20644)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5870])]) ).

fof(i_0_9331,plain,
    ! [X22286,X22287] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22287),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)),X22286))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X22287),X22286) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(X22287,X22286)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__neg__pos])]) ).

fof(i_0_9332,plain,
    ! [X23543,X23544,X23545] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23545),hAPP(hAPP(c_Set_Oinsert(X23545),X23544),X23543)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X23545),X23543)) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23545),X23543))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X23545),hAPP(hAPP(c_Set_Oinsert(X23545),X23544),X23543))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__insert])]) ).

cnf(i_0_9333,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_5871]) ).

fof(i_0_9334,plain,
    ! [X32797,X32798,X32799] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X32799)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32799),X32798))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X32799),X32797),c_Complete__Lattice_OInf__class_OInf(X32799,X32798)) = hAPP(hAPP(c_Finite__Set_Ofold(X32799,X32799,c_Lattices_Osemilattice__inf__class_Oinf(X32799)),X32797),X32798) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__Inf__fold__inf])]) ).

fof(i_0_9335,plain,
    ! [X32794,X32795,X32796] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X32796)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32796),X32795))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X32796),X32794),c_Complete__Lattice_OSup__class_OSup(X32796,X32795)) = hAPP(hAPP(c_Finite__Set_Ofold(X32796,X32796,c_Lattices_Osemilattice__sup__class_Osup(X32796)),X32794),X32795) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__Sup__fold__sup])]) ).

cnf(i_0_9336,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_9337,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_9338,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_9339,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_9340,plain,
    ! [X24083,X24084] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24084,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X24084,tc_HOL_Obool)),X24083)),X24083) = c_Orderings_Obot__class_Obot(tc_fun(X24084,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Compl__disjoint2]) ).

fof(i_0_9341,plain,
    ! [X26747,X26748] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26748,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X26748,tc_HOL_Obool)),X26747)),X26747) = c_Orderings_Otop__class_Otop(tc_fun(X26748,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Compl__partition2]) ).

fof(i_0_9342,plain,
    ! [X26674,X26675] : c_Sum__Type_OPlus(X26675,X26674,c_Orderings_Otop__class_Otop(tc_fun(X26675,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X26674,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X26675,X26674),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_UNIV__Plus__UNIV]) ).

fof(i_0_9343,plain,
    ! [X26547,X26548,X26549] :
      ( ~ class_Orderings_Oorder(X26549)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26549,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X26549,X26548,X26547)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X26549),X26547)) = c_Orderings_Obot__class_Obot(tc_fun(X26549,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I7_J])]) ).

fof(i_0_9344,plain,
    ! [X26557,X26558,X26559] :
      ( ~ class_Orderings_Oorder(X26559)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26559,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X26559,X26558,X26557)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X26559),X26557)) = c_Orderings_Obot__class_Obot(tc_fun(X26559,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I5_J])]) ).

fof(i_0_9345,plain,
    ! [X26408,X26409,X26410] :
      ( ~ class_Orderings_Oorder(X26410)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26410,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X26410,X26409,X26408)),hAPP(c_SetInterval_Oord__class_OatLeast(X26410),X26408)) = c_Orderings_Obot__class_Obot(tc_fun(X26410,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I6_J])]) ).

fof(i_0_9346,plain,
    ! [X21628,X21629,X21630] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X21630),X21629))
        | c_Random_Ominus__shift(X21628,X21630,X21629) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X21628),X21630)),X21629) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X21630),X21629))
        | c_Random_Ominus__shift(X21628,X21630,X21629) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X21630),X21629) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5872])]) ).

fof(i_0_9347,plain,
    ! [X20931,X20932] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20932),c_Groups_Ozero__class_Ozero(X20932)),hAPP(c_Int_Onumber__class_Onumber__of(X20932),X20931)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X20931))
        | ~ class_Int_Onumber__ring(X20932)
        | ~ class_Rings_Olinordered__idom(X20932) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X20931))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20932),c_Groups_Ozero__class_Ozero(X20932)),hAPP(c_Int_Onumber__class_Onumber__of(X20932),X20931)))
        | ~ class_Int_Onumber__ring(X20932)
        | ~ class_Rings_Olinordered__idom(X20932) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__special_I1_J])])]) ).

fof(i_0_9348,plain,
    ! [X20935,X20936] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20936),c_Groups_Ozero__class_Ozero(X20936)),hAPP(c_Int_Onumber__class_Onumber__of(X20936),X20935)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X20935))
        | ~ class_Int_Onumber__ring(X20936)
        | ~ class_Rings_Olinordered__idom(X20936) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X20935))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20936),c_Groups_Ozero__class_Ozero(X20936)),hAPP(c_Int_Onumber__class_Onumber__of(X20936),X20935)))
        | ~ class_Int_Onumber__ring(X20936)
        | ~ class_Rings_Olinordered__idom(X20936) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__special_I1_J])])]) ).

fof(i_0_9349,plain,
    ! [X19497,X19498,X19499] :
      ( ( ~ hBOOL(hAPP(X19499,c_Divides_Odiv__class_Omod(tc_Int_Oint,X19498,X19497)))
        | epred1_3(X19499,X19498,X19497) )
      & ( ~ epred1_3(X19499,X19498,X19497)
        | hBOOL(hAPP(X19499,c_Divides_Odiv__class_Omod(tc_Int_Oint,X19498,X19497))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5873])]) ).

fof(i_0_9350,plain,
    ! [X30896,X30897,X30898] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X30898,X30897)),X30896))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X30898),hAPP(c_Relation_ODomain(X30898,X30897),X30896))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Domain])]) ).

fof(i_0_9351,plain,
    ! [X28272,X28273,X28274] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X28274,X28273)),X28272))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X28273),hAPP(c_Relation_ORange(X28274,X28273),X28272))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Range])]) ).

fof(i_0_9352,plain,
    ! [X26866,X26867,X26868,X26869] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X26869,X26868,X26867),X26866))
      | X26867 != c_Orderings_Obot__class_Obot(tc_fun(X26869,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1Set__nonempty])]) ).

fof(i_0_9353,plain,
    ! [X21685,X21686] : hAPP(hAPP(c_Nitpick_Oint__gcd,X21686),X21685) = 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),X21686)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X21685)))),
    inference(variable_rename,[status(thm)],[fact_Nitpick_Oint__gcd__def]) ).

fof(i_0_9354,plain,
    ! [X30066,X30067,X30068,X30069,X30070] : hAPP(hAPP(c_List_Odrop(X30070),X30069),hAPP(hAPP(c_List_Omap(X30068,X30070),X30067),X30066)) = hAPP(hAPP(c_List_Omap(X30068,X30070),X30067),hAPP(hAPP(c_List_Odrop(X30068),X30069),X30066)),
    inference(variable_rename,[status(thm)],[fact_drop__map]) ).

fof(i_0_9355,plain,
    ! [X30056,X30057,X30058,X30059,X30060] : hAPP(hAPP(c_List_Otake(X30060),X30059),hAPP(hAPP(c_List_Omap(X30058,X30060),X30057),X30056)) = hAPP(hAPP(c_List_Omap(X30058,X30060),X30057),hAPP(hAPP(c_List_Otake(X30058),X30059),X30056)),
    inference(variable_rename,[status(thm)],[fact_take__map]) ).

fof(i_0_9356,plain,
    ! [X31195,X31196,X31197,X31198] : hAPP(c_List_Ofilter(X31198,X31197),hAPP(hAPP(c_List_Oappend(X31198),X31196),X31195)) = hAPP(hAPP(c_List_Oappend(X31198),hAPP(c_List_Ofilter(X31198,X31197),X31196)),hAPP(c_List_Ofilter(X31198,X31197),X31195)),
    inference(variable_rename,[status(thm)],[fact_filter__append]) ).

fof(i_0_9357,plain,
    ! [X29531,X29532] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X29532),X29531))
        | c_List_Oupto(X29532,X29531) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),X29532),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X29532),c_Groups_Oone__class_Oone(tc_Int_Oint)),X29531)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X29532),X29531))
        | c_List_Oupto(X29532,X29531) = c_List_Olist_ONil(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5874])]) ).

fof(i_0_9358,plain,
    ! [X28206,X28207,X28208,X28209,X28210] :
      ( ( ~ c_Wellfounded_Owf(X28207,X28206)
        | hBOOL(hAPP(hAPP(c_member(X28207),X28208),c_Wellfounded_Oacc(X28207,X28206))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X28210),esk299_2(X28209,X28210)),c_Wellfounded_Oacc(X28210,X28209)))
        | c_Wellfounded_Owf(X28210,X28209) ) ),
    inference(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_9359,plain,
    ! [X24391,X24392] :
      ( ~ class_Groups_Olinordered__ab__group__add(X24392)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24392),X24391))
      | X24391 = c_Orderings_Obot__class_Obot(tc_fun(X24392,tc_HOL_Obool))
      | hAPP(c_Groups_Ouminus__class_Ouminus(X24392),c_Big__Operators_Olinorder__class_OMin(X24392,X24391)) = c_Big__Operators_Olinorder__class_OMax(X24392,hAPP(c_Set_Oimage(X24392,X24392,c_Groups_Ouminus__class_Ouminus(X24392)),X24391)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__Min__eq__Max])]) ).

fof(i_0_9360,plain,
    ! [X24393,X24394] :
      ( ~ class_Groups_Olinordered__ab__group__add(X24394)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24394),X24393))
      | X24393 = c_Orderings_Obot__class_Obot(tc_fun(X24394,tc_HOL_Obool))
      | hAPP(c_Groups_Ouminus__class_Ouminus(X24394),c_Big__Operators_Olinorder__class_OMax(X24394,X24393)) = c_Big__Operators_Olinorder__class_OMin(X24394,hAPP(c_Set_Oimage(X24394,X24394,c_Groups_Ouminus__class_Ouminus(X24394)),X24393)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__Max__eq__Min])]) ).

fof(i_0_9361,plain,
    ! [X30851,X30852] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30852),c_Complete__Lattice_OSup__class_OSup(tc_fun(X30852,tc_HOL_Obool),X30851)))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X30852,tc_HOL_Obool)),X30851)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UnionD])]) ).

fof(i_0_9362,plain,
    ! [X19780,X19781] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X19781))
      | c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19781),X19780)),X19781) = 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_9363,plain,
    ! [X19473,X19474] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19474),c_Groups_Ozero__class_Ozero(X19474)),c_Groups_Osgn__class_Osgn(X19474,X19473)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19474),c_Groups_Ozero__class_Ozero(X19474)),X19473))
        | ~ class_Rings_Olinordered__idom(X19474) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19474),c_Groups_Ozero__class_Ozero(X19474)),X19473))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19474),c_Groups_Ozero__class_Ozero(X19474)),c_Groups_Osgn__class_Osgn(X19474,X19473)))
        | ~ class_Rings_Olinordered__idom(X19474) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__greater])])]) ).

cnf(i_0_9364,plain,
    c_Int_OBit0(X1) != c_Int_OBit1(X2),
    inference(split_conjunct,[status(thm)],[i_0_5875]) ).

cnf(i_0_9365,plain,
    c_Int_OBit1(X1) != c_Int_OBit0(X2),
    inference(split_conjunct,[status(thm)],[i_0_5876]) ).

fof(i_0_9366,plain,
    ! [X19380,X19381,X19382,X19383] :
      ( ~ class_Divides_Osemiring__div(X19383)
      | c_Divides_Odiv__class_Omod(X19383,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19383),X19382),X19381),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19383),X19382),X19380)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19383),X19382),c_Divides_Odiv__class_Omod(X19383,X19381,X19380)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__mult1])]) ).

fof(i_0_9367,plain,
    ! [X29879,X29880,X29881,X29882] :
      ( ( X29882 != c_Orderings_Obot__class_Obot(tc_fun(X29881,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29881,tc_fun(X29880,tc_HOL_Obool)),X29882),hAPP(c_COMBK(tc_fun(X29880,tc_HOL_Obool),X29881),X29879)) = c_Orderings_Otop__class_Otop(tc_fun(X29880,tc_HOL_Obool)) )
      & ( X29882 = c_Orderings_Obot__class_Obot(tc_fun(X29881,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29881,tc_fun(X29880,tc_HOL_Obool)),X29882),hAPP(c_COMBK(tc_fun(X29880,tc_HOL_Obool),X29881),X29879)) = X29879 ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__constant])]) ).

fof(i_0_9368,plain,
    ! [X25060,X25061,X25062,X25063] :
      ( ( X25063 != c_Orderings_Obot__class_Obot(tc_fun(X25062,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25062,tc_fun(X25061,tc_HOL_Obool)),X25063),hAPP(c_COMBK(tc_fun(X25061,tc_HOL_Obool),X25062),X25060)) = c_Orderings_Obot__class_Obot(tc_fun(X25061,tc_HOL_Obool)) )
      & ( X25063 = c_Orderings_Obot__class_Obot(tc_fun(X25062,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25062,tc_fun(X25061,tc_HOL_Obool)),X25063),hAPP(c_COMBK(tc_fun(X25061,tc_HOL_Obool),X25062),X25060)) = X25060 ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__constant])]) ).

fof(i_0_9369,plain,
    ! [X33671,X33672,X33673] : c_Random__Sequence_Oempty(X33673,X33672,X33671) = 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(X33673)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(X33673)),
    inference(variable_rename,[status(thm)],[fact_Random__Sequence_Oempty__def]) ).

fof(i_0_9370,plain,
    ! [X19653,X19654,X19655,X19656] :
      ( ( X19655 != c_Groups_Ozero__class_Ozero(X19656)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X19656),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19656),X19655),X19654)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19656),X19655),X19653)) = c_Groups_Ozero__class_Ozero(X19656)
        | ~ class_Divides_Osemiring__div(X19656) )
      & ( X19655 = c_Groups_Ozero__class_Ozero(X19656)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X19656),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19656),X19655),X19654)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19656),X19655),X19653)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X19656),X19654),X19653)
        | ~ class_Divides_Osemiring__div(X19656) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__mult1__if])])]) ).

fof(i_0_9371,plain,
    ! [X21351,X21352,X21353,X21354] :
      ( ~ class_Fields_Ofield__inverse__zero(X21354)
      | X21353 = c_Groups_Ozero__class_Ozero(X21354)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21354),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21354),X21353),X21352)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21354),X21353),X21351)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21354),X21352),X21351) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__divide__mult__cancel__left])]) ).

fof(i_0_9372,plain,
    ! [X21347,X21348,X21349,X21350] :
      ( ~ class_Fields_Ofield__inverse__zero(X21350)
      | X21349 = c_Groups_Ozero__class_Ozero(X21350)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21350),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21350),X21348),X21349)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21350),X21347),X21349)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21350),X21348),X21347) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__divide__mult__cancel__right])]) ).

fof(i_0_9373,plain,
    ! [X19639,X19640,X19641,X19642] :
      ( ~ class_Divides_Osemiring__div(X19642)
      | X19641 = c_Groups_Ozero__class_Ozero(X19642)
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X19642),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19642),X19641),X19640)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19642),X19641),X19639)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X19642),X19640),X19639) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__mult1])]) ).

fof(i_0_9374,plain,
    ! [X19643,X19644,X19645,X19646] :
      ( ~ class_Divides_Osemiring__div(X19646)
      | X19645 = c_Groups_Ozero__class_Ozero(X19646)
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X19646),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19646),X19644),X19645)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19646),X19643),X19645)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X19646),X19644),X19643) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__mult2])]) ).

cnf(i_0_9375,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_5877]) ).

fof(i_0_9376,plain,
    ! [X21845,X21846,X21847,X21848] : hAPP(c_Nat_Onat_Onat__rec(X21848,X21847,X21846),hAPP(c_Nat_OSuc,X21845)) = hAPP(hAPP(X21846,X21845),hAPP(c_Nat_Onat_Onat__rec(X21848,X21847,X21846),X21845)),
    inference(variable_rename,[status(thm)],[fact_nat__rec__Suc]) ).

fof(i_0_9377,plain,
    ! [X19161,X19162,X19163] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19163),X19162))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19163),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19162),X19161))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I3_J])]) ).

fof(i_0_9378,plain,
    ! [X19145,X19146,X19147] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19147),X19146))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19147),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19146),X19145))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__le__add1])]) ).

fof(i_0_9379,plain,
    ! [X19164,X19165,X19166] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19166),X19165))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19166),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19164),X19165))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I4_J])]) ).

fof(i_0_9380,plain,
    ! [X19142,X19143,X19144] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19144),X19143))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19144),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19142),X19143))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__le__add2])]) ).

fof(i_0_9381,plain,
    ! [X17606,X17607,X17608] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17608),X17607))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17608),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17607),X17606))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I1_J])]) ).

fof(i_0_9382,plain,
    ! [X17433,X17434,X17435] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17435),X17434))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17435),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17434),X17433))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__less__add1])]) ).

fof(i_0_9383,plain,
    ! [X17609,X17610,X17611] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17611),X17610))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17611),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17609),X17610))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I2_J])]) ).

fof(i_0_9384,plain,
    ! [X17430,X17431,X17432] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17432),X17431))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17432),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17430),X17431))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__less__add2])]) ).

fof(i_0_9385,plain,
    ! [X19431,X19432,X19433,X19434] :
      ( ~ class_Divides_Osemiring__div(X19434)
      | c_Divides_Odiv__class_Omod(X19434,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19434),X19433),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19434),X19432),X19431)),X19432) = c_Divides_Odiv__class_Omod(X19434,X19433,X19432) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__self2])]) ).

fof(i_0_9386,plain,
    ! [X19435,X19436,X19437,X19438] :
      ( ~ class_Divides_Osemiring__div(X19438)
      | c_Divides_Odiv__class_Omod(X19438,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19438),X19437),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19438),X19436),X19435)),X19435) = c_Divides_Odiv__class_Omod(X19438,X19437,X19435) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__self1])]) ).

fof(i_0_9387,plain,
    ! [X17586,X17587,X17589,X17590,X17591] :
      ( ( X17587 = hAPP(c_Nat_OSuc,esk24_2(X17586,X17587))
        | X17587 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17587),hAPP(c_Nat_OSuc,X17586))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk24_2(X17586,X17587)),X17586))
        | X17587 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17587),hAPP(c_Nat_OSuc,X17586))) )
      & ( X17590 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17590),hAPP(c_Nat_OSuc,X17589))) )
      & ( X17590 != hAPP(c_Nat_OSuc,X17591)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17591),X17589))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17590),hAPP(c_Nat_OSuc,X17589))) ) ),
    inference(distribute,[status(thm)],[inference(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_9388,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_5878]) ).

fof(i_0_9389,plain,
    ! [X33710,X33711,X33712,X33714,X33715,X33716] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X33711),X33712),c_Orderings_Otop__class_Otop(tc_fun(X33711,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(X33710,X33712))
        | hBOOL(hAPP(X33710,esk537_1(X33710))) )
      & ( hBOOL(hAPP(hAPP(c_member(X33716),esk538_2(X33714,X33716)),c_Orderings_Otop__class_Otop(tc_fun(X33716,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(X33714,X33715)) )
      & ( hBOOL(hAPP(X33714,esk538_2(X33714,X33716)))
        | ~ hBOOL(hAPP(X33714,X33715)) ) ),
    inference(distribute,[status(thm)],[inference(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_9390,plain,
    ! [X29310,X29311] :
      ( X29311 = c_List_Olist_ONil(X29310)
      | hAPP(c_List_Orotate1(X29310),X29311) = hAPP(hAPP(c_List_Oappend(X29310),hAPP(c_List_Otl(X29310),X29311)),hAPP(hAPP(c_List_Olist_OCons(X29310),hAPP(c_List_Ohd(X29310),X29311)),c_List_Olist_ONil(X29310))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rotate1__hd__tl])]) ).

cnf(i_0_9391,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_5879]) ).

fof(i_0_9392,plain,
    ! [X30309,X30310,X30311,X30312] :
      ( ~ class_Groups_Ocomm__monoid__add(X30312)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X30312),X30311),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X30310,X30309))) = hAPP(c_List_Omonoid__add__class_Olistsum(X30312),hAPP(hAPP(c_List_Omap(tc_Int_Oint,X30312),X30311),c_List_Oupto(X30310,X30309))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__set__upto__conv__listsum__int])]) ).

fof(i_0_9393,plain,
    ! [X30305,X30306,X30307,X30308] :
      ( ~ class_Groups_Ocomm__monoid__add(X30308)
      | hAPP(c_List_Omonoid__add__class_Olistsum(X30308),hAPP(hAPP(c_List_Omap(tc_Int_Oint,X30308),X30307),c_List_Oupto(X30306,X30305))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X30308),X30307),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X30306,X30305))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_interv__listsum__conv__setsum__set__int])]) ).

fof(i_0_9394,plain,
    ! [X23872,X23873,X23874,X23875] :
      ( ~ class_Lattices_Osemilattice__inf(X23875)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23875),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23875),X23874),X23873)),X23872) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23875),X23874),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23875),X23873),X23872)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf_Oassoc])]) ).

fof(i_0_9395,plain,
    ! [X23864,X23865,X23866,X23867] :
      ( ~ class_Lattices_Osemilattice__inf(X23867)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23867),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23867),X23866),X23865)),X23864) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23867),X23866),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23867),X23865),X23864)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__assoc])]) ).

fof(i_0_9396,plain,
    ! [X23868,X23869,X23870,X23871] :
      ( ~ class_Lattices_Olattice(X23871)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23871),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23871),X23870),X23869)),X23868) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23871),X23870),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23871),X23869),X23868)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I2_J])]) ).

fof(i_0_9397,plain,
    ! [X23016,X23017,X23018,X23019] :
      ( ~ class_Lattices_Olattice(X23019)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23019),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23019),X23018),X23017)),X23016) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23019),X23018),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23019),X23017),X23016)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I6_J])]) ).

fof(i_0_9398,plain,
    ! [X23020,X23021,X23022,X23023] :
      ( ~ class_Lattices_Osemilattice__sup(X23023)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23023),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23023),X23022),X23021)),X23020) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23023),X23022),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23023),X23021),X23020)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__assoc])]) ).

fof(i_0_9399,plain,
    ! [X23012,X23013,X23014,X23015] :
      ( ~ class_Lattices_Osemilattice__sup(X23015)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23015),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23015),X23014),X23013)),X23012) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23015),X23014),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23015),X23013),X23012)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup_Oassoc])]) ).

fof(i_0_9400,plain,
    ! [X22660,X22661,X22662,X22663] :
      ( ~ class_Orderings_Olinorder(X22663)
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X22663),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22663),X22662),X22661)),X22660) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X22663),X22662),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22663),X22661),X22660)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__assoc])]) ).

fof(i_0_9401,plain,
    ! [X22656,X22657,X22658,X22659] :
      ( ~ class_Orderings_Olinorder(X22659)
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X22659),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22659),X22658),X22657)),X22656) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X22659),X22658),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22659),X22657),X22656)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup_Oassoc])]) ).

fof(i_0_9402,plain,
    ! [X22397,X22398,X22399,X22400] :
      ( ~ class_Orderings_Olinorder(X22400)
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X22400),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22400),X22399),X22398)),X22397) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X22400),X22399),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22400),X22398),X22397)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf_Oassoc])]) ).

fof(i_0_9403,plain,
    ! [X22393,X22394,X22395,X22396] :
      ( ~ class_Orderings_Olinorder(X22396)
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X22396),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22396),X22395),X22394)),X22393) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X22396),X22395),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22396),X22394),X22393)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__assoc])]) ).

fof(i_0_9404,plain,
    ! [X20525,X20526,X20527] :
      ( ~ class_Groups_Omonoid__mult(X20527)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20527),hAPP(hAPP(c_Power_Opower__class_Opower(X20527),X20526),X20525)),X20526) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20527),X20526),hAPP(hAPP(c_Power_Opower__class_Opower(X20527),X20526),X20525)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__commutes])]) ).

fof(i_0_9405,plain,
    ! [X18191,X18192,X18193,X18194] :
      ( ~ class_Groups_Oab__semigroup__mult(X18194)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18194),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18194),X18193),X18192)),X18191) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18194),X18193),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18194),X18192),X18191)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__semigroup__mult__class_Omult__ac_I1_J])]) ).

fof(i_0_9406,plain,
    ! [X18151,X18152,X18153,X18154] :
      ( ~ class_Rings_Ocomm__semiring__1(X18154)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18154),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18154),X18153),X18152)),X18151) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18154),X18153),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18154),X18152),X18151)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J])]) ).

fof(i_0_9407,plain,
    ! [X17815,X17816,X17817,X17818] :
      ( ~ class_Rings_Ocomm__semiring__1(X17818)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17818),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17818),X17817),X17816)),X17815) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17818),X17817),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17818),X17816),X17815)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J])]) ).

fof(i_0_9408,plain,
    ! [X17321,X17322,X17323,X17324] :
      ( ~ class_Groups_Oab__semigroup__add(X17324)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17324),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17324),X17323),X17322)),X17321) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17324),X17323),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17324),X17322),X17321)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__semigroup__add__class_Oadd__ac_I1_J])]) ).

fof(i_0_9409,plain,
    ! [X21262,X21263,X21264,X21265] :
      ( ~ class_Rings_Odivision__ring(X21265)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21265),X21264),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21265),X21263),X21262)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21265),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21265),X21264),X21263)),X21262) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_times__divide__eq__right])]) ).

fof(i_0_9410,plain,
    ! [X18166,X18167,X18168,X18169] :
      ( ~ class_Rings_Ocomm__semiring__1(X18169)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18169),X18168),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18169),X18167),X18166)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18169),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18169),X18168),X18167)),X18166) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J])]) ).

fof(i_0_9411,plain,
    ! [X17819,X17820,X17821,X17822] :
      ( ~ class_Rings_Ocomm__semiring__1(X17822)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17822),X17821),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17822),X17820),X17819)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17822),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17822),X17821),X17820)),X17819) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J])]) ).

fof(i_0_9412,plain,
    ! [X31568,X31569,X31570] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X31570),X31569),hAPP(c_List_Oset(X31570),X31568)))
        | c_List_Oremdups(X31570,hAPP(hAPP(c_List_Olist_OCons(X31570),X31569),X31568)) = c_List_Oremdups(X31570,X31568) )
      & ( hBOOL(hAPP(hAPP(c_member(X31570),X31569),hAPP(c_List_Oset(X31570),X31568)))
        | c_List_Oremdups(X31570,hAPP(hAPP(c_List_Olist_OCons(X31570),X31569),X31568)) = hAPP(hAPP(c_List_Olist_OCons(X31570),X31569),c_List_Oremdups(X31570,X31568)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5880])]) ).

fof(i_0_9413,plain,
    ! [X29539,X29540] :
      ( X29540 = c_List_Olist_ONil(X29539)
      | c_List_Olast(X29539,X29540) = hAPP(hAPP(c_List_Onth(X29539),X29540),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29539)),X29540)),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_9414,plain,
    ! [X18213,X18214] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18213),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Int_Oring__1__class_Oof__int(X18214),X18213) = hAPP(c_Groups_Ouminus__class_Ouminus(X18214),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18214),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X18213))))
        | ~ class_Rings_Oring__1(X18214) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18213),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Int_Oring__1__class_Oof__int(X18214),X18213) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18214),hAPP(c_Int_Onat,X18213))
        | ~ class_Rings_Oring__1(X18214) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5881])])]) ).

fof(i_0_9415,plain,
    ! [X20951,X20952] :
      ( ~ class_Int_Onumber__ring(X20952)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X20951))
      | hBOOL(hAPP(hAPP(c_member(X20952),hAPP(c_Int_Onumber__class_Onumber__of(X20952),X20951)),c_Nat_Osemiring__1__class_ONats(X20952))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nats__number__of])]) ).

fof(i_0_9416,plain,
    ! [X25410,X25411] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25411),X25410))
      | hAPP(c_Finite__Set_Ocard(tc_fun(X25411,tc_HOL_Obool)),hAPP(c_Set_OPow(X25411),X25410)) = 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(X25411),X25410)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Pow])]) ).

fof(i_0_9417,plain,
    ! [X26415] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,X26415)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),X26415)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X26415),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_atLeast__Suc]) ).

fof(i_0_9418,plain,
    ! [X24099,X24100,X24101] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24101,tc_HOL_Obool)),X24100),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X24101,tc_HOL_Obool)),X24099)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24101,tc_HOL_Obool)),X24100),X24099),
    inference(variable_rename,[status(thm)],[fact_Diff__Compl]) ).

fof(i_0_9419,plain,
    ! [X24096,X24097,X24098] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24098,tc_HOL_Obool)),X24097),X24096) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24098,tc_HOL_Obool)),X24097),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X24098,tc_HOL_Obool)),X24096)),
    inference(variable_rename,[status(thm)],[fact_Diff__eq]) ).

fof(i_0_9420,plain,
    ! [X18924] :
      ( ~ class_Rings_Olinordered__semidom(X18924)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18924),c_Groups_Ozero__class_Ozero(X18924)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18924),c_Groups_Oone__class_Oone(X18924)),c_Groups_Oone__class_Oone(X18924)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__two])]) ).

fof(i_0_9421,plain,
    ! [X24810,X24811] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X24811,X24810)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24810),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24811),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(variable_rename,[status(thm)],[fact_card__greaterThanLessThan__int]) ).

fof(i_0_9422,plain,
    ! [X33416,X33417,X33418,X33419] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33419),X33418))
      | hAPP(hAPP(c_List_Onth(X33417),c_List_Oreplicate(X33417,X33418,X33416)),X33419) = X33416 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__replicate])]) ).

fof(i_0_9423,plain,
    ! [X24493,X24494,X24495] :
      ( ~ class_Orderings_Olinorder(X24495)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24495),X24494))
      | ~ hBOOL(hAPP(hAPP(c_member(X24495),X24493),X24494))
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X24495),X24493),c_Big__Operators_Olattice_OInf__fin(X24495,c_Orderings_Oord__class_Omin(X24495),X24494)) = X24493 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__Inf__absorb])]) ).

fof(i_0_9424,plain,
    ! [X24437,X24438,X24439] :
      ( ~ class_Orderings_Olinorder(X24439)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24439),X24438))
      | ~ hBOOL(hAPP(hAPP(c_member(X24439),X24437),X24438))
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X24439),X24437),c_Big__Operators_Olattice_OSup__fin(X24439,c_Orderings_Oord__class_Omax(X24439),X24438)) = X24437 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__Sup__absorb])]) ).

fof(i_0_9425,plain,
    ! [X18838,X18839] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18839),X18838),hAPP(c_Groups_Ouminus__class_Ouminus(X18839),X18838)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18839),X18838),c_Groups_Ozero__class_Ozero(X18839)))
        | ~ class_Groups_Olinordered__ab__group__add(X18839) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18839),X18838),c_Groups_Ozero__class_Ozero(X18839)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18839),X18838),hAPP(c_Groups_Ouminus__class_Ouminus(X18839),X18838)))
        | ~ class_Groups_Olinordered__ab__group__add(X18839) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__minus__self__iff])])]) ).

fof(i_0_9426,plain,
    ! [X18314,X18315] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18315),X18314),hAPP(c_Groups_Ouminus__class_Ouminus(X18315),X18314)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18315),X18314),c_Groups_Ozero__class_Ozero(X18315)))
        | ~ class_Rings_Olinordered__idom(X18315) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18315),X18314),c_Groups_Ozero__class_Ozero(X18315)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18315),X18314),hAPP(c_Groups_Ouminus__class_Ouminus(X18315),X18314)))
        | ~ class_Rings_Olinordered__idom(X18315) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__minus__self__iff])])]) ).

fof(i_0_9427,plain,
    ! [X24061,X24062,X24063] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24063,tc_HOL_Obool)),X24062),X24061) != c_Orderings_Obot__class_Obot(tc_fun(X24063,tc_HOL_Obool))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24063,tc_HOL_Obool)),X24062),X24061) = X24062 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Diff__triv])]) ).

fof(i_0_9428,plain,
    ! [X30557,X30558,X30559,X30560,X30561] :
      ( ~ class_Orderings_Olinorder(X30561)
      | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30560,X30561,X30559),X30558),X30557) != c_List_Olist_ONil(X30560) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insort__not__Nil])]) ).

fof(i_0_9429,plain,
    ! [X24731,X24732,X24733,X24734] :
      ( ~ class_Groups_Ocomm__monoid__mult(X24734)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24733),X24732))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24733,X24734),hAPP(c_COMBK(X24734,X24733),X24731)),X24732) = hAPP(hAPP(c_Power_Opower__class_Opower(X24734),X24731),hAPP(c_Finite__Set_Ocard(X24733),X24732)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__constant])]) ).

fof(i_0_9430,plain,
    ! [X33535,X33536] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X33536),X33535))
        | c_Lazy__Sequence_Osmall__lazy_H(X33536,X33535) = c_Lazy__Sequence_Oempty(tc_Int_Oint) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X33536),X33535))
        | c_Lazy__Sequence_Osmall__lazy_H(X33536,X33535) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),X33535),c_Lazy__Sequence_Osmall__lazy_H(X33536,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X33535),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5882])]) ).

fof(i_0_9431,plain,
    ! [X27051,X27052,X27053] :
      ( ~ class_Lattices_Oab__semigroup__idem__mult(X27053)
      | X27052 = c_Orderings_Obot__class_Obot(tc_fun(X27053,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27053),X27052))
      | hAPP(c_Finite__Set_Ofold1(X27053,c_Groups_Otimes__class_Otimes(X27053)),hAPP(hAPP(c_Set_Oinsert(X27053),X27051),X27052)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27053),X27051),hAPP(c_Finite__Set_Ofold1(X27053,c_Groups_Otimes__class_Otimes(X27053)),X27052)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1__insert__idem])]) ).

fof(i_0_9432,plain,
    ! [X25819,X25820,X25821,X25822] :
      ( ~ class_Orderings_Oorder(X25822)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25822,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X25822,X25821),X25820)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X25822,X25820),X25819)) = c_Orderings_Obot__class_Obot(tc_fun(X25822,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I11_J])]) ).

fof(i_0_9433,plain,
    ! [X21738,X21739] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21739),hAPP(c_Nat_OSuc,X21738)) = 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),X21739),X21738)),
    inference(variable_rename,[status(thm)],[fact_diff__Suc]) ).

fof(i_0_9434,plain,
    ! [X28367,X28368,X28369,X28370] : hAPP(hAPP(c_List_Oappend(X28370),hAPP(hAPP(c_List_Olist_OCons(X28370),X28369),X28368)),X28367) = hAPP(hAPP(c_List_Olist_OCons(X28370),X28369),hAPP(hAPP(c_List_Oappend(X28370),X28368),X28367)),
    inference(variable_rename,[status(thm)],[fact_append__Cons]) ).

fof(i_0_9435,plain,
    ! [X28179,X28180,X28181,X28182] : hAPP(hAPP(c_List_Oappend(X28182),hAPP(hAPP(c_List_Oappend(X28182),X28181),X28180)),X28179) = hAPP(hAPP(c_List_Oappend(X28182),X28181),hAPP(hAPP(c_List_Oappend(X28182),X28180),X28179)),
    inference(variable_rename,[status(thm)],[fact_append__assoc]) ).

fof(i_0_9436,plain,
    ! [X29387,X29388,X29389] :
      ( X29389 = c_List_Olist_ONil(X29388)
      | hAPP(hAPP(c_List_Otake(X29388),hAPP(c_Nat_OSuc,X29387)),X29389) = hAPP(hAPP(c_List_Olist_OCons(X29388),hAPP(c_List_Ohd(X29388),X29389)),hAPP(hAPP(c_List_Otake(X29388),X29387),hAPP(c_List_Otl(X29388),X29389))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__Suc])]) ).

fof(i_0_9437,plain,
    ! [X26155] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26155))
      | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26155) = 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,X26155))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__atLeastZeroLessThan__int])]) ).

fof(i_0_9438,plain,
    ! [X28733,X28734,X28735,X28736] :
      ( ( X28736 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Onth(X28735),hAPP(hAPP(c_List_Olist_OCons(X28735),X28734),X28733)),X28736) = X28734 )
      & ( X28736 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Onth(X28735),hAPP(hAPP(c_List_Olist_OCons(X28735),X28734),X28733)),X28736) = hAPP(hAPP(c_List_Onth(X28735),X28733),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X28736),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_9439,plain,
    ! [X23248,X23249,X23250,X23251] :
      ( ( X23251 != c_Orderings_Obot__class_Obot(tc_fun(X23250,tc_HOL_Obool))
        | hAPP(c_Set_Oimage(X23250,X23249,hAPP(c_COMBK(X23249,X23250),X23248)),X23251) = c_Orderings_Obot__class_Obot(tc_fun(X23249,tc_HOL_Obool)) )
      & ( X23251 = c_Orderings_Obot__class_Obot(tc_fun(X23250,tc_HOL_Obool))
        | hAPP(c_Set_Oimage(X23250,X23249,hAPP(c_COMBK(X23249,X23250),X23248)),X23251) = hAPP(hAPP(c_Set_Oinsert(X23249),X23248),c_Orderings_Obot__class_Obot(tc_fun(X23249,tc_HOL_Obool))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__constant__conv])]) ).

cnf(i_0_9440,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_5842]) ).

cnf(i_0_9441,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_5844]) ).

cnf(i_0_9442,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_5843]) ).

cnf(i_0_9443,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_5845]) ).

fof(i_0_9444,plain,
    ! [X30197,X30198,X30199,X30200] :
      ( ~ class_Groups_Ocomm__monoid__add(X30200)
      | ~ hBOOL(hAPP(c_List_Odistinct(X30199),X30198))
      | hAPP(c_List_Omonoid__add__class_Olistsum(X30200),hAPP(hAPP(c_List_Omap(X30199,X30200),X30197),X30198)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X30199,X30200),X30197),hAPP(c_List_Oset(X30199),X30198)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__distinct__conv__setsum__set])]) ).

fof(i_0_9445,plain,
    ! [X20537,X20538,X20539,X20540] :
      ( ~ class_Groups_Omonoid__mult(X20540)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X20540),X20539),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20538),X20537)) = hAPP(hAPP(c_Power_Opower__class_Opower(X20540),hAPP(hAPP(c_Power_Opower__class_Opower(X20540),X20539),X20538)),X20537) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__mult])]) ).

fof(i_0_9446,plain,
    ! [X20250,X20251,X20252,X20253] :
      ( ~ class_Rings_Ocomm__semiring__1(X20253)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X20253),hAPP(hAPP(c_Power_Opower__class_Opower(X20253),X20252),X20251)),X20250) = hAPP(hAPP(c_Power_Opower__class_Opower(X20253),X20252),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20251),X20250)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J])]) ).

fof(i_0_9447,plain,
    ! [X19402,X19403,X19404] :
      ( ~ class_Divides_Oring__div(X19404)
      | c_Divides_Odiv__class_Omod(X19404,hAPP(c_Groups_Ouminus__class_Ouminus(X19404),X19403),X19402) = c_Divides_Odiv__class_Omod(X19404,hAPP(c_Groups_Ouminus__class_Ouminus(X19404),c_Divides_Odiv__class_Omod(X19404,X19403,X19402)),X19402) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__minus__eq])]) ).

fof(i_0_9448,plain,
    ! [X29384,X29385,X29386] : hAPP(c_List_Otl(X29386),hAPP(hAPP(c_List_Otake(X29386),X29385),X29384)) = hAPP(hAPP(c_List_Otake(X29386),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X29385),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_List_Otl(X29386),X29384)),
    inference(variable_rename,[status(thm)],[fact_tl__take]) ).

fof(i_0_9449,plain,
    ! [X20581,X20582,X20583] :
      ( ~ class_Rings_Olinordered__idom(X20583)
      | hAPP(c_Groups_Oabs__class_Oabs(X20583),hAPP(hAPP(c_Power_Opower__class_Opower(X20583),hAPP(c_Groups_Ouminus__class_Ouminus(X20583),X20582)),X20581)) = hAPP(c_Groups_Oabs__class_Oabs(X20583),hAPP(hAPP(c_Power_Opower__class_Opower(X20583),X20582),X20581)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__power__minus])]) ).

cnf(i_0_9450,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_5883]) ).

cnf(i_0_9451,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_5884]) ).

fof(i_0_9452,plain,
    ! [X24379,X24380,X24381] :
      ( ~ class_Orderings_Olinorder(X24381)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24381),X24380))
      | hBOOL(hAPP(hAPP(c_member(X24381),X24379),X24380))
      | X24380 = c_Orderings_Obot__class_Obot(tc_fun(X24381,tc_HOL_Obool))
      | c_Big__Operators_Olinorder__class_OMin(X24381,hAPP(hAPP(c_Set_Oinsert(X24381),X24379),X24380)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X24381),X24379),c_Big__Operators_Olinorder__class_OMin(X24381,X24380)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5885])]) ).

fof(i_0_9453,plain,
    ! [X24312,X24313,X24314] :
      ( ~ class_Orderings_Olinorder(X24314)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24314),X24313))
      | hBOOL(hAPP(hAPP(c_member(X24314),X24312),X24313))
      | X24313 = c_Orderings_Obot__class_Obot(tc_fun(X24314,tc_HOL_Obool))
      | c_Big__Operators_Olinorder__class_OMax(X24314,hAPP(hAPP(c_Set_Oinsert(X24314),X24312),X24313)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X24314),X24312),c_Big__Operators_Olinorder__class_OMax(X24314,X24313)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5886])]) ).

fof(i_0_9454,plain,
    ! [X24306,X24307,X24308] :
      ( ~ class_Lattices_Olattice(X24308)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24308),X24307))
      | hBOOL(hAPP(hAPP(c_member(X24308),X24306),X24307))
      | X24307 = c_Orderings_Obot__class_Obot(tc_fun(X24308,tc_HOL_Obool))
      | c_Big__Operators_Olattice__class_OSup__fin(X24308,hAPP(hAPP(c_Set_Oinsert(X24308),X24306),X24307)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24308),X24306),c_Big__Operators_Olattice__class_OSup__fin(X24308,X24307)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5887])]) ).

fof(i_0_9455,plain,
    ! [X24309,X24310,X24311] :
      ( ~ class_Lattices_Olattice(X24311)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24311),X24310))
      | hBOOL(hAPP(hAPP(c_member(X24311),X24309),X24310))
      | X24310 = c_Orderings_Obot__class_Obot(tc_fun(X24311,tc_HOL_Obool))
      | c_Big__Operators_Olattice__class_OInf__fin(X24311,hAPP(hAPP(c_Set_Oinsert(X24311),X24309),X24310)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24311),X24309),c_Big__Operators_Olattice__class_OInf__fin(X24311,X24310)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5888])]) ).

fof(i_0_9456,plain,
    ! [X26729,X26730] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26730),c_Orderings_Otop__class_Otop(tc_fun(X26730,tc_HOL_Obool))))
      | hAPP(c_Finite__Set_Ocard(X26730),X26729) != hAPP(c_Finite__Set_Ocard(X26730),c_Orderings_Otop__class_Otop(tc_fun(X26730,tc_HOL_Obool)))
      | X26729 = c_Orderings_Otop__class_Otop(tc_fun(X26730,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__eq__UNIV__imp__eq__UNIV])]) ).

fof(i_0_9457,plain,
    ! [X28962,X28963,X28964,X28965] :
      ( ( X28965 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Odrop(X28964),X28965),hAPP(hAPP(c_List_Olist_OCons(X28964),X28963),X28962)) = hAPP(hAPP(c_List_Olist_OCons(X28964),X28963),X28962) )
      & ( X28965 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Odrop(X28964),X28965),hAPP(hAPP(c_List_Olist_OCons(X28964),X28963),X28962)) = hAPP(hAPP(c_List_Odrop(X28964),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X28965),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X28962) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_drop__Cons_H])]) ).

fof(i_0_9458,plain,
    ! [X20677] : 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,X20677))))),
    inference(variable_rename,[status(thm)],[fact_neg__zminus__int]) ).

fof(i_0_9459,plain,
    ! [X17036,X17037,X17038,X17039] :
      ( ( ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X17039),X17038),X17037),X17036))
        | X17038 = X17036
        | hBOOL(hAPP(X17037,X17036)) )
      & ( X17038 != X17036
        | hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X17039),X17038),X17037),X17036)) )
      & ( ~ hBOOL(hAPP(X17037,X17036))
        | hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X17039),X17038),X17037),X17036)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__code])])]) ).

fof(i_0_9460,plain,
    ! [X25881,X25882,X25883] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X25883),X25882),hAPP(c_SetInterval_Oord__class_OatMost(X25883),X25881)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25883),X25882),X25881))
        | ~ class_Orderings_Oord(X25883) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25883),X25882),X25881))
        | hBOOL(hAPP(hAPP(c_member(X25883),X25882),hAPP(c_SetInterval_Oord__class_OatMost(X25883),X25881)))
        | ~ class_Orderings_Oord(X25883) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atMost__iff])])]) ).

fof(i_0_9461,plain,
    ! [X26291,X26292,X26293] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X26293),X26292),hAPP(c_SetInterval_Oord__class_OatLeast(X26293),X26291)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26293),X26291),X26292))
        | ~ class_Orderings_Oord(X26293) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26293),X26291),X26292))
        | hBOOL(hAPP(hAPP(c_member(X26293),X26292),hAPP(c_SetInterval_Oord__class_OatLeast(X26293),X26291)))
        | ~ class_Orderings_Oord(X26293) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeast__iff])])]) ).

fof(i_0_9462,plain,
    ! [X26114,X26115,X26116] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X26116),X26115),hAPP(c_SetInterval_Oord__class_OlessThan(X26116),X26114)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26116),X26115),X26114))
        | ~ class_Orderings_Oord(X26116) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26116),X26115),X26114))
        | hBOOL(hAPP(hAPP(c_member(X26116),X26115),hAPP(c_SetInterval_Oord__class_OlessThan(X26116),X26114)))
        | ~ class_Orderings_Oord(X26116) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lessThan__iff])])]) ).

fof(i_0_9463,plain,
    ! [X26536,X26537,X26538] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X26538),X26537),hAPP(c_SetInterval_Oord__class_OgreaterThan(X26538),X26536)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26538),X26536),X26537))
        | ~ class_Orderings_Oord(X26538) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26538),X26536),X26537))
        | hBOOL(hAPP(hAPP(c_member(X26538),X26537),hAPP(c_SetInterval_Oord__class_OgreaterThan(X26538),X26536)))
        | ~ class_Orderings_Oord(X26538) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_greaterThan__iff])])]) ).

fof(i_0_9464,plain,
    ! [X25928,X25929,X25930] :
      ( ~ class_Groups_Oordered__ab__group__add(X25930)
      | hAPP(c_Set_Oimage(X25930,X25930,c_Groups_Ouminus__class_Ouminus(X25930)),c_SetInterval_Oord__class_OgreaterThanAtMost(X25930,X25929,X25928)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X25930,hAPP(c_Groups_Ouminus__class_Ouminus(X25930),X25928)),hAPP(c_Groups_Ouminus__class_Ouminus(X25930),X25929)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__uminus__greaterThanAtMost])]) ).

fof(i_0_9465,plain,
    ! [X26123,X26124,X26125,X26126,X26127] :
      ( ~ c_Finite__Set_Ofolding__one__idem(X26127,X26126,X26125)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26127),X26124))
      | ~ hBOOL(hAPP(hAPP(c_member(X26127),X26123),X26124))
      | hAPP(hAPP(X26126,X26123),hAPP(X26125,X26124)) = hAPP(X26125,X26124) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Oin__idem])]) ).

fof(i_0_9466,plain,
    ! [X24256,X24257,X24258] :
      ( ~ class_Orderings_Olinorder(X24258)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24258),X24257))
      | ~ hBOOL(hAPP(hAPP(c_member(X24258),X24256),X24257))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24258),X24256),c_Big__Operators_Olinorder__class_OMax(X24258,X24257))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max__ge])]) ).

fof(i_0_9467,plain,
    ! [X29565,X29566] :
      ( ~ class_Groups_Ocomm__monoid__add(X29566)
      | hAPP(c_List_Omonoid__add__class_Olistsum(X29566),X29565) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X29566),hAPP(c_List_Onth(X29566),X29565)),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(X29566)),X29565))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__setsum__nth])]) ).

fof(i_0_9468,plain,
    ! [X19830,X19831] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19831),X19830))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19830)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19831)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19830),X19831)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiff__int])]) ).

fof(i_0_9469,plain,
    ! [X18909] : 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)),X18909)),X18909) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[fact_odd__nonzero]) ).

fof(i_0_9470,plain,
    ! [X30946,X30947] : hAPP(c_Relation_OField(X30947),X30946) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X30947,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X30947,X30947),X30946)),hAPP(c_Relation_ORange(X30947,X30947),X30946)),
    inference(variable_rename,[status(thm)],[fact_Field__def]) ).

cnf(i_0_9471,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_5889]) ).

fof(i_0_9472,plain,
    ! [X25433,X25434] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X25434,X25433) = 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),X25434),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25433))),
    inference(variable_rename,[status(thm)],[fact_SetInterval_Otransfer__nat__int__set__functions_I2_J]) ).

fof(i_0_9473,plain,
    ! [X28493,X28494,X28495] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X28495))
        | c_List_Osublist(X28494,hAPP(hAPP(c_List_Olist_OCons(X28494),X28493),c_List_Olist_ONil(X28494)),X28495) = hAPP(hAPP(c_List_Olist_OCons(X28494),X28493),c_List_Olist_ONil(X28494)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X28495))
        | c_List_Osublist(X28494,hAPP(hAPP(c_List_Olist_OCons(X28494),X28493),c_List_Olist_ONil(X28494)),X28495) = c_List_Olist_ONil(X28494) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5890])]) ).

fof(i_0_9474,plain,
    ! [X19667,X19668] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19668))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19668),X19667)),X19668) = X19667 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__self1__is__m])]) ).

fof(i_0_9475,plain,
    ! [X19665,X19666] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19666))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19665),X19666)),X19666) = X19665 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__self__is__m])]) ).

cnf(i_0_9476,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_5891]) ).

cnf(i_0_9477,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_5892]) ).

fof(i_0_9478,plain,
    ! [X20144,X20145] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X20145,X20144) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,X20145,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X20144)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X20145,X20144) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,X20145,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X20144)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X20145,X20144)),X20144) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__zminus2__eq__if])]) ).

fof(i_0_9479,plain,
    ! [X26692,X26693] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26693,tc_HOL_Obool)),X26692),c_Orderings_Otop__class_Otop(tc_fun(X26693,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_subset__UNIV]) ).

fof(i_0_9480,plain,
    ! [X20636] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20636)))
        | 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),X20636)) = 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),X20636)))
        | 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),X20636)) = 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),X20636))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5893])]) ).

cnf(i_0_9481,plain,
    c_Relation_Osingle__valued(X1,X1,c_Relation_OId(X1)),
    inference(split_conjunct,[status(thm)],[i_0_5894]) ).

fof(i_0_9482,plain,
    ! [X18521,X18522,X18523] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X18523),X18522))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X18522),X18521))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X18523),X18521)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__trans])]) ).

fof(i_0_9483,plain,
    ! [X19079,X19080,X19081] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19081),X19080))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19080),X19079))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19081),X19079)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__trans])]) ).

fof(i_0_9484,plain,
    ! [X17170,X17171,X17172] :
      ( ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,X17172,X17171,X17170)
      | X17170 = X17172 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evaln__elim__cases_I1_J])]) ).

fof(i_0_9485,plain,
    ! [X18740,X18741] :
      ( ~ class_Rings_Ocomm__semiring__1(X18741)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18741),X18740),X18740) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18741),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18741),c_Groups_Oone__class_Oone(X18741)),c_Groups_Oone__class_Oone(X18741))),X18740) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J])]) ).

fof(i_0_9486,plain,
    ! [X18563,X18564,X18565] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18565),X18564),X18563))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18565),X18564),X18563))
        | ~ class_Orderings_Opreorder(X18565) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18565),X18563),X18564))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18565),X18564),X18563))
        | ~ class_Orderings_Opreorder(X18565) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18565),X18564),X18563))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18565),X18563),X18564))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18565),X18564),X18563))
        | ~ class_Orderings_Opreorder(X18565) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5895])])]) ).

fof(i_0_9487,plain,
    ! [X17419,X17420,X17421,X17422] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17422),X17421))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17420),X17421) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17422),X17419)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17420),X17419)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__eq__less])]) ).

fof(i_0_9488,plain,
    ! [X19112,X19113] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19113)),X19112))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19113),X19112)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__leD])]) ).

fof(i_0_9489,plain,
    ! [X19240,X19241] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19241),X19240))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19241)),X19240)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19241)),X19240))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19241),X19240)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__Suc__le])]) ).

fof(i_0_9490,plain,
    ! [X19236,X19237] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19237)),X19236))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19237),X19236)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19237),X19236))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19237)),X19236)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__eq])]) ).

fof(i_0_9491,plain,
    ! [X19228,X19229] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19229)),X19228))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19229),X19228)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__lessD])]) ).

fof(i_0_9492,plain,
    ! [X17536,X17537] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X17537)),X17536))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17537),X17536)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__lessD])]) ).

fof(i_0_9493,plain,
    ! [X24584,X24585,X24586] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24586),X24585))
      | hBOOL(hAPP(hAPP(c_member(X24586),X24584),X24585))
      | hAPP(c_Finite__Set_Ocard(X24586),hAPP(hAPP(c_Set_Oinsert(X24586),X24584),X24585)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X24586),X24585)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5896])]) ).

fof(i_0_9494,plain,
    ! [X28841,X28842,X28843,X28844] : hAPP(hAPP(c_List_Odrop(X28844),X28843),hAPP(hAPP(c_List_Odrop(X28844),X28842),X28841)) = hAPP(hAPP(c_List_Odrop(X28844),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X28843),X28842)),X28841),
    inference(variable_rename,[status(thm)],[fact_drop__drop]) ).

fof(i_0_9495,plain,
    ! [X28769,X28770,X28771,X28772] : hAPP(hAPP(c_List_Otake(X28772),X28771),hAPP(hAPP(c_List_Otake(X28772),X28770),X28769)) = hAPP(hAPP(c_List_Otake(X28772),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X28771),X28770)),X28769),
    inference(variable_rename,[status(thm)],[fact_take__take]) ).

fof(i_0_9496,plain,
    ! [X19537,X19538,X19539] :
      ( ( ~ hBOOL(hAPP(X19539,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19538),X19537)))
        | epred2_3(X19539,X19538,X19537) )
      & ( ~ epred2_3(X19539,X19538,X19537)
        | hBOOL(hAPP(X19539,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19538),X19537))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5897])]) ).

fof(i_0_9497,plain,
    ! [X31030,X31031,X31032] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X31032)
      | ~ hBOOL(hAPP(hAPP(c_member(X31032),X31031),X31030))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31032),c_Complete__Lattice_OInf__class_OInf(X31032,X31030)),X31031)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__lower])]) ).

fof(i_0_9498,plain,
    ! [X18881,X18883,X18884,X18886] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk42_1(X18881)))
        | hBOOL(hAPP(X18881,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18883))) )
      & ( ~ hBOOL(hAPP(X18881,esk42_1(X18881)))
        | hBOOL(hAPP(X18881,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18883))) )
      & ( ~ hBOOL(hAPP(X18884,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk43_1(X18884))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18886))
        | hBOOL(hAPP(X18884,X18886)) ) ),
    inference(distribute,[status(thm)],[inference(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_9499,plain,
    ! [X19596,X19597] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19597))
      | hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19597),X19596)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,X19597)),hAPP(c_Int_Onat,X19596)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__div__distrib])]) ).

fof(i_0_9500,plain,
    ! [X18710,X18711] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18711))
      | hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X18711),X18710)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,X18711)),hAPP(c_Int_Onat,X18710)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__distrib])]) ).

fof(i_0_9501,plain,
    ! [X25461,X25462] :
      ( ~ c_Nat__Transfer_Ois__nat(X25462)
      | ~ c_Nat__Transfer_Ois__nat(X25461)
      | c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X25462,X25461) = 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,X25462),hAPP(c_Int_Onat,X25461))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SetInterval_Otransfer__int__nat__set__functions])]) ).

fof(i_0_9502,plain,
    ! [X31307] :
      ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(X31307)),c_List_Otranspose__rel(X31307)),c_List_Olist_ONil(tc_List_Olist(X31307))))
      | c_List_Otranspose(X31307,c_List_Olist_ONil(tc_List_Olist(X31307))) = c_List_Olist_ONil(tc_List_Olist(X31307)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transpose_Opsimps_I1_J])]) ).

fof(i_0_9503,plain,
    ! [X19583,X19584,X19585] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19585),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19584,X19583)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19585),X19584),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19585),X19583)),
    inference(variable_rename,[status(thm)],[fact_mod__mult__distrib2]) ).

fof(i_0_9504,plain,
    ! [X23330,X23331] :
      ( ( X23331 != X23330
        | hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X23331) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X23330) )
      & ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X23331) != hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X23330)
        | X23331 = X23330 ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__relations_I3_J])]) ).

fof(i_0_9505,plain,
    ! [X28838,X28839,X28840] : hAPP(c_List_Oset(X28840),hAPP(hAPP(c_List_Oappend(X28840),X28839),X28838)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X28840,tc_HOL_Obool)),hAPP(c_List_Oset(X28840),X28839)),hAPP(c_List_Oset(X28840),X28838)),
    inference(variable_rename,[status(thm)],[fact_set__append]) ).

fof(i_0_9506,plain,
    ! [X17270,X17271] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17271),X17270))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X17271)),hAPP(c_Nat_OSuc,X17270))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mono])]) ).

fof(i_0_9507,plain,
    ! [X20781,X20782,X20783,X20784] :
      ( ( hAPP(hAPP(c_Set_Oinsert(X20784),X20783),X20782) != hAPP(hAPP(c_Set_Oinsert(X20784),X20783),X20781)
        | X20782 = X20781
        | hBOOL(hAPP(hAPP(c_member(X20784),X20783),X20781))
        | hBOOL(hAPP(hAPP(c_member(X20784),X20783),X20782)) )
      & ( X20782 != X20781
        | hAPP(hAPP(c_Set_Oinsert(X20784),X20783),X20782) = hAPP(hAPP(c_Set_Oinsert(X20784),X20783),X20781)
        | hBOOL(hAPP(hAPP(c_member(X20784),X20783),X20781))
        | hBOOL(hAPP(hAPP(c_member(X20784),X20783),X20782)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5898])])]) ).

fof(i_0_9508,plain,
    ! [X20565,X20566,X20567,X20568] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(X20568),X20567),X20566) != hAPP(hAPP(c_Power_Opower__class_Opower(X20568),X20567),X20565)
        | X20566 = X20565
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20568),c_Groups_Oone__class_Oone(X20568)),X20567))
        | ~ class_Rings_Olinordered__semidom(X20568) )
      & ( X20566 != X20565
        | hAPP(hAPP(c_Power_Opower__class_Opower(X20568),X20567),X20566) = hAPP(hAPP(c_Power_Opower__class_Opower(X20568),X20567),X20565)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20568),c_Groups_Oone__class_Oone(X20568)),X20567))
        | ~ class_Rings_Olinordered__semidom(X20568) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__inject__exp])])]) ).

fof(i_0_9509,plain,
    ! [X17115,X17116,X17117,X17118] : c_Hoare__Mirabelle_Otriple__valid(X17118,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17118),X17117),hAPP(c_Com_Ocom_OBODY,X17116)),X17115)),
    inference(variable_rename,[status(thm)],[fact_Body__triple__valid__0]) ).

fof(i_0_9510,plain,
    ! [X28591,X28592,X28593] : c_List_Olistset(X28593,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X28593,tc_HOL_Obool)),X28592),X28591)) = c_List_Oset__Cons(X28593,X28592,c_List_Olistset(X28593,X28591)),
    inference(variable_rename,[status(thm)],[fact_listset_Osimps_I2_J]) ).

fof(i_0_9511,plain,
    ! [X33707,X33708,X33709] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X33708),X33709),c_Orderings_Obot__class_Obot(tc_fun(X33708,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(X33707,X33709)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bex__empty])]) ).

fof(i_0_9512,plain,
    ! [X32888,X32889] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X32889)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32889),X32888))
      | c_Complete__Lattice_OInf__class_OInf(X32889,X32888) = hAPP(hAPP(c_Finite__Set_Ofold(X32889,X32889,c_Lattices_Osemilattice__inf__class_Oinf(X32889)),c_Orderings_Otop__class_Otop(X32889)),X32888) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fold__inf])]) ).

fof(i_0_9513,plain,
    ! [X32886,X32887] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X32887)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32887),X32886))
      | c_Complete__Lattice_OSup__class_OSup(X32887,X32886) = hAPP(hAPP(c_Finite__Set_Ofold(X32887,X32887,c_Lattices_Osemilattice__sup__class_Osup(X32887)),c_Orderings_Obot__class_Obot(X32887)),X32886) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fold__sup])]) ).

fof(i_0_9514,plain,
    ! [X20514,X20515] :
      ( ( X20515 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X20514),X20515) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( X20515 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X20514),X20515) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20514),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X20514),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20515),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_9515,plain,
    ! [X25488,X25489,X25490] :
      ( ~ class_Groups_Oordered__ab__group__add(X25490)
      | hAPP(c_Set_Oimage(X25490,X25490,c_Groups_Ouminus__class_Ouminus(X25490)),c_SetInterval_Oord__class_OatLeastAtMost(X25490,X25489,X25488)) = c_SetInterval_Oord__class_OatLeastAtMost(X25490,hAPP(c_Groups_Ouminus__class_Ouminus(X25490),X25488),hAPP(c_Groups_Ouminus__class_Ouminus(X25490),X25489)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__uminus__atLeastAtMost])]) ).

fof(i_0_9516,plain,
    ! [X24873,X24874,X24875] :
      ( ~ class_Groups_Oordered__ab__group__add(X24875)
      | hAPP(c_Set_Oimage(X24875,X24875,c_Groups_Ouminus__class_Ouminus(X24875)),c_SetInterval_Oord__class_OgreaterThanLessThan(X24875,X24874,X24873)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X24875,hAPP(c_Groups_Ouminus__class_Ouminus(X24875),X24873),hAPP(c_Groups_Ouminus__class_Ouminus(X24875),X24874)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__uminus__greaterThanLessThan])]) ).

fof(i_0_9517,plain,
    ! [X24552,X24553,X24554] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X24554),X24552),X24553))
        | hAPP(c_Finite__Set_Ocard(X24554),hAPP(hAPP(c_Set_Oinsert(X24554),X24552),X24553)) = hAPP(c_Finite__Set_Ocard(X24554),X24553)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24554),X24553)) )
      & ( hBOOL(hAPP(hAPP(c_member(X24554),X24552),X24553))
        | hAPP(c_Finite__Set_Ocard(X24554),hAPP(hAPP(c_Set_Oinsert(X24554),X24552),X24553)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X24554),X24553))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24554),X24553)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5899])])]) ).

fof(i_0_9518,plain,
    ! [X26139] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X26139)) = 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),X26139))),
    inference(variable_rename,[status(thm)],[fact_lessThan__Suc__eq__insert__0]) ).

fof(i_0_9519,plain,
    ! [X21827,X21828] : c_Code__Numeral_Odiv__mod__code__numeral(X21828,X21827) = 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),X21828),X21827)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X21828,X21827)),
    inference(variable_rename,[status(thm)],[fact_div__mod__code__numeral__def]) ).

fof(i_0_9520,plain,
    ! [X21854,X21855] : c_Divides_Odivmod__int(X21855,X21854) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X21855),X21854)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X21855,X21854)),
    inference(variable_rename,[status(thm)],[fact_divmod__int__mod__div]) ).

fof(i_0_9521,plain,
    ! [X19413,X19414] : 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,X19414,X19413)),X19413) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X19414),X19413),
    inference(variable_rename,[status(thm)],[fact_zminus__zmod]) ).

fof(i_0_9522,plain,
    ! [X18901,X18902] :
      ( ( hAPP(c_Int_Onat,X18902) != hAPP(c_Int_Onat,X18901)
        | X18902 = X18901
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18901))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18902)) )
      & ( X18902 != X18901
        | hAPP(c_Int_Onat,X18902) = hAPP(c_Int_Onat,X18901)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18901))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18902)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__relations_I1_J])])]) ).

fof(i_0_9523,plain,
    ! [X18887,X18888] :
      ( ( hAPP(c_Int_Onat,X18888) != hAPP(c_Int_Onat,X18887)
        | X18888 = X18887
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18887))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18888)) )
      & ( X18888 != X18887
        | hAPP(c_Int_Onat,X18888) = hAPP(c_Int_Onat,X18887)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18887))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18888)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__nat__nat__iff])])]) ).

fof(i_0_9524,plain,
    ! [X17908,X17909,X17911,X17912,X17913] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X17909),X17908))
        | X17908 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X17909),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,esk31_2(X17908,X17909)))) )
      & ( X17911 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X17912),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X17913)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X17912),X17911)) ) ),
    inference(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_9525,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_5900]) ).

fof(i_0_9526,plain,
    ! [X20053,X20054] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20054),X20053)),X20053) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20054),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20054,X20053)),
    inference(variable_rename,[status(thm)],[fact_div__mod__equality_H]) ).

fof(i_0_9527,plain,
    ! [X20027,X20028] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20028),X20027))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20027),X20028)),X20028) = X20027 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__diff__inverse2])]) ).

fof(i_0_9528,plain,
    ! [X18022] :
      ( ( ~ 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),X18022)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18022)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18022))
        | 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),X18022))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__int__conv])]) ).

fof(i_0_9529,plain,
    ! [X20516,X20517] :
      ( ( X20517 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20516))
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20517) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20516) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20516)))
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20517) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20516) )
      & ( X20517 != hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20516))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20516)))
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20517) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20516) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__eq__iff__number__of])])]) ).

fof(i_0_9530,plain,
    ! [X25431,X25432] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X25432,tc_HOL_Obool)),hAPP(c_Set_OPow(X25432),X25431)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X25432),X25431)) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25432),X25431))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X25432,tc_HOL_Obool)),hAPP(c_Set_OPow(X25432),X25431))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Pow__iff])]) ).

fof(i_0_9531,plain,
    ! [X30965,X30966,X30967,X30968,X30969] :
      ( ~ hBOOL(hAPP(hAPP(X30969,X30968),X30967))
      | hBOOL(hAPP(c_Predicate_ODomainP(X30966,X30965,X30969),X30968)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DomainP_Ointros])]) ).

fof(i_0_9532,plain,
    ! [X28307,X28308,X28309,X28310,X28311] :
      ( ~ hBOOL(hAPP(hAPP(X28311,X28310),X28309))
      | hBOOL(hAPP(c_Predicate_ORangeP(X28308,X28307,X28311),X28309)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_RangeP_Ointros])]) ).

fof(i_0_9533,plain,
    ! [X33315,X33316,X33317] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33317)),c_List_Osplice(X33317,X33316,X33315)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33317)),X33316)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33317)),X33315)),
    inference(variable_rename,[status(thm)],[fact_length__splice]) ).

fof(i_0_9534,plain,
    ! [X28482,X28483] :
      ( ( ~ 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(X28483)),X28482)))
        | X28482 != c_List_Olist_ONil(X28483) )
      & ( X28482 = c_List_Olist_ONil(X28483)
        | 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(X28483)),X28482))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_length__greater__0__conv])]) ).

fof(i_0_9535,plain,
    ! [X26385,X26386,X26387] :
      ( ~ class_Orderings_Oorder(X26387)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26387,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26387,X26386),X26385)),hAPP(c_SetInterval_Oord__class_OatLeast(X26387),X26385)) = c_Orderings_Obot__class_Obot(tc_fun(X26387,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I8_J])]) ).

fof(i_0_9536,plain,
    ! [X19230,X19231] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19230),hAPP(c_Nat_OSuc,X19231)))
        | X19230 = X19231
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19231),X19230)) )
      & ( X19230 != X19231
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19230),hAPP(c_Nat_OSuc,X19231)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19231),X19230)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__less__Suc__eq])])]) ).

fof(i_0_9537,plain,
    ! [X17256,X17257] :
      ( ( hBOOL(hAPP(X17257,esk20_2(X17256,X17257)))
        | hBOOL(hAPP(X17257,X17256))
        | ~ hBOOL(hAPP(X17257,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
      & ( ~ hBOOL(hAPP(X17257,hAPP(c_Nat_OSuc,esk20_2(X17256,X17257))))
        | hBOOL(hAPP(X17257,X17256))
        | ~ hBOOL(hAPP(X17257,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_nat__induct])])])]) ).

cnf(i_0_9538,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_5901]) ).

fof(i_0_9539,plain,
    ! [X19463,X19464] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19464))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19464),X19463))
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,X19464,X19463) = X19464 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__pos__pos__trivial])]) ).

fof(i_0_9540,plain,
    ! [X26165,X26166] :
      ( ~ class_Orderings_Oorder(X26166)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26166,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X26166),X26165)),hAPP(c_SetInterval_Oord__class_OatLeast(X26166),X26165)) = hAPP(hAPP(c_Set_Oinsert(X26166),X26165),c_Orderings_Obot__class_Obot(tc_fun(X26166,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atMost__Int__atLeast])]) ).

fof(i_0_9541,plain,
    ! [X17517,X17518] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17518),X17517))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17517),hAPP(c_Nat_OSuc,X17518))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17517),hAPP(c_Nat_OSuc,X17518)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17518),X17517)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5902])]) ).

cnf(i_0_9542,plain,
    hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(X1,X2))),
    inference(split_conjunct,[status(thm)],[i_0_5903]) ).

fof(i_0_9543,plain,
    ! [X28201,X28202,X28203] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28203)),hAPP(hAPP(c_List_Oappend(X28203),X28202),X28201)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28203)),X28202)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28203)),X28201)),
    inference(variable_rename,[status(thm)],[fact_length__append]) ).

fof(i_0_9544,plain,
    ! [X23447,X23448] :
      ( ( X23448 != X23447
        | hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X23448) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X23447)
        | ~ c_Nat__Transfer_Onat__set(X23447)
        | ~ c_Nat__Transfer_Onat__set(X23448) )
      & ( hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X23448) != hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X23447)
        | X23448 = X23447
        | ~ c_Nat__Transfer_Onat__set(X23447)
        | ~ c_Nat__Transfer_Onat__set(X23448) ) ),
    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_9545,plain,
    ! [X16958,X16959,X16960,X16961,X16962,X16963,X16964] :
      ( ( X16963 = X16960
        | hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X16964),X16963),X16962),X16961) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X16964),X16960),X16959),X16958) )
      & ( X16962 = X16959
        | hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X16964),X16963),X16962),X16961) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X16964),X16960),X16959),X16958) )
      & ( X16961 = X16958
        | hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X16964),X16963),X16962),X16961) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X16964),X16960),X16959),X16958) )
      & ( X16963 != X16960
        | X16962 != X16959
        | X16961 != X16958
        | hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X16964),X16963),X16962),X16961) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X16964),X16960),X16959),X16958) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_triple_Oinject])])]) ).

fof(i_0_9546,plain,
    ! [X24657,X24658,X24659,X24660,X24661] :
      ( ~ class_Rings_Ocomm__semiring__1(X24660)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24659),X24658))
      | ~ hBOOL(hAPP(hAPP(c_member(X24659),X24661),X24658))
      | hAPP(X24657,X24661) != c_Groups_Ozero__class_Ozero(X24660)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24659,X24660),X24657),X24658) = c_Groups_Ozero__class_Ozero(X24660) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__zero])])]) ).

fof(i_0_9547,plain,
    ! [X19603,X19604,X19605] :
      ( ( X19605 != 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),X19605),X19604)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19605),X19603)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X19605 = 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),X19605),X19604)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19605),X19603)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19604),X19603) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__div__cancel__disj])]) ).

fof(i_0_9548,plain,
    ! [X25438,X25439] : hBOOL(hAPP(hAPP(c_member(tc_fun(X25439,tc_HOL_Obool)),X25438),hAPP(c_Set_OPow(X25439),X25438))),
    inference(variable_rename,[status(thm)],[fact_Pow__top]) ).

fof(i_0_9549,plain,
    ! [X31674,X31675,X31676] : hAPP(c_List_Orev(X31676),hAPP(hAPP(c_List_Olist_OCons(X31676),X31675),X31674)) = hAPP(hAPP(c_List_Oappend(X31676),hAPP(c_List_Orev(X31676),X31674)),hAPP(hAPP(c_List_Olist_OCons(X31676),X31675),c_List_Olist_ONil(X31676))),
    inference(variable_rename,[status(thm)],[fact_rev_Osimps_I2_J]) ).

cnf(i_0_9550,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_5904]) ).

fof(i_0_9551,plain,
    ! [X19702,X19703] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19703),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)),X19703))
        | X19702 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19703),X19702) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19702),X19703))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19703))
        | X19702 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19703),X19702) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19703),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19703),X19702))
        | X19702 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19703),X19702) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19702),X19703))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19703),X19702))
        | X19702 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19703),X19702) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( X19702 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19703),X19702) = 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)),X19703))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19703),X19702))
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19703),X19702) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19703),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19702),X19703))
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19703),X19702) = 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_9552,plain,
    ! [X19689,X19690] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19690))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19690),X19689))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19690),X19689) = 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_9553,plain,
    ! [X24248,X24249] :
      ( ~ class_Lattices_Olattice(X24249)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24249),X24248))
      | X24248 = c_Orderings_Obot__class_Obot(tc_fun(X24249,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24249),c_Big__Operators_Olattice__class_OInf__fin(X24249,X24248)),c_Big__Operators_Olattice__class_OSup__fin(X24249,X24248))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__le__Sup])]) ).

fof(i_0_9554,plain,
    ! [X33401,X33402,X33403,X33404] : hAPP(hAPP(c_List_Omap(X33404,X33403),hAPP(c_COMBK(X33403,X33404),X33402)),X33401) = c_List_Oreplicate(X33403,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33404)),X33401),X33402),
    inference(variable_rename,[status(thm)],[fact_map__replicate__const]) ).

fof(i_0_9555,plain,
    ! [X33897,X33898,X33899,X33900,X33901] :
      ( ~ c_Equiv__Relations_Opart__equivp(X33901,X33900)
      | ~ hBOOL(hAPP(hAPP(X33900,X33899),X33898))
      | ~ hBOOL(hAPP(hAPP(X33900,X33898),X33897))
      | hBOOL(hAPP(hAPP(X33900,X33899),X33897)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_part__equivp__transp])]) ).

fof(i_0_9556,plain,
    ! [X33830,X33831,X33832,X33833,X33834] :
      ( ~ c_Predicate_Otransp(X33834,X33833)
      | ~ hBOOL(hAPP(hAPP(X33833,X33832),X33831))
      | ~ hBOOL(hAPP(hAPP(X33833,X33831),X33830))
      | hBOOL(hAPP(hAPP(X33833,X33832),X33830)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transpE])]) ).

fof(i_0_9557,plain,
    ! [X26898,X26899,X26900,X26901,X26902] :
      ( ~ c_Equiv__Relations_Oequivp(X26902,X26901)
      | ~ hBOOL(hAPP(hAPP(X26901,X26900),X26899))
      | ~ hBOOL(hAPP(hAPP(X26901,X26899),X26898))
      | hBOOL(hAPP(hAPP(X26901,X26900),X26898)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equivp__transp])]) ).

fof(i_0_9558,plain,
    ! [X26142,X26143,X26144,X26145,X26146] :
      ( ~ c_Finite__Set_Ofolding__one__idem(X26146,X26145,X26144)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26146),X26143))
      | X26143 = c_Orderings_Obot__class_Obot(tc_fun(X26146,tc_HOL_Obool))
      | hAPP(X26144,hAPP(hAPP(c_Set_Oinsert(X26146),X26142),X26143)) = hAPP(hAPP(X26145,X26142),hAPP(X26144,X26143)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Oinsert__idem])]) ).

fof(i_0_9559,plain,
    ! [X19398,X19399,X19400,X19401] :
      ( ~ class_Divides_Oring__div(X19401)
      | c_Divides_Odiv__class_Omod(X19401,X19400,X19399) != c_Divides_Odiv__class_Omod(X19401,X19398,X19399)
      | c_Divides_Odiv__class_Omod(X19401,hAPP(c_Groups_Ouminus__class_Ouminus(X19401),X19400),X19399) = c_Divides_Odiv__class_Omod(X19401,hAPP(c_Groups_Ouminus__class_Ouminus(X19401),X19398),X19399) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__minus__cong])]) ).

fof(i_0_9560,plain,
    ! [X30746,X30747] : hAPP(c_Set_Oimage(tc_List_Olist(X30747),tc_fun(X30747,tc_HOL_Obool),c_List_Oset(X30747)),hAPP(c_List_Oset(tc_List_Olist(X30747)),c_Enum_Osublists(X30747,X30746))) = hAPP(c_Set_OPow(X30747),hAPP(c_List_Oset(X30747),X30746)),
    inference(variable_rename,[status(thm)],[fact_sublists__powset]) ).

fof(i_0_9561,plain,
    ! [X31027,X31028] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X31028,tc_HOL_Obool),X31027) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X31028,tc_HOL_Obool),tc_fun(X31028,tc_HOL_Obool)),X31027),c_COMBI(tc_fun(X31028,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_Inter__def]) ).

fof(i_0_9562,plain,
    ! [X30811,X30812] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X30812,tc_HOL_Obool),X30811) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X30812,tc_HOL_Obool),tc_fun(X30812,tc_HOL_Obool)),X30811),c_COMBI(tc_fun(X30812,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_Union__def]) ).

fof(i_0_9563,plain,
    ! [X31723,X31724,X31725,X31726] :
      ( ( ~ hBOOL(hAPP(X31726,X31725))
        | c_List_OtakeWhile(X31724,X31726,hAPP(hAPP(c_List_Olist_OCons(X31724),X31725),X31723)) = hAPP(hAPP(c_List_Olist_OCons(X31724),X31725),c_List_OtakeWhile(X31724,X31726,X31723)) )
      & ( hBOOL(hAPP(X31726,X31725))
        | c_List_OtakeWhile(X31724,X31726,hAPP(hAPP(c_List_Olist_OCons(X31724),X31725),X31723)) = c_List_Olist_ONil(X31724) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5905])]) ).

fof(i_0_9564,plain,
    ! [X20436] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X20436)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | X20436 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( X20436 != 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),X20436)),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_9565,plain,
    ! [X19011] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19011)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | X19011 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X19011 != 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),X19011)),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_9566,plain,
    ! [X20520,X20521] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20521))
      | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,X20521)),X20520) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X20521),X20520)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J])]) ).

fof(i_0_9567,plain,
    ! [X20518,X20519] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20519))
      | hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X20519),X20518)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,X20519)),X20518) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__power__eq])]) ).

fof(i_0_9568,plain,
    ! [X19906,X19907,X19908] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19908),X19907)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19908),X19906)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19907),X19906),
    inference(variable_rename,[status(thm)],[fact_diff__cancel]) ).

fof(i_0_9569,plain,
    ! [X19909,X19910,X19911] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19911),X19910)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19909),X19910)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19911),X19909),
    inference(variable_rename,[status(thm)],[fact_diff__cancel2]) ).

fof(i_0_9570,plain,
    ! [X20266,X20267,X20268] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X20268),X20267)),X20266) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X20268),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20267),X20266)),
    inference(variable_rename,[status(thm)],[fact_zpower__zpower]) ).

fof(i_0_9571,plain,
    ! [X19903,X19904,X19905] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19905),X19904)),X19903) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19905),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19904),X19903)),
    inference(variable_rename,[status(thm)],[fact_diff__diff__left]) ).

fof(i_0_9572,plain,
    ! [X18148,X18149,X18150] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X18150),X18149)),X18148) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X18150),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X18149),X18148)),
    inference(variable_rename,[status(thm)],[fact_zmult__assoc]) ).

fof(i_0_9573,plain,
    ! [X18450,X18451,X18452] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18452),X18451)),X18450) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18452),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18451),X18450)),
    inference(variable_rename,[status(thm)],[fact_nat__mult__assoc]) ).

fof(i_0_9574,plain,
    ! [X18090,X18091,X18092] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18092),X18091)),X18090) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18092),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18091),X18090)),
    inference(variable_rename,[status(thm)],[fact_zadd__assoc]) ).

fof(i_0_9575,plain,
    ! [X17452,X17453,X17454] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17454),X17453)),X17452) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17454),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17453),X17452)),
    inference(variable_rename,[status(thm)],[fact_nat__add__assoc]) ).

fof(i_0_9576,plain,
    ! [X19573,X19574,X19575] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19575),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19574),X19573)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19575),X19574)),X19573),
    inference(variable_rename,[status(thm)],[fact_div__mult2__eq]) ).

fof(i_0_9577,plain,
    ! [X29220,X29221,X29222] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X29221),X29222),c_Orderings_Obot__class_Obot(tc_fun(X29221,tc_HOL_Obool))))
      | hBOOL(hAPP(X29220,X29222)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ball__empty])]) ).

fof(i_0_9578,plain,
    ! [X26133,X26134,X26135] :
      ( ~ class_Orderings_Oorder(X26135)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26135,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X26135),X26134)),c_SetInterval_Oord__class_OatLeastAtMost(X26135,X26134,X26133)) = c_Orderings_Obot__class_Obot(tc_fun(X26135,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I4_J])]) ).

fof(i_0_9579,plain,
    ! [X25972,X25973,X25974] :
      ( ~ class_Orderings_Oorder(X25974)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25974,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X25974),X25973)),c_SetInterval_Oord__class_OgreaterThanAtMost(X25974,X25973,X25972)) = c_Orderings_Obot__class_Obot(tc_fun(X25974,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I3_J])]) ).

fof(i_0_9580,plain,
    ! [X25975,X25976,X25977] :
      ( ~ class_Orderings_Oorder(X25977)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25977,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X25977),X25976)),c_SetInterval_Oord__class_OgreaterThanLessThan(X25977,X25976,X25975)) = c_Orderings_Obot__class_Obot(tc_fun(X25977,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I1_J])]) ).

fof(i_0_9581,plain,
    ! [X19469,X19470] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19470),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19469),X19470))
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,X19470,X19469) = X19470 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__neg__neg__trivial])]) ).

fof(i_0_9582,plain,
    ! [X29766,X29767,X29768,X29769] : hAPP(c_List_Oset(X29769),hAPP(hAPP(c_List_Omap(X29768,X29769),X29767),X29766)) = hAPP(c_Set_Oimage(X29768,X29769,X29767),hAPP(c_List_Oset(X29768),X29766)),
    inference(variable_rename,[status(thm)],[fact_set__map]) ).

fof(i_0_9583,plain,
    ! [X28884,X28885,X28886] : hAPP(hAPP(c_List_Oappend(X28886),hAPP(hAPP(c_List_Otake(X28886),X28885),X28884)),hAPP(hAPP(c_List_Odrop(X28886),X28885),X28884)) = X28884,
    inference(variable_rename,[status(thm)],[fact_append__take__drop__id]) ).

fof(i_0_9584,plain,
    ! [X18080] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18080)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[i_0_5906]) ).

fof(i_0_9585,plain,
    ! [X19571,X19572] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X19572),X19571) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19572,X19571)),X19571),
    inference(variable_rename,[status(thm)],[fact_mod__Suc__eq__Suc__mod]) ).

fof(i_0_9586,plain,
    ! [X17241,X17242] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(X17242,X17241)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X17242)),c_Com_Ocom_Ocom__size(X17241))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[fact_com_Osize_I4_J]) ).

fof(i_0_9587,plain,
    ! [X20939] :
      ( ( ~ 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),X20939)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X20939)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X20939))
        | 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),X20939))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__0__number__of])]) ).

fof(i_0_9588,plain,
    ! [X32732,X32733,X32734,X32735] :
      ( ( ~ c_List_Olist__ex(X32735,X32734,hAPP(hAPP(c_List_Oappend(X32735),X32733),X32732))
        | c_List_Olist__ex(X32735,X32734,X32733)
        | c_List_Olist__ex(X32735,X32734,X32732) )
      & ( ~ c_List_Olist__ex(X32735,X32734,X32733)
        | c_List_Olist__ex(X32735,X32734,hAPP(hAPP(c_List_Oappend(X32735),X32733),X32732)) )
      & ( ~ c_List_Olist__ex(X32735,X32734,X32732)
        | c_List_Olist__ex(X32735,X32734,hAPP(hAPP(c_List_Oappend(X32735),X32733),X32732)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__ex__append])])]) ).

fof(i_0_9589,plain,
    ! [X19680,X19681] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19681),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19680),X19681))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19681),X19680) = 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_9590,plain,
    ( c_Int_OMin = X1
    | c_Int_OMin != c_Int_OBit1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5907]) ).

cnf(i_0_9591,plain,
    ( X1 = c_Int_OMin
    | c_Int_OBit1(X1) != c_Int_OMin ),
    inference(split_conjunct,[status(thm)],[i_0_5908]) ).

fof(i_0_9592,plain,
    ! [X28765,X28766,X28767,X28768] : hAPP(hAPP(c_List_Otake(X28768),hAPP(c_Nat_OSuc,X28767)),hAPP(hAPP(c_List_Olist_OCons(X28768),X28766),X28765)) = hAPP(hAPP(c_List_Olist_OCons(X28768),X28766),hAPP(hAPP(c_List_Otake(X28768),X28767),X28765)),
    inference(variable_rename,[status(thm)],[fact_take__Suc__Cons]) ).

fof(i_0_9593,plain,
    ! [X33506,X33507,X33508] :
      ( ~ class_Lazy__Sequence_Osmall__lazy(X33508)
      | ~ class_Lazy__Sequence_Osmall__lazy(X33507)
      | c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_prod(X33508,X33507),X33506) = c_Lazy__Sequence_Oproduct(X33508,X33507,c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(X33508,X33506),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(X33507,X33506)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_small__lazy__prod__def])]) ).

fof(i_0_9594,plain,
    ! [X29719,X29720,X29721,X29722,X29723,X29724,X29725] :
      ( hAPP(hAPP(c_List_Omap(X29725,X29724),X29723),X29722) != hAPP(hAPP(c_List_Omap(X29721,X29724),X29720),X29719)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29725)),X29722) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29721)),X29719) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__eq__imp__length__eq])]) ).

cnf(i_0_9595,plain,
    c_Int_OBit1(X1) != c_Int_OPls,
    inference(split_conjunct,[status(thm)],[i_0_5909]) ).

cnf(i_0_9596,plain,
    c_Int_OPls != c_Int_OBit1(X1),
    inference(split_conjunct,[status(thm)],[i_0_5910]) ).

fof(i_0_9597,plain,
    ! [X30736,X30737] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X30737))),c_Enum_Osublists(X30737,X30736)) = 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(X30737)),X30736)),
    inference(variable_rename,[status(thm)],[fact_length__sublists]) ).

fof(i_0_9598,plain,
    ! [X23329] : 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)),X23329)) = X23329,
    inference(variable_rename,[status(thm)],[fact_transfer__int__nat__set__return__embed]) ).

fof(i_0_9599,plain,
    ! [X22209,X22210,X22211,X22212,X22213] :
      ( hAPP(c_Product__Type_Ofst(X22213,X22212),hAPP(hAPP(c_Product__Type_OPair(X22213,X22212),X22211),X22210)) != X22209
      | X22211 = X22209 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fst__eqD])]) ).

fof(i_0_9600,plain,
    ! [X22153,X22154,X22155,X22156,X22157] :
      ( hAPP(c_Product__Type_Osnd(X22157,X22156),hAPP(hAPP(c_Product__Type_OPair(X22157,X22156),X22155),X22154)) != X22153
      | X22154 = X22153 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_snd__eqD])]) ).

cnf(i_0_9601,plain,
    c_Relation_Osym(X1,c_Relation_OId(X1)),
    inference(split_conjunct,[status(thm)],[i_0_5911]) ).

cnf(i_0_9602,plain,
    c_Relation_Oantisym(X1,c_Relation_OId(X1)),
    inference(split_conjunct,[status(thm)],[i_0_5912]) ).

cnf(i_0_9603,plain,
    c_Relation_Otrans(X1,c_Relation_OId(X1)),
    inference(split_conjunct,[status(thm)],[i_0_5913]) ).

cnf(i_0_9604,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_5891]) ).

cnf(i_0_9605,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_5892]) ).

fof(i_0_9606,plain,
    ! [X23453] :
      ( ~ c_Nat__Transfer_Onat__set(X23453)
      | 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),X23453)) = X23453 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__return__embed])]) ).

fof(i_0_9607,plain,
    ! [X23466,X23467] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X23467,X23467)),X23466))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X23467),hAPP(c_Relation_OField(X23467),X23466))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Field])]) ).

fof(i_0_9608,plain,
    ! [X25925,X25926,X25927] :
      ( ~ class_Groups_Oordered__ab__group__add(X25927)
      | hAPP(c_Set_Oimage(X25927,X25927,c_Groups_Ouminus__class_Ouminus(X25927)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X25927,X25926),X25925)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X25927,hAPP(c_Groups_Ouminus__class_Ouminus(X25927),X25925),hAPP(c_Groups_Ouminus__class_Ouminus(X25927),X25926)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__uminus__atLeastLessThan])]) ).

fof(i_0_9609,plain,
    ! [X17529,X17530] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17530),X17529))
      | hAPP(c_Nat_OSuc,X17530) = X17529
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X17530)),X17529)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__lessI])]) ).

fof(i_0_9610,plain,
    ! [X23693,X23695,X23696,X23697] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X23693))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X23695),X23693))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X23695),esk117_1(X23693))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk118_2(X23696,X23697)),X23696))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X23696)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk118_2(X23696,X23697)),X23697))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X23696)) ) ),
    inference(distribute,[status(thm)],[inference(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_9611,plain,
    ! [X23699,X23701,X23702,X23703] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X23699))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X23701),X23699))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23701),esk119_1(X23699))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk120_2(X23702,X23703)),X23702))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X23702)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk120_2(X23702,X23703)),X23703))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X23702)) ) ),
    inference(distribute,[status(thm)],[inference(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_9612,plain,
    ! [X20274,X20275] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20274)))
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20275),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20274)) = hAPP(c_Int_Onumber__class_Onumber__of(X20275),X20274)
        | ~ class_Int_Onumber__ring(X20275) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20274)))
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20275),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20274)) = c_Groups_Ozero__class_Ozero(X20275)
        | ~ class_Int_Onumber__ring(X20275) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5914])])]) ).

fof(i_0_9613,plain,
    ! [X20447,X20448,X20449] :
      ( ~ class_Int_Onumber__ring(X20449)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20449),hAPP(c_Int_Onumber__class_Onumber__of(X20449),X20448)),hAPP(c_Int_Onumber__class_Onumber__of(X20449),X20447)) = hAPP(c_Int_Onumber__class_Onumber__of(X20449),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20448),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X20447))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__number__of__eq])]) ).

fof(i_0_9614,plain,
    ! [X30757,X30758,X30759] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X30759),X30758))
      | hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X30759)),c_Enum_On__lists(X30759,X30757,X30758))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__n__lists])]) ).

fof(i_0_9615,plain,
    ! [X24549,X24550,X24551] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24551),X24550))
      | hBOOL(hAPP(hAPP(c_member(X24551),X24549),X24550))
      | hAPP(c_Finite__Set_Ocard(X24551),hAPP(hAPP(c_Set_Oinsert(X24551),X24549),X24550)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X24551),X24550)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5915])]) ).

fof(i_0_9616,plain,
    ! [X18116] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,X18116)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18116)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18116))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,X18116))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__nat__eq])]) ).

fof(i_0_9617,plain,
    ! [X18590,X18591,X18592] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18592),X18591),X18590))
        | X18591 = X18590
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18592),X18591),X18590))
        | ~ class_Orderings_Olinorder(X18592) )
      & ( X18591 != X18590
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18592),X18591),X18590))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18592),X18591),X18590))
        | ~ class_Orderings_Olinorder(X18592) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5916])])]) ).

fof(i_0_9618,plain,
    ! [X29616,X29617,X29618] : c_List_Obutlast(X29618,hAPP(hAPP(c_List_Oappend(X29618),X29617),hAPP(hAPP(c_List_Olist_OCons(X29618),X29616),c_List_Olist_ONil(X29618)))) = X29617,
    inference(variable_rename,[status(thm)],[fact_butlast__snoc]) ).

fof(i_0_9619,plain,
    ! [X29525,X29526,X29527] : c_List_Olast(X29527,hAPP(hAPP(c_List_Oappend(X29527),X29526),hAPP(hAPP(c_List_Olist_OCons(X29527),X29525),c_List_Olist_ONil(X29527)))) = X29525,
    inference(variable_rename,[status(thm)],[fact_last__snoc]) ).

fof(i_0_9620,plain,
    ! [X32169,X32170] : hAPP(hAPP(c_Relation_Orel__comp(X32170,X32170,X32170),c_Transitive__Closure_Ortrancl(X32170,X32169)),c_Transitive__Closure_Ortrancl(X32170,X32169)) = c_Transitive__Closure_Ortrancl(X32170,X32169),
    inference(variable_rename,[status(thm)],[fact_rtrancl__idemp__self__comp]) ).

fof(i_0_9621,plain,
    ! [X22231,X22232,X22233] : hAPP(c_Product__Type_Ofst(X22233,X22232),X22231) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X22233,X22232,X22233),c_COMBK(X22233,X22232)),X22231),
    inference(variable_rename,[status(thm)],[fact_fst__def]) ).

fof(i_0_9622,plain,
    ! [X28701] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X28701)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X28701),tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[i_0_5917]) ).

fof(i_0_9623,plain,
    ! [X32517,X32518] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X32518,X32518)),X32517))
      | ~ c_Wellfounded_Oacyclic(X32518,X32517)
      | c_Wellfounded_Owf(X32518,hAPP(c_Relation_Oconverse(X32518,X32518),X32517)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__acyclic__wf__converse])]) ).

fof(i_0_9624,plain,
    ! [X18501,X18502,X18503] :
      ( ~ class_Orderings_Oorder(X18503)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18503),X18502),X18501))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18503),X18501),X18502))
      | X18501 = X18502 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I5_J])]) ).

fof(i_0_9625,plain,
    ! [X18494,X18495,X18496] :
      ( ~ class_Orderings_Oorder(X18496)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18496),X18495),X18494))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18496),X18494),X18495))
      | X18495 = X18494 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__antisym])]) ).

fof(i_0_9626,plain,
    ! [X18475,X18476,X18477] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18477),X18475),X18476))
        | X18475 = X18476
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18477),X18476),X18475))
        | ~ class_Orderings_Oorder(X18477) )
      & ( X18475 != X18476
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18477),X18475),X18476))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18477),X18476),X18475))
        | ~ class_Orderings_Oorder(X18477) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__antisym__conv])])]) ).

fof(i_0_9627,plain,
    ! [X18464,X18465,X18466] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18466),X18465),X18464))
        | X18465 != X18464
        | ~ class_Orderings_Oorder(X18466) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18466),X18464),X18465))
        | X18465 != X18464
        | ~ class_Orderings_Oorder(X18466) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18466),X18465),X18464))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18466),X18464),X18465))
        | X18465 = X18464
        | ~ class_Orderings_Oorder(X18466) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__eq__iff])])]) ).

fof(i_0_9628,plain,
    ! [X17876,X17877,X17878] :
      ( hBOOL(hAPP(X17878,X17877))
      | hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X17878,X17876)),X17877),X17877)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5918])]) ).

fof(i_0_9629,plain,
    ! [X19931,X19932] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19932),X19931))
      | c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19931,X19932) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19931),X19932),X19932) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__mod__geq])]) ).

fof(i_0_9630,plain,
    ! [X31129,X31130,X31131] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X31131),X31130),hAPP(c_List_Oset(X31131),X31129)))
      | c_List_Oinsert(X31131,X31130,X31129) = X31129 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__set__insert])]) ).

fof(i_0_9631,plain,
    ! [X31123,X31124,X31125] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X31125),X31124),hAPP(c_List_Oset(X31125),X31123)))
        | c_List_Oinsert(X31125,X31124,X31123) = X31123 )
      & ( hBOOL(hAPP(hAPP(c_member(X31125),X31124),hAPP(c_List_Oset(X31125),X31123)))
        | c_List_Oinsert(X31125,X31124,X31123) = hAPP(hAPP(c_List_Olist_OCons(X31125),X31124),X31123) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5919])]) ).

fof(i_0_9632,plain,
    ! [X20007,X20008] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20008),X20007))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X20007)),X20008) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20007),X20008)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__diff__le])]) ).

fof(i_0_9633,plain,
    ! [X17375,X17376,X17377] :
      ( ~ class_Orderings_Oorder(X17377)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17377),X17376),X17375))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17377),X17375),X17376)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5920])]) ).

fof(i_0_9634,plain,
    ! [X17390,X17391,X17392] :
      ( ~ class_Orderings_Opreorder(X17392)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17392),X17391),X17390))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17392),X17390),X17391)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5921])]) ).

fof(i_0_9635,plain,
    ! [X17387,X17388,X17389] :
      ( ~ class_Orderings_Opreorder(X17389)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17389),X17388),X17387))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17389),X17387),X17388)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5922])]) ).

fof(i_0_9636,plain,
    ! [X17378,X17379,X17380] :
      ( ~ class_Orderings_Opreorder(X17380)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17380),X17379),X17378))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17380),X17378),X17379)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5923])]) ).

fof(i_0_9637,plain,
    ! [X17348,X17349,X17350] :
      ( ~ class_Orderings_Opreorder(X17350)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17350),X17349),X17348))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17350),X17348),X17349)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5924])]) ).

fof(i_0_9638,plain,
    ! [X18554,X18555,X18556] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18556),X18555),X18554))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18556),X18554),X18555))
        | ~ class_Orderings_Olinorder(X18556) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18556),X18554),X18555))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18556),X18555),X18554))
        | ~ class_Orderings_Olinorder(X18556) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5925])])]) ).

fof(i_0_9639,plain,
    ! [X18584,X18585,X18586] :
      ( ~ class_Orderings_Olinorder(X18586)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18586),X18585),X18584))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18586),X18584),X18585)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5926])]) ).

fof(i_0_9640,plain,
    ! [X18551,X18552,X18553] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18553),X18552),X18551))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18553),X18551),X18552))
        | ~ class_Orderings_Olinorder(X18553) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18553),X18551),X18552))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18553),X18552),X18551))
        | ~ class_Orderings_Olinorder(X18553) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5927])])]) ).

fof(i_0_9641,plain,
    ! [X17405,X17406,X17407] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17407),X17406),X17405))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17407),X17405),X17406))
        | X17406 = X17405
        | ~ class_Orderings_Olinorder(X17407) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17407),X17405),X17406))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17407),X17406),X17405))
        | ~ class_Orderings_Olinorder(X17407) )
      & ( X17406 != X17405
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17407),X17406),X17405))
        | ~ class_Orderings_Olinorder(X17407) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5928])])]) ).

fof(i_0_9642,plain,
    ! [X20311,X20312] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X20312)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20312),hAPP(c_Groups_Ouminus__class_Ouminus(X20312),X20311)),hAPP(c_Groups_Oabs__class_Oabs(X20312),X20311))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__ge__minus__self])]) ).

fof(i_0_9643,plain,
    ! [X18763,X18764] :
      ( ~ class_Rings_Olinordered__ring(X18764)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18764),c_Groups_Ozero__class_Ozero(X18764)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18764),X18763),X18763))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__square])]) ).

fof(i_0_9644,plain,
    ! [X18729,X18730] :
      ( ~ class_Rings_Olinordered__semidom(X18730)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18730),X18729),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18730),X18729),c_Groups_Oone__class_Oone(X18730)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__one])]) ).

fof(i_0_9645,plain,
    ! [X20290,X20291] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20291),c_Groups_Ozero__class_Ozero(X20291)),hAPP(c_Groups_Oabs__class_Oabs(X20291),X20290)))
        | X20290 != c_Groups_Ozero__class_Ozero(X20291)
        | ~ class_Groups_Oordered__ab__group__add__abs(X20291) )
      & ( X20290 = c_Groups_Ozero__class_Ozero(X20291)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20291),c_Groups_Ozero__class_Ozero(X20291)),hAPP(c_Groups_Oabs__class_Oabs(X20291),X20290)))
        | ~ class_Groups_Oordered__ab__group__add__abs(X20291) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__abs__iff])])]) ).

fof(i_0_9646,plain,
    ! [X22040,X22041,X22042,X22043] :
      ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X22043,X22042),X22041))
      | ~ hBOOL(hAPP(hAPP(X22042,X22040),X22041))
      | hBOOL(hAPP(c_Wellfounded_Oaccp(X22043,X22042),X22040)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_accp__downward])]) ).

fof(i_0_9647,plain,
    ! [X20944,X20945] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20945),c_Int_OPls))
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20945)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20944)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20945),c_Int_OPls))
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20945)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20944)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20945),X20944)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5929])]) ).

fof(i_0_9648,plain,
    ! [X29009,X29010] :
      ( X29010 = c_List_Olist_ONil(X29009)
      | hBOOL(hAPP(hAPP(c_member(X29009),hAPP(c_List_Ohd(X29009),X29010)),hAPP(c_List_Oset(X29009),X29010))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hd__in__set])]) ).

fof(i_0_9649,plain,
    ! [X33513,X33514,X33515] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X33515)),c_Lazy__Sequence_Olazy__sequence_OInsert(X33515,X33514,X33513)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X33515)),X33513)),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_9650,plain,
    ! [X20342,X20343,X20344] :
      ( ~ class_Rings_Ocomm__semiring__1(X20344)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20344),hAPP(hAPP(c_Power_Opower__class_Opower(X20344),X20343),X20342)),X20343) = hAPP(hAPP(c_Power_Opower__class_Opower(X20344),X20343),hAPP(c_Nat_OSuc,X20342)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J])]) ).

fof(i_0_9651,plain,
    ! [X20572,X20573,X20574] :
      ( ~ class_Groups_Omonoid__mult(X20574)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X20574),X20573),hAPP(c_Nat_OSuc,X20572)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20574),hAPP(hAPP(c_Power_Opower__class_Opower(X20574),X20573),X20572)),X20573) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__Suc2])]) ).

fof(i_0_9652,plain,
    ! [X31893,X31894] :
      ( ~ class_Orderings_Olinorder(X31894)
      | c_List_Olinorder__class_Osorted__list__of__set(X31894,hAPP(c_List_Oset(X31894),X31893)) = c_List_Olinorder__class_Osort__key(X31894,X31894,c_COMBI(X31894),c_List_Oremdups(X31894,X31893)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__list__of__set__sort__remdups])]) ).

fof(i_0_9653,plain,
    ! [X17086,X17087,X17088,X17089] :
      ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17089),X17088),X17087))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17089),X17088),X17086))
      | X17086 = X17087 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_com__det])]) ).

fof(i_0_9654,plain,
    ! [X28394,X28395,X28396] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28396)),hAPP(hAPP(c_List_Olist_OCons(X28396),X28395),X28394)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28396)),X28394)),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_9655,plain,
    ! [X30768,X30769,X30770] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X30770))),c_Enum_On__lists(X30770,X30769,X30768)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30770)),X30768)),X30769),
    inference(variable_rename,[status(thm)],[fact_length__n__lists]) ).

fof(i_0_9656,plain,
    ! [X18875,X18876,X18878,X18879] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18876))
        | ~ hBOOL(hAPP(X18875,X18876))
        | hBOOL(hAPP(X18875,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk40_1(X18875)))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk41_1(X18878)))
        | ~ hBOOL(hAPP(X18878,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18879))) )
      & ( hBOOL(hAPP(X18878,esk41_1(X18878)))
        | ~ hBOOL(hAPP(X18878,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18879))) ) ),
    inference(distribute,[status(thm)],[inference(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_9657,plain,
    ! [X19232,X19233] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19233),X19232))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19233)),X19232)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__leI])]) ).

fof(i_0_9658,plain,
    ! [X24267,X24268,X24269] :
      ( ~ class_Lattices_Olattice(X24269)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24269),X24268))
      | ~ hBOOL(hAPP(hAPP(c_member(X24269),X24267),X24268))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24269),X24267),c_Big__Operators_Olattice__class_OInf__fin(X24269,X24268)) = c_Big__Operators_Olattice__class_OInf__fin(X24269,X24268) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oin__idem])]) ).

fof(i_0_9659,plain,
    ! [X24261,X24262,X24263] :
      ( ~ class_Lattices_Olattice(X24263)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24263),X24262))
      | ~ hBOOL(hAPP(hAPP(c_member(X24263),X24261),X24262))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24263),X24261),c_Big__Operators_Olattice__class_OSup__fin(X24263,X24262)) = c_Big__Operators_Olattice__class_OSup__fin(X24263,X24262) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oin__idem])]) ).

fof(i_0_9660,plain,
    ! [X24273,X24274,X24275] :
      ( ~ class_Orderings_Olinorder(X24275)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24275),X24274))
      | ~ hBOOL(hAPP(hAPP(c_member(X24275),X24273),X24274))
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X24275),X24273),c_Big__Operators_Olinorder__class_OMax(X24275,X24274)) = c_Big__Operators_Olinorder__class_OMax(X24275,X24274) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Oin__idem])]) ).

fof(i_0_9661,plain,
    ! [X24364,X24365,X24366] :
      ( ~ class_Orderings_Olinorder(X24366)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24366),X24365))
      | ~ hBOOL(hAPP(hAPP(c_member(X24366),X24364),X24365))
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X24366),X24364),c_Big__Operators_Olinorder__class_OMin(X24366,X24365)) = c_Big__Operators_Olinorder__class_OMin(X24366,X24365) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Oin__idem])]) ).

fof(i_0_9662,plain,
    ! [X30899,X30900,X30901] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X30901)
      | ~ hBOOL(hAPP(hAPP(c_member(X30901),X30900),X30899))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X30901),X30900),c_Complete__Lattice_OSup__class_OSup(X30901,X30899))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__upper])]) ).

cnf(i_0_9663,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_5930]) ).

fof(i_0_9664,plain,
    ! [X32728,X32729,X32730,X32731] :
      ( ( ~ c_List_Olist__ex(X32731,X32730,hAPP(hAPP(c_List_Olist_OCons(X32731),X32729),X32728))
        | hBOOL(hAPP(X32730,X32729))
        | c_List_Olist__ex(X32731,X32730,X32728) )
      & ( ~ hBOOL(hAPP(X32730,X32729))
        | c_List_Olist__ex(X32731,X32730,hAPP(hAPP(c_List_Olist_OCons(X32731),X32729),X32728)) )
      & ( ~ c_List_Olist__ex(X32731,X32730,X32728)
        | c_List_Olist__ex(X32731,X32730,hAPP(hAPP(c_List_Olist_OCons(X32731),X32729),X32728)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__ex__simps_I1_J])])]) ).

fof(i_0_9665,plain,
    ! [X26136,X26137,X26138] :
      ( ~ class_Orderings_Oorder(X26138)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26138,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X26138),X26137)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X26138,X26137),X26136)) = c_Orderings_Obot__class_Obot(tc_fun(X26138,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I2_J])]) ).

fof(i_0_9666,plain,
    ! [X24555,X24556] :
      ( ( X24555 != c_Orderings_Obot__class_Obot(tc_fun(X24556,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(X24556),X24555))) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X24556),X24555))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X24556),X24555))) )
      & ( X24555 = c_Orderings_Obot__class_Obot(tc_fun(X24556,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24556),X24555))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X24556),X24555))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__gt__0__iff])])]) ).

fof(i_0_9667,plain,
    ! [X28713,X28714,X28715,X28716] : hAPP(hAPP(c_List_Onth(X28716),hAPP(hAPP(c_List_Olist_OCons(X28716),X28715),X28714)),hAPP(c_Nat_OSuc,X28713)) = hAPP(hAPP(c_List_Onth(X28716),X28714),X28713),
    inference(variable_rename,[status(thm)],[fact_nth__Cons__Suc]) ).

fof(i_0_9668,plain,
    ! [X29770,X29771,X29772,X29773] : hAPP(hAPP(c_List_Omap(X29773,X29772),X29771),hAPP(c_List_Otl(X29773),X29770)) = hAPP(c_List_Otl(X29772),hAPP(hAPP(c_List_Omap(X29773,X29772),X29771),X29770)),
    inference(variable_rename,[status(thm)],[fact_map__tl]) ).

fof(i_0_9669,plain,
    ! [X31640,X31641,X31642,X31643] : hAPP(c_List_Orev(X31643),hAPP(hAPP(c_List_Omap(X31642,X31643),X31641),X31640)) = hAPP(hAPP(c_List_Omap(X31642,X31643),X31641),hAPP(c_List_Orev(X31642),X31640)),
    inference(variable_rename,[status(thm)],[fact_rev__map]) ).

fof(i_0_9670,plain,
    ! [X20769,X20770] : ~ hBOOL(hAPP(hAPP(c_member(X20770),X20769),c_Orderings_Obot__class_Obot(tc_fun(X20770,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[i_0_5931]) ).

fof(i_0_9671,plain,
    ! [X20716,X20717] : ~ hBOOL(hAPP(hAPP(c_member(X20717),X20716),c_Orderings_Obot__class_Obot(tc_fun(X20717,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[i_0_5932]) ).

fof(i_0_9672,plain,
    ! [X18889,X18890,X18892,X18893] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk44_1(X18889)))
        | ~ hBOOL(hAPP(X18889,X18890)) )
      & ( hBOOL(hAPP(X18889,hAPP(c_Int_Onat,esk44_1(X18889))))
        | ~ hBOOL(hAPP(X18889,X18890)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18893))
        | ~ hBOOL(hAPP(X18892,hAPP(c_Int_Onat,X18893)))
        | hBOOL(hAPP(X18892,esk45_1(X18892))) ) ),
    inference(distribute,[status(thm)],[inference(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_9673,plain,
    ! [X24531,X24532] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X24532),X24531)))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X24532),X24531)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__ge__0__finite])]) ).

cnf(i_0_9674,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_5868]) ).

fof(i_0_9675,plain,
    ! [X33169,X33170,X33171,X33172] :
      ( ( c_List_Olist__all(X33172,X33171,X33170)
        | ~ c_List_Olist__all(X33172,X33171,hAPP(hAPP(c_List_Oappend(X33172),X33170),X33169)) )
      & ( c_List_Olist__all(X33172,X33171,X33169)
        | ~ c_List_Olist__all(X33172,X33171,hAPP(hAPP(c_List_Oappend(X33172),X33170),X33169)) )
      & ( ~ c_List_Olist__all(X33172,X33171,X33170)
        | ~ c_List_Olist__all(X33172,X33171,X33169)
        | c_List_Olist__all(X33172,X33171,hAPP(hAPP(c_List_Oappend(X33172),X33170),X33169)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all__append])])]) ).

fof(i_0_9676,plain,
    ! [X20087] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20087))
      | hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20087),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = X20087 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__pred])]) ).

fof(i_0_9677,plain,
    ! [X17001,X17002,X17003] :
      ( hAPP(hAPP(c_Set_Oinsert(X17003),X17002),c_Orderings_Obot__class_Obot(tc_fun(X17003,tc_HOL_Obool))) != hAPP(hAPP(c_Set_Oinsert(X17003),X17001),c_Orderings_Obot__class_Obot(tc_fun(X17003,tc_HOL_Obool)))
      | X17002 = X17001 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_singleton__inject])]) ).

fof(i_0_9678,plain,
    ! [X30395] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X30395),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,X30395)) = X30395 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__inverse])]) ).

fof(i_0_9679,plain,
    ! [X21507,X21508,X21509,X21510] :
      ( ( X21508 = c_Groups_Ozero__class_Ozero(X21510)
        | X21509 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21510),hAPP(c_Int_Onumber__class_Onumber__of(X21510),X21507)),X21508)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21510),X21509),X21508) != hAPP(c_Int_Onumber__class_Onumber__of(X21510),X21507)
        | ~ class_Fields_Ofield__inverse__zero(X21510)
        | ~ class_Int_Onumber(X21510) )
      & ( X21508 != c_Groups_Ozero__class_Ozero(X21510)
        | hAPP(c_Int_Onumber__class_Onumber__of(X21510),X21507) = c_Groups_Ozero__class_Ozero(X21510)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21510),X21509),X21508) != hAPP(c_Int_Onumber__class_Onumber__of(X21510),X21507)
        | ~ class_Fields_Ofield__inverse__zero(X21510)
        | ~ class_Int_Onumber(X21510) )
      & ( X21508 = c_Groups_Ozero__class_Ozero(X21510)
        | X21508 != c_Groups_Ozero__class_Ozero(X21510)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21510),X21509),X21508) = hAPP(c_Int_Onumber__class_Onumber__of(X21510),X21507)
        | ~ class_Fields_Ofield__inverse__zero(X21510)
        | ~ class_Int_Onumber(X21510) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(X21510),X21507) != c_Groups_Ozero__class_Ozero(X21510)
        | X21508 != c_Groups_Ozero__class_Ozero(X21510)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21510),X21509),X21508) = hAPP(c_Int_Onumber__class_Onumber__of(X21510),X21507)
        | ~ class_Fields_Ofield__inverse__zero(X21510)
        | ~ class_Int_Onumber(X21510) )
      & ( X21508 = c_Groups_Ozero__class_Ozero(X21510)
        | X21509 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21510),hAPP(c_Int_Onumber__class_Onumber__of(X21510),X21507)),X21508)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21510),X21509),X21508) = hAPP(c_Int_Onumber__class_Onumber__of(X21510),X21507)
        | ~ class_Fields_Ofield__inverse__zero(X21510)
        | ~ class_Int_Onumber(X21510) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(X21510),X21507) != c_Groups_Ozero__class_Ozero(X21510)
        | X21509 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21510),hAPP(c_Int_Onumber__class_Onumber__of(X21510),X21507)),X21508)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21510),X21509),X21508) = hAPP(c_Int_Onumber__class_Onumber__of(X21510),X21507)
        | ~ class_Fields_Ofield__inverse__zero(X21510)
        | ~ class_Int_Onumber(X21510) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__eq__eq__number__of])])]) ).

fof(i_0_9680,plain,
    ! [X21511,X21512,X21513,X21514] :
      ( ( X21511 = c_Groups_Ozero__class_Ozero(X21514)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21514),hAPP(c_Int_Onumber__class_Onumber__of(X21514),X21513)),X21511) = X21512
        | hAPP(c_Int_Onumber__class_Onumber__of(X21514),X21513) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21514),X21512),X21511)
        | ~ class_Fields_Ofield__inverse__zero(X21514)
        | ~ class_Int_Onumber(X21514) )
      & ( X21511 != c_Groups_Ozero__class_Ozero(X21514)
        | hAPP(c_Int_Onumber__class_Onumber__of(X21514),X21513) = c_Groups_Ozero__class_Ozero(X21514)
        | hAPP(c_Int_Onumber__class_Onumber__of(X21514),X21513) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21514),X21512),X21511)
        | ~ class_Fields_Ofield__inverse__zero(X21514)
        | ~ class_Int_Onumber(X21514) )
      & ( X21511 = c_Groups_Ozero__class_Ozero(X21514)
        | X21511 != c_Groups_Ozero__class_Ozero(X21514)
        | hAPP(c_Int_Onumber__class_Onumber__of(X21514),X21513) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21514),X21512),X21511)
        | ~ class_Fields_Ofield__inverse__zero(X21514)
        | ~ class_Int_Onumber(X21514) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(X21514),X21513) != c_Groups_Ozero__class_Ozero(X21514)
        | X21511 != c_Groups_Ozero__class_Ozero(X21514)
        | hAPP(c_Int_Onumber__class_Onumber__of(X21514),X21513) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21514),X21512),X21511)
        | ~ class_Fields_Ofield__inverse__zero(X21514)
        | ~ class_Int_Onumber(X21514) )
      & ( X21511 = c_Groups_Ozero__class_Ozero(X21514)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21514),hAPP(c_Int_Onumber__class_Onumber__of(X21514),X21513)),X21511) != X21512
        | hAPP(c_Int_Onumber__class_Onumber__of(X21514),X21513) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21514),X21512),X21511)
        | ~ class_Fields_Ofield__inverse__zero(X21514)
        | ~ class_Int_Onumber(X21514) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(X21514),X21513) != c_Groups_Ozero__class_Ozero(X21514)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21514),hAPP(c_Int_Onumber__class_Onumber__of(X21514),X21513)),X21511) != X21512
        | hAPP(c_Int_Onumber__class_Onumber__of(X21514),X21513) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21514),X21512),X21511)
        | ~ class_Fields_Ofield__inverse__zero(X21514)
        | ~ class_Int_Onumber(X21514) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__divide__eq__number__of])])]) ).

fof(i_0_9681,plain,
    ! [X19110,X19111] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19111),hAPP(c_Nat_OSuc,X19110)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19111),X19110))
      | X19111 = hAPP(c_Nat_OSuc,X19110) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5933])]) ).

fof(i_0_9682,plain,
    ! [X19104,X19105] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19105),hAPP(c_Nat_OSuc,X19104)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19105),X19104))
        | X19105 = hAPP(c_Nat_OSuc,X19104) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19105),X19104))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19105),hAPP(c_Nat_OSuc,X19104))) )
      & ( X19105 != hAPP(c_Nat_OSuc,X19104)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19105),hAPP(c_Nat_OSuc,X19104))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__Suc__eq])])]) ).

fof(i_0_9683,plain,
    ! [X29630,X29631] :
      ( X29631 = c_List_Olist_ONil(X29630)
      | hAPP(hAPP(c_List_Oappend(X29630),c_List_Obutlast(X29630,X29631)),hAPP(hAPP(c_List_Olist_OCons(X29630),c_List_Olast(X29630,X29631)),c_List_Olist_ONil(X29630))) = X29631 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__butlast__last__id])]) ).

cnf(i_0_9684,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_5934]) ).

fof(i_0_9685,plain,
    ! [X22240,X22241,X22242] : hAPP(hAPP(c_Product__Type_OPair(X22242,X22241),hAPP(c_Product__Type_Ofst(X22242,X22241),X22240)),hAPP(c_Product__Type_Osnd(X22242,X22241),X22240)) = X22240,
    inference(variable_rename,[status(thm)],[fact_pair__collapse]) ).

fof(i_0_9686,plain,
    ! [X22237,X22238,X22239] : X22239 = hAPP(hAPP(c_Product__Type_OPair(X22238,X22237),hAPP(c_Product__Type_Ofst(X22238,X22237),X22239)),hAPP(c_Product__Type_Osnd(X22238,X22237),X22239)),
    inference(variable_rename,[status(thm)],[fact_surjective__pairing]) ).

fof(i_0_9687,plain,
    ! [X25931,X25932] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25932),X25931))
        | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X25932),hAPP(c_Nat_OSuc,X25931)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X25931),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X25932),X25931)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25932),X25931))
        | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X25932),hAPP(c_Nat_OSuc,X25931)) = 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_5935])]) ).

fof(i_0_9688,plain,
    ! [X30516,X30517,X30518,X30519] :
      ( ~ class_Orderings_Olinorder(X30519)
      | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30518,X30519,X30517),X30516),c_List_Olist_ONil(X30518)) = hAPP(hAPP(c_List_Olist_OCons(X30518),X30516),c_List_Olist_ONil(X30518)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insort__key_Osimps_I1_J])]) ).

fof(i_0_9689,plain,
    ! [X31737,X31738,X31739] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X31739),X31738))
      | hBOOL(hAPP(c_List_Odistinct(X31739),c_List_OtakeWhile(X31739,X31737,X31738))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__takeWhile])]) ).

fof(i_0_9690,plain,
    ! [X31126,X31127,X31128] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X31128),X31127))
      | hBOOL(hAPP(c_List_Odistinct(X31128),c_List_Oinsert(X31128,X31126,X31127))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__insert])]) ).

fof(i_0_9691,plain,
    ! [X30439,X30440,X30441] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X30441),X30440))
      | hBOOL(hAPP(c_List_Odistinct(X30441),c_List_Oremove1(X30441,X30439,X30440))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__remove1])]) ).

fof(i_0_9692,plain,
    ! [X29337,X29338,X29339] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X29339),X29338))
      | hBOOL(hAPP(c_List_Odistinct(X29339),c_List_Osublist(X29339,X29338,X29337))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__sublistI])]) ).

fof(i_0_9693,plain,
    ! [X33516,X33517,X33518,X33519] : c_Lazy__Sequence_Oappend(X33519,c_Lazy__Sequence_Olazy__sequence_OInsert(X33519,X33518,X33517),X33516) = c_Lazy__Sequence_Olazy__sequence_OInsert(X33519,X33518,c_Lazy__Sequence_Oappend(X33519,X33517,X33516)),
    inference(variable_rename,[status(thm)],[fact__01]) ).

fof(i_0_9694,plain,
    ! [X30435,X30436,X30437,X30438] : c_List_Oremove1(X30438,X30437,c_List_Oremove1(X30438,X30436,X30435)) = c_List_Oremove1(X30438,X30436,c_List_Oremove1(X30438,X30437,X30435)),
    inference(variable_rename,[status(thm)],[fact_remove1__commute]) ).

fof(i_0_9695,plain,
    ! [X32967,X32968,X32969,X32970,X32971,X32972] :
      ( ~ c_Finite__Set_Ofun__left__comm(X32972,X32971,X32970)
      | hAPP(hAPP(X32970,X32969),hAPP(hAPP(X32970,X32968),X32967)) = hAPP(hAPP(X32970,X32968),hAPP(hAPP(X32970,X32969),X32967)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofun__left__comm])]) ).

fof(i_0_9696,plain,
    ! [X24270,X24271,X24272] :
      ( ~ class_Lattices_Olattice(X24272)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24272),X24271))
      | ~ hBOOL(hAPP(hAPP(c_member(X24272),X24270),X24271))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24272),X24270),c_Big__Operators_Olattice__class_OSup__fin(X24272,X24271)) = X24270 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__Sup__absorb])]) ).

fof(i_0_9697,plain,
    ! [X24264,X24265,X24266] :
      ( ~ class_Lattices_Olattice(X24266)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24266),X24265))
      | ~ hBOOL(hAPP(hAPP(c_member(X24266),X24264),X24265))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24266),X24264),c_Big__Operators_Olattice__class_OInf__fin(X24266,X24265)) = X24264 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__Inf__absorb])]) ).

fof(i_0_9698,plain,
    ! [X31976] : c_Wellfounded_OwfP(X31976,hAPP(c_COMBK(tc_fun(X31976,tc_HOL_Obool),X31976),hAPP(c_COMBK(tc_HOL_Obool,X31976),c_fFalse))),
    inference(variable_rename,[status(thm)],[fact_wfP__empty]) ).

fof(i_0_9699,plain,
    ! [X34088,X34089] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk563_2(X34088,X34089)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
        | hBOOL(hAPP(X34089,X34088)) )
      & ( ~ hBOOL(hAPP(X34089,hAPP(c_Code__Numeral_Oof__nat,esk563_2(X34088,X34089))))
        | hBOOL(hAPP(X34089,X34088)) ) ),
    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_9700,plain,
    ! [X31191,X31192,X31193,X31194] :
      ( ( ~ hBOOL(hAPP(X31194,X31193))
        | hAPP(c_List_Ofilter(X31192,X31194),hAPP(hAPP(c_List_Olist_OCons(X31192),X31193),X31191)) = hAPP(hAPP(c_List_Olist_OCons(X31192),X31193),hAPP(c_List_Ofilter(X31192,X31194),X31191)) )
      & ( hBOOL(hAPP(X31194,X31193))
        | hAPP(c_List_Ofilter(X31192,X31194),hAPP(hAPP(c_List_Olist_OCons(X31192),X31193),X31191)) = hAPP(c_List_Ofilter(X31192,X31194),X31191) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5936])]) ).

fof(i_0_9701,plain,
    ! [X22844,X22845,X22846] :
      ( ~ class_Lattices_Olattice(X22846)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22846),X22845),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X22846),X22845),X22844))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__ord_I3_J])]) ).

fof(i_0_9702,plain,
    ! [X22847,X22848,X22849] :
      ( ~ class_Lattices_Osemilattice__sup(X22849)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22849),X22848),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X22849),X22848),X22847))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__ge1])]) ).

fof(i_0_9703,plain,
    ! [X22850,X22851,X22852] :
      ( ~ class_Lattices_Olattice(X22852)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22852),X22851),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X22852),X22850),X22851))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__ord_I4_J])]) ).

fof(i_0_9704,plain,
    ! [X22853,X22854,X22855] :
      ( ~ class_Lattices_Osemilattice__sup(X22855)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22855),X22854),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X22855),X22853),X22854))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__ge2])]) ).

fof(i_0_9705,plain,
    ! [X22562,X22563,X22564] :
      ( ~ class_Orderings_Olinorder(X22564)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22564),X22563),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22564),X22563),X22562))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__maxI1])]) ).

fof(i_0_9706,plain,
    ! [X22565,X22566,X22567] :
      ( ~ class_Orderings_Olinorder(X22567)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22567),X22566),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22567),X22565),X22566))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__maxI2])]) ).

fof(i_0_9707,plain,
    ! [X27712,X27713,X27714] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X27714),X27713),hAPP(c_Set_OCollect(X27714),X27712)))
      | hBOOL(hAPP(X27712,X27713)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_CollectE])]) ).

fof(i_0_9708,plain,
    ! [X27709,X27710,X27711] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X27711),X27710),hAPP(c_Set_OCollect(X27711),X27709)))
      | hBOOL(hAPP(X27709,X27710)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_CollectD])]) ).

fof(i_0_9709,plain,
    ! [X27706,X27707,X27708] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X27708),X27707),hAPP(c_Set_OCollect(X27708),X27706)))
        | hBOOL(hAPP(X27706,X27707)) )
      & ( ~ hBOOL(hAPP(X27706,X27707))
        | hBOOL(hAPP(hAPP(c_member(X27708),X27707),hAPP(c_Set_OCollect(X27708),X27706))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__Collect__eq])]) ).

fof(i_0_9710,plain,
    ! [X18724] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18724))
      | hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,X18724)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X18724)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__nat__eq__nat__zadd1])]) ).

cnf(i_0_9711,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_9712,plain,
    ! [X30442,X30443,X30444,X30445] :
      ( ( X30445 != X30444
        | c_List_Oremove1(X30443,X30445,hAPP(hAPP(c_List_Olist_OCons(X30443),X30444),X30442)) = X30442 )
      & ( X30445 = X30444
        | c_List_Oremove1(X30443,X30445,hAPP(hAPP(c_List_Olist_OCons(X30443),X30444),X30442)) = hAPP(hAPP(c_List_Olist_OCons(X30443),X30444),c_List_Oremove1(X30443,X30445,X30442)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_remove1_Osimps_I2_J])]) ).

fof(i_0_9713,plain,
    ! [X17534,X17535] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17535),hAPP(c_Nat_OSuc,X17534)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17535),X17534))
      | X17535 = X17534 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5937])]) ).

fof(i_0_9714,plain,
    ! [X17525,X17526] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17526),X17525))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17526),hAPP(c_Nat_OSuc,X17525)))
      | X17525 = X17526 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5938])]) ).

fof(i_0_9715,plain,
    ! [X17523,X17524] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17524),hAPP(c_Nat_OSuc,X17523)))
        | X17524 = X17523
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17524),X17523)) )
      & ( X17524 != X17523
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17524),hAPP(c_Nat_OSuc,X17523)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17524),X17523)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5939])])]) ).

fof(i_0_9716,plain,
    ! [X17519,X17520] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17520),hAPP(c_Nat_OSuc,X17519)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17520),X17519))
        | X17520 = X17519 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17520),X17519))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17520),hAPP(c_Nat_OSuc,X17519))) )
      & ( X17520 != X17519
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17520),hAPP(c_Nat_OSuc,X17519))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__eq])])]) ).

cnf(i_0_9717,plain,
    hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X2),c_Divides_Odivmod__nat(X1,X2))),
    inference(split_conjunct,[status(thm)],[i_0_5940]) ).

cnf(i_0_9718,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_5941]) ).

cnf(i_0_9719,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_5942]) ).

fof(i_0_9720,plain,
    ! [X25331,X25332,X25333] : hAPP(c_Relation_OImage(X25333,X25333,c_Relation_OId__on(X25333,X25332)),X25331) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25333,tc_HOL_Obool)),X25332),X25331),
    inference(variable_rename,[status(thm)],[fact_Image__Id__on]) ).

fof(i_0_9721,plain,
    ! [X23884,X23885,X23886,X23887] :
      ( ~ class_Lattices_Osemilattice__inf(X23887)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23887),X23886),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23887),X23885),X23884)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23887),X23885),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23887),X23886),X23884)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf_Oleft__commute])]) ).

fof(i_0_9722,plain,
    ! [X23876,X23877,X23878,X23879] :
      ( ~ class_Lattices_Osemilattice__inf(X23879)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23879),X23878),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23879),X23877),X23876)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23879),X23877),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23879),X23878),X23876)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__left__commute])]) ).

fof(i_0_9723,plain,
    ! [X23880,X23881,X23882,X23883] :
      ( ~ class_Lattices_Olattice(X23883)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23883),X23882),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23883),X23881),X23880)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23883),X23881),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23883),X23882),X23880)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I3_J])]) ).

fof(i_0_9724,plain,
    ! [X23004,X23005,X23006,X23007] :
      ( ~ class_Lattices_Olattice(X23007)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23007),X23006),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23007),X23005),X23004)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23007),X23005),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23007),X23006),X23004)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I7_J])]) ).

fof(i_0_9725,plain,
    ! [X23008,X23009,X23010,X23011] :
      ( ~ class_Lattices_Osemilattice__sup(X23011)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23011),X23010),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23011),X23009),X23008)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23011),X23009),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23011),X23010),X23008)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__left__commute])]) ).

fof(i_0_9726,plain,
    ! [X23000,X23001,X23002,X23003] :
      ( ~ class_Lattices_Osemilattice__sup(X23003)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23003),X23002),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23003),X23001),X23000)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23003),X23001),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23003),X23002),X23000)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup_Oleft__commute])]) ).

fof(i_0_9727,plain,
    ! [X22652,X22653,X22654,X22655] :
      ( ~ class_Orderings_Olinorder(X22655)
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X22655),X22654),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22655),X22653),X22652)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X22655),X22653),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22655),X22654),X22652)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__left__commute])]) ).

fof(i_0_9728,plain,
    ! [X22648,X22649,X22650,X22651] :
      ( ~ class_Orderings_Olinorder(X22651)
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X22651),X22650),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22651),X22649),X22648)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X22651),X22649),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22651),X22650),X22648)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup_Oleft__commute])]) ).

fof(i_0_9729,plain,
    ! [X22405,X22406,X22407,X22408] :
      ( ~ class_Orderings_Olinorder(X22408)
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X22408),X22407),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22408),X22406),X22405)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X22408),X22406),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22408),X22407),X22405)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf_Oleft__commute])]) ).

fof(i_0_9730,plain,
    ! [X22401,X22402,X22403,X22404] :
      ( ~ class_Orderings_Olinorder(X22404)
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X22404),X22403),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22404),X22402),X22401)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X22404),X22402),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22404),X22403),X22401)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__left__commute])]) ).

fof(i_0_9731,plain,
    ! [X18170,X18171,X18172,X18173] :
      ( ~ class_Rings_Ocomm__semiring__1(X18173)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18173),X18172),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18173),X18171),X18170)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18173),X18171),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18173),X18172),X18170)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J])]) ).

fof(i_0_9732,plain,
    ! [X17823,X17824,X17825,X17826] :
      ( ~ class_Rings_Ocomm__semiring__1(X17826)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17826),X17825),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17826),X17824),X17823)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17826),X17824),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17826),X17825),X17823)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J])]) ).

fof(i_0_9733,plain,
    ! [X18241,X18242,X18243] :
      ( ~ class_Groups_Ogroup__add(X18243)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18243),X18242),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18243),hAPP(c_Groups_Ouminus__class_Ouminus(X18243),X18242)),X18241)) = X18241 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__minus__cancel])]) ).

fof(i_0_9734,plain,
    ! [X19068,X19069,X19070] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19070),X19069) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19070),X19068)
        | X19069 = X19068
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19070)) )
      & ( X19069 != X19068
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19070),X19069) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19070),X19068)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19070)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__cancel1])])]) ).

fof(i_0_9735,plain,
    ! [X19238,X19239] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19239),hAPP(c_Nat_OSuc,X19238)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19239),X19238)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19239),X19238))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19239),hAPP(c_Nat_OSuc,X19238))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__eq__le])]) ).

fof(i_0_9736,plain,
    ! [X20541] : 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),X20541)) = 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),X20541))),
    inference(variable_rename,[status(thm)],[fact_one__div__nat__number__of]) ).

fof(i_0_9737,plain,
    ! [X18110,X18111,X18112,X18113,X18114] :
      ( ( X18110 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18112)
        | hBOOL(hAPP(X18111,X18112))
        | ~ hBOOL(hAPP(X18111,hAPP(c_Int_Onat,X18110))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18110),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(X18111,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(X18111,hAPP(c_Int_Onat,X18110))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18113),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | X18113 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk37_2(X18113,X18114))
        | hBOOL(hAPP(X18114,hAPP(c_Int_Onat,X18113))) )
      & ( ~ hBOOL(hAPP(X18114,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | X18113 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk37_2(X18113,X18114))
        | hBOOL(hAPP(X18114,hAPP(c_Int_Onat,X18113))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18113),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(X18114,esk37_2(X18113,X18114)))
        | hBOOL(hAPP(X18114,hAPP(c_Int_Onat,X18113))) )
      & ( ~ hBOOL(hAPP(X18114,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(X18114,esk37_2(X18113,X18114)))
        | hBOOL(hAPP(X18114,hAPP(c_Int_Onat,X18113))) ) ),
    inference(distribute,[status(thm)],[inference(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_9738,plain,
    ! [X29318,X29319,X29320] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X29320),X29319))
      | hBOOL(hAPP(c_List_Odistinct(X29320),hAPP(hAPP(c_List_Odrop(X29320),X29318),X29319))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__drop])]) ).

fof(i_0_9739,plain,
    ! [X29332,X29333,X29334] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X29334),X29333))
      | hBOOL(hAPP(c_List_Odistinct(X29334),hAPP(hAPP(c_List_Otake(X29334),X29332),X29333))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__take])]) ).

fof(i_0_9740,plain,
    ! [X23532,X23533,X23534] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23534),X23533))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X23534),hAPP(hAPP(c_Set_Oinsert(X23534),X23532),X23533))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite_OinsertI])]) ).

fof(i_0_9741,plain,
    ! [X25454,X25455] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X25455,X25454)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X25455),hAPP(c_Nat_OSuc,X25454)),
    inference(variable_rename,[status(thm)],[fact_image__Suc__atLeastAtMost]) ).

fof(i_0_9742,plain,
    ! [X29876,X29877,X29878] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29878,tc_fun(X29877,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X29878,tc_HOL_Obool))),X29876) = c_Orderings_Otop__class_Otop(tc_fun(X29877,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_INT__empty]) ).

fof(i_0_9743,plain,
    ! [X20512,X20513] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20513)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20512)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20513),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X20512))),
    inference(variable_rename,[status(thm)],[fact_minus__numeral__code_I6_J]) ).

fof(i_0_9744,plain,
    ! [X26749,X26750] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X26750,tc_HOL_Obool)),X26749) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26750,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X26750,tc_HOL_Obool))),X26749),
    inference(variable_rename,[status(thm)],[fact_Compl__eq__Diff__UNIV]) ).

fof(i_0_9745,plain,
    ! [X29730,X29731,X29732,X29733] : hAPP(hAPP(c_List_Omap(X29733,X29732),X29731),c_List_Obutlast(X29733,X29730)) = c_List_Obutlast(X29732,hAPP(hAPP(c_List_Omap(X29733,X29732),X29731),X29730)),
    inference(variable_rename,[status(thm)],[fact_map__butlast]) ).

fof(i_0_9746,plain,
    ! [X24362,X24363] :
      ( ~ class_Orderings_Olinorder(X24363)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24363),X24362))
      | X24362 = c_Orderings_Obot__class_Obot(tc_fun(X24363,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(X24363),c_Big__Operators_Olinorder__class_OMin(X24363,X24362)),X24362)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min__in])]) ).

fof(i_0_9747,plain,
    ! [X24259,X24260] :
      ( ~ class_Orderings_Olinorder(X24260)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24260),X24259))
      | X24259 = c_Orderings_Obot__class_Obot(tc_fun(X24260,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(X24260),c_Big__Operators_Olinorder__class_OMax(X24260,X24259)),X24259)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max__in])]) ).

fof(i_0_9748,plain,
    ! [X34086] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X34086),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
      | X34086 = hAPP(c_Code__Numeral_Onat__of,esk562_1(X34086)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__of__cases])])]) ).

fof(i_0_9749,plain,
    ! [X18895,X18897,X18898,X18900] :
      ( ( ~ hBOOL(hAPP(X18895,esk46_1(X18895)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18897))
        | hBOOL(hAPP(X18895,hAPP(c_Int_Onat,X18897))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk47_1(X18898)))
        | hBOOL(hAPP(X18898,X18900)) )
      & ( ~ hBOOL(hAPP(X18898,hAPP(c_Int_Onat,esk47_1(X18898))))
        | hBOOL(hAPP(X18898,X18900)) ) ),
    inference(distribute,[status(thm)],[inference(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_9750,plain,
    ! [X20774,X20775,X20776] : hBOOL(hAPP(hAPP(c_member(X20776),X20775),hAPP(hAPP(c_Set_Oinsert(X20776),X20775),X20774))),
    inference(variable_rename,[status(thm)],[fact_insertI1]) ).

fof(i_0_9751,plain,
    ! [X19606,X19607] :
      ( ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19607,X19606)) != X19606
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X19607),X19606) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19607,X19606)) = X19606
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X19607),X19606) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19607,X19606)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__Suc])]) ).

fof(i_0_9752,plain,
    ! [X34028] : c_Hilbert__Choice_Oinv__into(X34028,X34028,c_Orderings_Otop__class_Otop(tc_fun(X34028,tc_HOL_Obool)),c_Fun_Oid(X34028)) = c_Fun_Oid(X34028),
    inference(variable_rename,[status(thm)],[fact_inv__id]) ).

cnf(i_0_9753,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_5943]) ).

cnf(i_0_9754,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]) ).

fof(i_0_9755,plain,
    ! [X17040,X17041,X17042,X17043] : hAPP(hAPP(c_Set_Oinsert(X17043),X17042),hAPP(hAPP(c_Set_Oinsert(X17043),X17041),X17040)) = hAPP(hAPP(c_Set_Oinsert(X17043),X17041),hAPP(hAPP(c_Set_Oinsert(X17043),X17042),X17040)),
    inference(variable_rename,[status(thm)],[fact_insert__commute]) ).

fof(i_0_9756,plain,
    ! [X23651,X23652,X23653,X23654] :
      ( ~ c_Finite__Set_Ofolding__one(X23654,X23653,X23652)
      | hAPP(X23652,hAPP(hAPP(c_Set_Oinsert(X23654),X23651),c_Orderings_Obot__class_Obot(tc_fun(X23654,tc_HOL_Obool)))) = X23651 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one_Osingleton])]) ).

fof(i_0_9757,plain,
    ! [X20051,X20052] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20052),hAPP(c_Nat_OSuc,X20051)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20052),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X20051),
    inference(variable_rename,[status(thm)],[fact_diff__Suc__eq__diff__pred]) ).

fof(i_0_9758,plain,
    ! [X17851,X17852] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk27_2(X17851,X17852)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17852),X17851)) )
      & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17852),esk27_2(X17851,X17852)) = X17851
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17852),X17851)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__add__positive])])])]) ).

fof(i_0_9759,plain,
    ! [X32815,X32816,X32817,X32818] : hAPP(hAPP(c_Finite__Set_Ofold(X32818,X32817,X32816),X32815),c_Orderings_Obot__class_Obot(tc_fun(X32818,tc_HOL_Obool))) = X32815,
    inference(variable_rename,[status(thm)],[fact_fold__empty]) ).

fof(i_0_9760,plain,
    ! [X28835,X28836,X28837] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28837)),hAPP(hAPP(c_List_Odrop(X28837),X28836),X28835)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28837)),X28835)),X28836),
    inference(variable_rename,[status(thm)],[fact_length__drop]) ).

fof(i_0_9761,plain,
    ! [X28780,X28781,X28782] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28782)),hAPP(hAPP(c_List_Otake(X28782),X28781),X28780)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28782)),X28780)),X28781),
    inference(variable_rename,[status(thm)],[fact_length__take]) ).

cnf(i_0_9762,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_5945]) ).

fof(i_0_9763,plain,
    ! [X26773] :
      ( ~ class_Nat_Osemiring__char__0(X26773)
      | c_Fun_Oinj__on(tc_Nat_Onat,X26773,c_Nat_Osemiring__1__class_Oof__nat(X26773),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_9764,plain,
    ! [X17872,X17873,X17874,X17875] :
      ( hBOOL(hAPP(X17875,X17874))
      | c_Natural_Oevaln(c_Com_Ocom_OWhile(X17875,X17873),X17874,X17872,X17874) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5946])]) ).

fof(i_0_9765,plain,
    ! [X29351,X29352,X29353] : hAPP(hAPP(c_List_Otake(X29353),X29352),hAPP(c_List_Otl(X29353),X29351)) = hAPP(c_List_Otl(X29353),hAPP(hAPP(c_List_Otake(X29353),hAPP(c_Nat_OSuc,X29352)),X29351)),
    inference(variable_rename,[status(thm)],[fact_take__tl]) ).

fof(i_0_9766,plain,
    ! [X17848,X17849] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17849),X17848))
      | X17848 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17849),esk26_2(X17848,X17849))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__Suc__add])])]) ).

fof(i_0_9767,plain,
    ! [X17479,X17480,X17482,X17483,X17484] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17480),X17479))
        | X17479 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17480),esk23_2(X17479,X17480))) )
      & ( X17482 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17483),X17484))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17483),X17482)) ) ),
    inference(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_9768,plain,
    ! [X33454,X33455,X33456,X33457] : hAPP(hAPP(c_List_Odrop(X33457),X33456),c_List_Oreplicate(X33457,X33455,X33454)) = c_List_Oreplicate(X33457,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X33455),X33456),X33454),
    inference(variable_rename,[status(thm)],[fact_drop__replicate]) ).

fof(i_0_9769,plain,
    ! [X33464,X33465,X33466,X33467] : hAPP(hAPP(c_List_Otake(X33467),X33466),c_List_Oreplicate(X33467,X33465,X33464)) = c_List_Oreplicate(X33467,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X33466),X33465),X33464),
    inference(variable_rename,[status(thm)],[fact_take__replicate]) ).

cnf(i_0_9770,plain,
    ( c_Transitive__Closure_Otrancl(X1,X2) = X2
    | ~ c_Relation_Otrans(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5947]) ).

fof(i_0_9771,plain,
    ! [X25465,X25466,X25467] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(X25467,tc_HOL_Obool)) != c_SetInterval_Oord__class_OatLeastAtMost(X25467,X25466,X25465)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25467),X25466),X25465))
        | ~ class_Orderings_Oorder(X25467) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25467),X25466),X25465))
        | c_Orderings_Obot__class_Obot(tc_fun(X25467,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(X25467,X25466,X25465)
        | ~ class_Orderings_Oorder(X25467) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5948])])]) ).

fof(i_0_9772,plain,
    ! [X25317,X25318,X25319] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(X25319,tc_HOL_Obool)) != c_SetInterval_Oord__class_OgreaterThanAtMost(X25319,X25318,X25317)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25319),X25318),X25317))
        | ~ class_Orderings_Oorder(X25319) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25319),X25318),X25317))
        | c_Orderings_Obot__class_Obot(tc_fun(X25319,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X25319,X25318,X25317)
        | ~ class_Orderings_Oorder(X25319) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5949])])]) ).

fof(i_0_9773,plain,
    ! [X25468,X25469,X25470] :
      ( ( c_SetInterval_Oord__class_OatLeastAtMost(X25470,X25469,X25468) != c_Orderings_Obot__class_Obot(tc_fun(X25470,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25470),X25469),X25468))
        | ~ class_Orderings_Oorder(X25470) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25470),X25469),X25468))
        | c_SetInterval_Oord__class_OatLeastAtMost(X25470,X25469,X25468) = c_Orderings_Obot__class_Obot(tc_fun(X25470,tc_HOL_Obool))
        | ~ class_Orderings_Oorder(X25470) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5950])])]) ).

fof(i_0_9774,plain,
    ! [X25314,X25315,X25316] :
      ( ( c_SetInterval_Oord__class_OgreaterThanAtMost(X25316,X25315,X25314) != c_Orderings_Obot__class_Obot(tc_fun(X25316,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25316),X25315),X25314))
        | ~ class_Orderings_Oorder(X25316) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25316),X25315),X25314))
        | c_SetInterval_Oord__class_OgreaterThanAtMost(X25316,X25315,X25314) = c_Orderings_Obot__class_Obot(tc_fun(X25316,tc_HOL_Obool))
        | ~ class_Orderings_Oorder(X25316) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5951])])]) ).

fof(i_0_9775,plain,
    ! [X25655] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X25655) = 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),X25655))),
    inference(variable_rename,[status(thm)],[fact_SetInterval_Otransfer__nat__int__set__functions_I1_J]) ).

fof(i_0_9776,plain,
    ! [X33165,X33166,X33167,X33168] :
      ( ( hBOOL(hAPP(X33167,X33166))
        | ~ c_List_Olist__all(X33168,X33167,hAPP(hAPP(c_List_Olist_OCons(X33168),X33166),X33165)) )
      & ( c_List_Olist__all(X33168,X33167,X33165)
        | ~ c_List_Olist__all(X33168,X33167,hAPP(hAPP(c_List_Olist_OCons(X33168),X33166),X33165)) )
      & ( ~ hBOOL(hAPP(X33167,X33166))
        | ~ c_List_Olist__all(X33168,X33167,X33165)
        | c_List_Olist__all(X33168,X33167,hAPP(hAPP(c_List_Olist_OCons(X33168),X33166),X33165)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all__simps_I1_J])])]) ).

fof(i_0_9777,plain,
    ! [X21393,X21394,X21395] :
      ( ~ class_Fields_Olinordered__field(X21395)
      | X21394 = c_Groups_Ozero__class_Ozero(X21395)
      | hAPP(c_Groups_Oabs__class_Oabs(X21395),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21395),X21393),X21394)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21395),hAPP(c_Groups_Oabs__class_Oabs(X21395),X21393)),hAPP(c_Groups_Oabs__class_Oabs(X21395),X21394)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__abs__divide])]) ).

fof(i_0_9778,plain,
    ! [X32653,X32654] :
      ( ( hBOOL(hAPP(hAPP(c_member(X32654),esk464_2(X32653,X32654)),X32653))
        | hAPP(c_Finite__Set_Ocard(X32654),X32653) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32654),X32653)) )
      & ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Finite__Set_Ocard(X32654),X32653) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32654),X32653)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card_Oneutral])])])]) ).

fof(i_0_9779,plain,
    ! [X24081,X24082] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24082,tc_HOL_Obool)),X24081),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X24082,tc_HOL_Obool)),X24081)) = c_Orderings_Obot__class_Obot(tc_fun(X24082,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Compl__disjoint]) ).

fof(i_0_9780,plain,
    ! [X26745,X26746] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26746,tc_HOL_Obool)),X26745),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X26746,tc_HOL_Obool)),X26745)) = c_Orderings_Otop__class_Otop(tc_fun(X26746,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Compl__partition]) ).

fof(i_0_9781,plain,
    ! [X25659,X25660,X25661] : c_Fun_Oinj__on(X25661,X25660,X25659,c_Orderings_Obot__class_Obot(tc_fun(X25661,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_inj__on__empty]) ).

fof(i_0_9782,plain,
    ! [X18524,X18525] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X18525),X18524))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X18524),X18525))
      | X18525 = X18524 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__antisym])]) ).

fof(i_0_9783,plain,
    ! [X19082,X19083] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19083),X19082))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19082),X19083))
      | X19083 = X19082 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__antisym])]) ).

cnf(i_0_9784,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_5714]) ).

fof(i_0_9785,plain,
    ! [X20646] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20646))
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),X20646) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20646),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__minus1])]) ).

fof(i_0_9786,plain,
    ! [X24370,X24371,X24372] :
      ( ~ class_Orderings_Olinorder(X24372)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24372),X24371))
      | X24371 = c_Orderings_Obot__class_Obot(tc_fun(X24372,tc_HOL_Obool))
      | c_Big__Operators_Olinorder__class_OMin(X24372,hAPP(hAPP(c_Set_Oinsert(X24372),X24370),X24371)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X24372),X24370),c_Big__Operators_Olinorder__class_OMin(X24372,X24371)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min__insert])]) ).

fof(i_0_9787,plain,
    ! [X24288,X24289,X24290] :
      ( ~ class_Orderings_Olinorder(X24290)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24290),X24289))
      | X24289 = c_Orderings_Obot__class_Obot(tc_fun(X24290,tc_HOL_Obool))
      | c_Big__Operators_Olinorder__class_OMax(X24290,hAPP(hAPP(c_Set_Oinsert(X24290),X24288),X24289)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X24290),X24288),c_Big__Operators_Olinorder__class_OMax(X24290,X24289)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max__insert])]) ).

fof(i_0_9788,plain,
    ! [X24279,X24280,X24281] :
      ( ~ class_Lattices_Olattice(X24281)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24281),X24280))
      | X24280 = c_Orderings_Obot__class_Obot(tc_fun(X24281,tc_HOL_Obool))
      | c_Big__Operators_Olattice__class_OSup__fin(X24281,hAPP(hAPP(c_Set_Oinsert(X24281),X24279),X24280)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24281),X24279),c_Big__Operators_Olattice__class_OSup__fin(X24281,X24280)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oinsert__idem])]) ).

fof(i_0_9789,plain,
    ! [X24282,X24283,X24284] :
      ( ~ class_Lattices_Olattice(X24284)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24284),X24283))
      | X24283 = c_Orderings_Obot__class_Obot(tc_fun(X24284,tc_HOL_Obool))
      | c_Big__Operators_Olattice__class_OInf__fin(X24284,hAPP(hAPP(c_Set_Oinsert(X24284),X24282),X24283)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24284),X24282),c_Big__Operators_Olattice__class_OInf__fin(X24284,X24283)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oinsert__idem])]) ).

fof(i_0_9790,plain,
    ! [X22817,X22818,X22819] :
      ( ( X22818 = c_Orderings_Obot__class_Obot(tc_fun(X22819,tc_HOL_Obool))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22819,tc_HOL_Obool)),X22818),X22817) != c_Orderings_Obot__class_Obot(tc_fun(X22819,tc_HOL_Obool)) )
      & ( X22817 = c_Orderings_Obot__class_Obot(tc_fun(X22819,tc_HOL_Obool))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22819,tc_HOL_Obool)),X22818),X22817) != c_Orderings_Obot__class_Obot(tc_fun(X22819,tc_HOL_Obool)) )
      & ( X22818 != c_Orderings_Obot__class_Obot(tc_fun(X22819,tc_HOL_Obool))
        | X22817 != c_Orderings_Obot__class_Obot(tc_fun(X22819,tc_HOL_Obool))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22819,tc_HOL_Obool)),X22818),X22817) = c_Orderings_Obot__class_Obot(tc_fun(X22819,tc_HOL_Obool)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Un__empty])])]) ).

fof(i_0_9791,plain,
    ! [X29573,X29574,X29575] :
      ( ~ class_Groups_Omonoid__add(X29575)
      | hAPP(c_List_Omonoid__add__class_Olistsum(X29575),hAPP(hAPP(c_List_Oappend(X29575),X29574),X29573)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X29575),hAPP(c_List_Omonoid__add__class_Olistsum(X29575),X29574)),hAPP(c_List_Omonoid__add__class_Olistsum(X29575),X29573)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__append])]) ).

fof(i_0_9792,plain,
    ! [X21285,X21286,X21287] :
      ( ~ class_Fields_Olinordered__field__inverse__zero(X21287)
      | hAPP(c_Groups_Oabs__class_Oabs(X21287),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21287),X21286),X21285)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21287),hAPP(c_Groups_Oabs__class_Oabs(X21287),X21286)),hAPP(c_Groups_Oabs__class_Oabs(X21287),X21285)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__divide])]) ).

fof(i_0_9793,plain,
    ! [X20228,X20229,X20230] :
      ( ~ class_Rings_Olinordered__idom(X20230)
      | hAPP(c_Groups_Oabs__class_Oabs(X20230),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20230),X20229),X20228)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20230),hAPP(c_Groups_Oabs__class_Oabs(X20230),X20229)),hAPP(c_Groups_Oabs__class_Oabs(X20230),X20228)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__mult])]) ).

fof(i_0_9794,plain,
    ! [X24023,X24024,X24025] :
      ( ~ class_Lattices_Oboolean__algebra(X24025)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X24025),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24025),X24024),X24023)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24025),hAPP(c_Groups_Ouminus__class_Ouminus(X24025),X24024)),hAPP(c_Groups_Ouminus__class_Ouminus(X24025),X24023)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__inf])]) ).

fof(i_0_9795,plain,
    ! [X24026,X24027,X24028] :
      ( ~ class_Lattices_Oboolean__algebra(X24028)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X24028),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24028),X24027),X24026)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24028),hAPP(c_Groups_Ouminus__class_Ouminus(X24028),X24027)),hAPP(c_Groups_Ouminus__class_Ouminus(X24028),X24026)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__sup])]) ).

fof(i_0_9796,plain,
    ! [X22704,X22705,X22706] :
      ( ~ class_Groups_Olinordered__ab__group__add(X22706)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X22706),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22706),X22705),X22704)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X22706),hAPP(c_Groups_Ouminus__class_Ouminus(X22706),X22705)),hAPP(c_Groups_Ouminus__class_Ouminus(X22706),X22704)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__max__eq__min])]) ).

fof(i_0_9797,plain,
    ! [X22707,X22708,X22709] :
      ( ~ class_Groups_Olinordered__ab__group__add(X22709)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X22709),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22709),X22708),X22707)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X22709),hAPP(c_Groups_Ouminus__class_Ouminus(X22709),X22708)),hAPP(c_Groups_Ouminus__class_Ouminus(X22709),X22707)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__min__eq__max])]) ).

fof(i_0_9798,plain,
    ! [X18247,X18248,X18249] :
      ( ~ class_Groups_Oab__group__add(X18249)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X18249),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18249),X18248),X18247)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18249),hAPP(c_Groups_Ouminus__class_Ouminus(X18249),X18248)),hAPP(c_Groups_Ouminus__class_Ouminus(X18249),X18247)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__add__distrib])]) ).

fof(i_0_9799,plain,
    ! [X18244,X18245,X18246] :
      ( ~ class_Groups_Ogroup__add(X18246)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X18246),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18246),X18245),X18244)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18246),hAPP(c_Groups_Ouminus__class_Ouminus(X18246),X18244)),hAPP(c_Groups_Ouminus__class_Ouminus(X18246),X18245)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__add])]) ).

cnf(i_0_9800,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_5520]) ).

cnf(i_0_9801,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_5952]) ).

fof(i_0_9802,plain,
    ! [X25451,X25452,X25453] : hAPP(c_Set_Oimage(X25452,tc_fun(X25452,tc_HOL_Obool),X25453),X25451) != hAPP(c_Set_OPow(X25452),X25451),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cantors__paradox])]) ).

fof(i_0_9803,plain,
    ! [X19317,X19318,X19319] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19317,tc_HOL_Obool)),X19319),X19318))
        | X19319 != X19318 )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19317,tc_HOL_Obool)),X19318),X19319))
        | X19319 != X19318 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5953])])]) ).

fof(i_0_9804,plain,
    ! [X19307,X19308,X19309] :
      ( X19309 != X19308
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19307,tc_HOL_Obool)),X19309),X19308)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equalityD1])]) ).

fof(i_0_9805,plain,
    ! [X19310,X19311,X19312] :
      ( X19312 != X19311
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19310,tc_HOL_Obool)),X19311),X19312)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equalityD2])]) ).

fof(i_0_9806,plain,
    ! [X19101] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19101)),X19101)),
    inference(variable_rename,[status(thm)],[i_0_5954]) ).

fof(i_0_9807,plain,
    ! [X19789,X19790] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19790))
        | c_SMT_Oz3div(X19789,X19790) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19789),X19790) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19790))
        | c_SMT_Oz3div(X19789,X19790) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19789),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X19790))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5955])]) ).

fof(i_0_9808,plain,
    ! [X29523,X29524] :
      ( X29524 = c_List_Olist_ONil(X29523)
      | hBOOL(hAPP(hAPP(c_member(X29523),c_List_Olast(X29523,X29524)),hAPP(c_List_Oset(X29523),X29524))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__in__set])]) ).

fof(i_0_9809,plain,
    ! [X18671,X18672,X18673] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X18673)),X18672) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X18673)),X18671)
        | X18672 = X18671 )
      & ( X18672 != X18671
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X18673)),X18672) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X18673)),X18671) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mult__cancel1])]) ).

fof(i_0_9810,plain,
    ! [X21941,X21942,X21943,X21944,X21945,X21946] :
      ( ( X21944 = X21942
        | hAPP(hAPP(c_Product__Type_OPair(X21946,X21945),X21944),X21943) != hAPP(hAPP(c_Product__Type_OPair(X21946,X21945),X21942),X21941) )
      & ( X21943 = X21941
        | hAPP(hAPP(c_Product__Type_OPair(X21946,X21945),X21944),X21943) != hAPP(hAPP(c_Product__Type_OPair(X21946,X21945),X21942),X21941) )
      & ( X21944 != X21942
        | X21943 != X21941
        | hAPP(hAPP(c_Product__Type_OPair(X21946,X21945),X21944),X21943) = hAPP(hAPP(c_Product__Type_OPair(X21946,X21945),X21942),X21941) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pair__eq])])]) ).

fof(i_0_9811,plain,
    ! [X21935,X21936,X21937,X21938,X21939,X21940] :
      ( ( X21938 = X21936
        | hAPP(hAPP(c_Product__Type_OPair(X21940,X21939),X21938),X21937) != hAPP(hAPP(c_Product__Type_OPair(X21940,X21939),X21936),X21935) )
      & ( X21937 = X21935
        | hAPP(hAPP(c_Product__Type_OPair(X21940,X21939),X21938),X21937) != hAPP(hAPP(c_Product__Type_OPair(X21940,X21939),X21936),X21935) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pair__inject])])]) ).

fof(i_0_9812,plain,
    ! [X20146,X20147] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X20147,X20146) != 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),X20147),X20146) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X20147,X20146) = 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),X20147),X20146) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20146),c_Divides_Odiv__class_Omod(tc_Int_Oint,X20147,X20146)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__zminus1__eq__if])]) ).

fof(i_0_9813,plain,
    ! [X19897,X19898] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19898),X19897))
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19898,X19897) = X19898 )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19898),X19897))
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19898,X19897) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19898),X19897),X19897) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5956])]) ).

fof(i_0_9814,plain,
    ! [X19895,X19896] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19896),X19895))
      | c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19896,X19895) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19896),X19895),X19895) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5957])]) ).

fof(i_0_9815,plain,
    ! [X31120,X31121,X31122] :
      ( hBOOL(hAPP(hAPP(c_member(X31122),X31121),hAPP(c_List_Oset(X31122),X31120)))
      | c_List_Oinsert(X31122,X31121,X31120) = hAPP(hAPP(c_List_Olist_OCons(X31122),X31121),X31120) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5958])]) ).

fof(i_0_9816,plain,
    ! [X19302,X19303] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19303,tc_HOL_Obool)),X19302),X19302)),
    inference(variable_rename,[status(thm)],[fact_subset__refl]) ).

fof(i_0_9817,plain,
    ! [X25795,X25796] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X25796),X25795)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X25796)),hAPP(c_Nat_OSuc,X25795)),
    inference(variable_rename,[status(thm)],[fact_image__Suc__atLeastLessThan]) ).

fof(i_0_9818,plain,
    ! [X31657,X31658,X31659] : hAPP(c_List_Orev(X31659),hAPP(hAPP(c_List_Oappend(X31659),X31658),X31657)) = hAPP(hAPP(c_List_Oappend(X31659),hAPP(c_List_Orev(X31659),X31657)),hAPP(c_List_Orev(X31659),X31658)),
    inference(variable_rename,[status(thm)],[fact_rev__append]) ).

fof(i_0_9819,plain,
    ! [X29304,X29305,X29306,X29307] :
      ( hAPP(c_List_Orotate1(X29307),c_List_Olist_ONil(X29307)) = c_List_Olist_ONil(X29307)
      & hAPP(c_List_Orotate1(X29306),hAPP(hAPP(c_List_Olist_OCons(X29306),X29305),X29304)) = hAPP(hAPP(c_List_Oappend(X29306),X29304),hAPP(hAPP(c_List_Olist_OCons(X29306),X29305),c_List_Olist_ONil(X29306))) ),
    inference(variable_rename,[status(thm)],[fact_rotate__simps]) ).

fof(i_0_9820,plain,
    ! [X19108,X19109] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19109),X19108))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19109),hAPP(c_Nat_OSuc,X19108))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__SucI])]) ).

fof(i_0_9821,plain,
    ! [X19234,X19235] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19235),X19234))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19235),hAPP(c_Nat_OSuc,X19234))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__less__Suc])]) ).

fof(i_0_9822,plain,
    ! [X17527,X17528] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17528),X17527))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17528),hAPP(c_Nat_OSuc,X17527))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__SucI])]) ).

fof(i_0_9823,plain,
    ! [X29535,X29536] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X29536,X29535) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X29536),c_Groups_Oone__class_Oone(tc_Int_Oint)),X29535)),
    inference(variable_rename,[status(thm)],[fact_greaterThanAtMost__upto]) ).

fof(i_0_9824,plain,
    ! [X20942,X20943] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20943),X20942),X20942) != c_Groups_Ozero__class_Ozero(X20943)
        | X20942 = c_Groups_Ozero__class_Ozero(X20943)
        | ~ hBOOL(hAPP(hAPP(c_member(X20943),X20942),c_Int_Oring__1__class_OInts(X20943)))
        | ~ class_Int_Oring__char__0(X20943) )
      & ( X20942 != c_Groups_Ozero__class_Ozero(X20943)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20943),X20942),X20942) = c_Groups_Ozero__class_Ozero(X20943)
        | ~ hBOOL(hAPP(hAPP(c_member(X20943),X20942),c_Int_Oring__1__class_OInts(X20943)))
        | ~ class_Int_Oring__char__0(X20943) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__double__eq__0__iff])])]) ).

fof(i_0_9825,plain,
    ! [X20680] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20680))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),X20680) = 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_9826,plain,
    ! [X23921,X23922,X23923] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23923,tc_HOL_Obool)),X23922),X23921) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23923,tc_HOL_Obool)),X23921),X23922),
    inference(variable_rename,[status(thm)],[fact_Int__commute]) ).

fof(i_0_9827,plain,
    ! [X22936,X22937,X22938] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22938,tc_HOL_Obool)),X22937),X22936) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22938,tc_HOL_Obool)),X22936),X22937),
    inference(variable_rename,[status(thm)],[fact_Un__commute]) ).

fof(i_0_9828,plain,
    ! [X17209,X17210,X17211,X17212,X17213] : c_Hoare__Mirabelle_Otriple_Otriple__size(X17213,X17212,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17213),X17211),X17210),X17209)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_triple_Osize_I1_J]) ).

fof(i_0_9829,plain,
    ! [X18100] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk36_1(X18100)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18100)) )
      & ( X18100 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk36_1(X18100))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18100)) ) ),
    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_9830,plain,
    ! [X21355,X21356,X21357,X21358,X21359] :
      ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21359),X21356),X21358) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21359),X21355),X21357)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21359),X21356),X21357) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21359),X21355),X21358)
        | X21357 = c_Groups_Ozero__class_Ozero(X21359)
        | X21358 = c_Groups_Ozero__class_Ozero(X21359)
        | ~ class_Fields_Ofield(X21359) )
      & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21359),X21356),X21357) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21359),X21355),X21358)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21359),X21356),X21358) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21359),X21355),X21357)
        | X21357 = c_Groups_Ozero__class_Ozero(X21359)
        | X21358 = c_Groups_Ozero__class_Ozero(X21359)
        | ~ class_Fields_Ofield(X21359) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_frac__eq__eq])])]) ).

fof(i_0_9831,plain,
    ! [X20150,X20151] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20151),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20150),X20151)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20150),c_Divides_Odiv__class_Omod(tc_Int_Oint,X20150,X20151)),
    inference(variable_rename,[status(thm)],[fact_zmult__div__cancel]) ).

fof(i_0_9832,plain,
    ! [X20055,X20056] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20056),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20055),X20056)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20055),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20055,X20056)),
    inference(variable_rename,[status(thm)],[fact_mult__div__cancel]) ).

fof(i_0_9833,plain,
    ! [X30393,X30394] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X30394),X30393) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X30394)),hAPP(c_Code__Numeral_Onat__of,X30393))),
    inference(variable_rename,[status(thm)],[fact_minus__code__numeral__def]) ).

fof(i_0_9834,plain,
    ! [X30398,X30399] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X30399),X30398) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X30399)),hAPP(c_Code__Numeral_Onat__of,X30398))),
    inference(variable_rename,[status(thm)],[fact_div__code__numeral__def]) ).

fof(i_0_9835,plain,
    ! [X30400,X30401] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),X30401),X30400) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X30401)),hAPP(c_Code__Numeral_Onat__of,X30400))),
    inference(variable_rename,[status(thm)],[fact_times__code__numeral__def]) ).

fof(i_0_9836,plain,
    ! [X30396,X30397] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X30397),X30396) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X30397)),hAPP(c_Code__Numeral_Onat__of,X30396))),
    inference(variable_rename,[status(thm)],[fact_plus__code__numeral__def]) ).

fof(i_0_9837,plain,
    ! [X19921,X19922] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19922),X19921))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19921),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19921),X19922)) = X19922 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__diff__cancel])]) ).

fof(i_0_9838,plain,
    ! [X20035,X20036] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20036),X20035))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20036),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20035),X20036)) = X20035 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__diff__inverse])]) ).

fof(i_0_9839,plain,
    ! [X17264,X17265,X17266,X17267] : c_Nat_Onat_Onat__case(X17267,X17266,X17265,hAPP(c_Nat_OSuc,X17264)) = hAPP(X17265,X17264),
    inference(variable_rename,[status(thm)],[fact_nat__case__Suc]) ).

fof(i_0_9840,plain,
    ! [X29576,X29577,X29578] :
      ( ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X29576) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X29577),hAPP(c_List_Oset(tc_Nat_Onat),X29576)))
        | X29577 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk348_1(X29578)),hAPP(c_List_Oset(tc_Nat_Onat),X29578)))
        | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X29578) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( esk348_1(X29578) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X29578) = 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_9841,plain,
    ! [X18599,X18600,X18601] :
      ( ~ class_Orderings_Oorder(X18601)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18601),X18600),X18599))
      | X18599 = X18600
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18601),X18600),X18599)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I11_J])]) ).

fof(i_0_9842,plain,
    ! [X18596,X18597,X18598] :
      ( ~ class_Orderings_Oorder(X18598)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18598),X18597),X18596))
      | X18597 = X18596
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18598),X18597),X18596)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__neq__trans])]) ).

fof(i_0_9843,plain,
    ! [X18593,X18594,X18595] :
      ( ~ class_Orderings_Oorder(X18595)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18595),X18594),X18593))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18595),X18594),X18593))
      | X18594 = X18593 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__imp__less__or__eq])]) ).

fof(i_0_9844,plain,
    ! [X18578,X18579,X18580] :
      ( ~ class_Orderings_Oorder(X18580)
      | X18579 = X18578
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18580),X18579),X18578))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18580),X18579),X18578)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__neq__le__trans])]) ).

fof(i_0_9845,plain,
    ! [X18566,X18567,X18568] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18568),X18567),X18566))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18568),X18567),X18566))
        | X18567 = X18566
        | ~ class_Orderings_Oorder(X18568) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18568),X18567),X18566))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18568),X18567),X18566))
        | ~ class_Orderings_Oorder(X18568) )
      & ( X18567 != X18566
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18568),X18567),X18566))
        | ~ class_Orderings_Oorder(X18568) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__less])])]) ).

fof(i_0_9846,plain,
    ! [X18560,X18561,X18562] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18562),X18561),X18560))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18562),X18561),X18560))
        | ~ class_Orderings_Oorder(X18562) )
      & ( X18561 != X18560
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18562),X18561),X18560))
        | ~ class_Orderings_Oorder(X18562) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18562),X18561),X18560))
        | X18561 = X18560
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18562),X18561),X18560))
        | ~ class_Orderings_Oorder(X18562) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__le])])]) ).

fof(i_0_9847,plain,
    ! [X18575,X18576,X18577] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18577),X18576),X18575))
        | X18576 = X18575
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18577),X18576),X18575))
        | ~ class_Orderings_Olinorder(X18577) )
      & ( X18576 != X18575
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18577),X18576),X18575))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18577),X18576),X18575))
        | ~ class_Orderings_Olinorder(X18577) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5959])])]) ).

fof(i_0_9848,plain,
    ! [X18581,X18582,X18583] :
      ( ~ class_Orderings_Oorder(X18583)
      | X18582 = X18581
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18583),X18581),X18582))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18583),X18581),X18582)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I12_J])]) ).

fof(i_0_9849,plain,
    ! [X20392,X20393,X20394] :
      ( ~ class_Int_Onumber__ring(X20394)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20394),hAPP(c_Int_Onumber__class_Onumber__of(X20394),X20393)),hAPP(c_Int_Onumber__class_Onumber__of(X20394),X20392)) = hAPP(c_Int_Onumber__class_Onumber__of(X20394),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20393),X20392)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_arith__simps_I32_J])]) ).

fof(i_0_9850,plain,
    ! [X20368,X20369,X20370] :
      ( ~ class_Int_Onumber__ring(X20370)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20370),hAPP(c_Int_Onumber__class_Onumber__of(X20370),X20369)),hAPP(c_Int_Onumber__class_Onumber__of(X20370),X20368)) = hAPP(c_Int_Onumber__class_Onumber__of(X20370),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20369),X20368)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__number__of__eq])]) ).

fof(i_0_9851,plain,
    ! [X20400,X20401,X20402] :
      ( ~ class_Int_Onumber__ring(X20402)
      | hAPP(c_Int_Onumber__class_Onumber__of(X20402),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20401),X20400)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20402),hAPP(c_Int_Onumber__class_Onumber__of(X20402),X20401)),hAPP(c_Int_Onumber__class_Onumber__of(X20402),X20400)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__diff])]) ).

fof(i_0_9852,plain,
    ! [X20395,X20396,X20397] :
      ( ~ class_Int_Onumber__ring(X20397)
      | hAPP(c_Int_Onumber__class_Onumber__of(X20397),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20396),X20395)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20397),hAPP(c_Int_Onumber__class_Onumber__of(X20397),X20396)),hAPP(c_Int_Onumber__class_Onumber__of(X20397),X20395)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__mult])]) ).

fof(i_0_9853,plain,
    ! [X20365,X20366,X20367] :
      ( ~ class_Int_Onumber__ring(X20367)
      | hAPP(c_Int_Onumber__class_Onumber__of(X20367),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20366),X20365)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20367),hAPP(c_Int_Onumber__class_Onumber__of(X20367),X20366)),hAPP(c_Int_Onumber__class_Onumber__of(X20367),X20365)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__add])]) ).

fof(i_0_9854,plain,
    ! [X19819,X19820,X19821] :
      ( ~ class_Rings_Oring__1(X19821)
      | hAPP(c_Int_Oring__1__class_Oof__int(X19821),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X19820),X19819)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19821),hAPP(c_Int_Oring__1__class_Oof__int(X19821),X19820)),hAPP(c_Int_Oring__1__class_Oof__int(X19821),X19819)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__diff])]) ).

fof(i_0_9855,plain,
    ! [X18179,X18180,X18181] :
      ( ~ class_Rings_Oring__1(X18181)
      | hAPP(c_Int_Oring__1__class_Oof__int(X18181),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X18180),X18179)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18181),hAPP(c_Int_Oring__1__class_Oof__int(X18181),X18180)),hAPP(c_Int_Oring__1__class_Oof__int(X18181),X18179)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__mult])]) ).

fof(i_0_9856,plain,
    ! [X18412,X18413,X18414] :
      ( ~ class_Rings_Oring__1(X18414)
      | hAPP(c_Int_Oring__1__class_Oof__int(X18414),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18413),X18412)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18414),hAPP(c_Int_Oring__1__class_Oof__int(X18414),X18413)),hAPP(c_Int_Oring__1__class_Oof__int(X18414),X18412)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__add])]) ).

fof(i_0_9857,plain,
    ! [X18210,X18211,X18212] :
      ( ~ class_Rings_Osemiring__1(X18212)
      | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18212),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18211),X18210)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18212),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18212),X18211)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18212),X18210)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__mult])]) ).

fof(i_0_9858,plain,
    ! [X18035,X18036,X18037] :
      ( ~ class_Rings_Osemiring__1(X18037)
      | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18037),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18036),X18035)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18037),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18037),X18036)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18037),X18035)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__add])]) ).

fof(i_0_9859,plain,
    ! [X30685,X30686,X30687] : c_Enum_Oproduct(X30687,X30686,c_List_Olist_ONil(X30687),X30685) = c_List_Olist_ONil(tc_prod(X30687,X30686)),
    inference(variable_rename,[status(thm)],[fact_product_Osimps_I1_J]) ).

fof(i_0_9860,plain,
    ! [X21596,X21597] :
      ( ~ class_Fields_Ofield__inverse__zero(X21597)
      | ~ class_Int_Onumber__ring(X21597)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21597),hAPP(c_Int_Onumber__class_Onumber__of(X21597),c_Int_OMin)),X21596) = hAPP(c_Groups_Ouminus__class_Ouminus(X21597),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21597),c_Groups_Oone__class_Oone(X21597)),X21596)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus1__divide])]) ).

fof(i_0_9861,plain,
    ! [X26196,X26197,X26198] :
      ( ~ class_Groups_Ocomm__monoid__add(X26198)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26197,X26198),hAPP(c_COMBK(X26198,X26197),c_Groups_Ozero__class_Ozero(X26198))),X26196) = c_Groups_Ozero__class_Ozero(X26198) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__0])]) ).

fof(i_0_9862,plain,
    ! [X24632,X24633,X24634] :
      ( ~ class_Groups_Ocomm__monoid__mult(X24634)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24633,X24634),hAPP(c_COMBK(X24634,X24633),c_Groups_Oone__class_Oone(X24634))),X24632) = c_Groups_Oone__class_Oone(X24634) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__1])]) ).

fof(i_0_9863,plain,
    ! [X26065,X26066] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26066),c_Groups_Oone__class_Oone(tc_Int_Oint))),X26065) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X26066,X26065),
    inference(variable_rename,[status(thm)],[fact_atLeastPlusOneLessThan__greaterThanLessThan__int]) ).

fof(i_0_9864,plain,
    ! [X18587,X18588,X18589] :
      ( ~ class_Orderings_Opreorder(X18589)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18589),X18588),X18587))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18589),X18588),X18587)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__le])]) ).

fof(i_0_9865,plain,
    ! [X33384,X33385,X33386] :
      ( X33386 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | hAPP(c_List_Otl(X33385),c_List_Oreplicate(X33385,X33386,X33384)) = c_List_Oreplicate(X33385,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X33386),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X33384) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_tl__replicate])]) ).

fof(i_0_9866,plain,
    ! [X21887,X21888] : hAPP(c_Divides_OnegateSnd,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X21888),X21887)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X21888),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21887)),
    inference(variable_rename,[status(thm)],[fact_negateSnd__eq]) ).

fof(i_0_9867,plain,
    ! [X20678,X20679] :
      ( ~ class_Int_Onumber__ring(X20679)
      | ~ class_Rings_Olinordered__idom(X20679)
      | hAPP(c_Groups_Oabs__class_Oabs(X20679),hAPP(hAPP(c_Power_Opower__class_Opower(X20679),hAPP(c_Int_Onumber__class_Onumber__of(X20679),c_Int_OMin)),X20678)) = c_Groups_Oone__class_Oone(X20679) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__power__minus__one])]) ).

fof(i_0_9868,plain,
    ! [X25803,X25804,X25805] :
      ( ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X25805,X25804),X25803) != c_Orderings_Obot__class_Obot(tc_fun(X25805,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25805),X25804),X25803))
        | ~ class_Orderings_Oorder(X25805) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25805),X25804),X25803))
        | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X25805,X25804),X25803) = c_Orderings_Obot__class_Obot(tc_fun(X25805,tc_HOL_Obool))
        | ~ class_Orderings_Oorder(X25805) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5960])])]) ).

fof(i_0_9869,plain,
    ! [X25800,X25801,X25802] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(X25802,tc_HOL_Obool)) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X25802,X25801),X25800)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25802),X25801),X25800))
        | ~ class_Orderings_Oorder(X25802) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25802),X25801),X25800))
        | c_Orderings_Obot__class_Obot(tc_fun(X25802,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X25802,X25801),X25800)
        | ~ class_Orderings_Oorder(X25802) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5961])])]) ).

cnf(i_0_9870,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_5962]) ).

fof(i_0_9871,plain,
    ! [X23936,X23937] :
      ( ~ c_Nat__Transfer_Onat__set(X23937)
      | ~ c_Nat__Transfer_Onat__set(X23936)
      | c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X23937),X23936)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J])]) ).

fof(i_0_9872,plain,
    ! [X23440,X23441] :
      ( ~ c_Nat__Transfer_Onat__set(X23441)
      | ~ c_Nat__Transfer_Onat__set(X23440)
      | c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X23441),X23440)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J])]) ).

fof(i_0_9873,plain,
    ! [X18918,X18919,X18921,X18922,X18923] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X18919),X18918))
        | X18918 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18919),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk48_2(X18918,X18919))) )
      & ( X18921 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18922),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18923))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X18922),X18921)) ) ),
    inference(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_9874,plain,
    ! [X33405,X33406,X33407,X33408,X33409] : hAPP(hAPP(c_List_Omap(X33409,X33408),X33407),c_List_Oreplicate(X33409,X33406,X33405)) = c_List_Oreplicate(X33408,X33406,hAPP(X33407,X33405)),
    inference(variable_rename,[status(thm)],[fact_map__replicate]) ).

fof(i_0_9875,plain,
    ! [X31163,X31164,X31165,X31166] : hAPP(c_List_Ofilter(X31166,X31165),c_List_Oremove1(X31166,X31164,X31163)) = c_List_Oremove1(X31166,X31164,hAPP(c_List_Ofilter(X31166,X31165),X31163)),
    inference(variable_rename,[status(thm)],[fact_filter__remove1]) ).

fof(i_0_9876,plain,
    ! [X29632,X29633,X29634,X29635] :
      ( ( X29632 != c_List_Olist_ONil(X29635)
        | hAPP(hAPP(c_List_Oappend(X29635),X29634),hAPP(hAPP(c_List_Olist_OCons(X29635),X29633),c_List_Olist_ONil(X29635))) != X29632 )
      & ( c_List_Obutlast(X29635,X29632) = X29634
        | hAPP(hAPP(c_List_Oappend(X29635),X29634),hAPP(hAPP(c_List_Olist_OCons(X29635),X29633),c_List_Olist_ONil(X29635))) != X29632 )
      & ( c_List_Olast(X29635,X29632) = X29633
        | hAPP(hAPP(c_List_Oappend(X29635),X29634),hAPP(hAPP(c_List_Olist_OCons(X29635),X29633),c_List_Olist_ONil(X29635))) != X29632 )
      & ( X29632 = c_List_Olist_ONil(X29635)
        | c_List_Obutlast(X29635,X29632) != X29634
        | c_List_Olast(X29635,X29632) != X29633
        | hAPP(hAPP(c_List_Oappend(X29635),X29634),hAPP(hAPP(c_List_Olist_OCons(X29635),X29633),c_List_Olist_ONil(X29635))) = X29632 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_snoc__eq__iff__butlast])])]) ).

fof(i_0_9877,plain,
    ! [X18432] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18432),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | X18432 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,esk38_1(X18432)))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_negD])])]) ).

fof(i_0_9878,plain,
    ! [X20913,X20914] :
      ( ~ class_Int_Onumber__ring(X20914)
      | hBOOL(hAPP(hAPP(c_member(X20914),hAPP(c_Int_Onumber__class_Onumber__of(X20914),X20913)),c_Int_Oring__1__class_OInts(X20914))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__number__of])]) ).

fof(i_0_9879,plain,
    ! [X20923,X20924] :
      ( ~ class_Rings_Oring__1(X20924)
      | hBOOL(hAPP(hAPP(c_member(X20924),hAPP(c_Int_Oring__1__class_Oof__int(X20924),X20923)),c_Int_Oring__1__class_OInts(X20924))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__of__int])]) ).

fof(i_0_9880,plain,
    ! [X21009,X21010] :
      ( ~ class_Rings_Osemiring__1(X21010)
      | hBOOL(hAPP(hAPP(c_member(X21010),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X21010),X21009)),c_Nat_Osemiring__1__class_ONats(X21010))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__in__Nats])]) ).

fof(i_0_9881,plain,
    ! [X20918,X20919] :
      ( ~ class_Rings_Oring__1(X20919)
      | hBOOL(hAPP(hAPP(c_member(X20919),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20919),X20918)),c_Int_Oring__1__class_OInts(X20919))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__of__nat])]) ).

fof(i_0_9882,plain,
    ! [X20155] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20155))
      | hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20155),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X20155 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__diff__1])]) ).

fof(i_0_9883,plain,
    ! [X20154] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20154))
      | X20154 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20154),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_9884,plain,
    ! [X30385] : hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X30385)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_nat__of]) ).

fof(i_0_9885,plain,
    ! [X19659,X19660,X19661] :
      ( ~ class_Divides_Osemiring__div(X19661)
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X19661),c_Divides_Odiv__class_Omod(X19661,X19660,X19659)),X19659) = c_Groups_Ozero__class_Ozero(X19661) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__div__trivial])]) ).

fof(i_0_9886,plain,
    ! [X21753] : c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),X21753) = 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),X21753),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[fact_negDivAlg__minus1]) ).

fof(i_0_9887,plain,
    ! [X33499,X33500,X33501] : hAPP(c_List_Oset(X33501),c_List_Oreplicate(X33501,hAPP(c_Nat_OSuc,X33500),X33499)) = hAPP(hAPP(c_Set_Oinsert(X33501),X33499),c_Orderings_Obot__class_Obot(tc_fun(X33501,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_set__replicate__Suc]) ).

fof(i_0_9888,plain,
    ! [X25506,X25507] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25507))
      | c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X25507,X25506)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SetInterval_Otransfer__nat__int__set__function__closures])]) ).

fof(i_0_9889,plain,
    ! [X24485,X24486] :
      ( ~ class_Orderings_Olinorder(X24486)
      | c_Big__Operators_Olattice_OInf__fin(X24486,c_Orderings_Oord__class_Omin(X24486),hAPP(hAPP(c_Set_Oinsert(X24486),X24485),c_Orderings_Obot__class_Obot(tc_fun(X24486,tc_HOL_Obool)))) = X24485 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Osingleton])]) ).

fof(i_0_9890,plain,
    ! [X24429,X24430] :
      ( ~ class_Orderings_Olinorder(X24430)
      | c_Big__Operators_Olattice_OSup__fin(X24430,c_Orderings_Oord__class_Omax(X24430),hAPP(hAPP(c_Set_Oinsert(X24430),X24429),c_Orderings_Obot__class_Obot(tc_fun(X24430,tc_HOL_Obool)))) = X24429 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Osingleton])]) ).

fof(i_0_9891,plain,
    ! [X18542] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X18542))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18542)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18542))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X18542)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__one__le__iff__zero__less])]) ).

fof(i_0_9892,plain,
    ! [X23819,X23820] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23820,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X23820,tc_HOL_Obool))),X23819) = c_Orderings_Obot__class_Obot(tc_fun(X23820,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Int__empty__left]) ).

fof(i_0_9893,plain,
    ! [X26694,X26695] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26695,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X26695,tc_HOL_Obool))),X26694) = c_Orderings_Otop__class_Otop(tc_fun(X26695,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Un__UNIV__left]) ).

fof(i_0_9894,plain,
    ! [X20247,X20248] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20248,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X20248,tc_HOL_Obool))),X20247) = c_Orderings_Obot__class_Obot(tc_fun(X20248,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_empty__Diff]) ).

fof(i_0_9895,plain,
    ! [X27263,X27264,X27265] : hAPP(hAPP(c_Product__Type_OSigma(X27265,X27264),c_Orderings_Obot__class_Obot(tc_fun(X27265,tc_HOL_Obool))),X27263) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27265,X27264),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Sigma__empty1]) ).

fof(i_0_9896,plain,
    ! [X19167] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19167),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19167),X19167))),
    inference(variable_rename,[status(thm)],[fact_le__square]) ).

fof(i_0_9897,plain,
    ! [X19157,X19158] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19158),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19158),X19157))),
    inference(variable_rename,[status(thm)],[fact_le__add1]) ).

fof(i_0_9898,plain,
    ! [X19159,X19160] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19160),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19159),X19160))),
    inference(variable_rename,[status(thm)],[fact_le__add2]) ).

fof(i_0_9899,plain,
    ! [X21503,X21504,X21505,X21506] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(X21506),X21504) = c_Groups_Ozero__class_Ozero(X21506)
        | X21505 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21506),X21503),hAPP(c_Int_Onumber__class_Onumber__of(X21506),X21504))
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21506),X21505),hAPP(c_Int_Onumber__class_Onumber__of(X21506),X21504)) != X21503
        | ~ class_Fields_Ofield__inverse__zero(X21506)
        | ~ class_Int_Onumber(X21506) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(X21506),X21504) != c_Groups_Ozero__class_Ozero(X21506)
        | X21503 = c_Groups_Ozero__class_Ozero(X21506)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21506),X21505),hAPP(c_Int_Onumber__class_Onumber__of(X21506),X21504)) != X21503
        | ~ class_Fields_Ofield__inverse__zero(X21506)
        | ~ class_Int_Onumber(X21506) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(X21506),X21504) = c_Groups_Ozero__class_Ozero(X21506)
        | hAPP(c_Int_Onumber__class_Onumber__of(X21506),X21504) != c_Groups_Ozero__class_Ozero(X21506)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21506),X21505),hAPP(c_Int_Onumber__class_Onumber__of(X21506),X21504)) = X21503
        | ~ class_Fields_Ofield__inverse__zero(X21506)
        | ~ class_Int_Onumber(X21506) )
      & ( X21503 != c_Groups_Ozero__class_Ozero(X21506)
        | hAPP(c_Int_Onumber__class_Onumber__of(X21506),X21504) != c_Groups_Ozero__class_Ozero(X21506)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21506),X21505),hAPP(c_Int_Onumber__class_Onumber__of(X21506),X21504)) = X21503
        | ~ class_Fields_Ofield__inverse__zero(X21506)
        | ~ class_Int_Onumber(X21506) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(X21506),X21504) = c_Groups_Ozero__class_Ozero(X21506)
        | X21505 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21506),X21503),hAPP(c_Int_Onumber__class_Onumber__of(X21506),X21504))
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21506),X21505),hAPP(c_Int_Onumber__class_Onumber__of(X21506),X21504)) = X21503
        | ~ class_Fields_Ofield__inverse__zero(X21506)
        | ~ class_Int_Onumber(X21506) )
      & ( X21503 != c_Groups_Ozero__class_Ozero(X21506)
        | X21505 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21506),X21503),hAPP(c_Int_Onumber__class_Onumber__of(X21506),X21504))
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21506),X21505),hAPP(c_Int_Onumber__class_Onumber__of(X21506),X21504)) = X21503
        | ~ class_Fields_Ofield__inverse__zero(X21506)
        | ~ class_Int_Onumber(X21506) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__eq__eq__number__of1])])]) ).

fof(i_0_9900,plain,
    ! [X21515,X21516,X21517,X21518] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(X21518),X21515) = c_Groups_Ozero__class_Ozero(X21518)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21518),X21517),hAPP(c_Int_Onumber__class_Onumber__of(X21518),X21515)) = X21516
        | X21517 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21518),X21516),hAPP(c_Int_Onumber__class_Onumber__of(X21518),X21515))
        | ~ class_Fields_Ofield__inverse__zero(X21518)
        | ~ class_Int_Onumber(X21518) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(X21518),X21515) != c_Groups_Ozero__class_Ozero(X21518)
        | X21517 = c_Groups_Ozero__class_Ozero(X21518)
        | X21517 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21518),X21516),hAPP(c_Int_Onumber__class_Onumber__of(X21518),X21515))
        | ~ class_Fields_Ofield__inverse__zero(X21518)
        | ~ class_Int_Onumber(X21518) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(X21518),X21515) = c_Groups_Ozero__class_Ozero(X21518)
        | hAPP(c_Int_Onumber__class_Onumber__of(X21518),X21515) != c_Groups_Ozero__class_Ozero(X21518)
        | X21517 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21518),X21516),hAPP(c_Int_Onumber__class_Onumber__of(X21518),X21515))
        | ~ class_Fields_Ofield__inverse__zero(X21518)
        | ~ class_Int_Onumber(X21518) )
      & ( X21517 != c_Groups_Ozero__class_Ozero(X21518)
        | hAPP(c_Int_Onumber__class_Onumber__of(X21518),X21515) != c_Groups_Ozero__class_Ozero(X21518)
        | X21517 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21518),X21516),hAPP(c_Int_Onumber__class_Onumber__of(X21518),X21515))
        | ~ class_Fields_Ofield__inverse__zero(X21518)
        | ~ class_Int_Onumber(X21518) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(X21518),X21515) = c_Groups_Ozero__class_Ozero(X21518)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21518),X21517),hAPP(c_Int_Onumber__class_Onumber__of(X21518),X21515)) != X21516
        | X21517 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21518),X21516),hAPP(c_Int_Onumber__class_Onumber__of(X21518),X21515))
        | ~ class_Fields_Ofield__inverse__zero(X21518)
        | ~ class_Int_Onumber(X21518) )
      & ( X21517 != c_Groups_Ozero__class_Ozero(X21518)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21518),X21517),hAPP(c_Int_Onumber__class_Onumber__of(X21518),X21515)) != X21516
        | X21517 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21518),X21516),hAPP(c_Int_Onumber__class_Onumber__of(X21518),X21515))
        | ~ class_Fields_Ofield__inverse__zero(X21518)
        | ~ class_Int_Onumber(X21518) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__divide__eq__number__of1])])]) ).

fof(i_0_9901,plain,
    ! [X17413,X17414,X17415] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17414),X17415))
        | hBOOL(hAPP(hAPP(X17413,X17414),X17415))
        | X17415 = X17414
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17415),X17414)) )
      & ( ~ hBOOL(hAPP(hAPP(X17413,X17414),X17415))
        | hBOOL(hAPP(hAPP(X17413,X17414),X17415))
        | X17415 = X17414
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17415),X17414)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17414),X17415))
        | hBOOL(hAPP(hAPP(X17413,X17414),X17415))
        | ~ hBOOL(hAPP(hAPP(X17413,X17414),X17415))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17415),X17414)) )
      & ( ~ hBOOL(hAPP(hAPP(X17413,X17414),X17415))
        | hBOOL(hAPP(hAPP(X17413,X17414),X17415))
        | ~ hBOOL(hAPP(hAPP(X17413,X17414),X17415))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17415),X17414)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17414),X17415))
        | hBOOL(hAPP(hAPP(X17413,X17414),X17415))
        | X17415 = X17414
        | ~ hBOOL(hAPP(hAPP(X17413,X17414),X17415)) )
      & ( ~ hBOOL(hAPP(hAPP(X17413,X17414),X17415))
        | hBOOL(hAPP(hAPP(X17413,X17414),X17415))
        | X17415 = X17414
        | ~ hBOOL(hAPP(hAPP(X17413,X17414),X17415)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17414),X17415))
        | hBOOL(hAPP(hAPP(X17413,X17414),X17415))
        | ~ hBOOL(hAPP(hAPP(X17413,X17414),X17415))
        | ~ hBOOL(hAPP(hAPP(X17413,X17414),X17415)) )
      & ( ~ hBOOL(hAPP(hAPP(X17413,X17414),X17415))
        | hBOOL(hAPP(hAPP(X17413,X17414),X17415))
        | ~ hBOOL(hAPP(hAPP(X17413,X17414),X17415))
        | ~ hBOOL(hAPP(hAPP(X17413,X17414),X17415)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__cases])])]) ).

fof(i_0_9902,plain,
    ! [X24524] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X24524) = 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)),X24524)),
    inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J]) ).

fof(i_0_9903,plain,
    ! [X28371,X28372,X28373,X28374,X28375,X28376] :
      ( hAPP(hAPP(c_List_Olist_OCons(X28376),X28375),X28374) != X28373
      | X28372 != hAPP(hAPP(c_List_Oappend(X28376),X28374),X28371)
      | hAPP(hAPP(c_List_Olist_OCons(X28376),X28375),X28372) = hAPP(hAPP(c_List_Oappend(X28376),X28373),X28371) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cons__eq__appendI])]) ).

fof(i_0_9904,plain,
    ! [X28151,X28152,X28153,X28154,X28155,X28156] :
      ( hAPP(hAPP(c_List_Oappend(X28156),X28155),X28154) != X28153
      | X28152 != hAPP(hAPP(c_List_Oappend(X28156),X28154),X28151)
      | hAPP(hAPP(c_List_Oappend(X28156),X28155),X28152) = hAPP(hAPP(c_List_Oappend(X28156),X28153),X28151) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__eq__appendI])]) ).

fof(i_0_9905,plain,
    ! [X18093,X18094,X18095] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18095),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18094),X18093)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18094),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18095),X18093)),
    inference(variable_rename,[status(thm)],[fact_zadd__left__commute]) ).

fof(i_0_9906,plain,
    ! [X17455,X17456,X17457] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17457),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17456),X17455)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17456),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17457),X17455)),
    inference(variable_rename,[status(thm)],[fact_nat__add__left__commute]) ).

fof(i_0_9907,plain,
    ! [X29533,X29534] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X29534),X29533) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X29534,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X29533),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(variable_rename,[status(thm)],[fact_atLeastLessThan__upto]) ).

fof(i_0_9908,plain,
    ! [X22710,X22711] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22711),X22710)),X22710) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X22711),X22710),
    inference(variable_rename,[status(thm)],[fact_nat__minus__add__max]) ).

fof(i_0_9909,plain,
    ! [X22754] :
      ( ~ class_Orderings_Olinorder(X22754)
      | c_Orderings_Oord_Omax(X22754,hAPP(c_COMBC(X22754,X22754,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X22754))) = c_Orderings_Oord__class_Omin(X22754) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dual__max])]) ).

fof(i_0_9910,plain,
    ! [X22730] :
      ( ~ class_Orderings_Olinorder(X22730)
      | c_Orderings_Oord_Omin(X22730,hAPP(c_COMBC(X22730,X22730,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X22730))) = c_Orderings_Oord__class_Omax(X22730) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dual__min])]) ).

fof(i_0_9911,plain,
    ! [X29583] :
      ( ~ class_Groups_Omonoid__add(X29583)
      | c_List_Omonoid__add__class_Olistsum(X29583) = c_List_Ofoldl(X29583,X29583,c_Groups_Oplus__class_Oplus(X29583),c_Groups_Ozero__class_Ozero(X29583)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__foldl])]) ).

fof(i_0_9912,plain,
    ! [X19647,X19648,X19649] :
      ( ~ class_Divides_Osemiring__div(X19649)
      | X19648 = c_Groups_Ozero__class_Ozero(X19649)
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X19649),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19649),X19648),X19647)),X19648) = X19647 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__self1__is__id])]) ).

fof(i_0_9913,plain,
    ! [X19650,X19651,X19652] :
      ( ~ class_Divides_Osemiring__div(X19652)
      | X19651 = c_Groups_Ozero__class_Ozero(X19652)
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X19652),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19652),X19650),X19651)),X19651) = X19650 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__self2__is__id])]) ).

fof(i_0_9914,plain,
    ! [X20024,X20025,X20026] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20025),X20026) != X20024
        | X20025 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20024),X20026)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20026),X20025)) )
      & ( X20025 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20024),X20026)
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20025),X20026) = X20024
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20026),X20025)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__diff__is__add])])]) ).

fof(i_0_9915,plain,
    ! [X19417,X19418] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X19418,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X19417)) = 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),X19418),X19417)),
    inference(variable_rename,[status(thm)],[fact_zmod__zminus2]) ).

fof(i_0_9916,plain,
    ! [X31547,X31548,X31549] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X31549),X31548))
      | c_List_Oremove1(X31549,X31547,c_List_Oremdups(X31549,X31548)) = c_List_Oremdups(X31549,c_List_Oremove1(X31549,X31547,X31548)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_remove1__remdups])]) ).

fof(i_0_9917,plain,
    ! [X32019,X32020] :
      ( ( c_Wellfounded_Oacyclic(X32020,X32019)
        | ~ c_Nitpick_Owf_H(X32020,X32019) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X32020,X32020)),X32019))
        | c_Nitpick_Ounknown(tc_HOL_Obool)
        | ~ c_Nitpick_Owf_H(X32020,X32019) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X32020,X32020)),X32019))
        | ~ c_Wellfounded_Oacyclic(X32020,X32019)
        | c_Nitpick_Owf_H(X32020,X32019) )
      & ( ~ c_Nitpick_Ounknown(tc_HOL_Obool)
        | ~ c_Wellfounded_Oacyclic(X32020,X32019)
        | c_Nitpick_Owf_H(X32020,X32019) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nitpick_Owf_H__def])])]) ).

fof(i_0_9918,plain,
    ! [X32015,X32016] :
      ( ( ~ c_Wellfounded_Owf(X32016,X32015)
        | c_Wellfounded_Oacyclic(X32016,X32015)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X32016,X32016)),X32015)) )
      & ( ~ c_Wellfounded_Oacyclic(X32016,X32015)
        | c_Wellfounded_Owf(X32016,X32015)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X32016,X32016)),X32015)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__iff__acyclic__if__finite])])]) ).

fof(i_0_9919,plain,
    ! [X32017,X32018] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X32018,X32018)),X32017))
      | ~ c_Wellfounded_Oacyclic(X32018,X32017)
      | c_Wellfounded_Owf(X32018,X32017) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__acyclic__wf])]) ).

fof(i_0_9920,plain,
    ! [X31605,X31606] : c_Fun_Oinj__on(tc_List_Olist(X31606),tc_List_Olist(X31606),c_List_Orev(X31606),X31605),
    inference(variable_rename,[status(thm)],[fact_inj__on__rev]) ).

fof(i_0_9921,plain,
    ! [X31143,X31144,X31145] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X31145),X31144))
      | hBOOL(hAPP(c_List_Odistinct(X31145),hAPP(c_List_Ofilter(X31145,X31143),X31144))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__filter])]) ).

fof(i_0_9922,plain,
    ! [X17214,X17215,X17216,X17217] : hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(X17217)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X17217),X17216),X17215),X17214)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_triple_Osize_I2_J]) ).

fof(i_0_9923,plain,
    ! [X26881,X26882,X26883,X26884,X26885,X26886,X26887,X26890] :
      ( ( ~ hBOOL(hAPP(hAPP(X26881,X26883),X26884))
        | hAPP(X26881,X26883) = hAPP(X26881,X26884)
        | ~ c_Equiv__Relations_Oequivp(X26882,X26881) )
      & ( hAPP(X26881,X26885) != hAPP(X26881,X26886)
        | hBOOL(hAPP(hAPP(X26881,X26885),X26886))
        | ~ c_Equiv__Relations_Oequivp(X26882,X26881) )
      & ( ~ hBOOL(hAPP(hAPP(X26887,esk253_1(X26887)),esk254_1(X26887)))
        | hAPP(X26887,esk253_1(X26887)) != hAPP(X26887,esk254_1(X26887))
        | c_Equiv__Relations_Oequivp(X26890,X26887) )
      & ( hBOOL(hAPP(hAPP(X26887,esk253_1(X26887)),esk254_1(X26887)))
        | hAPP(X26887,esk253_1(X26887)) = hAPP(X26887,esk254_1(X26887))
        | c_Equiv__Relations_Oequivp(X26890,X26887) ) ),
    inference(distribute,[status(thm)],[inference(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_9924,plain,
    ! [X19855,X19856,X19857] :
      ( ~ class_Groups_Ogroup__add(X19857)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19857),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19857),X19856),X19855)),X19855) = X19856 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__diff__cancel])]) ).

fof(i_0_9925,plain,
    ! [X19852,X19853,X19854] :
      ( ~ class_Groups_Ogroup__add(X19854)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19854),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19854),X19853),X19852)),X19852) = X19853 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__add__cancel])]) ).

fof(i_0_9926,plain,
    ! [X31864,X31865,X31866] :
      ( ~ class_Orderings_Olinorder(X31866)
      | c_List_Olinorder__class_Osort__key(X31865,X31866,X31864,c_List_Olist_ONil(X31865)) = c_List_Olist_ONil(X31865) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sort__key__simps_I1_J])]) ).

fof(i_0_9927,plain,
    ! [X30902,X30903,X30904] : hAPP(c_Set_Oimage(tc_prod(X30904,X30903),X30904,c_Product__Type_Ofst(X30904,X30903)),X30902) = hAPP(c_Relation_ODomain(X30904,X30903),X30902),
    inference(variable_rename,[status(thm)],[fact_fst__eq__Domain]) ).

fof(i_0_9928,plain,
    ! [X28275,X28276,X28277] : hAPP(c_Set_Oimage(tc_prod(X28277,X28276),X28276,c_Product__Type_Osnd(X28277,X28276)),X28275) = hAPP(c_Relation_ORange(X28277,X28276),X28275),
    inference(variable_rename,[status(thm)],[fact_snd__eq__Range]) ).

fof(i_0_9929,plain,
    ! [X17259,X17260] :
      ( ( hBOOL(hAPP(X17260,hAPP(c_Nat_OSuc,esk21_2(X17259,X17260))))
        | hBOOL(hAPP(X17260,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(X17260,X17259)) )
      & ( ~ hBOOL(hAPP(X17260,esk21_2(X17259,X17260)))
        | hBOOL(hAPP(X17260,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(X17260,X17259)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__induct])])])]) ).

fof(i_0_9930,plain,
    ! [X32466,X32467,X32468] :
      ( ( ~ c_Relation_Orefl__on(X32468,X32467,hAPP(c_Relation_Oconverse(X32468,X32468),X32466))
        | c_Relation_Orefl__on(X32468,X32467,X32466) )
      & ( ~ c_Relation_Orefl__on(X32468,X32467,X32466)
        | c_Relation_Orefl__on(X32468,X32467,hAPP(c_Relation_Oconverse(X32468,X32468),X32466)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__on__converse])]) ).

fof(i_0_9931,plain,
    ! [X32444,X32445,X32446] :
      ( ( ~ c_Relation_Ototal__on(X32446,X32445,hAPP(c_Relation_Oconverse(X32446,X32446),X32444))
        | c_Relation_Ototal__on(X32446,X32445,X32444) )
      & ( ~ c_Relation_Ototal__on(X32446,X32445,X32444)
        | c_Relation_Ototal__on(X32446,X32445,hAPP(c_Relation_Oconverse(X32446,X32446),X32444)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_total__on__converse])]) ).

fof(i_0_9932,plain,
    ! [X17830,X17831,X17832] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OLocal(X17832,X17831,X17830)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X17830)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[fact_com_Osize_I11_J]) ).

fof(i_0_9933,plain,
    ! [X24525] :
      ( ~ c_Nat__Transfer_Onat__set(X24525)
      | hAPP(c_Finite__Set_Ocard(tc_Int_Oint),X24525) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X24525)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J])]) ).

fof(i_0_9934,plain,
    ! [X23451,X23452] :
      ( ~ c_Nat__Transfer_Onat__set(X23452)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X23451),X23452))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23451)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J])]) ).

fof(i_0_9935,plain,
    ! [X23442,X23443,X23444] :
      ( ( ~ c_Nat__Transfer_Onat__set(X23442)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X23443),X23442))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23443)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk113_1(X23444)),X23444))
        | c_Nat__Transfer_Onat__set(X23444) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk113_1(X23444)))
        | c_Nat__Transfer_Onat__set(X23444) ) ),
    inference(distribute,[status(thm)],[inference(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_9936,plain,
    ! [X27614] : c_Relation_Orefl__on(X27614,c_Orderings_Obot__class_Obot(tc_fun(X27614,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27614,X27614),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_refl__on__empty]) ).

fof(i_0_9937,plain,
    ! [X26477,X26478] : hAPP(c_Finite__Set_Ocard(X26478),X26477) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26478,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,X26478),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X26477),
    inference(variable_rename,[status(thm)],[fact_card__eq__setsum]) ).

fof(i_0_9938,plain,
    ! [X21870,X21871,X21872,X21873] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X21873,X21872),X21871))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X21873,X21872),X21870))
      | X21871 = X21870 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__nat__rel__unique])]) ).

fof(i_0_9939,plain,
    ! [X25662,X25663] :
      ( ~ class_Groups_Oordered__ab__group__add(X25663)
      | c_Fun_Oinj__on(X25663,X25663,c_Groups_Ouminus__class_Ouminus(X25663),X25662) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__uminus])]) ).

fof(i_0_9940,plain,
    ! [X30402,X30403] : c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X30403,X30402) = hAPP(c_Code__Numeral_Oof__nat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Code__Numeral_Onat__of,X30403),hAPP(c_Code__Numeral_Onat__of,X30402))),
    inference(variable_rename,[status(thm)],[fact_mod__code__numeral__def]) ).

fof(i_0_9941,plain,
    ! [X28710,X28711,X28712] : hAPP(hAPP(c_List_Onth(X28712),hAPP(hAPP(c_List_Olist_OCons(X28712),X28711),X28710)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X28711,
    inference(variable_rename,[status(thm)],[fact_nth__Cons__0]) ).

fof(i_0_9942,plain,
    ! [X33949,X33950] :
      ( ( hBOOL(hAPP(hAPP(X33949,esk554_2(X33949,X33950)),esk554_2(X33949,X33950)))
        | ~ c_Equiv__Relations_Opart__equivp(X33950,X33949) )
      & ( c_Predicate_Osymp(X33950,X33949)
        | ~ c_Equiv__Relations_Opart__equivp(X33950,X33949) )
      & ( c_Predicate_Otransp(X33950,X33949)
        | ~ c_Equiv__Relations_Opart__equivp(X33950,X33949) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5963])])])]) ).

fof(i_0_9943,plain,
    ! [X33943,X33944,X33946,X33947,X33948] :
      ( ( hBOOL(hAPP(hAPP(X33943,esk553_2(X33943,X33944)),esk553_2(X33943,X33944)))
        | ~ c_Equiv__Relations_Opart__equivp(X33944,X33943) )
      & ( c_Predicate_Osymp(X33944,X33943)
        | ~ c_Equiv__Relations_Opart__equivp(X33944,X33943) )
      & ( c_Predicate_Otransp(X33944,X33943)
        | ~ c_Equiv__Relations_Opart__equivp(X33944,X33943) )
      & ( ~ hBOOL(hAPP(hAPP(X33946,X33948),X33948))
        | ~ c_Predicate_Osymp(X33947,X33946)
        | ~ c_Predicate_Otransp(X33947,X33946)
        | c_Equiv__Relations_Opart__equivp(X33947,X33946) ) ),
    inference(distribute,[status(thm)],[inference(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_9944,plain,
    ! [X23234,X23235,X23236,X23237] :
      ( ( hAPP(c_Set_Oimage(X23237,X23236,X23235),X23234) != c_Orderings_Obot__class_Obot(tc_fun(X23236,tc_HOL_Obool))
        | X23234 = c_Orderings_Obot__class_Obot(tc_fun(X23237,tc_HOL_Obool)) )
      & ( X23234 != c_Orderings_Obot__class_Obot(tc_fun(X23237,tc_HOL_Obool))
        | hAPP(c_Set_Oimage(X23237,X23236,X23235),X23234) = c_Orderings_Obot__class_Obot(tc_fun(X23236,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__is__empty])]) ).

fof(i_0_9945,plain,
    ! [X23227,X23228,X23229,X23230] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(X23230,tc_HOL_Obool)) != hAPP(c_Set_Oimage(X23229,X23230,X23228),X23227)
        | X23227 = c_Orderings_Obot__class_Obot(tc_fun(X23229,tc_HOL_Obool)) )
      & ( X23227 != c_Orderings_Obot__class_Obot(tc_fun(X23229,tc_HOL_Obool))
        | c_Orderings_Obot__class_Obot(tc_fun(X23230,tc_HOL_Obool)) = hAPP(c_Set_Oimage(X23229,X23230,X23228),X23227) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_empty__is__image])]) ).

fof(i_0_9946,plain,
    ! [X28620,X28621] : c_List_Olistrelp(X28621,X28620,c_List_Olist_ONil(X28621),c_List_Olist_ONil(X28621)),
    inference(variable_rename,[status(thm)],[fact_listrelp_Oequations_I1_J]) ).

fof(i_0_9947,plain,
    ! [X28618,X28619] : c_List_Olistrelp(X28619,X28618,c_List_Olist_ONil(X28619),c_List_Olist_ONil(X28619)),
    inference(variable_rename,[status(thm)],[fact_listrelp_ONil]) ).

fof(i_0_9948,plain,
    ! [X30097,X30098,X30099,X30100] :
      ( X30100 = c_List_Olist_ONil(X30099)
      | hAPP(c_List_Ohd(X30098),hAPP(hAPP(c_List_Omap(X30099,X30098),X30097),X30100)) = hAPP(X30097,hAPP(c_List_Ohd(X30099),X30100)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hd__map])]) ).

fof(i_0_9949,plain,
    ! [X17232,X17233,X17234] :
      ( ~ class_Rings_Osemiring__1(X17234)
      | c_Nat_Osemiring__1__class_Oof__nat__aux(X17234,X17233,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X17232) = X17232 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__aux_Osimps_I1_J])]) ).

fof(i_0_9950,plain,
    ! [X25482,X25483,X25484,X25485] :
      ( ( X25484 = X25483
        | c_SetInterval_Oord__class_OatLeastAtMost(X25485,X25484,X25483) != hAPP(hAPP(c_Set_Oinsert(X25485),X25482),c_Orderings_Obot__class_Obot(tc_fun(X25485,tc_HOL_Obool)))
        | ~ class_Orderings_Oorder(X25485) )
      & ( X25483 = X25482
        | c_SetInterval_Oord__class_OatLeastAtMost(X25485,X25484,X25483) != hAPP(hAPP(c_Set_Oinsert(X25485),X25482),c_Orderings_Obot__class_Obot(tc_fun(X25485,tc_HOL_Obool)))
        | ~ class_Orderings_Oorder(X25485) )
      & ( X25484 != X25483
        | X25483 != X25482
        | c_SetInterval_Oord__class_OatLeastAtMost(X25485,X25484,X25483) = hAPP(hAPP(c_Set_Oinsert(X25485),X25482),c_Orderings_Obot__class_Obot(tc_fun(X25485,tc_HOL_Obool)))
        | ~ class_Orderings_Oorder(X25485) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastAtMost__singleton__iff])])]) ).

fof(i_0_9951,plain,
    ! [X33310,X33311,X33312,X33313,X33314] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(X33314),X33313),X33312),X33311),X33310) = c_New__DSequence_Opos__single(X33314,X33313),
    inference(variable_rename,[status(thm)],[fact_pos__single__def]) ).

fof(i_0_9952,plain,
    ! [X33291,X33292,X33293,X33294,X33295] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(X33295),X33294),X33293),X33292),X33291) = c_New__DSequence_Oneg__single(X33295,X33294),
    inference(variable_rename,[status(thm)],[fact_neg__single__def]) ).

fof(i_0_9953,plain,
    ! [X20542,X20543,X20544] :
      ( ~ class_Rings_Olinordered__idom(X20544)
      | hAPP(c_Groups_Oabs__class_Oabs(X20544),hAPP(hAPP(c_Power_Opower__class_Opower(X20544),X20543),X20542)) = hAPP(hAPP(c_Power_Opower__class_Opower(X20544),hAPP(c_Groups_Oabs__class_Oabs(X20544),X20543)),X20542) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__abs])]) ).

fof(i_0_9954,plain,
    ! [X21278,X21279,X21280] :
      ( ~ class_Rings_Odivision__ring(X21280)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X21280),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21280),X21279),X21278)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21280),hAPP(c_Groups_Ouminus__class_Ouminus(X21280),X21279)),X21278) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__divide__left])]) ).

fof(i_0_9955,plain,
    ! [X18182,X18183,X18184] :
      ( ~ class_Rings_Oring(X18184)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X18184),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18184),X18183),X18182)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18184),hAPP(c_Groups_Ouminus__class_Ouminus(X18184),X18183)),X18182) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__mult__left])]) ).

fof(i_0_9956,plain,
    ! [X20665,X20666,X20667,X20668] : hAPP(hAPP(c_Power_Opower_Opower(X20668,X20667,X20666),X20665),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X20667,
    inference(variable_rename,[status(thm)],[fact_power_Opower_Opower__0]) ).

fof(i_0_9957,plain,
    ! [X31917,X31918,X31919] : c_List_Omaps(X31919,X31918,X31917,c_List_Olist_ONil(X31919)) = c_List_Olist_ONil(X31918),
    inference(variable_rename,[status(thm)],[fact_maps__simps_I2_J]) ).

cnf(i_0_9958,plain,
    ( X1 = X2
    | c_Code__Numeral_OSuc__code__numeral(X1) != c_Code__Numeral_OSuc__code__numeral(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5964]) ).

fof(i_0_9959,plain,
    ! [X25471,X25472,X25473] :
      ( ~ class_Orderings_Oorder(X25473)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25473),X25472),X25471))
      | c_SetInterval_Oord__class_OatLeastAtMost(X25473,X25471,X25472) = c_Orderings_Obot__class_Obot(tc_fun(X25473,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastatMost__empty])]) ).

fof(i_0_9960,plain,
    ! [X25311,X25312,X25313] :
      ( ~ class_Orderings_Oorder(X25313)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25313),X25312),X25311))
      | c_SetInterval_Oord__class_OgreaterThanAtMost(X25313,X25311,X25312) = c_Orderings_Obot__class_Obot(tc_fun(X25313,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_greaterThanAtMost__empty])]) ).

fof(i_0_9961,plain,
    ! [X24870,X24871,X24872] :
      ( ~ class_Orderings_Oorder(X24872)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24872),X24871),X24870))
      | c_SetInterval_Oord__class_OgreaterThanLessThan(X24872,X24870,X24871) = c_Orderings_Obot__class_Obot(tc_fun(X24872,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_greaterThanLessThan__empty])]) ).

fof(i_0_9962,plain,
    ! [X29348,X29349,X29350] :
      ( X29350 = c_List_Olist_ONil(X29349)
      | hAPP(c_List_Otl(X29349),hAPP(hAPP(c_List_Oappend(X29349),X29350),X29348)) = hAPP(hAPP(c_List_Oappend(X29349),hAPP(c_List_Otl(X29349),X29350)),X29348) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_tl__append2])]) ).

fof(i_0_9963,plain,
    ! [X19627,X19628] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19628,X19627)),X19627) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[fact_zmod__zdiv__trivial]) ).

fof(i_0_9964,plain,
    ! [X22222,X22223,X22224,X22225] :
      ( ( hAPP(c_Product__Type_Ofst(X22223,X22222),X22225) = hAPP(c_Product__Type_Ofst(X22223,X22222),X22224)
        | X22225 != X22224 )
      & ( hAPP(c_Product__Type_Osnd(X22223,X22222),X22225) = hAPP(c_Product__Type_Osnd(X22223,X22222),X22224)
        | X22225 != X22224 )
      & ( hAPP(c_Product__Type_Ofst(X22223,X22222),X22225) != hAPP(c_Product__Type_Ofst(X22223,X22222),X22224)
        | hAPP(c_Product__Type_Osnd(X22223,X22222),X22225) != hAPP(c_Product__Type_Osnd(X22223,X22222),X22224)
        | X22225 = X22224 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pair__fst__snd__eq])])]) ).

fof(i_0_9965,plain,
    ! [X22218,X22219,X22220,X22221] :
      ( hAPP(c_Product__Type_Ofst(X22221,X22220),X22219) != hAPP(c_Product__Type_Ofst(X22221,X22220),X22218)
      | hAPP(c_Product__Type_Osnd(X22221,X22220),X22219) != hAPP(c_Product__Type_Osnd(X22221,X22220),X22218)
      | X22219 = X22218 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_prod__eqI])]) ).

fof(i_0_9966,plain,
    ! [X27908,X27909] : c_Fun_Oinj__on(X27909,X27909,c_Fun_Oid(X27909),X27908),
    inference(variable_rename,[status(thm)],[fact_inj__on__id]) ).

fof(i_0_9967,plain,
    ! [X25701,X25702] : c_Fun_Oinj__on(X25702,X25702,c_COMBI(X25702),X25701),
    inference(variable_rename,[status(thm)],[fact_inj__on__id2]) ).

fof(i_0_9968,plain,
    ! [X19422,X19423,X19424] :
      ( ~ class_Rings_Olinordered__idom(X19424)
      | c_Groups_Osgn__class_Osgn(X19424,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19424),X19423),X19422)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19424),c_Groups_Osgn__class_Osgn(X19424,X19423)),c_Groups_Osgn__class_Osgn(X19424,X19422)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__times])]) ).

fof(i_0_9969,plain,
    ! [X31483,X31484,X31485] :
      ( ~ class_Orderings_Olinorder(X31485)
      | ~ c_List_Olinorder__class_Osorted(X31485,X31484)
      | ~ hBOOL(hAPP(c_List_Odistinct(X31485),X31484))
      | ~ c_List_Olinorder__class_Osorted(X31485,X31483)
      | ~ hBOOL(hAPP(c_List_Odistinct(X31485),X31483))
      | hAPP(c_List_Oset(X31485),X31484) != hAPP(c_List_Oset(X31485),X31483)
      | X31484 = X31483 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__distinct__set__unique])]) ).

fof(i_0_9970,plain,
    ! [X28854,X28855,X28856,X28857] : hAPP(hAPP(c_List_Odrop(X28857),hAPP(c_Nat_OSuc,X28856)),hAPP(hAPP(c_List_Olist_OCons(X28857),X28855),X28854)) = hAPP(hAPP(c_List_Odrop(X28857),X28856),X28854),
    inference(variable_rename,[status(thm)],[fact_drop__Suc__Cons]) ).

cnf(i_0_9971,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_9972,plain,
    ! [X20231,X20232,X20233] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X20233)
      | hAPP(c_Groups_Oabs__class_Oabs(X20233),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20233),X20232),X20231)) = hAPP(c_Groups_Oabs__class_Oabs(X20233),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20233),X20231),X20232)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__minus__commute])]) ).

cnf(i_0_9973,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_5965]) ).

fof(i_0_9974,plain,
    ! [X21800,X21801,X21802] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X21802,X21801,X21800,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = X21801,
    inference(variable_rename,[status(thm)],[fact_code__numeral_Orecs_I1_J]) ).

fof(i_0_9975,plain,
    ! [X21616,X21617,X21618] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X21618,X21617,X21616,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = X21617,
    inference(variable_rename,[status(thm)],[fact_code__numeral_Osimps_I4_J]) ).

fof(i_0_9976,plain,
    ! [X17597,X17598,X17599] : c_Nat_Onat_Onat__case(X17599,X17598,X17597,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X17598,
    inference(variable_rename,[status(thm)],[fact_nat__case__0]) ).

fof(i_0_9977,plain,
    ! [X19555,X19556] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19556)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19555)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19556),X19555)),
    inference(variable_rename,[status(thm)],[fact_Divides_Otransfer__int__nat__functions_I1_J]) ).

fof(i_0_9978,plain,
    ! [X20490,X20491] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20491)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20490)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20491),X20490)),
    inference(variable_rename,[status(thm)],[fact_times__numeral__code_I5_J]) ).

fof(i_0_9979,plain,
    ! [X18914,X18915] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18915)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18914)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18915),X18914)),
    inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J]) ).

fof(i_0_9980,plain,
    ! [X18910,X18911] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18911)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18910)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18911),X18910)),
    inference(variable_rename,[status(thm)],[fact_zmult__int]) ).

fof(i_0_9981,plain,
    ! [X20488,X20489] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20489)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20488)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20489),X20488)),
    inference(variable_rename,[status(thm)],[fact_plus__numeral__code_I9_J]) ).

fof(i_0_9982,plain,
    ! [X18076,X18077] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18077)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18076)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18077),X18076)),
    inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J]) ).

fof(i_0_9983,plain,
    ! [X17919,X17920] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X17920)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X17919)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17920),X17919)),
    inference(variable_rename,[status(thm)],[fact_zadd__int]) ).

cnf(i_0_9984,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_5966]) ).

fof(i_0_9985,plain,
    ! [X18299,X18300] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18300),X18299)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X18300)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X18299)),
    inference(variable_rename,[status(thm)],[fact_zminus__zadd__distrib]) ).

fof(i_0_9986,plain,
    ! [X19557,X19558] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19558),X19557)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19558)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19557)),
    inference(variable_rename,[status(thm)],[fact_zdiv__int]) ).

fof(i_0_9987,plain,
    ! [X18912,X18913] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18913),X18912)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18913)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18912)),
    inference(variable_rename,[status(thm)],[fact_int__mult]) ).

fof(i_0_9988,plain,
    ! [X33397,X33398,X33399,X33400] :
      ( ( ~ hBOOL(hAPP(X33400,X33399))
        | hAPP(c_List_Ofilter(X33398,X33400),c_List_Oreplicate(X33398,X33397,X33399)) = c_List_Oreplicate(X33398,X33397,X33399) )
      & ( hBOOL(hAPP(X33400,X33399))
        | hAPP(c_List_Ofilter(X33398,X33400),c_List_Oreplicate(X33398,X33397,X33399)) = c_List_Olist_ONil(X33398) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5967])]) ).

fof(i_0_9989,plain,
    ! [X26698,X26699] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26699,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X26699,tc_HOL_Obool))),X26698) = X26698,
    inference(variable_rename,[status(thm)],[fact_Int__UNIV__left]) ).

fof(i_0_9990,plain,
    ! [X22822,X22823] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22823,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X22823,tc_HOL_Obool))),X22822) = X22822,
    inference(variable_rename,[status(thm)],[fact_Un__empty__left]) ).

fof(i_0_9991,plain,
    ! [X19019,X19020] :
      ( ( X19020 = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19020),X19019) != 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)),X19020)) )
      & ( X19019 = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19020),X19019) != 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)),X19020)) )
      & ( X19020 != c_Groups_Oone__class_Oone(tc_Int_Oint)
        | X19019 != c_Groups_Oone__class_Oone(tc_Int_Oint)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19020),X19019) = 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)),X19020)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__zmult__eq__1__iff])])]) ).

cnf(i_0_9992,plain,
    c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls),
    inference(split_conjunct,[status(thm)],[fact_succ__Pls]) ).

fof(i_0_9993,plain,
    ! [X27007,X27008,X27009] : hAPP(c_Finite__Set_Ofold1(X27009,X27008),hAPP(hAPP(c_Set_Oinsert(X27009),X27007),c_Orderings_Obot__class_Obot(tc_fun(X27009,tc_HOL_Obool)))) = X27007,
    inference(variable_rename,[status(thm)],[fact_fold1__singleton]) ).

fof(i_0_9994,plain,
    ! [X29726,X29727,X29728,X29729] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29729)),hAPP(hAPP(c_List_Omap(X29728,X29729),X29727),X29726)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29728)),X29726),
    inference(variable_rename,[status(thm)],[fact_length__map]) ).

fof(i_0_9995,plain,
    ! [X29082,X29083,X29084,X29085] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29085)),hAPP(hAPP(c_List_Olist__update(X29085,X29084),X29083),X29082)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29085)),X29084),
    inference(variable_rename,[status(thm)],[fact_length__list__update]) ).

fof(i_0_9996,plain,
    ! [X17207,X17208] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,X17208,X17207,X17208),
    inference(variable_rename,[status(thm)],[fact_evaln_Oequations_I1_J]) ).

fof(i_0_9997,plain,
    ! [X17168,X17169] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,X17169,X17168,X17169),
    inference(variable_rename,[status(thm)],[fact_evaln_OSkip]) ).

fof(i_0_9998,plain,
    ! [X20200,X20201,X20202] :
      ( ~ class_Rings_Oring__1(X20202)
      | hAPP(c_Int_Oring__1__class_Oof__int(X20202),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X20201),X20200)) = hAPP(hAPP(c_Power_Opower__class_Opower(X20202),hAPP(c_Int_Oring__1__class_Oof__int(X20202),X20201)),X20200) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__power])]) ).

fof(i_0_9999,plain,
    ! [X20534,X20535,X20536] :
      ( ~ class_Rings_Osemiring__1(X20536)
      | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20536),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X20535),X20534)) = hAPP(hAPP(c_Power_Opower__class_Opower(X20536),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20536),X20535)),X20534) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__power])]) ).

fof(i_0_10000,plain,
    ! [X18692,X18693] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X18693),X18692))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18693),X18692)) )
      & ( X18693 != X18692
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18693),X18692)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X18693),X18692))
        | X18693 = X18692
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18693),X18692)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__le])])]) ).

fof(i_0_10001,plain,
    ! [X19122,X19123] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19123),X19122))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19123),X19122)) )
      & ( X19123 != X19122
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19123),X19122)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19123),X19122))
        | X19123 = X19122
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19123),X19122)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__le])])]) ).

fof(i_0_10002,plain,
    ! [X19120,X19121] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19121),X19120))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19121),X19120))
        | X19121 = X19120 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19121),X19120))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19121),X19120)) )
      & ( X19121 != X19120
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19121),X19120)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__eq__less__or__eq])])]) ).

fof(i_0_10003,plain,
    ! [X19116,X19117] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19117),X19116))
      | X19117 = X19116
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19117),X19116)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__neq__implies__less])]) ).

cnf(i_0_10004,plain,
    ( c_List_Oembed__list(c_List_Oreturn__list(X1)) = X1
    | ~ c_List_Onat__list(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5968]) ).

fof(i_0_10005,plain,
    ! [X27003,X27004,X27005,X27006] :
      ( X27006 != c_Finite__Set_Ofold1(X27005,X27004)
      | hAPP(X27006,hAPP(hAPP(c_Set_Oinsert(X27005),X27003),c_Orderings_Obot__class_Obot(tc_fun(X27005,tc_HOL_Obool)))) = X27003 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1__singleton__def])]) ).

fof(i_0_10006,plain,
    ! [X29382,X29383] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29383)),hAPP(c_List_Otl(X29383),X29382)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29383)),X29382)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[fact_length__tl]) ).

fof(i_0_10007,plain,
    ! [X27656,X27657,X27658,X27659,X27660] :
      ( ~ c_Finite__Set_Ofun__left__comm__idem(X27660,X27659,X27658)
      | hAPP(hAPP(X27658,X27657),hAPP(hAPP(X27658,X27657),X27656)) = hAPP(hAPP(X27658,X27657),X27656) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofun__left__idem])]) ).

fof(i_0_10008,plain,
    ! [X23446] : 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)),X23446)),
    inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J]) ).

fof(i_0_10009,plain,
    ! [X25423,X25424] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X25424,X25423))),
    inference(variable_rename,[status(thm)],[fact_finite__atLeastAtMost__int]) ).

fof(i_0_10010,plain,
    ! [X25291,X25292] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X25292,X25291))),
    inference(variable_rename,[status(thm)],[fact_finite__greaterThanAtMost__int]) ).

fof(i_0_10011,plain,
    ! [X24826,X24827] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X24827,X24826))),
    inference(variable_rename,[status(thm)],[fact_finite__greaterThanLessThan__int]) ).

fof(i_0_10012,plain,
    ! [X25421,X25422] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X25422,X25421))),
    inference(variable_rename,[status(thm)],[fact_finite__atLeastAtMost]) ).

fof(i_0_10013,plain,
    ! [X25289,X25290] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X25290,X25289))),
    inference(variable_rename,[status(thm)],[fact_finite__greaterThanAtMost]) ).

fof(i_0_10014,plain,
    ! [X24943,X24944] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X24944,X24943))),
    inference(variable_rename,[status(thm)],[fact_finite__greaterThanLessThan]) ).

fof(i_0_10015,plain,
    ! [X17592] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17592),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
        | X17592 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X17592 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17592),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_10016,plain,
    ! [X26024] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X26024),
    inference(variable_rename,[status(thm)],[fact_inj__Suc]) ).

fof(i_0_10017,plain,
    ! [X19124,X19125] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19125),X19124))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19125),X19124)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I5_J])]) ).

fof(i_0_10018,plain,
    ! [X19118,X19119] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19119),X19118))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19119),X19118)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__le__nat])]) ).

fof(i_0_10019,plain,
    ! [X19114,X19115] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19115),X19114))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19115),X19114)) )
      & ( X19115 != X19114
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19115),X19114)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__or__eq__imp__le])])]) ).

fof(i_0_10020,plain,
    ! [X25797,X25798,X25799] :
      ( ~ class_Orderings_Oorder(X25799)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25799),X25798),X25797))
      | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X25799,X25797),X25798) = c_Orderings_Obot__class_Obot(tc_fun(X25799,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__empty])]) ).

fof(i_0_10021,plain,
    ! [X22275,X22276,X22277] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X22277),X22276),hAPP(c_fequal,X22275)))
        | X22276 = X22275 )
      & ( X22276 != X22275
        | hBOOL(hAPP(hAPP(c_member(X22277),X22276),hAPP(c_fequal,X22275))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__mem])]) ).

fof(i_0_10022,plain,
    ! [X30101,X30102,X30103,X30104] :
      ( X30104 = c_List_Olist_ONil(X30103)
      | c_List_Olast(X30102,hAPP(hAPP(c_List_Omap(X30103,X30102),X30101),X30104)) = hAPP(X30101,c_List_Olast(X30103,X30104)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__map])]) ).

cnf(i_0_10023,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_5969]) ).

fof(i_0_10024,plain,
    ! [X18238,X18239,X18240] :
      ( ~ class_Groups_Ogroup__add(X18240)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18240),hAPP(c_Groups_Ouminus__class_Ouminus(X18240),X18239)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18240),X18239),X18238)) = X18238 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__add__cancel])]) ).

fof(i_0_10025,plain,
    ! [X20763,X20764,X20765,X20766,X20767] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X20764),X20765),X20763))
        | X20763 != c_Orderings_Obot__class_Obot(tc_fun(X20764,tc_HOL_Obool)) )
      & ( X20766 = c_Orderings_Obot__class_Obot(tc_fun(X20767,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_member(X20767),esk75_2(X20766,X20767)),X20766)) ) ),
    inference(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_10026,plain,
    ! [X20757,X20758,X20760,X20761,X20762] :
      ( ( hBOOL(hAPP(hAPP(c_member(X20758),esk74_2(X20757,X20758)),X20757))
        | X20757 = c_Orderings_Obot__class_Obot(tc_fun(X20758,tc_HOL_Obool)) )
      & ( X20760 != c_Orderings_Obot__class_Obot(tc_fun(X20761,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(X20761),X20762),X20760)) ) ),
    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_5970])])])])]) ).

fof(i_0_10027,plain,
    ! [X30448,X30449,X30450] :
      ( hBOOL(hAPP(hAPP(c_member(X30450),X30449),hAPP(c_List_Oset(X30450),X30448)))
      | c_List_Oremove1(X30450,X30449,X30448) = X30448 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5971])]) ).

cnf(i_0_10028,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_5972]) ).

fof(i_0_10029,plain,
    ! [X18437,X18438] :
      ( ~ class_Rings_Oring__1(X18438)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18437))
      | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18438),hAPP(c_Int_Onat,X18437)) = hAPP(c_Int_Oring__1__class_Oof__int(X18438),X18437) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__nat])]) ).

fof(i_0_10030,plain,
    ! [X19415,X19416] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X19416),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X19415)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X19416,X19415)),
    inference(variable_rename,[status(thm)],[fact_zmod__zminus__zminus]) ).

fof(i_0_10031,plain,
    ! [X19635,X19636] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19636),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19635)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19636,X19635)),
    inference(variable_rename,[status(thm)],[fact_Divides_Otransfer__int__nat__functions_I2_J]) ).

fof(i_0_10032,plain,
    ! [X19637,X19638] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19638,X19637)) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19638),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19637)),
    inference(variable_rename,[status(thm)],[fact_zmod__int]) ).

fof(i_0_10033,plain,
    ! [X19282,X19283] :
      ( ( X19282 != c_Groups_Ozero__class_Ozero(X19283)
        | c_Groups_Osgn__class_Osgn(X19283,X19282) = c_Groups_Ozero__class_Ozero(X19283)
        | ~ class_Groups_Osgn__if(X19283) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19283),c_Groups_Ozero__class_Ozero(X19283)),X19282))
        | c_Groups_Osgn__class_Osgn(X19283,X19282) = c_Groups_Oone__class_Oone(X19283)
        | X19282 = c_Groups_Ozero__class_Ozero(X19283)
        | ~ class_Groups_Osgn__if(X19283) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19283),c_Groups_Ozero__class_Ozero(X19283)),X19282))
        | c_Groups_Osgn__class_Osgn(X19283,X19282) = hAPP(c_Groups_Ouminus__class_Ouminus(X19283),c_Groups_Oone__class_Oone(X19283))
        | X19282 = c_Groups_Ozero__class_Ozero(X19283)
        | ~ class_Groups_Osgn__if(X19283) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5973])])]) ).

fof(i_0_10034,plain,
    ! [X29584,X29585] :
      ( ~ class_Groups_Ocomm__monoid__add(X29585)
      | ~ hBOOL(hAPP(c_List_Odistinct(X29585),X29584))
      | hAPP(c_List_Omonoid__add__class_Olistsum(X29585),X29584) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X29585,X29585),c_COMBI(X29585)),hAPP(c_List_Oset(X29585),X29584)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__listsum__conv__Setsum])]) ).

fof(i_0_10035,plain,
    ! [X20339,X20340,X20341] :
      ( ~ class_Rings_Ocomm__semiring__1(X20341)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20341),X20340),hAPP(hAPP(c_Power_Opower__class_Opower(X20341),X20340),X20339)) = hAPP(hAPP(c_Power_Opower__class_Opower(X20341),X20340),hAPP(c_Nat_OSuc,X20339)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J])]) ).

fof(i_0_10036,plain,
    ! [X20569,X20570,X20571] :
      ( ~ class_Power_Opower(X20571)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X20571),X20570),hAPP(c_Nat_OSuc,X20569)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20571),X20570),hAPP(hAPP(c_Power_Opower__class_Opower(X20571),X20570),X20569)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__Suc])]) ).

fof(i_0_10037,plain,
    ! [X20336,X20337,X20338] :
      ( ~ class_Rings_Ocomm__semiring__1(X20338)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X20338),X20337),hAPP(c_Nat_OSuc,X20336)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20338),X20337),hAPP(hAPP(c_Power_Opower__class_Opower(X20338),X20337),X20336)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J])]) ).

fof(i_0_10038,plain,
    ! [X26555,X26556] :
      ( ~ class_Groups_Oordered__ab__group__add(X26556)
      | hAPP(c_Set_Oimage(X26556,X26556,c_Groups_Ouminus__class_Ouminus(X26556)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X26556),X26555)) = hAPP(c_SetInterval_Oord__class_OlessThan(X26556),hAPP(c_Groups_Ouminus__class_Ouminus(X26556),X26555)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__uminus__greaterThan])]) ).

fof(i_0_10039,plain,
    ! [X26413,X26414] :
      ( ~ class_Groups_Oordered__ab__group__add(X26414)
      | hAPP(c_Set_Oimage(X26414,X26414,c_Groups_Ouminus__class_Ouminus(X26414)),hAPP(c_SetInterval_Oord__class_OatLeast(X26414),X26413)) = hAPP(c_SetInterval_Oord__class_OatMost(X26414),hAPP(c_Groups_Ouminus__class_Ouminus(X26414),X26413)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__uminus__atLeast])]) ).

fof(i_0_10040,plain,
    ! [X26553,X26554] :
      ( ~ class_Groups_Oordered__ab__group__add(X26554)
      | hAPP(c_Set_Oimage(X26554,X26554,c_Groups_Ouminus__class_Ouminus(X26554)),hAPP(c_SetInterval_Oord__class_OlessThan(X26554),X26553)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X26554),hAPP(c_Groups_Ouminus__class_Ouminus(X26554),X26553)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__uminus__lessThan])]) ).

fof(i_0_10041,plain,
    ! [X26411,X26412] :
      ( ~ class_Groups_Oordered__ab__group__add(X26412)
      | hAPP(c_Set_Oimage(X26412,X26412,c_Groups_Ouminus__class_Ouminus(X26412)),hAPP(c_SetInterval_Oord__class_OatMost(X26412),X26411)) = hAPP(c_SetInterval_Oord__class_OatLeast(X26412),hAPP(c_Groups_Ouminus__class_Ouminus(X26412),X26411)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__uminus__atMost])]) ).

fof(i_0_10042,plain,
    ! [X33480,X33481,X33482] : c_List_Oreplicate(X33482,hAPP(c_Nat_OSuc,X33481),X33480) = hAPP(hAPP(c_List_Olist_OCons(X33482),X33480),c_List_Oreplicate(X33482,X33481,X33480)),
    inference(variable_rename,[status(thm)],[fact_replicate__Suc]) ).

cnf(i_0_10043,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_5974]) ).

cnf(i_0_10044,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_5975]) ).

cnf(i_0_10045,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_5975]) ).

fof(i_0_10046,plain,
    ! [X19516,X19517] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19517))
        | c_SMT_Oz3mod(X19516,X19517) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X19516,X19517) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19517))
        | c_SMT_Oz3mod(X19516,X19517) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X19516,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X19517)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5976])]) ).

fof(i_0_10047,plain,
    ! [X33496,X33497,X33498] :
      ( X33498 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | hAPP(c_List_Oset(X33497),c_List_Oreplicate(X33497,X33498,X33496)) = hAPP(hAPP(c_Set_Oinsert(X33497),X33496),c_Orderings_Obot__class_Obot(tc_fun(X33497,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__replicate])]) ).

fof(i_0_10048,plain,
    ! [X33493,X33494,X33495] :
      ( ( X33495 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_List_Oset(X33494),c_List_Oreplicate(X33494,X33495,X33493)) = c_Orderings_Obot__class_Obot(tc_fun(X33494,tc_HOL_Obool)) )
      & ( X33495 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_List_Oset(X33494),c_List_Oreplicate(X33494,X33495,X33493)) = hAPP(hAPP(c_Set_Oinsert(X33494),X33493),c_Orderings_Obot__class_Obot(tc_fun(X33494,tc_HOL_Obool))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__replicate__conv__if])]) ).

fof(i_0_10049,plain,
    ! [X20282,X20283] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X20283)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20283),c_Groups_Ozero__class_Ozero(X20283)),X20282))
      | hAPP(c_Groups_Oabs__class_Oabs(X20283),X20282) = X20282 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__nonneg])]) ).

fof(i_0_10050,plain,
    ! [X20288,X20289] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X20289)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20289),c_Groups_Ozero__class_Ozero(X20289)),X20288))
      | hAPP(c_Groups_Oabs__class_Oabs(X20289),X20288) = X20288 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__pos])]) ).

fof(i_0_10051,plain,
    ! [X20432,X20433] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20433),X20432),c_Groups_Ozero__class_Ozero(X20433)))
        | hAPP(c_Groups_Oabs__class_Oabs(X20433),X20432) = hAPP(c_Groups_Ouminus__class_Ouminus(X20433),X20432)
        | ~ class_Groups_Oabs__if(X20433) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20433),X20432),c_Groups_Ozero__class_Ozero(X20433)))
        | hAPP(c_Groups_Oabs__class_Oabs(X20433),X20432) = X20432
        | ~ class_Groups_Oabs__if(X20433) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5977])])]) ).

fof(i_0_10052,plain,
    ! [X20428,X20429] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X20429)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20429),X20428),c_Groups_Ozero__class_Ozero(X20429)))
      | hAPP(c_Groups_Oabs__class_Oabs(X20429),X20428) = hAPP(c_Groups_Ouminus__class_Ouminus(X20429),X20428) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__nonpos])]) ).

fof(i_0_10053,plain,
    ! [X20434,X20435] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X20435)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20435),X20434),c_Groups_Ozero__class_Ozero(X20435)))
      | hAPP(c_Groups_Oabs__class_Oabs(X20435),X20434) = hAPP(c_Groups_Ouminus__class_Ouminus(X20435),X20434) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__neg])]) ).

fof(i_0_10054,plain,
    ! [X19286,X19287] :
      ( ~ class_Rings_Olinordered__idom(X19287)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19287),X19286),c_Groups_Ozero__class_Ozero(X19287)))
      | c_Groups_Osgn__class_Osgn(X19287,X19286) = hAPP(c_Groups_Ouminus__class_Ouminus(X19287),c_Groups_Oone__class_Oone(X19287)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__neg])]) ).

fof(i_0_10055,plain,
    ! [X19284,X19285] :
      ( ( c_Groups_Osgn__class_Osgn(X19285,X19284) != hAPP(c_Groups_Ouminus__class_Ouminus(X19285),c_Groups_Oone__class_Oone(X19285))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19285),X19284),c_Groups_Ozero__class_Ozero(X19285)))
        | ~ class_Rings_Olinordered__idom(X19285) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19285),X19284),c_Groups_Ozero__class_Ozero(X19285)))
        | c_Groups_Osgn__class_Osgn(X19285,X19284) = hAPP(c_Groups_Ouminus__class_Ouminus(X19285),c_Groups_Oone__class_Oone(X19285))
        | ~ class_Rings_Olinordered__idom(X19285) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__1__neg])])]) ).

fof(i_0_10056,plain,
    ! [X33902,X33903,X33904,X33905] :
      ( ~ c_Equiv__Relations_Opart__equivp(X33905,X33904)
      | ~ hBOOL(hAPP(hAPP(X33904,X33903),X33902))
      | hBOOL(hAPP(hAPP(X33904,X33902),X33903)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_part__equivp__symp])]) ).

fof(i_0_10057,plain,
    ! [X33859,X33860,X33861,X33862] :
      ( ~ c_Predicate_Osymp(X33862,X33861)
      | ~ hBOOL(hAPP(hAPP(X33861,X33860),X33859))
      | hBOOL(hAPP(hAPP(X33861,X33859),X33860)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sympE])]) ).

fof(i_0_10058,plain,
    ! [X26894,X26895,X26896,X26897] :
      ( ~ c_Equiv__Relations_Oequivp(X26897,X26896)
      | ~ hBOOL(hAPP(hAPP(X26896,X26895),X26894))
      | hBOOL(hAPP(hAPP(X26896,X26894),X26895)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equivp__symp])]) ).

fof(i_0_10059,plain,
    ! [X29622,X29623] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29623)),c_List_Obutlast(X29623,X29622)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29623)),X29622)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[fact_length__butlast]) ).

fof(i_0_10060,plain,
    ! [X18526] :
      ( ~ class_Rings_Olinordered__semidom(X18526)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18526),c_Groups_Oone__class_Oone(X18526)),c_Groups_Ozero__class_Ozero(X18526))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5978])]) ).

fof(i_0_10061,plain,
    ! [X18726] :
      ( ~ class_Rings_Olinordered__semidom(X18726)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18726),c_Groups_Oone__class_Oone(X18726)),c_Groups_Ozero__class_Ozero(X18726))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5979])]) ).

fof(i_0_10062,plain,
    ! [X20005,X20006] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20006),X20005))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20005),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20006),X20005)) = X20006 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5980])]) ).

fof(i_0_10063,plain,
    ! [X28646,X28647] : hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X28647)),c_List_Olist_ONil(X28647)),c_List_Olists(X28647,X28646))),
    inference(variable_rename,[status(thm)],[fact_lists_ONil]) ).

fof(i_0_10064,plain,
    ! [X19495,X19496] :
      ( ( c_Groups_Osgn__class_Osgn(X19496,X19495) != c_Groups_Oone__class_Oone(X19496)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19496),c_Groups_Ozero__class_Ozero(X19496)),X19495))
        | ~ class_Rings_Olinordered__idom(X19496) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19496),c_Groups_Ozero__class_Ozero(X19496)),X19495))
        | c_Groups_Osgn__class_Osgn(X19496,X19495) = c_Groups_Oone__class_Oone(X19496)
        | ~ class_Rings_Olinordered__idom(X19496) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__1__pos])])]) ).

fof(i_0_10065,plain,
    ! [X19493,X19494] :
      ( ~ class_Rings_Olinordered__idom(X19494)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19494),c_Groups_Ozero__class_Ozero(X19494)),X19493))
      | c_Groups_Osgn__class_Osgn(X19494,X19493) = c_Groups_Oone__class_Oone(X19494) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__pos])]) ).

fof(i_0_10066,plain,
    ! [X21383,X21384,X21385] :
      ( ~ class_Rings_Odivision__ring(X21385)
      | X21384 = c_Groups_Ozero__class_Ozero(X21385)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21385),hAPP(c_Groups_Ouminus__class_Ouminus(X21385),X21383)),hAPP(c_Groups_Ouminus__class_Ouminus(X21385),X21384)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21385),X21383),X21384) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__minus__divide__divide])]) ).

fof(i_0_10067,plain,
    ! [X28668] : c_List_Olists(X28668,c_Orderings_Obot__class_Obot(tc_fun(X28668,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X28668)),c_List_Olist_ONil(X28668)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X28668),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_lists__empty]) ).

fof(i_0_10068,plain,
    ! [X28558] : c_List_Olistset(X28558,c_List_Olist_ONil(tc_fun(X28558,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X28558)),c_List_Olist_ONil(X28558)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X28558),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_listset_Osimps_I1_J]) ).

fof(i_0_10069,plain,
    ! [X27682,X27683,X27684] :
      ( ~ hBOOL(hAPP(X27684,X27683))
      | hBOOL(hAPP(hAPP(c_member(X27682),X27683),hAPP(c_Set_OCollect(X27682),X27684))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_CollectI])]) ).

fof(i_0_10070,plain,
    ! [X31644,X31645] :
      ( ( ~ hBOOL(hAPP(c_List_Odistinct(X31645),hAPP(c_List_Orev(X31645),X31644)))
        | hBOOL(hAPP(c_List_Odistinct(X31645),X31644)) )
      & ( ~ hBOOL(hAPP(c_List_Odistinct(X31645),X31644))
        | hBOOL(hAPP(c_List_Odistinct(X31645),hAPP(c_List_Orev(X31645),X31644))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__rev])]) ).

fof(i_0_10071,plain,
    ! [X29316,X29317] :
      ( ( ~ hBOOL(hAPP(c_List_Odistinct(X29317),hAPP(c_List_Orotate1(X29317),X29316)))
        | hBOOL(hAPP(c_List_Odistinct(X29317),X29316)) )
      & ( ~ hBOOL(hAPP(c_List_Odistinct(X29317),X29316))
        | hBOOL(hAPP(c_List_Odistinct(X29317),hAPP(c_List_Orotate1(X29317),X29316))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct1__rotate])]) ).

fof(i_0_10072,plain,
    ! [X23996,X23997] : hAPP(hAPP(c_Equiv__Relations_Oquotient(X23997),c_Orderings_Obot__class_Obot(tc_fun(X23997,tc_HOL_Obool))),X23996) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X23997,tc_HOL_Obool),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_quotient__empty]) ).

fof(i_0_10073,plain,
    ! [X27960,X27961] : hAPP(c_Product__Type_Oprod_Oprod__case(X27961,X27960,tc_prod(X27961,X27960)),c_Product__Type_OPair(X27961,X27960)) = c_Fun_Oid(tc_prod(X27961,X27960)),
    inference(variable_rename,[status(thm)],[fact_split__Pair]) ).

fof(i_0_10074,plain,
    ! [X23767,X23768,X23769] :
      ( ~ class_Lattices_Osemilattice__inf(X23769)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23769),X23768),X23767))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23769),X23768),X23767) = X23768 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__absorb1])]) ).

fof(i_0_10075,plain,
    ! [X23752,X23753,X23754] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23754),X23753),X23752))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23754),X23753),X23752) = X23753
        | ~ class_Lattices_Osemilattice__inf(X23754) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23754),X23753),X23752) != X23753
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23754),X23753),X23752))
        | ~ class_Lattices_Osemilattice__inf(X23754) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__iff__inf])])]) ).

fof(i_0_10076,plain,
    ! [X23770,X23771,X23772] :
      ( ~ class_Lattices_Osemilattice__inf(X23772)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23772),X23771),X23770))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23772),X23770),X23771) = X23771 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__absorb2])]) ).

fof(i_0_10077,plain,
    ! [X22871,X22872,X22873] :
      ( ~ class_Lattices_Osemilattice__sup(X22873)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22873),X22872),X22871))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X22873),X22872),X22871) = X22871 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__absorb2])]) ).

fof(i_0_10078,plain,
    ! [X22856,X22857,X22858] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22858),X22857),X22856))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X22858),X22857),X22856) = X22856
        | ~ class_Lattices_Osemilattice__sup(X22858) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X22858),X22857),X22856) != X22856
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22858),X22857),X22856))
        | ~ class_Lattices_Osemilattice__sup(X22858) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__iff__sup])])]) ).

fof(i_0_10079,plain,
    ! [X22874,X22875,X22876] :
      ( ~ class_Lattices_Osemilattice__sup(X22876)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22876),X22875),X22874))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X22876),X22874),X22875) = X22874 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__absorb1])]) ).

fof(i_0_10080,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),X22584),X22583) = X22583 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__absorb2])]) ).

fof(i_0_10081,plain,
    ! [X22568,X22569,X22570] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22570),X22569),X22568))
        | hAPP(hAPP(c_Orderings_Oord__class_Omax(X22570),X22569),X22568) = X22568
        | ~ class_Orderings_Olinorder(X22570) )
      & ( hAPP(hAPP(c_Orderings_Oord__class_Omax(X22570),X22569),X22568) != X22568
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22570),X22569),X22568))
        | ~ class_Orderings_Olinorder(X22570) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__iff__sup])])]) ).

fof(i_0_10082,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),X22586),X22587) = X22586 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__absorb1])]) ).

fof(i_0_10083,plain,
    ! [X22484,X22485,X22486] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22486),X22485),X22484))
        | hAPP(hAPP(c_Orderings_Oord__class_Omin(X22486),X22485),X22484) = X22485
        | ~ class_Orderings_Olinorder(X22486) )
      & ( hAPP(hAPP(c_Orderings_Oord__class_Omin(X22486),X22485),X22484) != X22485
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22486),X22485),X22484))
        | ~ class_Orderings_Olinorder(X22486) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__iff__inf])])]) ).

fof(i_0_10084,plain,
    ! [X22469,X22470,X22471] :
      ( ~ class_Orderings_Olinorder(X22471)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22471),X22470),X22469))
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X22471),X22470),X22469) = X22470 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__absorb1])]) ).

fof(i_0_10085,plain,
    ! [X22466,X22467,X22468] :
      ( ~ class_Orderings_Olinorder(X22468)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22468),X22467),X22466))
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X22468),X22466),X22467) = X22467 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__absorb2])]) ).

fof(i_0_10086,plain,
    ! [X31036,X31037] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X31037)
      | c_Complete__Lattice_OInf__class_OInf(X31037,hAPP(hAPP(c_Set_Oinsert(X31037),X31036),c_Orderings_Obot__class_Obot(tc_fun(X31037,tc_HOL_Obool)))) = X31036 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__singleton])]) ).

fof(i_0_10087,plain,
    ! [X30906,X30907] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X30907)
      | c_Complete__Lattice_OSup__class_OSup(X30907,hAPP(hAPP(c_Set_Oinsert(X30907),X30906),c_Orderings_Obot__class_Obot(tc_fun(X30907,tc_HOL_Obool)))) = X30906 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__singleton])]) ).

fof(i_0_10088,plain,
    ! [X24357,X24358] :
      ( ~ class_Orderings_Olinorder(X24358)
      | c_Big__Operators_Olinorder__class_OMin(X24358,hAPP(hAPP(c_Set_Oinsert(X24358),X24357),c_Orderings_Obot__class_Obot(tc_fun(X24358,tc_HOL_Obool)))) = X24357 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Osingleton])]) ).

fof(i_0_10089,plain,
    ! [X24250,X24251] :
      ( ~ class_Orderings_Olinorder(X24251)
      | c_Big__Operators_Olinorder__class_OMax(X24251,hAPP(hAPP(c_Set_Oinsert(X24251),X24250),c_Orderings_Obot__class_Obot(tc_fun(X24251,tc_HOL_Obool)))) = X24250 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Osingleton])]) ).

fof(i_0_10090,plain,
    ! [X24254,X24255] :
      ( ~ class_Lattices_Olattice(X24255)
      | c_Big__Operators_Olattice__class_OSup__fin(X24255,hAPP(hAPP(c_Set_Oinsert(X24255),X24254),c_Orderings_Obot__class_Obot(tc_fun(X24255,tc_HOL_Obool)))) = X24254 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Osingleton])]) ).

fof(i_0_10091,plain,
    ! [X24252,X24253] :
      ( ~ class_Lattices_Olattice(X24253)
      | c_Big__Operators_Olattice__class_OInf__fin(X24253,hAPP(hAPP(c_Set_Oinsert(X24253),X24252),c_Orderings_Obot__class_Obot(tc_fun(X24253,tc_HOL_Obool)))) = X24252 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Osingleton])]) ).

fof(i_0_10092,plain,
    ! [X18869,X18870] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X18870)),X18869) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18869),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18870),X18869)),
    inference(variable_rename,[status(thm)],[fact_mult__Suc]) ).

fof(i_0_10093,plain,
    ! [X16965,X16966,X16967,X16968] :
      ( ~ c_Hoare__Mirabelle_Ohoare__derivs(X16968,X16967,X16966)
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(X16968,X16965,X16967)
      | c_Hoare__Mirabelle_Ohoare__derivs(X16968,X16965,X16966) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_cut])]) ).

cnf(i_0_10094,plain,
    ( c_Int_OBit1(X1) = c_Int_OMin
    | X1 != c_Int_OMin ),
    inference(split_conjunct,[status(thm)],[i_0_5908]) ).

cnf(i_0_10095,plain,
    ( c_Int_OMin = c_Int_OBit1(X1)
    | c_Int_OMin != X1 ),
    inference(split_conjunct,[status(thm)],[i_0_5907]) ).

cnf(i_0_10096,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_5761]) ).

fof(i_0_10097,plain,
    ! [X19901,X19902] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19902),X19901)),X19902) = X19901,
    inference(variable_rename,[status(thm)],[fact_diff__add__inverse]) ).

fof(i_0_10098,plain,
    ! [X19899,X19900] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19900),X19899)),X19899) = X19900,
    inference(variable_rename,[status(thm)],[fact_diff__add__inverse2]) ).

fof(i_0_10099,plain,
    ! [X33509,X33510,X33511,X33512] : hAPP(c_New__DSequence_Opos__union(X33512,X33511,X33510),X33509) = c_Lazy__Sequence_Oappend(X33512,hAPP(X33511,X33509),hAPP(X33510,X33509)),
    inference(variable_rename,[status(thm)],[fact_New__DSequence_Opos__union__def]) ).

fof(i_0_10100,plain,
    ! [X30798,X30799,X30800] :
      ( ~ c_Equiv__Relations_Oequiv(X30800,X30799,X30798)
      | c_Complete__Lattice_OSup__class_OSup(tc_fun(X30800,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(X30800),X30799),X30798)) = X30799 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Union__quotient])]) ).

fof(i_0_10101,plain,
    ! [X21275,X21276,X21277] :
      ( ~ class_Fields_Ofield__inverse__zero(X21277)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21277),hAPP(c_Groups_Ouminus__class_Ouminus(X21277),X21276)),hAPP(c_Groups_Ouminus__class_Ouminus(X21277),X21275)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21277),X21276),X21275) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__divide__divide])]) ).

fof(i_0_10102,plain,
    ! [X20226,X20227] :
      ( ~ class_Rings_Olinordered__idom(X20227)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20227),hAPP(c_Groups_Oabs__class_Oabs(X20227),X20226)),hAPP(c_Groups_Oabs__class_Oabs(X20227),X20226)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20227),X20226),X20226) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__mult__self])]) ).

fof(i_0_10103,plain,
    ! [X18155,X18156,X18157] :
      ( ~ class_Rings_Oring(X18157)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18157),hAPP(c_Groups_Ouminus__class_Ouminus(X18157),X18156)),hAPP(c_Groups_Ouminus__class_Ouminus(X18157),X18155)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18157),X18156),X18155) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__mult__minus])]) ).

fof(i_0_10104,plain,
    ! [X18161,X18162,X18163] :
      ( ~ class_Rings_Oring(X18163)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18163),hAPP(c_Groups_Ouminus__class_Ouminus(X18163),X18162)),X18161) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18163),X18162),hAPP(c_Groups_Ouminus__class_Ouminus(X18163),X18161)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__mult__commute])]) ).

fof(i_0_10105,plain,
    ! [X31983,X31984,X31985,X31986,X31987] :
      ( ( ~ c_Wellfounded_OwfP(X31984,X31983)
        | hBOOL(hAPP(c_Wellfounded_Oaccp(X31984,X31983),X31985)) )
      & ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X31987,X31986),esk414_2(X31986,X31987)))
        | c_Wellfounded_OwfP(X31987,X31986) ) ),
    inference(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_10106,plain,
    ! [X21386,X21387,X21388] :
      ( ~ class_Rings_Odivision__ring(X21388)
      | X21387 = c_Groups_Ozero__class_Ozero(X21388)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X21388),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21388),X21386),X21387)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21388),X21386),hAPP(c_Groups_Ouminus__class_Ouminus(X21388),X21387)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__minus__divide__right])]) ).

cnf(i_0_10107,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_5981]) ).

fof(i_0_10108,plain,
    ! [X23998,X23999,X24000] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X24000,tc_HOL_Obool),tc_HOL_Obool)) != hAPP(hAPP(c_Equiv__Relations_Oquotient(X24000),X23999),X23998)
        | X23999 = c_Orderings_Obot__class_Obot(tc_fun(X24000,tc_HOL_Obool)) )
      & ( X23999 != c_Orderings_Obot__class_Obot(tc_fun(X24000,tc_HOL_Obool))
        | c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X24000,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(X24000),X23999),X23998) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_quotient__is__empty2])]) ).

fof(i_0_10109,plain,
    ! [X24001,X24002,X24003] :
      ( ( hAPP(hAPP(c_Equiv__Relations_Oquotient(X24003),X24002),X24001) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X24003,tc_HOL_Obool),tc_HOL_Obool))
        | X24002 = c_Orderings_Obot__class_Obot(tc_fun(X24003,tc_HOL_Obool)) )
      & ( X24002 != c_Orderings_Obot__class_Obot(tc_fun(X24003,tc_HOL_Obool))
        | hAPP(hAPP(c_Equiv__Relations_Oquotient(X24003),X24002),X24001) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X24003,tc_HOL_Obool),tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_quotient__is__empty])]) ).

fof(i_0_10110,plain,
    ! [X25351,X25352] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X25352,X25351)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X25351),X25352)),
    inference(variable_rename,[status(thm)],[fact_card__greaterThanAtMost__int]) ).

fof(i_0_10111,plain,
    ! [X17408,X17409,X17410] :
      ( ( X17409 = X17408
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17410),X17409),X17408))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17410),X17408),X17409))
        | ~ class_Orderings_Olinorder(X17410) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17410),X17409),X17408))
        | X17409 != X17408
        | ~ class_Orderings_Olinorder(X17410) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17410),X17408),X17409))
        | X17409 != X17408
        | ~ class_Orderings_Olinorder(X17410) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__neq__iff])])]) ).

fof(i_0_10112,plain,
    ! [X17803,X17804,X17805] :
      ( ~ class_Rings_Olinordered__idom(X17805)
      | X17804 = X17803
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17805),X17804),X17803))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17805),X17803),X17804)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5982])]) ).

fof(i_0_10113,plain,
    ! [X17402,X17403,X17404] :
      ( ~ class_Orderings_Olinorder(X17404)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17404),X17403),X17402))
      | X17403 = X17402
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17404),X17402),X17403)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__less__linear])]) ).

fof(i_0_10114,plain,
    ! [X17399,X17400,X17401] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17401),X17399),X17400))
        | X17399 = X17400
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17401),X17400),X17399))
        | ~ class_Orderings_Olinorder(X17401) )
      & ( X17399 != X17400
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17401),X17399),X17400))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17401),X17400),X17399))
        | ~ class_Orderings_Olinorder(X17401) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5983])])]) ).

fof(i_0_10115,plain,
    ! [X17396,X17397,X17398] :
      ( ~ class_Orderings_Olinorder(X17398)
      | X17397 = X17396
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17398),X17397),X17396))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17398),X17396),X17397)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5984])]) ).

fof(i_0_10116,plain,
    ! [X17345,X17346,X17347] :
      ( ~ class_Orderings_Olinorder(X17347)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17347),X17346),X17345))
      | X17346 = X17345
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17347),X17345),X17346)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5985])]) ).

fof(i_0_10117,plain,
    ! [X19320,X19321,X19322] :
      ( ~ class_Divides_Osemiring__div(X19322)
      | c_Divides_Odiv__class_Omod(X19322,c_Divides_Odiv__class_Omod(X19322,X19321,X19320),X19320) = c_Divides_Odiv__class_Omod(X19322,X19321,X19320) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mod__trivial])]) ).

fof(i_0_10118,plain,
    ! [X23821,X23822] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23822,tc_HOL_Obool)),X23821),c_Orderings_Obot__class_Obot(tc_fun(X23822,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X23822,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Int__empty__right]) ).

fof(i_0_10119,plain,
    ! [X26696,X26697] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26697,tc_HOL_Obool)),X26696),c_Orderings_Otop__class_Otop(tc_fun(X26697,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X26697,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Un__UNIV__right]) ).

fof(i_0_10120,plain,
    ! [X26722,X26723] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26723,tc_HOL_Obool)),X26722),c_Orderings_Otop__class_Otop(tc_fun(X26723,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X26723,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Diff__UNIV]) ).

fof(i_0_10121,plain,
    ! [X30864,X30865] : hAPP(c_Relation_ODomain(X30865,X30864),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X30865,X30864),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X30865,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Domain__empty]) ).

fof(i_0_10122,plain,
    ! [X28265,X28266] : hAPP(c_Relation_ORange(X28266,X28265),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X28266,X28265),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X28265,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Range__empty]) ).

fof(i_0_10123,plain,
    ! [X22214,X22215,X22216,X22217] : hAPP(c_Product__Type_Ofst(X22217,X22216),hAPP(hAPP(c_Product__Type_OPair(X22217,X22216),X22215),X22214)) = X22215,
    inference(variable_rename,[status(thm)],[fact_fst__conv]) ).

fof(i_0_10124,plain,
    ! [X22149,X22150,X22151,X22152] : hAPP(c_Product__Type_Osnd(X22152,X22151),hAPP(hAPP(c_Product__Type_OPair(X22152,X22151),X22150),X22149)) = X22149,
    inference(variable_rename,[status(thm)],[fact_snd__conv]) ).

cnf(i_0_10125,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_10126,plain,
    ! [X19151,X19152,X19154,X19155,X19156] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19152),X19151))
        | X19151 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19152),esk49_2(X19151,X19152)) )
      & ( X19154 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19155),X19156)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19155),X19154)) ) ),
    inference(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_10127,plain,
    ! [X20789,X20790,X20791] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X20791),X20790),X20789))
      | hAPP(hAPP(c_Set_Oinsert(X20791),X20790),X20789) = X20789 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__absorb])]) ).

fof(i_0_10128,plain,
    ! [X17047,X17048] : c_Set_Othe__elem(X17048,hAPP(hAPP(c_Set_Oinsert(X17048),X17047),c_Orderings_Obot__class_Obot(tc_fun(X17048,tc_HOL_Obool)))) = X17047,
    inference(variable_rename,[status(thm)],[fact_the__elem__eq]) ).

fof(i_0_10129,plain,
    ! [X18513,X18514,X18515] :
      ( ~ class_Orderings_Olinorder(X18515)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18515),X18514),X18513))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18515),X18513),X18514)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5986])]) ).

fof(i_0_10130,plain,
    ! [X18461,X18462,X18463] :
      ( ~ class_Orderings_Olinorder(X18463)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18463),X18462),X18461))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18463),X18461),X18462)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__linear])]) ).

fof(i_0_10131,plain,
    ! [X18569,X18570,X18571] :
      ( ~ class_Orderings_Olinorder(X18571)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18571),X18570),X18569))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18571),X18569),X18570)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5987])]) ).

fof(i_0_10132,plain,
    ! [X18572,X18573,X18574] :
      ( ~ class_Orderings_Olinorder(X18574)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18574),X18573),X18572))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18574),X18572),X18573)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5988])]) ).

fof(i_0_10133,plain,
    ! [X18557,X18558,X18559] :
      ( ~ class_Orderings_Olinorder(X18559)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18559),X18558),X18557))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18559),X18557),X18558)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__le__less__linear])]) ).

cnf(i_0_10134,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_5989]) ).

cnf(i_0_10135,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_5990]) ).

fof(i_0_10136,plain,
    ! [X29570,X29571,X29572] :
      ( ~ class_Groups_Omonoid__add(X29572)
      | hAPP(c_List_Omonoid__add__class_Olistsum(X29572),hAPP(hAPP(c_List_Olist_OCons(X29572),X29571),X29570)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X29572),X29571),hAPP(c_List_Omonoid__add__class_Olistsum(X29572),X29570)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__simps_I2_J])]) ).

fof(i_0_10137,plain,
    ! [X21272,X21273,X21274] :
      ( ~ class_Fields_Ofield__inverse__zero(X21274)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X21274),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21274),X21273),X21272)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21274),X21273),hAPP(c_Groups_Ouminus__class_Ouminus(X21274),X21272)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__divide__right])]) ).

fof(i_0_10138,plain,
    ! [X18185,X18186,X18187] :
      ( ~ class_Rings_Oring(X18187)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X18187),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18187),X18186),X18185)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18187),X18186),hAPP(c_Groups_Ouminus__class_Ouminus(X18187),X18185)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__mult__right])]) ).

fof(i_0_10139,plain,
    ! [X30485,X30486] : c_List_Opartition(X30486,X30485,c_List_Olist_ONil(X30486)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30486),tc_List_Olist(X30486)),c_List_Olist_ONil(X30486)),c_List_Olist_ONil(X30486)),
    inference(variable_rename,[status(thm)],[fact_partition_Osimps_I1_J]) ).

cnf(i_0_10140,plain,
    c_Int_Osucc(c_Int_Opred(X1)) = X1,
    inference(split_conjunct,[status(thm)],[i_0_5991]) ).

fof(i_0_10141,plain,
    ! [X28794,X28795,X28796] : hAPP(hAPP(c_List_Otake(X28796),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(X28796),X28795),X28794)) = hAPP(hAPP(c_List_Olist_OCons(X28796),X28795),c_List_Olist_ONil(X28796)),
    inference(variable_rename,[status(thm)],[fact_take__1__Cons]) ).

fof(i_0_10142,plain,
    ! [X33890,X33891,X33892,X33893] :
      ( ~ c_Relation_Osym(X33893,X33892)
      | c_Relation_Osym(X33891,hAPP(hAPP(c_Relation_Oinv__image(X33893,X33891),X33892),X33890)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sym__inv__image])]) ).

fof(i_0_10143,plain,
    ! [X33798,X33799,X33800,X33801] :
      ( ~ c_Relation_Otrans(X33801,X33800)
      | c_Relation_Otrans(X33799,hAPP(hAPP(c_Relation_Oinv__image(X33801,X33799),X33800),X33798)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__inv__image])]) ).

fof(i_0_10144,plain,
    ! [X28107,X28108,X28109,X28110] :
      ( ~ c_Wellfounded_Owf(X28110,X28109)
      | c_Wellfounded_Owf(X28108,hAPP(hAPP(c_Relation_Oinv__image(X28110,X28108),X28109),X28107)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__inv__image])]) ).

fof(i_0_10145,plain,
    ! [X23079,X23080,X23081,X23082] :
      ( ~ c_FunDef_Oreduction__pair(X23082,X23081)
      | c_FunDef_Oreduction__pair(X23080,hAPP(hAPP(c_FunDef_Orp__inv__image(X23082,X23080),X23081),X23079)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rp__inv__image__rp])]) ).

fof(i_0_10146,plain,
    ! [X19339,X19340,X19341] :
      ( ~ class_Divides_Osemiring__div(X19341)
      | c_Divides_Odiv__class_Omod(X19341,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19341),X19340),X19339),X19340) = c_Divides_Odiv__class_Omod(X19341,X19339,X19340) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__self1])]) ).

fof(i_0_10147,plain,
    ! [X19336,X19337,X19338] :
      ( ~ class_Divides_Osemiring__div(X19338)
      | c_Divides_Odiv__class_Omod(X19338,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19338),X19337),X19336),X19336) = c_Divides_Odiv__class_Omod(X19338,X19337,X19336) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__self2])]) ).

fof(i_0_10148,plain,
    ! [X28868,X28869,X28870,X28871,X28872] :
      ( hAPP(hAPP(c_List_Odrop(X28872),X28871),X28870) != hAPP(hAPP(c_List_Olist_OCons(X28872),X28869),X28868)
      | hAPP(hAPP(c_List_Onth(X28872),X28870),X28871) = X28869 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__via__drop])]) ).

fof(i_0_10149,plain,
    ! [X22612,X22613] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X22613)),hAPP(c_Nat_OSuc,X22612)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X22613),X22612)),
    inference(variable_rename,[status(thm)],[fact_max__Suc__Suc]) ).

fof(i_0_10150,plain,
    ! [X22391,X22392] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X22392)),hAPP(c_Nat_OSuc,X22391)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X22392),X22391)),
    inference(variable_rename,[status(thm)],[fact_min__Suc__Suc]) ).

fof(i_0_10151,plain,
    ! [X30268,X30269] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X30269)),hAPP(c_Code__Numeral_Oof__nat,X30268)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30269),X30268)),
    inference(variable_rename,[status(thm)],[fact_times__code__numeral__code]) ).

fof(i_0_10152,plain,
    ! [X30287,X30288] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X30288)),hAPP(c_Code__Numeral_Oof__nat,X30287)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30288),X30287)),
    inference(variable_rename,[status(thm)],[fact_plus__code__numeral__code]) ).

fof(i_0_10153,plain,
    ! [X20510,X20511] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20511)),X20510) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X20511),X20510)),
    inference(variable_rename,[status(thm)],[fact_zpower__int]) ).

fof(i_0_10154,plain,
    ! [X20506,X20507] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20507)),X20506) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X20507),X20506)),
    inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J]) ).

fof(i_0_10155,plain,
    ! [X18164,X18165] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X18165)),X18164) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X18165),X18164)),
    inference(variable_rename,[status(thm)],[fact_zmult__zminus]) ).

fof(i_0_10156,plain,
    ! [X20508,X20509] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X20509),X20508)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20509)),X20508),
    inference(variable_rename,[status(thm)],[fact_int__power]) ).

fof(i_0_10157,plain,
    ! [X31132,X31133,X31134] : hAPP(c_List_Oset(X31134),c_List_Oinsert(X31134,X31133,X31132)) = hAPP(hAPP(c_Set_Oinsert(X31134),X31133),hAPP(c_List_Oset(X31134),X31132)),
    inference(variable_rename,[status(thm)],[fact_List_Oset__insert]) ).

cnf(i_0_10158,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_5992]) ).

fof(i_0_10159,plain,
    ! [X33327,X33328,X33329] : c_List_Osplice(X33329,hAPP(hAPP(c_List_Olist_OCons(X33329),X33328),X33327),c_List_Olist_ONil(X33329)) = hAPP(hAPP(c_List_Olist_OCons(X33329),X33328),X33327),
    inference(variable_rename,[status(thm)],[fact_splice_Osimps_I2_J]) ).

fof(i_0_10160,plain,
    ! [X20286,X20287] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X20287)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20287),c_Groups_Ozero__class_Ozero(X20287)),hAPP(c_Groups_Oabs__class_Oabs(X20287),X20286))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__ge__zero])]) ).

fof(i_0_10161,plain,
    ! [X18848,X18849] :
      ( ~ class_Rings_Olinordered__semidom(X18849)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18849),c_Groups_Ozero__class_Ozero(X18849)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18849),X18848))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__imp__of__nat])]) ).

fof(i_0_10162,plain,
    ! [X18846,X18847] :
      ( ~ class_Rings_Olinordered__semidom(X18847)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18847),c_Groups_Ozero__class_Ozero(X18847)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18847),X18846))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__0__le__iff])]) ).

fof(i_0_10163,plain,
    ! [X23894,X23895,X23896] :
      ( ~ class_Lattices_Osemilattice__inf(X23896)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23896),X23895),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23896),X23895),X23894)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23896),X23895),X23894) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf_Oleft__idem])]) ).

fof(i_0_10164,plain,
    ! [X23888,X23889,X23890] :
      ( ~ class_Lattices_Osemilattice__inf(X23890)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23890),X23889),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23890),X23889),X23888)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23890),X23889),X23888) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__left__idem])]) ).

fof(i_0_10165,plain,
    ! [X23891,X23892,X23893] :
      ( ~ class_Lattices_Olattice(X23893)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23893),X23892),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23893),X23892),X23891)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23893),X23892),X23891) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I4_J])]) ).

fof(i_0_10166,plain,
    ! [X22994,X22995,X22996] :
      ( ~ class_Lattices_Olattice(X22996)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X22996),X22995),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X22996),X22995),X22994)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X22996),X22995),X22994) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I8_J])]) ).

fof(i_0_10167,plain,
    ! [X22997,X22998,X22999] :
      ( ~ class_Lattices_Osemilattice__sup(X22999)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X22999),X22998),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X22999),X22998),X22997)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X22999),X22998),X22997) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__left__idem])]) ).

fof(i_0_10168,plain,
    ! [X22991,X22992,X22993] :
      ( ~ class_Lattices_Osemilattice__sup(X22993)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X22993),X22992),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X22993),X22992),X22991)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X22993),X22992),X22991) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup_Oleft__idem])]) ).

fof(i_0_10169,plain,
    ! [X22645,X22646,X22647] :
      ( ~ class_Orderings_Olinorder(X22647)
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X22647),X22646),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22647),X22646),X22645)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X22647),X22646),X22645) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__left__idem])]) ).

fof(i_0_10170,plain,
    ! [X22642,X22643,X22644] :
      ( ~ class_Orderings_Olinorder(X22644)
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X22644),X22643),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22644),X22643),X22642)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X22644),X22643),X22642) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup_Oleft__idem])]) ).

fof(i_0_10171,plain,
    ! [X22412,X22413,X22414] :
      ( ~ class_Orderings_Olinorder(X22414)
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X22414),X22413),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22414),X22413),X22412)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X22414),X22413),X22412) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf_Oleft__idem])]) ).

fof(i_0_10172,plain,
    ! [X22409,X22410,X22411] :
      ( ~ class_Orderings_Olinorder(X22411)
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X22411),X22410),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22411),X22410),X22409)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X22411),X22410),X22409) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__left__idem])]) ).

fof(i_0_10173,plain,
    ! [X19475,X19476,X19477] :
      ( ~ class_Lattices_Oab__semigroup__idem__mult(X19477)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19477),X19476),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19477),X19476),X19475)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19477),X19476),X19475) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__idem])]) ).

fof(i_0_10174,plain,
    ! [X32092,X32093,X32095] :
      ( ( hAPP(c_List_Oset(X32093),esk432_2(X32092,X32093)) = X32092
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32093),X32092))
        | ~ class_Orderings_Olinorder(X32093) )
      & ( c_List_Olinorder__class_Osorted(X32093,esk432_2(X32092,X32093))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32093),X32092))
        | ~ class_Orderings_Olinorder(X32093) )
      & ( hBOOL(hAPP(c_List_Odistinct(X32093),esk432_2(X32092,X32093)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32093),X32092))
        | ~ class_Orderings_Olinorder(X32093) )
      & ( hAPP(c_List_Oset(X32093),X32095) != X32092
        | ~ c_List_Olinorder__class_Osorted(X32093,X32095)
        | ~ hBOOL(hAPP(c_List_Odistinct(X32093),X32095))
        | X32095 = esk432_2(X32092,X32093)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32093),X32092))
        | ~ class_Orderings_Olinorder(X32093) ) ),
    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_10175,plain,
    ! [X29321,X29322,X29323] : hAPP(hAPP(c_List_Odrop(X29323),X29322),hAPP(c_List_Otl(X29323),X29321)) = hAPP(c_List_Otl(X29323),hAPP(hAPP(c_List_Odrop(X29323),X29322),X29321)),
    inference(variable_rename,[status(thm)],[fact_drop__tl]) ).

fof(i_0_10176,plain,
    ! [X29324,X29325,X29326] : hAPP(c_List_Otl(X29326),hAPP(hAPP(c_List_Odrop(X29326),X29325),X29324)) = hAPP(hAPP(c_List_Odrop(X29326),X29325),hAPP(c_List_Otl(X29326),X29324)),
    inference(variable_rename,[status(thm)],[fact_tl__drop]) ).

fof(i_0_10177,plain,
    ! [X28847,X28848,X28849] : hAPP(c_List_Oset(X28849),hAPP(hAPP(c_List_Olist_OCons(X28849),X28848),X28847)) = hAPP(hAPP(c_Set_Oinsert(X28849),X28848),hAPP(c_List_Oset(X28849),X28847)),
    inference(variable_rename,[status(thm)],[fact_List_Oset_Osimps_I2_J]) ).

fof(i_0_10178,plain,
    ! [X25508,X25509] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X25509,X25508)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X25508)),X25509),
    inference(variable_rename,[status(thm)],[fact_card__atLeastAtMost]) ).

fof(i_0_10179,plain,
    ! [X20771,X20772,X20773] :
      ( X20773 != c_Orderings_Obot__class_Obot(tc_fun(X20772,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_member(X20772),X20771),X20773)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5993])]) ).

fof(i_0_10180,plain,
    ! [X27945] : hAPP(c_Set_Oimage(X27945,X27945,c_Fun_Oid(X27945)),c_Orderings_Otop__class_Otop(tc_fun(X27945,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X27945,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_surj__id]) ).

fof(i_0_10181,plain,
    ! [X30258,X30259,X30261,X30262,X30263] :
      ( ( ~ hBOOL(hAPP(X30259,c_Hilbert__Choice_OEps(X30258,X30259)))
        | hBOOL(hAPP(X30259,esk359_2(X30258,X30259))) )
      & ( ~ hBOOL(hAPP(X30262,X30263))
        | hBOOL(hAPP(X30262,c_Hilbert__Choice_OEps(X30261,X30262))) ) ),
    inference(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_10182,plain,
    ! [X31152,X31153,X31154] : hAPP(c_Product__Type_Ofst(tc_List_Olist(X31154),tc_List_Olist(X31154)),c_List_Opartition(X31154,X31153,X31152)) = hAPP(c_List_Ofilter(X31154,X31153),X31152),
    inference(variable_rename,[status(thm)],[fact_partition__filter1]) ).

fof(i_0_10183,plain,
    ! [X20649] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,X20649))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20649)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20649))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X20649)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5994])]) ).

fof(i_0_10184,plain,
    ! [X34091] :
      ( X34091 = hAPP(c_Code__Numeral_Oof__nat,esk564_1(X34091))
      & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk564_1(X34091)),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_5995])])]) ).

fof(i_0_10185,plain,
    ! [X26658,X26659] : hBOOL(hAPP(hAPP(c_member(X26659),X26658),c_Orderings_Otop__class_Otop(tc_fun(X26659,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_iso__tuple__UNIV__I]) ).

fof(i_0_10186,plain,
    ! [X26637,X26638] : hBOOL(hAPP(hAPP(c_member(X26638),X26637),c_Orderings_Otop__class_Otop(tc_fun(X26638,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_UNIV__I]) ).

fof(i_0_10187,plain,
    ! [X18444,X18445] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18445))
        | X18445 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18444)
        | hAPP(c_Int_Onat,X18445) != X18444 )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18445))
        | X18444 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Int_Onat,X18445) != X18444 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18445))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18445))
        | hAPP(c_Int_Onat,X18445) = X18444 )
      & ( X18444 != 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)),X18445))
        | hAPP(c_Int_Onat,X18445) = X18444 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18445))
        | X18445 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18444)
        | hAPP(c_Int_Onat,X18445) = X18444 )
      & ( X18444 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X18445 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18444)
        | hAPP(c_Int_Onat,X18445) = X18444 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5996])])]) ).

fof(i_0_10188,plain,
    ! [X19029,X19030] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19029))
        | X19029 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19030)
        | X19030 != hAPP(c_Int_Onat,X19029) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19029))
        | X19030 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X19030 != hAPP(c_Int_Onat,X19029) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19029))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19029))
        | X19030 = hAPP(c_Int_Onat,X19029) )
      & ( X19030 != 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)),X19029))
        | X19030 = hAPP(c_Int_Onat,X19029) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19029))
        | X19029 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19030)
        | X19030 = hAPP(c_Int_Onat,X19029) )
      & ( X19030 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X19029 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19030)
        | X19030 = hAPP(c_Int_Onat,X19029) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5997])])]) ).

fof(i_0_10189,plain,
    ! [X19327,X19328,X19329] :
      ( ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X19329,tc_HOL_Obool)),X19328) != hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X19329,tc_HOL_Obool)),X19327)
        | X19328 = X19327 )
      & ( X19328 != X19327
        | hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X19329,tc_HOL_Obool)),X19328) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X19329,tc_HOL_Obool)),X19327) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Compl__eq__Compl__iff])]) ).

fof(i_0_10190,plain,
    ! [X21719,X21720,X21721,X21722] :
      ( ~ class_Groups_Ouminus(X21722)
      | hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X21721,X21722)),X21720),X21719) = hAPP(c_Groups_Ouminus__class_Ouminus(X21722),hAPP(X21720,X21719)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__Compl__def])]) ).

fof(i_0_10191,plain,
    ! [X19485,X19486,X19487,X19488] :
      ( ~ class_Groups_Ouminus(X19488)
      | hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X19487,X19488)),X19486),X19485) = hAPP(c_Groups_Ouminus__class_Ouminus(X19488),hAPP(X19486,X19485)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_uminus__apply])]) ).

fof(i_0_10192,plain,
    ! [X19018] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19018))
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X19018)) = X19018 )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19018))
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X19018)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5998])]) ).

fof(i_0_10193,plain,
    ! [X19015] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19015))
      | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X19015)) = X19015 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__0__le])]) ).

fof(i_0_10194,plain,
    ! [X20152,X20153] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20153),X20152))
        | c_Nat__Transfer_Otsub(X20152,X20153) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20152),X20153) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20153),X20152))
        | c_Nat__Transfer_Otsub(X20152,X20153) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5999])]) ).

fof(i_0_10195,plain,
    ! [X20059,X20060] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20060),X20059))
      | c_Nat__Transfer_Otsub(X20059,X20060) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20059),X20060) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_tsub__eq])]) ).

fof(i_0_10196,plain,
    ! [X30291,X30292] : hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,hAPP(c_Code__Numeral_Oof__nat,X30292)),hAPP(c_Code__Numeral_Oof__nat,X30291)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X30292),X30291)),
    inference(variable_rename,[status(thm)],[fact_subtract__code__numeral__code]) ).

fof(i_0_10197,plain,
    ! [X19016,X19017] :
      ( ( X19017 = hAPP(c_Int_Onat,X19016)
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19017) != X19016 )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19016))
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19017) != X19016 )
      & ( X19017 != hAPP(c_Int_Onat,X19016)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19016))
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19017) = X19016 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__eq__iff])])]) ).

fof(i_0_10198,plain,
    ! [X27083,X27084,X27085,X27086] :
      ( ~ c_Big__Operators_Osemilattice__big(X27086,X27085,X27084)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27086),X27083))
      | hAPP(X27084,X27083) = hAPP(c_Finite__Set_Ofold1(X27086,X27085),X27083) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_semilattice__big_OF__eq])]) ).

fof(i_0_10199,plain,
    ! [X27010,X27011,X27012,X27013] :
      ( ~ c_Finite__Set_Ofolding__one(X27013,X27012,X27011)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27013),X27010))
      | hAPP(X27011,X27010) = hAPP(c_Finite__Set_Ofold1(X27013,X27012),X27010) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one_Oeq__fold])]) ).

fof(i_0_10200,plain,
    ! [X20687,X20688] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20687)))
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20688),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20687)) = c_Groups_Ozero__class_Ozero(X20688)
        | ~ class_Int_Onumber__ring(X20688) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20687)))
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20688),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20687)) = hAPP(c_Int_Onumber__class_Onumber__of(X20688),X20687)
        | ~ class_Int_Onumber__ring(X20688) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6000])])]) ).

fof(i_0_10201,plain,
    ! [X31029] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X31029,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X31029,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X31029,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Inter__UNIV]) ).

fof(i_0_10202,plain,
    ! [X31013] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X31013,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X31013,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X31013,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Inter__empty]) ).

fof(i_0_10203,plain,
    ! [X30793] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X30793,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X30793,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X30793,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Union__UNIV]) ).

fof(i_0_10204,plain,
    ! [X30848] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X30848,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X30848,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X30848,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Union__empty]) ).

cnf(i_0_10205,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_5714]) ).

fof(i_0_10206,plain,
    ! [X17044,X17045,X17046] : hAPP(hAPP(c_Set_Oinsert(X17046),X17045),hAPP(hAPP(c_Set_Oinsert(X17046),X17045),X17044)) = hAPP(hAPP(c_Set_Oinsert(X17046),X17045),X17044),
    inference(variable_rename,[status(thm)],[fact_insert__absorb2]) ).

cnf(i_0_10207,plain,
    c_Int_OBit1(c_Int_OMin) = c_Int_OMin,
    inference(split_conjunct,[status(thm)],[fact_Bit1__Min]) ).

fof(i_0_10208,plain,
    ! [X29904,X29905,X29906,X29907] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X29907)
      | X29906 = c_Orderings_Obot__class_Obot(tc_fun(X29905,tc_HOL_Obool))
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X29905,X29907),X29906),hAPP(c_COMBK(X29907,X29905),X29904)) = X29904 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF__const])]) ).

fof(i_0_10209,plain,
    ! [X25046,X25047,X25048,X25049] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X25049)
      | X25048 = c_Orderings_Obot__class_Obot(tc_fun(X25047,tc_HOL_Obool))
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25047,X25049),X25048),hAPP(c_COMBK(X25049,X25047),X25046)) = X25046 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUP__const])]) ).

cnf(i_0_10210,plain,
    ~ hBOOL(hAPP(hAPP(c_List_Omember(X1),c_List_Olist_ONil(X1)),X2)),
    inference(split_conjunct,[status(thm)],[i_0_6001]) ).

fof(i_0_10211,plain,
    ! [X26628,X26629,X26630] :
      ( ~ class_Lattices_Oboolean__algebra(X26630)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X26630),X26629),X26628) != c_Orderings_Obot__class_Obot(X26630)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X26630),X26629),X26628) != c_Orderings_Otop__class_Otop(X26630)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X26630),X26629) = X26628 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__unique])]) ).

fof(i_0_10212,plain,
    ! [X18867,X18868] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18868),hAPP(c_Nat_OSuc,X18867)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18868),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18868),X18867)),
    inference(variable_rename,[status(thm)],[fact_mult__Suc__right]) ).

cnf(i_0_10213,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_6002]) ).

fof(i_0_10214,plain,
    ! [X26030] : 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)),X26030))),
    inference(variable_rename,[status(thm)],[fact_finite__atLeastZeroLessThan__int]) ).

fof(i_0_10215,plain,
    ! [X31308,X31309] : c_List_Otranspose(X31309,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X31309)),c_List_Olist_ONil(X31309)),X31308)) = c_List_Otranspose(X31309,X31308),
    inference(variable_rename,[status(thm)],[fact_transpose_Osimps_I2_J]) ).

fof(i_0_10216,plain,
    ! [X31159,X31160,X31161,X31162] :
      ( hBOOL(hAPP(X31162,X31161))
      | c_List_Oremove1(X31160,X31161,hAPP(c_List_Ofilter(X31160,X31162),X31159)) = hAPP(c_List_Ofilter(X31160,X31162),X31159) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6003])]) ).

fof(i_0_10217,plain,
    ! [X23286] : hAPP(c_Relation_OField(X23286),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X23286,X23286),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X23286,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Field__empty]) ).

fof(i_0_10218,plain,
    ! [X19576,X19577] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19577),X19576))
      | c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19577,X19576) = X19577 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__less])]) ).

fof(i_0_10219,plain,
    ! [X25512,X25513] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25513),c_Groups_Oone__class_Oone(tc_Int_Oint)),X25512) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X25513,X25512),
    inference(variable_rename,[status(thm)],[fact_atLeastPlusOneAtMost__greaterThanAtMost__int]) ).

fof(i_0_10220,plain,
    ! [X31040,X31041,X31042] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X31042)
      | c_Complete__Lattice_OInf__class_OInf(X31042,hAPP(hAPP(c_Set_Oinsert(X31042),X31041),X31040)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X31042),X31041),c_Complete__Lattice_OInf__class_OInf(X31042,X31040)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__insert])]) ).

fof(i_0_10221,plain,
    ! [X30908,X30909,X30910] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X30910)
      | c_Complete__Lattice_OSup__class_OSup(X30910,hAPP(hAPP(c_Set_Oinsert(X30910),X30909),X30908)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X30910),X30909),c_Complete__Lattice_OSup__class_OSup(X30910,X30908)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__insert])]) ).

fof(i_0_10222,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_10223,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_10224,plain,
    ! [X31523,X31524,X31525] : c_List_Oinsert(X31525,X31524,c_List_Oremdups(X31525,X31523)) = c_List_Oremdups(X31525,c_List_Oinsert(X31525,X31524,X31523)),
    inference(variable_rename,[status(thm)],[fact_insert__remdups]) ).

fof(i_0_10225,plain,
    ! [X33181,X33182,X33183] :
      ( ( ~ c_List_Olist__all(X33183,X33182,hAPP(c_List_Orev(X33183),X33181))
        | c_List_Olist__all(X33183,X33182,X33181) )
      & ( ~ c_List_Olist__all(X33183,X33182,X33181)
        | c_List_Olist__all(X33183,X33182,hAPP(c_List_Orev(X33183),X33181)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all__rev])]) ).

fof(i_0_10226,plain,
    ! [X32744,X32745,X32746] :
      ( ( ~ c_List_Olist__ex(X32746,X32745,hAPP(c_List_Orev(X32746),X32744))
        | c_List_Olist__ex(X32746,X32745,X32744) )
      & ( ~ c_List_Olist__ex(X32746,X32745,X32744)
        | c_List_Olist__ex(X32746,X32745,hAPP(c_List_Orev(X32746),X32744)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__ex__rev])]) ).

fof(i_0_10227,plain,
    ! [X29604,X29605,X29606] :
      ( ( X29606 != c_List_Olist_ONil(X29605)
        | c_List_Obutlast(X29605,hAPP(hAPP(c_List_Olist_OCons(X29605),X29604),X29606)) = c_List_Olist_ONil(X29605) )
      & ( X29606 = c_List_Olist_ONil(X29605)
        | c_List_Obutlast(X29605,hAPP(hAPP(c_List_Olist_OCons(X29605),X29604),X29606)) = hAPP(hAPP(c_List_Olist_OCons(X29605),X29604),c_List_Obutlast(X29605,X29606)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_butlast_Osimps_I2_J])]) ).

fof(i_0_10228,plain,
    ! [X29607,X29608,X29609] :
      ( ( X29609 != c_List_Olist_ONil(X29608)
        | c_List_Obutlast(X29608,hAPP(hAPP(c_List_Oappend(X29608),X29607),X29609)) = c_List_Obutlast(X29608,X29607) )
      & ( X29609 = c_List_Olist_ONil(X29608)
        | c_List_Obutlast(X29608,hAPP(hAPP(c_List_Oappend(X29608),X29607),X29609)) = hAPP(hAPP(c_List_Oappend(X29608),X29607),c_List_Obutlast(X29608,X29609)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_butlast__append])]) ).

fof(i_0_10229,plain,
    ! [X27159,X27160,X27161] : hAPP(c_Set_Ovimage(X27161,X27160,X27159),c_Orderings_Otop__class_Otop(tc_fun(X27160,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X27161,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_vimage__UNIV]) ).

fof(i_0_10230,plain,
    ! [X27134,X27135,X27136] : hAPP(c_Set_Ovimage(X27136,X27135,X27134),c_Orderings_Obot__class_Obot(tc_fun(X27135,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X27136,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_vimage__empty]) ).

fof(i_0_10231,plain,
    ! [X23143,X23144,X23145] : hAPP(c_Relation_OImage(X23145,X23144,X23143),c_Orderings_Obot__class_Obot(tc_fun(X23145,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X23144,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Image__empty]) ).

fof(i_0_10232,plain,
    ! [X23231,X23232,X23233] : hAPP(c_Set_Oimage(X23233,X23232,X23231),c_Orderings_Obot__class_Obot(tc_fun(X23233,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X23232,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_image__empty]) ).

fof(i_0_10233,plain,
    ! [X28659,X28660,X28661] :
      ( ~ c_Relation_Orefl__on(X28661,X28660,X28659)
      | c_Relation_Orefl__on(tc_List_Olist(X28661),c_List_Olists(X28661,X28660),c_List_Olistrel(X28661,X28659)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__refl__on])]) ).

fof(i_0_10234,plain,
    ! [X28656,X28657,X28658] :
      ( ~ c_Equiv__Relations_Oequiv(X28658,X28657,X28656)
      | c_Equiv__Relations_Oequiv(tc_List_Olist(X28658),c_List_Olists(X28658,X28657),c_List_Olistrel(X28658,X28656)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__listrel])]) ).

fof(i_0_10235,plain,
    ! [X20741,X20742,X20743] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X20743),X20742),X20741))
        | hBOOL(hAPP(X20741,X20742)) )
      & ( ~ hBOOL(hAPP(X20741,X20742))
        | hBOOL(hAPP(hAPP(c_member(X20743),X20742),X20741)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__def])]) ).

fof(i_0_10236,plain,
    ! [X17627,X17628,X17629] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(X17629,X17628,X17627)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X17627)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[fact_com_Osize_I3_J]) ).

cnf(i_0_10237,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_6004]) ).

fof(i_0_10238,plain,
    ! [X20000,X20001] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20001),X20000) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20001),X20000)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20001),X20000))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20001),X20000) = 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_10239,plain,
    ! [X19998,X19999] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19999),X19998))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19999),X19998) = 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_10240,plain,
    ! [X19601,X19602] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19602),X19601))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19602),X19601) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__less])]) ).

fof(i_0_10241,plain,
    ! [X26700,X26701] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26701,tc_HOL_Obool)),X26700),c_Orderings_Otop__class_Otop(tc_fun(X26701,tc_HOL_Obool))) = X26700,
    inference(variable_rename,[status(thm)],[fact_Int__UNIV__right]) ).

fof(i_0_10242,plain,
    ! [X22820,X22821] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22821,tc_HOL_Obool)),X22820),c_Orderings_Obot__class_Obot(tc_fun(X22821,tc_HOL_Obool))) = X22820,
    inference(variable_rename,[status(thm)],[fact_Un__empty__right]) ).

fof(i_0_10243,plain,
    ! [X20245,X20246] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20246,tc_HOL_Obool)),X20245),c_Orderings_Obot__class_Obot(tc_fun(X20246,tc_HOL_Obool))) = X20245,
    inference(variable_rename,[status(thm)],[fact_Diff__empty]) ).

fof(i_0_10244,plain,
    ! [X19325,X19326] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X19326,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X19326,tc_HOL_Obool)),X19325)) = X19325,
    inference(variable_rename,[status(thm)],[fact_double__complement]) ).

fof(i_0_10245,plain,
    ! [X21965,X21966] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(X21966,X21966),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X21965) = X21965,
    inference(variable_rename,[status(thm)],[fact_rel__pow__1]) ).

fof(i_0_10246,plain,
    ! [X20686] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20686)))
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20686)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20686)))
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20686)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20686) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6005])]) ).

fof(i_0_10247,plain,
    ! [X29092,X29093,X29094] : hAPP(hAPP(c_List_Olist__update(X29094,X29093),X29092),hAPP(hAPP(c_List_Onth(X29094),X29093),X29092)) = X29093,
    inference(variable_rename,[status(thm)],[fact_list__update__id]) ).

fof(i_0_10248,plain,
    ! [X18126,X18127,X18128] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18128),X18127),X18127) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18128),X18126),X18126)
        | X18127 = X18126
        | X18127 = hAPP(c_Groups_Ouminus__class_Ouminus(X18128),X18126)
        | ~ class_Rings_Oidom(X18128) )
      & ( X18127 != X18126
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18128),X18127),X18127) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18128),X18126),X18126)
        | ~ class_Rings_Oidom(X18128) )
      & ( X18127 != hAPP(c_Groups_Ouminus__class_Ouminus(X18128),X18126)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18128),X18127),X18127) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18128),X18126),X18126)
        | ~ class_Rings_Oidom(X18128) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_square__eq__iff])])]) ).

fof(i_0_10249,plain,
    ! [X17507,X17508] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X17508)),X17507) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17508),X17507)),
    inference(variable_rename,[status(thm)],[fact_add__Suc]) ).

fof(i_0_10250,plain,
    ! [X29595,X29596,X29597] : hAPP(hAPP(c_List_Odrop(X29597),X29596),c_List_Obutlast(X29597,X29595)) = c_List_Obutlast(X29597,hAPP(hAPP(c_List_Odrop(X29597),X29596),X29595)),
    inference(variable_rename,[status(thm)],[fact_drop__butlast]) ).

fof(i_0_10251,plain,
    ! [X29598,X29599,X29600] : c_List_Obutlast(X29600,hAPP(hAPP(c_List_Odrop(X29600),X29599),X29598)) = hAPP(hAPP(c_List_Odrop(X29600),X29599),c_List_Obutlast(X29600,X29598)),
    inference(variable_rename,[status(thm)],[fact_butlast__drop]) ).

fof(i_0_10252,plain,
    ! [X30304] :
      ( ( X30304 = 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)),X30304)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X30304))
        | X30304 != 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_10253,plain,
    ! [X30861,X30862,X30863] :
      ( ( hAPP(c_Relation_ODomain(X30863,X30862),X30861) != c_Orderings_Obot__class_Obot(tc_fun(X30863,tc_HOL_Obool))
        | X30861 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X30863,X30862),tc_HOL_Obool)) )
      & ( X30861 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X30863,X30862),tc_HOL_Obool))
        | hAPP(c_Relation_ODomain(X30863,X30862),X30861) = c_Orderings_Obot__class_Obot(tc_fun(X30863,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Domain__empty__iff])]) ).

fof(i_0_10254,plain,
    ! [X28262,X28263,X28264] :
      ( ( hAPP(c_Relation_ORange(X28264,X28263),X28262) != c_Orderings_Obot__class_Obot(tc_fun(X28263,tc_HOL_Obool))
        | X28262 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X28264,X28263),tc_HOL_Obool)) )
      & ( X28262 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X28264,X28263),tc_HOL_Obool))
        | hAPP(c_Relation_ORange(X28264,X28263),X28262) = c_Orderings_Obot__class_Obot(tc_fun(X28263,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Range__empty__iff])]) ).

fof(i_0_10255,plain,
    ! [X20441] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20441),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X20441) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X20441) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20441),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X20441) = X20441 ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6006])]) ).

fof(i_0_10256,plain,
    ! [X20398,X20399] :
      ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20399),X20398)) != c_Groups_Oone__class_Oone(tc_Int_Oint)
      | hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X20399) = 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_10257,plain,
    ! [X18081,X18082] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18082),X18081))
      | X18082 = X18081
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18081),X18082)) ),
    inference(variable_rename,[status(thm)],[fact_zless__linear]) ).

fof(i_0_10258,plain,
    ! [X17460,X17461] :
      ( ( X17461 = X17460
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17461),X17460))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17460),X17461)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17461),X17460))
        | X17461 != X17460 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17460),X17461))
        | X17461 != X17460 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__neq__iff])])]) ).

fof(i_0_10259,plain,
    ! [X17441,X17442] :
      ( X17442 = X17441
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17442),X17441))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17441),X17442)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6007])]) ).

fof(i_0_10260,plain,
    ! [X26063,X26064] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X26064),X26063)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26063),X26064)),
    inference(variable_rename,[status(thm)],[fact_card__atLeastLessThan__int]) ).

cnf(i_0_10261,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_6008]) ).

fof(i_0_10262,plain,
    ! [X20218,X20219] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X20219)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20219),X20218),hAPP(c_Groups_Oabs__class_Oabs(X20219),X20218))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__ge__self])]) ).

fof(i_0_10263,plain,
    ! [X24969,X24970] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X24970,X24969)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24969),hAPP(c_Nat_OSuc,X24970)),
    inference(variable_rename,[status(thm)],[fact_card__greaterThanLessThan]) ).

fof(i_0_10264,plain,
    ! [X33867,X33868,X33869] :
      ( ~ hBOOL(hAPP(hAPP(X33868,X33869),X33869))
      | ~ c_Predicate_Osymp(X33867,X33868)
      | ~ c_Predicate_Otransp(X33867,X33868)
      | c_Equiv__Relations_Opart__equivp(X33867,X33868) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_part__equivpI])])]) ).

fof(i_0_10265,plain,
    ! [X18519,X18520] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X18520),X18519))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X18519),X18520)) ),
    inference(variable_rename,[status(thm)],[fact_zle__linear]) ).

fof(i_0_10266,plain,
    ! [X19075,X19076] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19076),X19075))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19075),X19076)) ),
    inference(variable_rename,[status(thm)],[fact_nat__le__linear]) ).

fof(i_0_10267,plain,
    ! [X19588,X19589] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X19589)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X19588)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19589),X19588),
    inference(variable_rename,[status(thm)],[fact_zdiv__zminus__zminus]) ).

fof(i_0_10268,plain,
    ! [X19586,X19587] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19587),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X19586)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X19587)),X19586),
    inference(variable_rename,[status(thm)],[fact_zdiv__zminus2]) ).

fof(i_0_10269,plain,
    ! [X29354,X29355,X29356] : hAPP(hAPP(c_List_Odrop(X29356),hAPP(c_Nat_OSuc,X29355)),X29354) = hAPP(hAPP(c_List_Odrop(X29356),X29355),hAPP(c_List_Otl(X29356),X29354)),
    inference(variable_rename,[status(thm)],[fact_drop__Suc]) ).

fof(i_0_10270,plain,
    ! [X17854] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17854))
      | X17854 = hAPP(c_Nat_OSuc,esk28_1(X17854)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gr0__implies__Suc])])]) ).

fof(i_0_10271,plain,
    ! [X17593,X17595,X17596] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17593))
        | X17593 = hAPP(c_Nat_OSuc,esk25_1(X17593)) )
      & ( X17595 != hAPP(c_Nat_OSuc,X17596)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17595)) ) ),
    inference(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_10272,plain,
    ! [X27029,X27030] :
      ( ~ class_Orderings_Olinorder(X27030)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27030),X27029))
      | c_Big__Operators_Olattice_OInf__fin(X27030,c_Orderings_Oord__class_Omin(X27030),X27029) = hAPP(c_Finite__Set_Ofold1(X27030,c_Orderings_Oord__class_Omin(X27030)),X27029) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_OF__eq])]) ).

fof(i_0_10273,plain,
    ! [X27031,X27032] :
      ( ~ class_Orderings_Olinorder(X27032)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27032),X27031))
      | c_Big__Operators_Olattice_OSup__fin(X27032,c_Orderings_Oord__class_Omax(X27032),X27031) = hAPP(c_Finite__Set_Ofold1(X27032,c_Orderings_Oord__class_Omax(X27032)),X27031) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_OF__eq])]) ).

fof(i_0_10274,plain,
    ! [X32981] :
      ( ~ class_Orderings_Olinorder(X32981)
      | c_Finite__Set_Ofun__left__comm(X32981,tc_List_Olist(X32981),c_List_Olinorder__class_Oinsort__key(X32981,X32981,c_COMBI(X32981))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__insort])]) ).

fof(i_0_10275,plain,
    ! [X19288] :
      ( ( X19288 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Groups_Osgn__class_Osgn(tc_Int_Oint,X19288) = 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)),X19288))
        | c_Groups_Osgn__class_Osgn(tc_Int_Oint,X19288) = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | X19288 = 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)),X19288))
        | c_Groups_Osgn__class_Osgn(tc_Int_Oint,X19288) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))
        | X19288 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6009])])]) ).

fof(i_0_10276,plain,
    ! [X33935,X33936,X33937] :
      ( ~ c_Relation_Orefl__on(X33937,X33936,X33935)
      | ~ c_Relation_Osym(X33937,X33935)
      | ~ c_Relation_Otrans(X33937,X33935)
      | c_Equiv__Relations_Oequiv(X33937,X33936,X33935) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equivI])]) ).

fof(i_0_10277,plain,
    ! [X33932,X33933,X33934] :
      ( ( c_Relation_Orefl__on(X33934,X33933,X33932)
        | ~ c_Equiv__Relations_Oequiv(X33934,X33933,X33932) )
      & ( c_Relation_Osym(X33934,X33932)
        | ~ c_Equiv__Relations_Oequiv(X33934,X33933,X33932) )
      & ( c_Relation_Otrans(X33934,X33932)
        | ~ c_Equiv__Relations_Oequiv(X33934,X33933,X33932) )
      & ( ~ c_Relation_Orefl__on(X33934,X33933,X33932)
        | ~ c_Relation_Osym(X33934,X33932)
        | ~ c_Relation_Otrans(X33934,X33932)
        | c_Equiv__Relations_Oequiv(X33934,X33933,X33932) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__def])])]) ).

fof(i_0_10278,plain,
    ! [X29335,X29336] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X29336),X29335))
      | hBOOL(hAPP(c_List_Odistinct(X29336),hAPP(c_List_Otl(X29336),X29335))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__tl])]) ).

fof(i_0_10279,plain,
    ! [X26058,X26059] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X26059),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26058),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X26059,X26058),
    inference(variable_rename,[status(thm)],[fact_atLeastLessThanPlusOne__atLeastAtMost__int]) ).

fof(i_0_10280,plain,
    ! [X20650] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X20650))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20650),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20650),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,X20650)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__def])]) ).

fof(i_0_10281,plain,
    ! [X29360,X29361] :
      ( hAPP(c_Finite__Set_Ocard(X29361),hAPP(c_List_Oset(X29361),X29360)) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29361)),X29360)
      | hBOOL(hAPP(c_List_Odistinct(X29361),X29360)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__distinct])]) ).

fof(i_0_10282,plain,
    ! [X20061,X20062] : c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20062),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20061)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20062),X20061)),
    inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J]) ).

fof(i_0_10283,plain,
    ! [X31654,X31655,X31656] :
      ( ( hAPP(hAPP(c_List_Olist_OCons(X31656),X31655),c_List_Olist_ONil(X31656)) != hAPP(c_List_Orev(X31656),X31654)
        | X31654 = hAPP(hAPP(c_List_Olist_OCons(X31656),X31655),c_List_Olist_ONil(X31656)) )
      & ( X31654 != hAPP(hAPP(c_List_Olist_OCons(X31656),X31655),c_List_Olist_ONil(X31656))
        | hAPP(hAPP(c_List_Olist_OCons(X31656),X31655),c_List_Olist_ONil(X31656)) = hAPP(c_List_Orev(X31656),X31654) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_singleton__rev__conv])]) ).

fof(i_0_10284,plain,
    ! [X31651,X31652,X31653] :
      ( ( hAPP(c_List_Orev(X31653),X31652) != hAPP(hAPP(c_List_Olist_OCons(X31653),X31651),c_List_Olist_ONil(X31653))
        | X31652 = hAPP(hAPP(c_List_Olist_OCons(X31653),X31651),c_List_Olist_ONil(X31653)) )
      & ( X31652 != hAPP(hAPP(c_List_Olist_OCons(X31653),X31651),c_List_Olist_ONil(X31653))
        | hAPP(c_List_Orev(X31653),X31652) = hAPP(hAPP(c_List_Olist_OCons(X31653),X31651),c_List_Olist_ONil(X31653)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__singleton__conv])]) ).

fof(i_0_10285,plain,
    ! [X17833,X17834] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OWhile(X17834,X17833)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X17833)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[fact_com_Osize_I14_J]) ).

fof(i_0_10286,plain,
    ! [X32464,X32465] : c_List_Olistrel1(X32465,hAPP(c_Relation_Oconverse(X32465,X32465),X32464)) = hAPP(c_Relation_Oconverse(tc_List_Olist(X32465),tc_List_Olist(X32465)),c_List_Olistrel1(X32465,X32464)),
    inference(variable_rename,[status(thm)],[fact_listrel1__converse]) ).

fof(i_0_10287,plain,
    ! [X19858,X19859,X19860] :
      ( ~ class_Groups_Oab__group__add(X19860)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X19860),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19860),X19859),X19858)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19860),X19858),X19859) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__diff__eq])]) ).

cnf(i_0_10288,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_5803]) ).

fof(i_0_10289,plain,
    ! [X33410,X33411,X33412] : hAPP(c_List_Orev(X33412),c_List_Oreplicate(X33412,X33411,X33410)) = c_List_Oreplicate(X33412,X33411,X33410),
    inference(variable_rename,[status(thm)],[fact_rev__replicate]) ).

fof(i_0_10290,plain,
    ! [X28212,X28213,X28214] :
      ( ~ c_Wellfounded_Owf(X28214,X28213)
      | hBOOL(hAPP(hAPP(c_member(X28214),X28212),c_Wellfounded_Oacc(X28214,X28213))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc__wfD])]) ).

fof(i_0_10291,plain,
    ! [X18832,X18833] :
      ( ~ class_Rings_Ocomm__ring__1(X18833)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X18833),X18832) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18833),hAPP(c_Groups_Ouminus__class_Ouminus(X18833),c_Groups_Oone__class_Oone(X18833))),X18832) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J])]) ).

fof(i_0_10292,plain,
    ! [X26022,X26023] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X26023),X26022))),
    inference(variable_rename,[status(thm)],[fact_finite__atLeastLessThan__int]) ).

fof(i_0_10293,plain,
    ! [X25664,X25665] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X25665),X25664))),
    inference(variable_rename,[status(thm)],[fact_finite__atLeastLessThan]) ).

fof(i_0_10294,plain,
    ! [X33644,X33645,X33646] :
      ( ( ~ c_List_Olist__all(tc_Int_Oint,X33646,c_List_Oupto(X33645,X33644))
        | c_List_Oall__interval__int(X33646,X33645,X33644) )
      & ( ~ c_List_Oall__interval__int(X33646,X33645,X33644)
        | c_List_Olist__all(tc_Int_Oint,X33646,c_List_Oupto(X33645,X33644)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all__iff__all__interval__int])]) ).

fof(i_0_10295,plain,
    ! [X32660,X32661,X32662] :
      ( ( ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X32661),X32660))
        | hBOOL(hAPP(X32660,X32662))
        | ~ class_Enum_Oenum(X32661) )
      & ( ~ hBOOL(hAPP(X32660,esk466_2(X32660,X32661)))
        | hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X32661),X32660))
        | ~ class_Enum_Oenum(X32661) ) ),
    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_10296,plain,
    ! [X32656,X32657,X32659] :
      ( ( ~ hBOOL(hAPP(X32656,esk465_2(X32656,X32657)))
        | hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X32657),X32656))
        | ~ class_Enum_Oenum(X32657) )
      & ( ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X32657),X32656))
        | hBOOL(hAPP(X32656,X32659))
        | ~ class_Enum_Oenum(X32657) ) ),
    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_10297,plain,
    ! [X17840] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),hAPP(c_Nat_OSuc,X17840)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X17840)),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_10298,plain,
    c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_6010]) ).

fof(i_0_10299,plain,
    ! [X17393,X17394,X17395] :
      ( ~ class_Orderings_Oorder(X17395)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17395),X17394),X17393))
      | X17394 != X17393 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__neq])]) ).

fof(i_0_10300,plain,
    ! [X17384,X17385,X17386] :
      ( ~ class_Orderings_Oorder(X17386)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17386),X17385),X17384))
      | X17385 != X17384 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq])]) ).

fof(i_0_10301,plain,
    ! [X17381,X17382,X17383] :
      ( ~ class_Orderings_Oorder(X17383)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17383),X17382),X17381))
      | X17381 != X17382 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq2])]) ).

cnf(i_0_10302,plain,
    c_Wellfounded_Owf(X1,hAPP(c_Wellfounded_Omeasure(X1),X2)),
    inference(split_conjunct,[status(thm)],[i_0_6011]) ).

fof(i_0_10303,plain,
    ! [X33420,X33421,X33422,X33423,X33424] :
      ( ( X33423 = X33421
        | c_List_Oreplicate(X33424,X33423,X33422) != c_List_Oreplicate(X33424,X33421,X33420) )
      & ( X33423 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X33422 = X33420
        | c_List_Oreplicate(X33424,X33423,X33422) != c_List_Oreplicate(X33424,X33421,X33420) )
      & ( X33423 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X33423 != X33421
        | c_List_Oreplicate(X33424,X33423,X33422) = c_List_Oreplicate(X33424,X33421,X33420) )
      & ( X33422 != X33420
        | X33423 != X33421
        | c_List_Oreplicate(X33424,X33423,X33422) = c_List_Oreplicate(X33424,X33421,X33420) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_replicate__eq__replicate])])]) ).

fof(i_0_10304,plain,
    ! [X19814,X19815,X19816,X19817,X19818] :
      ( ( X19817 != X19816
        | X19815 = X19814
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19818),X19817),X19816) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19818),X19815),X19814)
        | ~ class_Groups_Oab__group__add(X19818) )
      & ( X19815 != X19814
        | X19817 = X19816
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19818),X19817),X19816) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19818),X19815),X19814)
        | ~ class_Groups_Oab__group__add(X19818) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__eq])])]) ).

fof(i_0_10305,plain,
    ! [X17090,X17091,X17092] :
      ( ~ c_Hoare__Mirabelle_Otriple__valid(X17092,hAPP(c_Nat_OSuc,X17091),X17090)
      | c_Hoare__Mirabelle_Otriple__valid(X17092,X17091,X17090) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_triple__valid__Suc])]) ).

fof(i_0_10306,plain,
    ! [X31635,X31636,X31637] : hAPP(c_List_Orev(X31637),hAPP(c_List_Ofilter(X31637,X31636),X31635)) = hAPP(c_List_Ofilter(X31637,X31636),hAPP(c_List_Orev(X31637),X31635)),
    inference(variable_rename,[status(thm)],[fact_rev__filter]) ).

fof(i_0_10307,plain,
    ! [X19457,X19458] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X19458),X19457) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,X19458,X19457) != 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_10308,plain,
    ! [X19455,X19456] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X19456,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X19455)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,X19456,X19455) != 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_10309,plain,
    ! [X17411,X17412] :
      ( ~ class_Orderings_Opreorder(X17412)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17412),X17411),X17411)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6012])]) ).

fof(i_0_10310,plain,
    ! [X17512] :
      ( ( X17512 = 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)),X17512)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17512))
        | X17512 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neq0__conv])]) ).

fof(i_0_10311,plain,
    ! [X30760,X30761] :
      ( ( X30761 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Enum_On__lists(X30760,X30761,c_List_Olist_ONil(X30760)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X30760)),c_List_Olist_ONil(X30760)),c_List_Olist_ONil(tc_List_Olist(X30760))) )
      & ( X30761 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Enum_On__lists(X30760,X30761,c_List_Olist_ONil(X30760)) = c_List_Olist_ONil(tc_List_Olist(X30760)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_n__lists__Nil])]) ).

fof(i_0_10312,plain,
    ! [X17313,X17314,X17315,X17316] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17316),X17315),X17314) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17316),X17313),X17314)
        | X17315 = X17313
        | ~ class_Groups_Ocancel__semigroup__add(X17316) )
      & ( X17315 != X17313
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17316),X17315),X17314) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17316),X17313),X17314)
        | ~ class_Groups_Ocancel__semigroup__add(X17316) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__cancel])])]) ).

fof(i_0_10313,plain,
    ! [X17280,X17281,X17282,X17283] :
      ( ~ class_Groups_Ocancel__semigroup__add(X17283)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17283),X17282),X17281) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17283),X17280),X17281)
      | X17282 = X17280 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__imp__eq])]) ).

fof(i_0_10314,plain,
    ! [X17284,X17285,X17286,X17287] :
      ( ~ class_Groups_Ocancel__ab__semigroup__add(X17287)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17287),X17286),X17285) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17287),X17286),X17284)
      | X17285 = X17284 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__imp__eq])]) ).

fof(i_0_10315,plain,
    ! [X17317,X17318,X17319,X17320] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17320),X17319),X17318) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17320),X17319),X17317)
        | X17318 = X17317
        | ~ class_Groups_Ocancel__semigroup__add(X17320) )
      & ( X17318 != X17317
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17320),X17319),X17318) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17320),X17319),X17317)
        | ~ class_Groups_Ocancel__semigroup__add(X17320) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__cancel])])]) ).

fof(i_0_10316,plain,
    ! [X17288,X17289,X17290,X17291] :
      ( ~ class_Groups_Ocancel__semigroup__add(X17291)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17291),X17290),X17289) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17291),X17290),X17288)
      | X17289 = X17288 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__imp__eq])]) ).

fof(i_0_10317,plain,
    ! [X33520,X33521,X33522,X33523,X33524] :
      ( ( X33523 = X33521
        | c_Lazy__Sequence_Olazy__sequence_OInsert(X33524,X33523,X33522) != c_Lazy__Sequence_Olazy__sequence_OInsert(X33524,X33521,X33520) )
      & ( X33522 = X33520
        | c_Lazy__Sequence_Olazy__sequence_OInsert(X33524,X33523,X33522) != c_Lazy__Sequence_Olazy__sequence_OInsert(X33524,X33521,X33520) )
      & ( X33523 != X33521
        | X33522 != X33520
        | c_Lazy__Sequence_Olazy__sequence_OInsert(X33524,X33523,X33522) = c_Lazy__Sequence_Olazy__sequence_OInsert(X33524,X33521,X33520) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lazy__sequence_Oinject])])]) ).

fof(i_0_10318,plain,
    ! [X17681,X17682,X17683,X17684,X17685,X17686] :
      ( ( X17686 = X17683
        | c_Com_Ocom_OLocal(X17686,X17685,X17684) != c_Com_Ocom_OLocal(X17683,X17682,X17681) )
      & ( X17685 = X17682
        | c_Com_Ocom_OLocal(X17686,X17685,X17684) != c_Com_Ocom_OLocal(X17683,X17682,X17681) )
      & ( X17684 = X17681
        | c_Com_Ocom_OLocal(X17686,X17685,X17684) != c_Com_Ocom_OLocal(X17683,X17682,X17681) )
      & ( X17686 != X17683
        | X17685 != X17682
        | X17684 != X17681
        | c_Com_Ocom_OLocal(X17686,X17685,X17684) = c_Com_Ocom_OLocal(X17683,X17682,X17681) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_com_Osimps_I2_J])])]) ).

fof(i_0_10319,plain,
    ! [X17675,X17676,X17677,X17678,X17679,X17680] :
      ( ( X17680 = X17677
        | c_Com_Ocom_OCond(X17680,X17679,X17678) != c_Com_Ocom_OCond(X17677,X17676,X17675) )
      & ( X17679 = X17676
        | c_Com_Ocom_OCond(X17680,X17679,X17678) != c_Com_Ocom_OCond(X17677,X17676,X17675) )
      & ( X17678 = X17675
        | c_Com_Ocom_OCond(X17680,X17679,X17678) != c_Com_Ocom_OCond(X17677,X17676,X17675) )
      & ( X17680 != X17677
        | X17679 != X17676
        | X17678 != X17675
        | c_Com_Ocom_OCond(X17680,X17679,X17678) = c_Com_Ocom_OCond(X17677,X17676,X17675) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_com_Osimps_I4_J])])]) ).

fof(i_0_10320,plain,
    ! [X17325,X17326,X17327,X17328,X17329,X17330] :
      ( ( X17330 = X17327
        | c_Com_Ocom_OCall(X17330,X17329,X17328) != c_Com_Ocom_OCall(X17327,X17326,X17325) )
      & ( X17329 = X17326
        | c_Com_Ocom_OCall(X17330,X17329,X17328) != c_Com_Ocom_OCall(X17327,X17326,X17325) )
      & ( X17328 = X17325
        | c_Com_Ocom_OCall(X17330,X17329,X17328) != c_Com_Ocom_OCall(X17327,X17326,X17325) )
      & ( X17330 != X17327
        | X17329 != X17326
        | X17328 != X17325
        | c_Com_Ocom_OCall(X17330,X17329,X17328) = c_Com_Ocom_OCall(X17327,X17326,X17325) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_com_Osimps_I7_J])])]) ).

fof(i_0_10321,plain,
    ! [X19013] :
      ( ( hAPP(c_Int_Onat,X19013) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19013),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19013),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Int_Onat,X19013) = 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_10322,plain,
    ! [X19012] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19012),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | hAPP(c_Int_Onat,X19012) = 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_10323,plain,
    ! [X21468] :
      ( ( ~ c_Nat__Transfer_Ois__nat(X21468)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21468)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21468))
        | c_Nat__Transfer_Ois__nat(X21468) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_is__nat__def])]) ).

fof(i_0_10324,plain,
    ! [X17505,X17506] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17506),hAPP(c_Nat_OSuc,X17505)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17506),X17505)),
    inference(variable_rename,[status(thm)],[fact_add__Suc__right]) ).

fof(i_0_10325,plain,
    ! [X17669,X17670,X17671,X17672,X17673,X17674] : c_Com_Ocom_OLocal(X17674,X17673,X17672) != c_Com_Ocom_OCond(X17671,X17670,X17669),
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I36_J]) ).

fof(i_0_10326,plain,
    ! [X17753,X17754,X17755,X17756,X17757,X17758] : c_Com_Ocom_OLocal(X17758,X17757,X17756) != c_Com_Ocom_OCall(X17755,X17754,X17753),
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I42_J]) ).

fof(i_0_10327,plain,
    ! [X17663,X17664,X17665,X17666,X17667,X17668] : c_Com_Ocom_OCond(X17668,X17667,X17666) != c_Com_Ocom_OLocal(X17665,X17664,X17663),
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I37_J]) ).

fof(i_0_10328,plain,
    ! [X17747,X17748,X17749,X17750,X17751,X17752] : c_Com_Ocom_OCall(X17752,X17751,X17750) != c_Com_Ocom_OLocal(X17749,X17748,X17747),
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I43_J]) ).

fof(i_0_10329,plain,
    ! [X17791,X17792,X17793,X17794,X17795,X17796] : c_Com_Ocom_OCond(X17796,X17795,X17794) != c_Com_Ocom_OCall(X17793,X17792,X17791),
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I56_J]) ).

fof(i_0_10330,plain,
    ! [X17785,X17786,X17787,X17788,X17789,X17790] : c_Com_Ocom_OCall(X17790,X17789,X17788) != c_Com_Ocom_OCond(X17787,X17786,X17785),
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I57_J]) ).

fof(i_0_10331,plain,
    ! [X28336,X28337] : hAPP(c_List_Olexn(X28337,X28336),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(X28337),tc_List_Olist(X28337)),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_lexn_Osimps_I1_J]) ).

fof(i_0_10332,plain,
    ! [X18874] : 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),X18874))),
    inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J]) ).

fof(i_0_10333,plain,
    ! [X18873] : 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),X18873))),
    inference(variable_rename,[status(thm)],[fact_zero__zle__int]) ).

fof(i_0_10334,plain,
    ! [X20243,X20244] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X20244,tc_HOL_Obool)),X20243),X20243) = c_Orderings_Obot__class_Obot(tc_fun(X20244,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Diff__cancel]) ).

fof(i_0_10335,plain,
    ! [X33835] : c_Relation_Oantisym(X33835,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X33835,X33835),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_antisym__empty]) ).

fof(i_0_10336,plain,
    ! [X28106] : c_Wellfounded_Owf(X28106,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X28106,X28106),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_wf__empty]) ).

fof(i_0_10337,plain,
    ! [X25479,X25480,X25481] :
      ( ~ class_Orderings_Oorder(X25481)
      | X25480 != X25479
      | c_SetInterval_Oord__class_OatLeastAtMost(X25481,X25480,X25479) = hAPP(hAPP(c_Set_Oinsert(X25481),X25480),c_Orderings_Obot__class_Obot(tc_fun(X25481,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastAtMost__singleton_H])]) ).

fof(i_0_10338,plain,
    ! [X31578,X31579] :
      ( ( hAPP(c_List_Oset(X31579),c_List_Olinorder__class_Osorted__list__of__set(X31579,X31578)) = X31578
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31579),X31578))
        | ~ class_Orderings_Olinorder(X31579) )
      & ( c_List_Olinorder__class_Osorted(X31579,c_List_Olinorder__class_Osorted__list__of__set(X31579,X31578))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31579),X31578))
        | ~ class_Orderings_Olinorder(X31579) )
      & ( hBOOL(hAPP(c_List_Odistinct(X31579),c_List_Olinorder__class_Osorted__list__of__set(X31579,X31578)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31579),X31578))
        | ~ class_Orderings_Olinorder(X31579) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__list__of__set])])]) ).

fof(i_0_10339,plain,
    ! [X19428,X19429,X19430] :
      ( ~ class_Divides_Osemiring__div(X19430)
      | c_Divides_Odiv__class_Omod(X19430,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19430),X19429),X19428),X19429) = c_Groups_Ozero__class_Ozero(X19430) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__self1__is__0])]) ).

fof(i_0_10340,plain,
    ! [X19425,X19426,X19427] :
      ( ~ class_Divides_Osemiring__div(X19427)
      | c_Divides_Odiv__class_Omod(X19427,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19427),X19426),X19425),X19425) = c_Groups_Ozero__class_Ozero(X19427) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__self2__is__0])]) ).

fof(i_0_10341,plain,
    ! [X29610,X29611] :
      ( X29611 = c_List_Olist_ONil(X29610)
      | ~ hBOOL(hAPP(c_List_Odistinct(X29610),X29611))
      | hBOOL(hAPP(c_List_Odistinct(X29610),c_List_Obutlast(X29610,X29611))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__butlast])]) ).

fof(i_0_10342,plain,
    ! [X25328,X25329] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X25329,X25328)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25328),X25329),
    inference(variable_rename,[status(thm)],[fact_card__greaterThanAtMost]) ).

fof(i_0_10343,plain,
    ! [X28356,X28357,X28358,X28359,X28360] :
      ( ( X28359 = X28357
        | hAPP(hAPP(c_List_Olist_OCons(X28360),X28359),X28358) != hAPP(hAPP(c_List_Olist_OCons(X28360),X28357),X28356) )
      & ( X28358 = X28356
        | hAPP(hAPP(c_List_Olist_OCons(X28360),X28359),X28358) != hAPP(hAPP(c_List_Olist_OCons(X28360),X28357),X28356) )
      & ( X28359 != X28357
        | X28358 != X28356
        | hAPP(hAPP(c_List_Olist_OCons(X28360),X28359),X28358) = hAPP(hAPP(c_List_Olist_OCons(X28360),X28357),X28356) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list_Oinject])])]) ).

fof(i_0_10344,plain,
    ! [X28157,X28158,X28159,X28160] :
      ( ( hAPP(hAPP(c_List_Oappend(X28160),X28159),X28158) != hAPP(hAPP(c_List_Oappend(X28160),X28157),X28158)
        | X28159 = X28157 )
      & ( X28159 != X28157
        | hAPP(hAPP(c_List_Oappend(X28160),X28159),X28158) = hAPP(hAPP(c_List_Oappend(X28160),X28157),X28158) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__same__eq])]) ).

fof(i_0_10345,plain,
    ! [X28161,X28162,X28163,X28164] :
      ( ( hAPP(hAPP(c_List_Oappend(X28164),X28163),X28162) != hAPP(hAPP(c_List_Oappend(X28164),X28163),X28161)
        | X28162 = X28161 )
      & ( X28162 != X28161
        | hAPP(hAPP(c_List_Oappend(X28164),X28163),X28162) = hAPP(hAPP(c_List_Oappend(X28164),X28163),X28161) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_same__append__eq])]) ).

fof(i_0_10346,plain,
    ! [X25486,X25487] :
      ( ~ class_Orderings_Oorder(X25487)
      | c_SetInterval_Oord__class_OatLeastAtMost(X25487,X25486,X25486) = hAPP(hAPP(c_Set_Oinsert(X25487),X25486),c_Orderings_Obot__class_Obot(tc_fun(X25487,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastAtMost__singleton])]) ).

fof(i_0_10347,plain,
    ! [X29499,X29500] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X29500),X29499))
      | c_List_Oupto(X29499,X29500) = c_List_Olist_ONil(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_upto__empty])]) ).

fof(i_0_10348,plain,
    ! [X30762,X30763] : c_Enum_On__lists(X30763,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X30762) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X30763)),c_List_Olist_ONil(X30763)),c_List_Olist_ONil(tc_List_Olist(X30763))),
    inference(variable_rename,[status(thm)],[fact_n__lists_Osimps_I1_J]) ).

fof(i_0_10349,plain,
    ! [X25880] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,X25880)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X25880)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X25880)),
    inference(variable_rename,[status(thm)],[fact_atMost__Suc]) ).

fof(i_0_10350,plain,
    ! [X34097,X34098] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X34098),X34097))
        | c_Quickcheck_Obeyond(X34098,X34097) = X34097 )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X34098),X34097))
        | c_Quickcheck_Obeyond(X34098,X34097) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6013])]) ).

fof(i_0_10351,plain,
    ! [X20925] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20925) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20925),c_Int_OPls)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20925),c_Int_OPls))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20925) = 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_10352,plain,
    ! [X20676] :
      ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20676)))
      | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20676) = 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_10353,plain,
    ! [X20926] :
      ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20926)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20926),c_Int_OPls)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20926),c_Int_OPls))
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20926) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__0__number__of])]) ).

cnf(i_0_10354,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_6014]) ).

fof(i_0_10355,plain,
    ! [X23974,X23975,X23976] :
      ( ~ class_Lattices_Olattice(X23976)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23976),X23975),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23976),X23975),X23974)) = X23975 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__absorb])]) ).

fof(i_0_10356,plain,
    ! [X23977,X23978,X23979] :
      ( ~ class_Lattices_Olattice(X23979)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23979),X23978),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23979),X23978),X23977)) = X23978 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__inf__absorb])]) ).

fof(i_0_10357,plain,
    ! [X22555,X22556,X22557] :
      ( ~ class_Orderings_Olinorder(X22557)
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X22557),X22556),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22557),X22556),X22555)) = X22556 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__inf__absorb])]) ).

fof(i_0_10358,plain,
    ! [X22552,X22553,X22554] :
      ( ~ class_Orderings_Olinorder(X22554)
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X22554),X22553),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22554),X22553),X22552)) = X22553 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__sup__absorb])]) ).

fof(i_0_10359,plain,
    ! [X33349,X33350,X33351] : c_Predicate_Oconversep(X33351,X33350,c_Predicate_Oconversep(X33350,X33351,X33349)) = X33349,
    inference(variable_rename,[status(thm)],[fact_conversep__conversep]) ).

fof(i_0_10360,plain,
    ! [X19089] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19089),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | X19089 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X19089 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19089),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_10361,plain,
    ! [X28862,X28863,X28864] : hAPP(hAPP(c_List_Odrop(X28864),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(X28864),X28863),X28862)) = X28862,
    inference(variable_rename,[status(thm)],[fact_drop__1__Cons]) ).

fof(i_0_10362,plain,
    ! [X19887,X19888] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19888)),hAPP(c_Nat_OSuc,X19887)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19888),X19887),
    inference(variable_rename,[status(thm)],[fact_diff__Suc__Suc]) ).

fof(i_0_10363,plain,
    ! [X17509,X17510] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X17510)),X17509) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17510),hAPP(c_Nat_OSuc,X17509)),
    inference(variable_rename,[status(thm)],[fact_add__Suc__shift]) ).

fof(i_0_10364,plain,
    ! [X27000,X27001,X27002] : hAPP(c_Finite__Set_Ofold1(X27002,X27001),X27000) = c_HOL_OThe(X27002,c_Finite__Set_Ofold1Set(X27002,X27001,X27000)),
    inference(variable_rename,[status(thm)],[fact_fold1__def]) ).

fof(i_0_10365,plain,
    ! [X19449,X19450,X19452,X19453,X19454] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X19450,X19449) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | X19450 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19449),esk51_2(X19449,X19450)) )
      & ( X19453 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19452),X19454)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,X19453,X19452) = 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_10366,plain,
    ! [X19620,X19621,X19623,X19624,X19625] :
      ( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19621,X19620) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X19621 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19620),esk57_2(X19620,X19621)) )
      & ( X19624 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19623),X19625)
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19624,X19623) = 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_10367,plain,
    ! [X23449,X23450] :
      ( ~ c_Nat__Transfer_Onat__set(X23450)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X23449),X23450))
      | c_Nat__Transfer_Ois__nat(X23449) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J])]) ).

fof(i_0_10368,plain,
    ! [X33882,X33883] :
      ( ( ~ c_Relation_Osym(X33883,hAPP(c_Relation_Oconverse(X33883,X33883),X33882))
        | c_Relation_Osym(X33883,X33882) )
      & ( ~ c_Relation_Osym(X33883,X33882)
        | c_Relation_Osym(X33883,hAPP(c_Relation_Oconverse(X33883,X33883),X33882)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sym__converse])]) ).

fof(i_0_10369,plain,
    ! [X33825,X33826] :
      ( ( ~ c_Relation_Oantisym(X33826,hAPP(c_Relation_Oconverse(X33826,X33826),X33825))
        | c_Relation_Oantisym(X33826,X33825) )
      & ( ~ c_Relation_Oantisym(X33826,X33825)
        | c_Relation_Oantisym(X33826,hAPP(c_Relation_Oconverse(X33826,X33826),X33825)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_antisym__converse])]) ).

fof(i_0_10370,plain,
    ! [X33804,X33805] :
      ( ( ~ c_Relation_Otrans(X33805,hAPP(c_Relation_Oconverse(X33805,X33805),X33804))
        | c_Relation_Otrans(X33805,X33804) )
      & ( ~ c_Relation_Otrans(X33805,X33804)
        | c_Relation_Otrans(X33805,hAPP(c_Relation_Oconverse(X33805,X33805),X33804)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__converse])]) ).

fof(i_0_10371,plain,
    ! [X32411,X32412] :
      ( ( ~ c_Wellfounded_Oacyclic(X32412,hAPP(c_Relation_Oconverse(X32412,X32412),X32411))
        | c_Wellfounded_Oacyclic(X32412,X32411) )
      & ( ~ c_Wellfounded_Oacyclic(X32412,X32411)
        | c_Wellfounded_Oacyclic(X32412,hAPP(c_Relation_Oconverse(X32412,X32412),X32411)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acyclic__converse])]) ).

fof(i_0_10372,plain,
    ! [X17513] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17513),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[i_0_6015]) ).

fof(i_0_10373,plain,
    ! [X17511] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17511),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[i_0_6016]) ).

fof(i_0_10374,plain,
    ! [X17268] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17268),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[i_0_6017]) ).

fof(i_0_10375,plain,
    ! [X29362,X29363] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X29363),X29362))
      | hAPP(c_Finite__Set_Ocard(X29363),hAPP(c_List_Oset(X29363),X29362)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29363)),X29362) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__card])]) ).

fof(i_0_10376,plain,
    ! [X31526,X31527] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31527)),c_List_Oremdups(X31527,X31526)) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31527)),X31526)
        | c_List_Oremdups(X31527,X31526) = X31526 )
      & ( c_List_Oremdups(X31527,X31526) != X31526
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31527)),c_List_Oremdups(X31527,X31526)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31527)),X31526) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_length__remdups__eq])]) ).

fof(i_0_10377,plain,
    ! [X32479,X32480,X32481] : hAPP(c_Relation_ODomain(X32481,X32480),hAPP(c_Relation_Oconverse(X32480,X32481),X32479)) = hAPP(c_Relation_ORange(X32480,X32481),X32479),
    inference(variable_rename,[status(thm)],[fact_Domain__converse]) ).

fof(i_0_10378,plain,
    ! [X32482,X32483,X32484] : hAPP(c_Relation_ORange(X32484,X32483),hAPP(c_Relation_Oconverse(X32483,X32484),X32482)) = hAPP(c_Relation_ODomain(X32483,X32484),X32482),
    inference(variable_rename,[status(thm)],[fact_Range__converse]) ).

fof(i_0_10379,plain,
    ! [X32405,X32406] : c_Transitive__Closure_Ortrancl(X32406,hAPP(c_Relation_Oconverse(X32406,X32406),X32405)) = hAPP(c_Relation_Oconverse(X32406,X32406),c_Transitive__Closure_Ortrancl(X32406,X32405)),
    inference(variable_rename,[status(thm)],[fact_rtrancl__converse]) ).

fof(i_0_10380,plain,
    ! [X31518,X31519,X31520] : c_List_Oremdups(X31520,hAPP(c_List_Ofilter(X31520,X31519),X31518)) = hAPP(c_List_Ofilter(X31520,X31519),c_List_Oremdups(X31520,X31518)),
    inference(variable_rename,[status(thm)],[fact_remdups__filter]) ).

fof(i_0_10381,plain,
    ! [X32476,X32477,X32478] : hAPP(c_Relation_ORange(X32478,X32477),X32476) = hAPP(c_Relation_ODomain(X32477,X32478),hAPP(c_Relation_Oconverse(X32478,X32477),X32476)),
    inference(variable_rename,[status(thm)],[fact_Range__def]) ).

fof(i_0_10382,plain,
    ! [X32011,X32012,X32013] :
      ( ( ~ hBOOL(hAPP(X32011,X32013))
        | hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X32012),X32011))
        | ~ class_Enum_Oenum(X32012) )
      & ( ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X32012),X32011))
        | hBOOL(hAPP(X32011,esk416_2(X32011,X32012)))
        | ~ class_Enum_Oenum(X32012) ) ),
    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_10383,plain,
    ! [X32007,X32008,X32010] :
      ( ( ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X32008),X32007))
        | hBOOL(hAPP(X32007,esk415_2(X32007,X32008)))
        | ~ class_Enum_Oenum(X32008) )
      & ( ~ hBOOL(hAPP(X32007,X32010))
        | hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X32008),X32007))
        | ~ class_Enum_Oenum(X32008) ) ),
    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_10384,plain,
    ! [X29061,X29062,X29063,X29064] :
      ( ( hAPP(hAPP(c_List_Olist__update(X29064,X29063),X29062),X29061) != c_List_Olist_ONil(X29064)
        | X29063 = c_List_Olist_ONil(X29064) )
      & ( X29063 != c_List_Olist_ONil(X29064)
        | hAPP(hAPP(c_List_Olist__update(X29064,X29063),X29062),X29061) = c_List_Olist_ONil(X29064) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__update__nonempty])]) ).

fof(i_0_10385,plain,
    ! [X30093,X30094,X30095,X30096] :
      ( ( hAPP(hAPP(c_List_Omap(X30096,X30095),X30094),X30093) != c_List_Olist_ONil(X30095)
        | X30093 = c_List_Olist_ONil(X30096) )
      & ( X30093 != c_List_Olist_ONil(X30096)
        | hAPP(hAPP(c_List_Omap(X30096,X30095),X30094),X30093) = c_List_Olist_ONil(X30095) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__is__Nil__conv])]) ).

fof(i_0_10386,plain,
    ! [X30086,X30087,X30088,X30089] :
      ( ( c_List_Olist_ONil(X30089) != hAPP(hAPP(c_List_Omap(X30088,X30089),X30087),X30086)
        | X30086 = c_List_Olist_ONil(X30088) )
      & ( X30086 != c_List_Olist_ONil(X30088)
        | c_List_Olist_ONil(X30089) = hAPP(hAPP(c_List_Omap(X30088,X30089),X30087),X30086) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nil__is__map__conv])]) ).

fof(i_0_10387,plain,
    ! [X19879,X19880] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19880),X19879) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19879),X19880) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | X19880 = X19879 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diffs0__imp__equal])]) ).

fof(i_0_10388,plain,
    ! [X26238,X26239,X26240] :
      ( ~ class_Groups_Ocomm__monoid__add(X26240)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26239,X26240),X26238),c_Orderings_Obot__class_Obot(tc_fun(X26239,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(X26240) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__empty])]) ).

fof(i_0_10389,plain,
    ! [X26235,X26236,X26237] :
      ( ~ class_Groups_Ocomm__monoid__add(X26237)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26236,X26237),X26235),c_Orderings_Obot__class_Obot(tc_fun(X26236,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(X26237) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum_Oempty])]) ).

fof(i_0_10390,plain,
    ! [X24671,X24672,X24673] :
      ( ~ class_Groups_Ocomm__monoid__mult(X24673)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24672,X24673),X24671),c_Orderings_Obot__class_Obot(tc_fun(X24672,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(X24673) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__empty])]) ).

fof(i_0_10391,plain,
    ! [X24668,X24669,X24670] :
      ( ~ class_Groups_Ocomm__monoid__mult(X24670)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24669,X24670),X24668),c_Orderings_Obot__class_Obot(tc_fun(X24669,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(X24670) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod_Oempty])]) ).

fof(i_0_10392,plain,
    ! [X17514,X17515] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17515),X17514))
      | X17514 != 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_10393,plain,
    ! [X26678] :
      ( ~ class_Finite__Set_Ofinite(X26678)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X26678),c_Orderings_Otop__class_Otop(tc_fun(X26678,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV])]) ).

fof(i_0_10394,plain,
    ! [X21343,X21344,X21345,X21346] :
      ( ( X21344 = c_Groups_Ozero__class_Ozero(X21346)
        | X21345 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21346),X21343),X21344)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21346),X21345),X21344) != X21343
        | ~ class_Fields_Ofield__inverse__zero(X21346) )
      & ( X21344 != c_Groups_Ozero__class_Ozero(X21346)
        | X21343 = c_Groups_Ozero__class_Ozero(X21346)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21346),X21345),X21344) != X21343
        | ~ class_Fields_Ofield__inverse__zero(X21346) )
      & ( X21344 = c_Groups_Ozero__class_Ozero(X21346)
        | X21344 != c_Groups_Ozero__class_Ozero(X21346)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21346),X21345),X21344) = X21343
        | ~ class_Fields_Ofield__inverse__zero(X21346) )
      & ( X21343 != c_Groups_Ozero__class_Ozero(X21346)
        | X21344 != c_Groups_Ozero__class_Ozero(X21346)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21346),X21345),X21344) = X21343
        | ~ class_Fields_Ofield__inverse__zero(X21346) )
      & ( X21344 = c_Groups_Ozero__class_Ozero(X21346)
        | X21345 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21346),X21343),X21344)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21346),X21345),X21344) = X21343
        | ~ class_Fields_Ofield__inverse__zero(X21346) )
      & ( X21343 != c_Groups_Ozero__class_Ozero(X21346)
        | X21345 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21346),X21343),X21344)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21346),X21345),X21344) = X21343
        | ~ class_Fields_Ofield__inverse__zero(X21346) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__eq__eq])])]) ).

fof(i_0_10395,plain,
    ! [X21339,X21340,X21341,X21342] :
      ( ( X21339 = c_Groups_Ozero__class_Ozero(X21342)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21342),X21341),X21339) = X21340
        | X21341 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21342),X21340),X21339)
        | ~ class_Fields_Ofield__inverse__zero(X21342) )
      & ( X21339 != c_Groups_Ozero__class_Ozero(X21342)
        | X21341 = c_Groups_Ozero__class_Ozero(X21342)
        | X21341 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21342),X21340),X21339)
        | ~ class_Fields_Ofield__inverse__zero(X21342) )
      & ( X21339 = c_Groups_Ozero__class_Ozero(X21342)
        | X21339 != c_Groups_Ozero__class_Ozero(X21342)
        | X21341 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21342),X21340),X21339)
        | ~ class_Fields_Ofield__inverse__zero(X21342) )
      & ( X21341 != c_Groups_Ozero__class_Ozero(X21342)
        | X21339 != c_Groups_Ozero__class_Ozero(X21342)
        | X21341 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21342),X21340),X21339)
        | ~ class_Fields_Ofield__inverse__zero(X21342) )
      & ( X21339 = c_Groups_Ozero__class_Ozero(X21342)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21342),X21341),X21339) != X21340
        | X21341 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21342),X21340),X21339)
        | ~ class_Fields_Ofield__inverse__zero(X21342) )
      & ( X21341 != c_Groups_Ozero__class_Ozero(X21342)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21342),X21341),X21339) != X21340
        | X21341 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21342),X21340),X21339)
        | ~ class_Fields_Ofield__inverse__zero(X21342) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__divide__eq])])]) ).

fof(i_0_10396,plain,
    ! [X19003,X19004] :
      ( ~ class_Rings_Osemiring__1(X19004)
      | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X19004),hAPP(c_Nat_OSuc,X19003)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19004),c_Groups_Oone__class_Oone(X19004)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X19004),X19003)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__Suc])]) ).

fof(i_0_10397,plain,
    ! [X17253] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X17253))),
    inference(variable_rename,[status(thm)],[fact_zero__less__Suc]) ).

fof(i_0_10398,plain,
    ! [X17438,X17439] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17439),X17438))
      | X17438 != X17439 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__not__refl2])]) ).

fof(i_0_10399,plain,
    ! [X17436,X17437] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17437),X17436))
      | X17437 != X17436 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__not__refl3])]) ).

cnf(i_0_10400,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_6018]) ).

fof(i_0_10401,plain,
    ! [X25891] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X25891),hAPP(c_Nat_OSuc,X25891)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X25891),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_atLeastLessThan__singleton]) ).

cnf(i_0_10402,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_5520]) ).

fof(i_0_10403,plain,
    ! [X31715,X31716,X31717] :
      ( ~ class_Orderings_Olinorder(X31717)
      | ~ c_List_Olinorder__class_Osorted(X31717,X31716)
      | c_List_Olinorder__class_Osorted(X31717,c_List_OtakeWhile(X31717,X31715,X31716)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__takeWhile])]) ).

fof(i_0_10404,plain,
    ! [X31539,X31540,X31541] :
      ( ~ class_Orderings_Olinorder(X31541)
      | ~ c_List_Olinorder__class_Osorted(X31541,X31540)
      | c_List_Olinorder__class_Osorted(X31541,c_List_Oremove1(X31541,X31539,X31540)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__remove1])]) ).

fof(i_0_10405,plain,
    ! [X18661,X18662,X18663] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18663),X18662) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18661),X18662)
        | X18663 = X18661
        | X18662 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X18663 != X18661
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18663),X18662) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18661),X18662) )
      & ( X18662 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18663),X18662) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18661),X18662) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__cancel2])])]) ).

fof(i_0_10406,plain,
    ! [X19265,X19266,X19267] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19267),X19266) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19267),X19265)
        | X19267 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X19266 = X19265 )
      & ( X19267 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19267),X19266) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19267),X19265) )
      & ( X19266 != X19265
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19267),X19266) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19267),X19265) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__cancel__disj])])]) ).

fof(i_0_10407,plain,
    ! [X18664,X18665,X18666] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18666),X18665) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18666),X18664)
        | X18665 = X18664
        | X18666 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X18665 != X18664
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18666),X18665) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18666),X18664) )
      & ( X18666 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18666),X18665) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18666),X18664) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__cancel1])])]) ).

fof(i_0_10408,plain,
    ! [X29006,X29007,X29008] :
      ( ( X29008 != c_List_Olist_ONil(X29007)
        | hAPP(c_List_Ohd(X29007),hAPP(hAPP(c_List_Oappend(X29007),X29008),X29006)) = hAPP(c_List_Ohd(X29007),X29006) )
      & ( X29008 = c_List_Olist_ONil(X29007)
        | hAPP(c_List_Ohd(X29007),hAPP(hAPP(c_List_Oappend(X29007),X29008),X29006)) = hAPP(c_List_Ohd(X29007),X29008) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hd__append])]) ).

fof(i_0_10409,plain,
    ! [X17083,X17084] :
      ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X17084),X17083))
      | X17083 = X17084 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_evalc__elim__cases_I1_J])]) ).

fof(i_0_10410,plain,
    ! [X20412,X20413] :
      ( ~ class_Rings_Olinordered__idom(X20413)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20413),c_Groups_Osgn__class_Osgn(X20413,X20412)),hAPP(c_Groups_Oabs__class_Oabs(X20413),X20412)) = X20412 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__sgn__abs])]) ).

fof(i_0_10411,plain,
    ! [X21008] :
      ( ~ class_Rings_Osemiring__1(X21008)
      | hBOOL(hAPP(hAPP(c_member(X21008),c_Groups_Oone__class_Oone(X21008)),c_Nat_Osemiring__1__class_ONats(X21008))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nats__1])]) ).

fof(i_0_10412,plain,
    ! [X20915] :
      ( ~ class_Rings_Oring__1(X20915)
      | hBOOL(hAPP(hAPP(c_member(X20915),c_Groups_Oone__class_Oone(X20915)),c_Int_Oring__1__class_OInts(X20915))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__1])]) ).

fof(i_0_10413,plain,
    ! [X21001] :
      ( ~ class_Rings_Osemiring__1(X21001)
      | hBOOL(hAPP(hAPP(c_member(X21001),c_Groups_Ozero__class_Ozero(X21001)),c_Nat_Osemiring__1__class_ONats(X21001))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nats__0])]) ).

fof(i_0_10414,plain,
    ! [X20903] :
      ( ~ class_Rings_Oring__1(X20903)
      | hBOOL(hAPP(hAPP(c_member(X20903),c_Groups_Ozero__class_Ozero(X20903)),c_Int_Oring__1__class_OInts(X20903))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__0])]) ).

fof(i_0_10415,plain,
    ! [X18527] :
      ( ~ class_Rings_Olinordered__semidom(X18527)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18527),c_Groups_Ozero__class_Ozero(X18527)),c_Groups_Oone__class_Oone(X18527))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__one])]) ).

fof(i_0_10416,plain,
    ! [X18725] :
      ( ~ class_Rings_Olinordered__semidom(X18725)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18725),c_Groups_Ozero__class_Ozero(X18725)),c_Groups_Oone__class_Oone(X18725))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__one])]) ).

fof(i_0_10417,plain,
    ! [X21364,X21365,X21366,X21367] :
      ( ~ class_Rings_Odivision__ring(X21367)
      | X21366 = c_Groups_Ozero__class_Ozero(X21367)
      | X21365 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21367),X21364),X21366)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21367),X21365),X21366) = X21364 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__eq__imp])]) ).

fof(i_0_10418,plain,
    ! [X21368,X21369,X21370,X21371] :
      ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21371),X21369),X21370) != X21368
        | X21369 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21371),X21368),X21370)
        | X21370 = c_Groups_Ozero__class_Ozero(X21371)
        | ~ class_Rings_Odivision__ring(X21371) )
      & ( X21369 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21371),X21368),X21370)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21371),X21369),X21370) = X21368
        | X21370 = c_Groups_Ozero__class_Ozero(X21371)
        | ~ class_Rings_Odivision__ring(X21371) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__divide__eq__eq])])]) ).

fof(i_0_10419,plain,
    ! [X21372,X21373,X21374,X21375] :
      ( ( X21373 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21375),X21372),X21374)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21375),X21373),X21374) = X21372
        | X21374 = c_Groups_Ozero__class_Ozero(X21375)
        | ~ class_Rings_Odivision__ring(X21375) )
      & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21375),X21373),X21374) != X21372
        | X21373 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21375),X21372),X21374)
        | X21374 = c_Groups_Ozero__class_Ozero(X21375)
        | ~ class_Rings_Odivision__ring(X21375) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__eq__divide__eq])])]) ).

fof(i_0_10420,plain,
    ! [X21360,X21361,X21362,X21363] :
      ( ~ class_Rings_Odivision__ring(X21363)
      | X21362 = c_Groups_Ozero__class_Ozero(X21363)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21363),X21361),X21362) != X21360
      | X21361 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21363),X21360),X21362) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__divide__imp])]) ).

fof(i_0_10421,plain,
    ! [X19985,X19986,X19987] :
      ( ~ class_Groups_Ogroup__add(X19987)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19987),X19986),hAPP(c_Groups_Ouminus__class_Ouminus(X19987),X19985)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19987),X19986),X19985) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__minus__eq__add])]) ).

fof(i_0_10422,plain,
    ! [X24020,X24021,X24022] :
      ( ~ class_Lattices_Oboolean__algebra(X24022)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X24022),X24021),X24020) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24022),X24021),hAPP(c_Groups_Ouminus__class_Ouminus(X24022),X24020)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__eq])]) ).

fof(i_0_10423,plain,
    ! [X19976,X19977,X19978] :
      ( ~ class_Rings_Ocomm__ring__1(X19978)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19978),X19977),X19976) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19978),X19977),hAPP(c_Groups_Ouminus__class_Ouminus(X19978),X19976)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J])]) ).

fof(i_0_10424,plain,
    ! [X19982,X19983,X19984] :
      ( ~ class_Groups_Oab__group__add(X19984)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19984),X19983),X19982) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19984),X19983),hAPP(c_Groups_Ouminus__class_Ouminus(X19984),X19982)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__diff__minus])]) ).

fof(i_0_10425,plain,
    ! [X19979,X19980,X19981] :
      ( ~ class_Groups_Ogroup__add(X19981)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19981),X19980),X19979) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19981),X19980),hAPP(c_Groups_Ouminus__class_Ouminus(X19981),X19979)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__def])]) ).

fof(i_0_10426,plain,
    ! [X20653,X20654] :
      ( ~ class_Int_Onumber__ring(X20654)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20654),hAPP(c_Int_Onumber__class_Onumber__of(X20654),c_Int_OMin)),X20653) = hAPP(c_Groups_Ouminus__class_Ouminus(X20654),X20653) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__minus1])]) ).

fof(i_0_10427,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_10428,plain,
    ! [X17466] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17466),X17466)),
    inference(variable_rename,[status(thm)],[i_0_6019]) ).

fof(i_0_10429,plain,
    ! [X17440] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17440),X17440)),
    inference(variable_rename,[status(thm)],[i_0_6020]) ).

fof(i_0_10430,plain,
    ! [X29003,X29004,X29005] :
      ( X29005 = c_List_Olist_ONil(X29004)
      | hAPP(c_List_Ohd(X29004),hAPP(hAPP(c_List_Oappend(X29004),X29005),X29003)) = hAPP(c_List_Ohd(X29004),X29005) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hd__append2])]) ).

cnf(i_0_10431,plain,
    ( X1 = X2
    | c_Int_OBit0(X1) != c_Int_OBit0(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6021]) ).

fof(i_0_10432,plain,
    ! [X17446,X17447,X17448] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17448),X17447) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17446),X17447)
        | X17448 = X17446 )
      & ( X17448 != X17446
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17448),X17447) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17446),X17447) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__right__cancel])]) ).

fof(i_0_10433,plain,
    ! [X17449,X17450,X17451] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17451),X17450) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17451),X17449)
        | X17450 = X17449 )
      & ( X17450 != X17449
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17451),X17450) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17451),X17449) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel])]) ).

fof(i_0_10434,plain,
    ! [X27759,X27760] : hAPP(c_Set_OCollect(X27760),hAPP(c_fequal,X27759)) = hAPP(hAPP(c_Set_Oinsert(X27760),X27759),c_Orderings_Obot__class_Obot(tc_fun(X27760,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_singleton__conv2]) ).

fof(i_0_10435,plain,
    ! [X31473,X31474,X31475] :
      ( ~ class_Orderings_Olinorder(X31475)
      | ~ c_List_Olinorder__class_Osorted(X31475,X31474)
      | c_List_Olinorder__class_Osorted(X31475,hAPP(hAPP(c_List_Odrop(X31475),X31473),X31474)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__drop])]) ).

fof(i_0_10436,plain,
    ! [X31476,X31477,X31478] :
      ( ~ class_Orderings_Olinorder(X31478)
      | ~ c_List_Olinorder__class_Osorted(X31478,X31477)
      | c_List_Olinorder__class_Osorted(X31478,hAPP(hAPP(c_List_Otake(X31478),X31476),X31477)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__take])]) ).

fof(i_0_10437,plain,
    ! [X23542] : hBOOL(hAPP(c_Finite__Set_Ofinite(X23542),c_Orderings_Obot__class_Obot(tc_fun(X23542,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_finite_Oequations_I1_J]) ).

fof(i_0_10438,plain,
    ! [X23535] : hBOOL(hAPP(c_Finite__Set_Ofinite(X23535),c_Orderings_Obot__class_Obot(tc_fun(X23535,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_finite_OemptyI]) ).

fof(i_0_10439,plain,
    ! [X25459,X25460] : hAPP(c_Set_OPow(X25460),X25459) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X25460,tc_HOL_Obool),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Pow__not__empty]) ).

fof(i_0_10440,plain,
    ! [X26245,X26246,X26247,X26248] :
      ( ~ class_Groups_Ocomm__monoid__add(X26248)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X26247),X26246))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26247,X26248),X26245),X26246) = c_Groups_Ozero__class_Ozero(X26248) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6022])]) ).

fof(i_0_10441,plain,
    ! [X26241,X26242,X26243,X26244] :
      ( ~ class_Groups_Ocomm__monoid__add(X26244)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X26243),X26242))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X26243,X26244),X26241),X26242) = c_Groups_Ozero__class_Ozero(X26244) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6023])]) ).

fof(i_0_10442,plain,
    ! [X24678,X24679,X24680,X24681] :
      ( ~ class_Groups_Ocomm__monoid__mult(X24681)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X24680),X24679))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24680,X24681),X24678),X24679) = c_Groups_Oone__class_Oone(X24681) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6024])]) ).

fof(i_0_10443,plain,
    ! [X24674,X24675,X24676,X24677] :
      ( ~ class_Groups_Ocomm__monoid__mult(X24677)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X24676),X24675))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X24676,X24677),X24674),X24675) = c_Groups_Oone__class_Oone(X24677) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6025])]) ).

fof(i_0_10444,plain,
    ! [X26741] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X26741,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X26741,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X26741,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Compl__UNIV__eq]) ).

fof(i_0_10445,plain,
    ! [X26742] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X26742,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X26742,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X26742,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Compl__empty__eq]) ).

fof(i_0_10446,plain,
    ! [X26654] : hAPP(c_Set_OPow(X26654),c_Orderings_Otop__class_Otop(tc_fun(X26654,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X26654,tc_HOL_Obool),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Pow__UNIV]) ).

fof(i_0_10447,plain,
    ! [X25330] : c_Relation_OId__on(X25330,c_Orderings_Obot__class_Obot(tc_fun(X25330,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X25330,X25330),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Id__on__empty]) ).

fof(i_0_10448,plain,
    ! [X23924,X23925] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X23925,tc_HOL_Obool)),X23924),X23924) = X23924,
    inference(variable_rename,[status(thm)],[fact_Int__absorb]) ).

fof(i_0_10449,plain,
    ! [X22934,X22935] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X22935,tc_HOL_Obool)),X22934),X22934) = X22934,
    inference(variable_rename,[status(thm)],[fact_Un__absorb]) ).

fof(i_0_10450,plain,
    ! [X31989,X31990] :
      ( ~ c_Wellfounded_Owf(X31990,X31989)
      | c_Wellfounded_OwfP(X31990,c_FunDef_Oin__rel(X31990,X31990,X31989)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__in__rel])]) ).

fof(i_0_10451,plain,
    ! [X28184,X28185,X28186] :
      ( ~ c_Wellfounded_Owf(X28186,X28185)
      | c_Wellfounded_Owf(X28186,c_Wellfounded_Omlex__prod(X28186,X28184,X28185)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__mlex])]) ).

fof(i_0_10452,plain,
    ! [X20647] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20647))),
    inference(variable_rename,[status(thm)],[i_0_6026]) ).

fof(i_0_10453,plain,
    ! [X33938,X33939,X33940] :
      ( ( c_Relation_Orefl__on(X33940,X33939,X33938)
        | ~ c_Equiv__Relations_Oequiv(X33940,X33939,X33938) )
      & ( c_Relation_Osym(X33940,X33938)
        | ~ c_Equiv__Relations_Oequiv(X33940,X33939,X33938) )
      & ( c_Relation_Otrans(X33940,X33938)
        | ~ c_Equiv__Relations_Oequiv(X33940,X33939,X33938) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6027])])]) ).

fof(i_0_10454,plain,
    ! [X27025,X27026] :
      ( ~ class_Orderings_Olinorder(X27026)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27026),X27025))
      | c_Big__Operators_Olinorder__class_OMin(X27026,X27025) = hAPP(c_Finite__Set_Ofold1(X27026,c_Orderings_Oord__class_Omin(X27026)),X27025) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_OF__eq])]) ).

fof(i_0_10455,plain,
    ! [X27027,X27028] :
      ( ~ class_Orderings_Olinorder(X27028)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27028),X27027))
      | c_Big__Operators_Olinorder__class_OMax(X27028,X27027) = hAPP(c_Finite__Set_Ofold1(X27028,c_Orderings_Oord__class_Omax(X27028)),X27027) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_OF__eq])]) ).

fof(i_0_10456,plain,
    ! [X27021,X27022] :
      ( ~ class_Lattices_Olattice(X27022)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27022),X27021))
      | c_Big__Operators_Olattice__class_OSup__fin(X27022,X27021) = hAPP(c_Finite__Set_Ofold1(X27022,c_Lattices_Osemilattice__sup__class_Osup(X27022)),X27021) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_OF__eq])]) ).

fof(i_0_10457,plain,
    ! [X27023,X27024] :
      ( ~ class_Lattices_Olattice(X27024)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27024),X27023))
      | c_Big__Operators_Olattice__class_OInf__fin(X27024,X27023) = hAPP(c_Finite__Set_Ofold1(X27024,c_Lattices_Osemilattice__inf__class_Oinf(X27024)),X27023) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_OF__eq])]) ).

fof(i_0_10458,plain,
    ! [X17269] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17269),hAPP(c_Nat_OSuc,X17269))),
    inference(variable_rename,[status(thm)],[fact_lessI]) ).

fof(i_0_10459,plain,
    ! [X33425,X33426,X33427] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X33427)),c_List_Oreplicate(X33427,X33426,X33425)) = X33426,
    inference(variable_rename,[status(thm)],[fact_length__replicate]) ).

fof(i_0_10460,plain,
    ! [X24018,X24019] :
      ( ~ class_Lattices_Oboolean__algebra(X24019)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24019),hAPP(c_Groups_Ouminus__class_Ouminus(X24019),X24018)),X24018) = c_Orderings_Obot__class_Obot(X24019) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__inf__bot])]) ).

fof(i_0_10461,plain,
    ! [X26780,X26781] :
      ( ~ class_Lattices_Oboolean__algebra(X26781)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X26781),hAPP(c_Groups_Ouminus__class_Ouminus(X26781),X26780)),X26780) = c_Orderings_Otop__class_Otop(X26781) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__sup__top])]) ).

fof(i_0_10462,plain,
    ! [X18319,X18320] :
      ( ~ class_Groups_Oab__group__add(X18320)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18320),hAPP(c_Groups_Ouminus__class_Ouminus(X18320),X18319)),X18319) = c_Groups_Ozero__class_Ozero(X18320) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__left__minus])]) ).

fof(i_0_10463,plain,
    ! [X18321,X18322] :
      ( ~ class_Groups_Ogroup__add(X18322)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18322),hAPP(c_Groups_Ouminus__class_Ouminus(X18322),X18321)),X18321) = c_Groups_Ozero__class_Ozero(X18322) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_left__minus])]) ).

fof(i_0_10464,plain,
    ! [X29520,X29521,X29522] :
      ( X29522 != c_List_Olist_ONil(X29521)
      | c_List_Olast(X29521,hAPP(hAPP(c_List_Oappend(X29521),X29520),X29522)) = c_List_Olast(X29521,X29520) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__appendL])]) ).

fof(i_0_10465,plain,
    ! [X29514,X29515,X29516] :
      ( ( X29516 != c_List_Olist_ONil(X29515)
        | c_List_Olast(X29515,hAPP(hAPP(c_List_Oappend(X29515),X29514),X29516)) = c_List_Olast(X29515,X29514) )
      & ( X29516 = c_List_Olist_ONil(X29515)
        | c_List_Olast(X29515,hAPP(hAPP(c_List_Oappend(X29515),X29514),X29516)) = c_List_Olast(X29515,X29516) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__append])]) ).

fof(i_0_10466,plain,
    ! [X19996,X19997] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19997),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19997),X19996)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_diff__add__0]) ).

fof(i_0_10467,plain,
    ! [X28787,X28788,X28789] : c_List_Osublist(X28789,X28788,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X28787)) = hAPP(hAPP(c_List_Otake(X28789),X28787),X28788),
    inference(variable_rename,[status(thm)],[fact_sublist__upt__eq__take]) ).

fof(i_0_10468,plain,
    ! [X18659,X18660] :
      ( ~ class_Orderings_Obot(X18660)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18660),c_Orderings_Obot__class_Obot(X18660)),X18659)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bot__least])]) ).

fof(i_0_10469,plain,
    ! [X22089,X22090] :
      ( X22090 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22089,X22090),c_Divides_Odivmod__int(X22089,X22090))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__int__correct])]) ).

fof(i_0_10470,plain,
    ! [X21900,X21901] :
      ( ( X21901 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Opdivmod(X21900,X21901) = 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),X21900)) )
      & ( X21901 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Opdivmod(X21900,X21901) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X21900),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X21901)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pdivmod__posDivAlg])]) ).

fof(i_0_10471,plain,
    ! [X31453,X31454] :
      ( ~ class_Orderings_Olinorder(X31454)
      | c_List_Olinorder__class_Osorted(X31454,hAPP(hAPP(c_List_Olist_OCons(X31454),X31453),c_List_Olist_ONil(X31454))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__single])]) ).

fof(i_0_10472,plain,
    ! [X29508,X29509,X29510] :
      ( X29510 = c_List_Olist_ONil(X29509)
      | c_List_Olast(X29509,hAPP(hAPP(c_List_Olist_OCons(X29509),X29508),X29510)) = c_List_Olast(X29509,X29510) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__ConsR])]) ).

fof(i_0_10473,plain,
    ! [X29505,X29506,X29507] :
      ( ( X29507 != c_List_Olist_ONil(X29506)
        | c_List_Olast(X29506,hAPP(hAPP(c_List_Olist_OCons(X29506),X29505),X29507)) = X29505 )
      & ( X29507 = c_List_Olist_ONil(X29506)
        | c_List_Olast(X29506,hAPP(hAPP(c_List_Olist_OCons(X29506),X29505),X29507)) = c_List_Olast(X29506,X29507) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last_Osimps])]) ).

fof(i_0_10474,plain,
    ! [X29517,X29518,X29519] :
      ( X29519 = c_List_Olist_ONil(X29518)
      | c_List_Olast(X29518,hAPP(hAPP(c_List_Oappend(X29518),X29517),X29519)) = c_List_Olast(X29518,X29519) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__appendR])]) ).

fof(i_0_10475,plain,
    ! [X21679,X21680] :
      ( ( X21680 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Nitpick_Onat__gcd(X21679,X21680) = X21679 )
      & ( X21680 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Nitpick_Onat__gcd(X21679,X21680) = c_Nitpick_Onat__gcd(X21680,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21679,X21680)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__gcd_Osimps])]) ).

fof(i_0_10476,plain,
    ! [X25823,X25824] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X25824)),X25823) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X25824,X25823),
    inference(variable_rename,[status(thm)],[fact_atLeastSucLessThan__greaterThanLessThan]) ).

fof(i_0_10477,plain,
    ! [X25793,X25794] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X25794),X25793)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25793),X25794),
    inference(variable_rename,[status(thm)],[fact_card__atLeastLessThan]) ).

fof(i_0_10478,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_10479,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_10480,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_10481,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_10482,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_10483,plain,
    ! [X29068,X29069,X29070] : hAPP(hAPP(c_List_Ozip(X29070,X29069),c_List_Olist_ONil(X29070)),X29068) = c_List_Olist_ONil(tc_prod(X29070,X29069)),
    inference(variable_rename,[status(thm)],[fact_zip__Nil]) ).

fof(i_0_10484,plain,
    ! [X26861,X26862] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X26862,tc_HOL_Obool)),X26861)),
    inference(variable_rename,[status(thm)],[fact_top1I]) ).

fof(i_0_10485,plain,
    ! [X27937,X27938] : hAPP(c_Set_Ovimage(X27938,X27938,c_Fun_Oid(X27938)),X27937) = X27937,
    inference(variable_rename,[status(thm)],[fact_vimage__id]) ).

fof(i_0_10486,plain,
    ! [X27141,X27142] : hAPP(c_Set_Ovimage(X27142,X27142,c_COMBI(X27142)),X27141) = X27141,
    inference(variable_rename,[status(thm)],[fact_vimage__ident]) ).

fof(i_0_10487,plain,
    ! [X27943,X27944] : hAPP(c_Set_Oimage(X27944,X27944,c_Fun_Oid(X27944)),X27943) = X27943,
    inference(variable_rename,[status(thm)],[fact_image__id]) ).

fof(i_0_10488,plain,
    ! [X23191,X23192] : hAPP(c_Set_Oimage(X23192,X23192,c_COMBI(X23192)),X23191) = X23191,
    inference(variable_rename,[status(thm)],[fact_image__ident]) ).

fof(i_0_10489,plain,
    ! [X32174,X32175] : c_Relation_Orefl__on(X32175,c_Orderings_Otop__class_Otop(tc_fun(X32175,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X32175,X32174)),
    inference(variable_rename,[status(thm)],[fact_refl__rtrancl]) ).

fof(i_0_10490,plain,
    ! [X33461,X33462,X33463] :
      ( X33463 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | hAPP(c_List_Ohd(X33462),c_List_Oreplicate(X33462,X33463,X33461)) = X33461 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hd__replicate])]) ).

cnf(i_0_10491,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_6028]) ).

cnf(i_0_10492,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_6029]) ).

fof(i_0_10493,plain,
    ! [X34308,X34309] :
      ( ~ hBOOL(hAPP(hAPP(c_fimplies,X34309),X34308))
      | ~ hBOOL(X34309)
      | hBOOL(X34308) ),
    inference(variable_rename,[status(thm)],[i_0_6030]) ).

fof(i_0_10494,plain,
    ! [X26544,X26545] :
      ( ~ class_Orderings_Olinorder(X26545)
      | hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X26545,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X26545),X26544)) = hAPP(c_SetInterval_Oord__class_OatMost(X26545),X26544) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Compl__greaterThan])]) ).

fof(i_0_10495,plain,
    ! [X26314,X26315] :
      ( ~ class_Orderings_Olinorder(X26315)
      | hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X26315,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X26315),X26314)) = hAPP(c_SetInterval_Oord__class_OlessThan(X26315),X26314) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Compl__atLeast])]) ).

fof(i_0_10496,plain,
    ! [X26316,X26317] :
      ( ~ class_Orderings_Olinorder(X26317)
      | hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X26317,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X26317),X26316)) = hAPP(c_SetInterval_Oord__class_OatLeast(X26317),X26316) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Compl__lessThan])]) ).

fof(i_0_10497,plain,
    ! [X26542,X26543] :
      ( ~ class_Orderings_Olinorder(X26543)
      | hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X26543,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X26543),X26542)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X26543),X26542) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Compl__atMost])]) ).

fof(i_0_10498,plain,
    ! [X24529,X24530] :
      ( ( hAPP(c_Finite__Set_Ocard(X24530),X24529) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X24529 = c_Orderings_Obot__class_Obot(tc_fun(X24530,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24530),X24529)) )
      & ( X24529 != c_Orderings_Obot__class_Obot(tc_fun(X24530,tc_HOL_Obool))
        | hAPP(c_Finite__Set_Ocard(X24530),X24529) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X24530),X24529))
        | hAPP(c_Finite__Set_Ocard(X24530),X24529) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6031])])]) ).

fof(i_0_10499,plain,
    ! [X16956,X16957] : c_Hoare__Mirabelle_Ohoare__derivs(X16957,X16956,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X16957),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_hoare__derivs_Oequations_I1_J]) ).

fof(i_0_10500,plain,
    ! [X16954,X16955] : c_Hoare__Mirabelle_Ohoare__derivs(X16955,X16954,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X16955),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_empty]) ).

fof(i_0_10501,plain,
    ! [X31068,X31069] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X31069)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31069),X31068))
      | X31068 = c_Orderings_Obot__class_Obot(tc_fun(X31069,tc_HOL_Obool))
      | c_Big__Operators_Olattice__class_OInf__fin(X31069,X31068) = c_Complete__Lattice_OInf__class_OInf(X31069,X31068) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin__Inf])]) ).

fof(i_0_10502,plain,
    ! [X30951,X30952] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X30952)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30952),X30951))
      | X30951 = c_Orderings_Obot__class_Obot(tc_fun(X30952,tc_HOL_Obool))
      | c_Big__Operators_Olattice__class_OSup__fin(X30952,X30951) = c_Complete__Lattice_OSup__class_OSup(X30952,X30951) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin__Sup])]) ).

fof(i_0_10503,plain,
    ! [X20900,X20901] :
      ( ~ class_Int_Onumber__ring(X20901)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20901),hAPP(c_Int_Onumber__class_Onumber__of(X20901),c_Int_OPls)),X20900) = X20900 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__numeral__0])]) ).

fof(i_0_10504,plain,
    ! [X17582,X17583] :
      ( ( X17583 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X17583 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17583),X17582) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( X17582 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | X17583 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17583),X17582) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( X17583 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X17582 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17583),X17582) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( X17582 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | X17582 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17583),X17582) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( X17583 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | X17582 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17583),X17582) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( X17583 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X17582 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17583),X17582) = 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_10505,plain,
    ! [X17584,X17585] :
      ( ( X17585 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X17585 = 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),X17585),X17584) )
      & ( X17584 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | X17585 = 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),X17585),X17584) )
      & ( X17585 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X17584 = 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),X17585),X17584) )
      & ( X17584 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | X17584 = 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),X17585),X17584) )
      & ( X17585 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | X17584 != 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),X17585),X17584) )
      & ( X17585 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X17584 != 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),X17585),X17584) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__is__add])])]) ).

fof(i_0_10506,plain,
    ! [X30255,X30256,X30257] :
      ( ~ hBOOL(hAPP(X30256,X30257))
      | hBOOL(hAPP(X30256,c_Hilbert__Choice_OEps(X30255,X30256))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_someI__ex])])]) ).

fof(i_0_10507,plain,
    ! [X30252,X30253,X30254] :
      ( ~ hBOOL(hAPP(X30253,X30254))
      | hBOOL(hAPP(X30253,c_Hilbert__Choice_OEps(X30252,X30253))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_tfl__some])])]) ).

fof(i_0_10508,plain,
    ! [X30249,X30250,X30251] :
      ( ~ hBOOL(hAPP(X30251,X30250))
      | hBOOL(hAPP(X30251,c_Hilbert__Choice_OEps(X30249,X30251))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_someI])]) ).

fof(i_0_10509,plain,
    ! [X34302,X34303] :
      ( ~ hBOOL(hAPP(hAPP(c_fdisj,X34303),X34302))
      | hBOOL(X34303)
      | hBOOL(X34302) ),
    inference(variable_rename,[status(thm)],[i_0_6032]) ).

fof(i_0_10510,plain,
    ! [X25504,X25505] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X25505),X25504) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X25505,X25504),
    inference(variable_rename,[status(thm)],[fact_atLeastSucAtMost__greaterThanAtMost]) ).

fof(i_0_10511,plain,
    ! [X18834,X18835] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18835),X18834),X18834) != c_Groups_Oone__class_Oone(X18835)
        | X18834 = c_Groups_Oone__class_Oone(X18835)
        | X18834 = hAPP(c_Groups_Ouminus__class_Ouminus(X18835),c_Groups_Oone__class_Oone(X18835))
        | ~ class_Rings_Oring__1__no__zero__divisors(X18835) )
      & ( X18834 != c_Groups_Oone__class_Oone(X18835)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18835),X18834),X18834) = c_Groups_Oone__class_Oone(X18835)
        | ~ class_Rings_Oring__1__no__zero__divisors(X18835) )
      & ( X18834 != hAPP(c_Groups_Ouminus__class_Ouminus(X18835),c_Groups_Oone__class_Oone(X18835))
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18835),X18834),X18834) = c_Groups_Oone__class_Oone(X18835)
        | ~ class_Rings_Oring__1__no__zero__divisors(X18835) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_square__eq__1__iff])])]) ).

fof(i_0_10512,plain,
    ! [X16951,X16952] :
      ( hAPP(X16952,esk1_2(X16951,X16952)) != hAPP(X16951,esk1_2(X16951,X16952))
      | X16952 = X16951 ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ext])])]) ).

fof(i_0_10513,plain,
    ! [X29065,X29066,X29067] : hAPP(hAPP(c_List_Ozip(X29067,X29066),X29065),c_List_Olist_ONil(X29066)) = c_List_Olist_ONil(tc_prod(X29067,X29066)),
    inference(variable_rename,[status(thm)],[fact_zip_Osimps_I1_J]) ).

fof(i_0_10514,plain,
    ! [X26104,X26105,X26106,X26107] :
      ( ~ c_Finite__Set_Ofolding__one__idem(X26107,X26106,X26105)
      | hAPP(hAPP(X26106,X26104),X26104) = X26104 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Oidem])]) ).

fof(i_0_10515,plain,
    ! [X30740] : c_Enum_Osublists(X30740,c_List_Olist_ONil(X30740)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X30740)),c_List_Olist_ONil(X30740)),c_List_Olist_ONil(tc_List_Olist(X30740))),
    inference(variable_rename,[status(thm)],[fact_sublists_Osimps_I1_J]) ).

fof(i_0_10516,plain,
    ! [X17243,X17244,X17245] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCall(X17245,X17244,X17243)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_com_Osize_I16_J]) ).

fof(i_0_10517,plain,
    ! [X26676,X26677] :
      ( ~ class_Orderings_Otop(X26677)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26677),X26676),c_Orderings_Otop__class_Otop(X26677))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_top__greatest])]) ).

fof(i_0_10518,plain,
    ! [X29511,X29512,X29513] :
      ( X29513 != c_List_Olist_ONil(X29512)
      | c_List_Olast(X29512,hAPP(hAPP(c_List_Olist_OCons(X29512),X29511),X29513)) = X29511 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__ConsL])]) ).

fof(i_0_10519,plain,
    ! [X33458,X33459,X33460] :
      ( X33460 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | c_List_Olast(X33459,c_List_Oreplicate(X33459,X33460,X33458)) = X33458 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__replicate])]) ).

fof(i_0_10520,plain,
    ! [X21842,X21843,X21844] : hAPP(c_Nat_Onat_Onat__rec(X21844,X21843,X21842),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X21843,
    inference(variable_rename,[status(thm)],[fact_nat__rec__0]) ).

fof(i_0_10521,plain,
    ! [X16993,X16994,X16995] : hAPP(hAPP(c_Set_Oinsert(X16995),X16994),X16993) != c_Orderings_Obot__class_Obot(tc_fun(X16995,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_insert__not__empty]) ).

fof(i_0_10522,plain,
    ! [X16990,X16991,X16992] : c_Orderings_Obot__class_Obot(tc_fun(X16992,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(X16992),X16991),X16990),
    inference(variable_rename,[status(thm)],[fact_empty__not__insert]) ).

fof(i_0_10523,plain,
    ! [X34294,X34295] :
      ( ~ hBOOL(hAPP(hAPP(c_fconj,X34295),X34294))
      | hBOOL(X34295) ),
    inference(variable_rename,[status(thm)],[i_0_6033]) ).

fof(i_0_10524,plain,
    ! [X34296,X34297] :
      ( ~ hBOOL(hAPP(hAPP(c_fconj,X34297),X34296))
      | hBOOL(X34296) ),
    inference(variable_rename,[status(thm)],[i_0_6034]) ).

fof(i_0_10525,plain,
    ! [X19021] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X19021)) = 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),X19021)),
    inference(variable_rename,[status(thm)],[fact_int__Suc]) ).

fof(i_0_10526,plain,
    ! [X20046,X20047] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20047),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X20046)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20047),X20046),
    inference(variable_rename,[status(thm)],[fact_diff__int__def__symmetric]) ).

fof(i_0_10527,plain,
    ! [X20048,X20049] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20049),X20048) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20049),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X20048)),
    inference(variable_rename,[status(thm)],[fact_diff__int__def]) ).

fof(i_0_10528,plain,
    ! [X29327,X29328,X29329] : hAPP(c_List_Otl(X29329),hAPP(hAPP(c_List_Olist_OCons(X29329),X29328),X29327)) = X29327,
    inference(variable_rename,[status(thm)],[fact_tl_Osimps_I2_J]) ).

fof(i_0_10529,plain,
    ! [X29000,X29001,X29002] : hAPP(c_List_Ohd(X29002),hAPP(hAPP(c_List_Olist_OCons(X29002),X29001),X29000)) = X29001,
    inference(variable_rename,[status(thm)],[fact_hd_Osimps]) ).

fof(i_0_10530,plain,
    ! [X20557,X20558,X20559] :
      ( ( X20558 = c_Groups_Ozero__class_Ozero(X20559)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X20559),X20558),X20557) != c_Groups_Ozero__class_Ozero(X20559)
        | ~ class_Power_Opower(X20559)
        | ~ class_Rings_Omult__zero(X20559)
        | ~ class_Rings_Ono__zero__divisors(X20559)
        | ~ class_Rings_Ozero__neq__one(X20559) )
      & ( X20557 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X20559),X20558),X20557) != c_Groups_Ozero__class_Ozero(X20559)
        | ~ class_Power_Opower(X20559)
        | ~ class_Rings_Omult__zero(X20559)
        | ~ class_Rings_Ono__zero__divisors(X20559)
        | ~ class_Rings_Ozero__neq__one(X20559) )
      & ( X20558 != c_Groups_Ozero__class_Ozero(X20559)
        | X20557 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X20559),X20558),X20557) = c_Groups_Ozero__class_Ozero(X20559)
        | ~ class_Power_Opower(X20559)
        | ~ class_Rings_Omult__zero(X20559)
        | ~ class_Rings_Ono__zero__divisors(X20559)
        | ~ class_Rings_Ozero__neq__one(X20559) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__eq__0__iff])])]) ).

fof(i_0_10531,plain,
    ! [X21293,X21294] :
      ( ~ c_Nat__Transfer_Ois__nat(X21294)
      | ~ c_Nat__Transfer_Ois__nat(X21293)
      | c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,X21294,X21293)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__int__nat__function__closures_I2_J])]) ).

fof(i_0_10532,plain,
    ! [X27727,X27728,X27729,X27730,X27732] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(X27728,tc_HOL_Obool)) != hAPP(c_Set_OCollect(X27728),X27727)
        | ~ hBOOL(hAPP(X27727,X27729)) )
      & ( hBOOL(hAPP(X27730,esk290_1(X27730)))
        | c_Orderings_Obot__class_Obot(tc_fun(X27732,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X27732),X27730) ) ),
    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_6035])])])])]) ).

fof(i_0_10533,plain,
    ! [X27721,X27722,X27723,X27724,X27726] :
      ( ( hAPP(c_Set_OCollect(X27722),X27721) != c_Orderings_Obot__class_Obot(tc_fun(X27722,tc_HOL_Obool))
        | ~ hBOOL(hAPP(X27721,X27723)) )
      & ( hBOOL(hAPP(X27724,esk289_1(X27724)))
        | hAPP(c_Set_OCollect(X27726),X27724) = c_Orderings_Obot__class_Obot(tc_fun(X27726,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_6036])])])])]) ).

fof(i_0_10534,plain,
    ! [X34286,X34287] :
      ( ~ hBOOL(hAPP(hAPP(c_fequal,X34287),X34286))
      | X34287 = X34286 ),
    inference(variable_rename,[status(thm)],[i_0_6037]) ).

fof(i_0_10535,plain,
    ! [X21534,X21535] :
      ( ~ class_Fields_Ofield__inverse__zero(X21535)
      | ~ class_Int_Onumber__ring(X21535)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21535),X21534),hAPP(c_Int_Onumber__class_Onumber__of(X21535),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(X21535),X21534) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__minus1])]) ).

fof(i_0_10536,plain,
    ! [X28328,X28329,X28330] :
      ( ~ c_Wellfounded_Owf(X28330,X28329)
      | c_Wellfounded_Owf(tc_List_Olist(X28330),hAPP(c_List_Olexn(X28330,X28329),X28328)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__lexn])]) ).

fof(i_0_10537,plain,
    ! [X29058,X29059,X29060] : hAPP(hAPP(c_List_Olist__update(X29060,c_List_Olist_ONil(X29060)),X29059),X29058) = c_List_Olist_ONil(X29060),
    inference(variable_rename,[status(thm)],[fact_list__update_Osimps_I1_J]) ).

fof(i_0_10538,plain,
    ! [X29055,X29056,X29057] : hAPP(hAPP(c_List_Olist__update(X29057,c_List_Olist_ONil(X29057)),X29056),X29055) = c_List_Olist_ONil(X29057),
    inference(variable_rename,[status(thm)],[fact_list__update__code_I1_J]) ).

fof(i_0_10539,plain,
    ! [X20493] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X20493) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[fact_power__Suc__0]) ).

fof(i_0_10540,plain,
    ! [X31135,X31136] : c_List_Oinsert(X31136,X31135,c_List_Olist_ONil(X31136)) = hAPP(hAPP(c_List_Olist_OCons(X31136),X31135),c_List_Olist_ONil(X31136)),
    inference(variable_rename,[status(thm)],[fact_insert__Nil]) ).

fof(i_0_10541,plain,
    ! [X28811,X28812] : hBOOL(hAPP(c_Finite__Set_Ofinite(X28812),hAPP(c_List_Oset(X28812),X28811))),
    inference(variable_rename,[status(thm)],[fact_finite__set]) ).

fof(i_0_10542,plain,
    ! [X32449,X32450,X32451] : hAPP(c_Relation_Oconverse(X32451,X32450),hAPP(c_Relation_Oconverse(X32450,X32451),X32449)) = X32449,
    inference(variable_rename,[status(thm)],[fact_converse__converse]) ).

fof(i_0_10543,plain,
    ! [X26113] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X26113)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X26113),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X26113)),
    inference(variable_rename,[status(thm)],[fact_lessThan__Suc]) ).

fof(i_0_10544,plain,
    ! [X32453,X32454] : hAPP(c_Relation_OField(X32454),hAPP(c_Relation_Oconverse(X32454,X32454),X32453)) = hAPP(c_Relation_OField(X32454),X32453),
    inference(variable_rename,[status(thm)],[fact_Field__converse]) ).

fof(i_0_10545,plain,
    ! [X20406,X20407] :
      ( ~ class_Int_Onumber__ring(X20407)
      | hAPP(c_Int_Onumber__class_Onumber__of(X20407),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X20406)) = hAPP(c_Groups_Ouminus__class_Ouminus(X20407),hAPP(c_Int_Onumber__class_Onumber__of(X20407),X20406)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__minus])]) ).

fof(i_0_10546,plain,
    ! [X18188,X18189] :
      ( ~ class_Rings_Oring__1(X18189)
      | hAPP(c_Int_Oring__1__class_Oof__int(X18189),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X18188)) = hAPP(c_Groups_Ouminus__class_Ouminus(X18189),hAPP(c_Int_Oring__1__class_Oof__int(X18189),X18188)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__minus])]) ).

fof(i_0_10547,plain,
    ! [X20408,X20409] :
      ( ~ class_Int_Onumber__ring(X20409)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X20409),hAPP(c_Int_Onumber__class_Onumber__of(X20409),X20408)) = hAPP(c_Int_Onumber__class_Onumber__of(X20409),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X20408)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_arith__simps_I30_J])]) ).

fof(i_0_10548,plain,
    ! [X20494,X20495] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X20495),X20494) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | X20494 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X20495 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( X20494 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X20495),X20494) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( X20495 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X20495),X20494) = 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_10549,plain,
    ! [X18467,X18468,X18469] :
      ( ~ class_Orderings_Opreorder(X18469)
      | X18468 != X18467
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18469),X18468),X18467)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__eq__refl])]) ).

fof(i_0_10550,plain,
    ! [X17835,X17836] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(X17836,X17835)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X17835)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[fact_com_Osize_I6_J]) ).

fof(i_0_10551,plain,
    ! [X18316,X18317,X18318] :
      ( ~ class_Groups_Ogroup__add(X18318)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18318),X18317),X18316) != c_Groups_Ozero__class_Ozero(X18318)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X18318),X18317) = X18316 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__unique])]) ).

fof(i_0_10552,plain,
    ! [X18323,X18324,X18325] :
      ( ( X18324 != hAPP(c_Groups_Ouminus__class_Ouminus(X18325),X18323)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18325),X18324),X18323) = c_Groups_Ozero__class_Ozero(X18325)
        | ~ class_Groups_Ogroup__add(X18325) )
      & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18325),X18324),X18323) != c_Groups_Ozero__class_Ozero(X18325)
        | X18324 = hAPP(c_Groups_Ouminus__class_Ouminus(X18325),X18323)
        | ~ class_Groups_Ogroup__add(X18325) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__neg__iff__add__eq__0])])]) ).

fof(i_0_10553,plain,
    ! [X31571,X31572] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31572)),c_List_Oremdups(X31572,X31571)) = hAPP(c_Finite__Set_Ocard(X31572),hAPP(c_List_Oset(X31572),X31571)),
    inference(variable_rename,[status(thm)],[fact_length__remdups__card__conv]) ).

fof(i_0_10554,plain,
    ! [X27715] : c_Orderings_Otop__class_Otop(tc_fun(X27715,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X27715),hAPP(c_COMBK(tc_HOL_Obool,X27715),c_fTrue)),
    inference(variable_rename,[status(thm)],[fact_UNIV__def]) ).

fof(i_0_10555,plain,
    ! [X27733] : c_Orderings_Obot__class_Obot(tc_fun(X27733,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X27733),hAPP(c_COMBK(tc_HOL_Obool,X27733),c_fFalse)),
    inference(variable_rename,[status(thm)],[fact_empty__def]) ).

fof(i_0_10556,plain,
    ! [X25463,X25464] :
      ( ~ c_Nat__Transfer_Ois__nat(X25464)
      | c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X25464,X25463)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SetInterval_Otransfer__int__nat__set__function__closures])]) ).

fof(i_0_10557,plain,
    ! [X20655,X20656] :
      ( ~ class_Int_Onumber__ring(X20656)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20656),X20655),hAPP(c_Int_Onumber__class_Onumber__of(X20656),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(X20656),X20655) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__minus1__right])]) ).

fof(i_0_10558,plain,
    ! [X18844,X18845] :
      ( ( X18845 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18845),X18844) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( X18844 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18845),X18844) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( X18845 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | X18844 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18845),X18844) = 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_10559,plain,
    ! [X17837] : c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,X17837)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(X17837)),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_10560,plain,
    ! [X18446,X18447] :
      ( ~ class_Orderings_Opreorder(X18447)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18447),X18446),X18446)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__refl])]) ).

fof(i_0_10561,plain,
    ! [X26062] : 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)),X26062)) = hAPP(c_Int_Onat,X26062),
    inference(variable_rename,[status(thm)],[fact_card__atLeastZeroLessThan__int]) ).

fof(i_0_10562,plain,
    ! [X17246,X17247,X17248] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCall(X17248,X17247,X17246)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_com_Osize_I8_J]) ).

fof(i_0_10563,plain,
    ! [X18396] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X18396)),X18396) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[fact_zadd__zminus__inverse2]) ).

fof(i_0_10564,plain,
    ! [X25790,X25791] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X25791),hAPP(c_Nat_OSuc,X25790)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X25791,X25790),
    inference(variable_rename,[status(thm)],[fact_atLeastLessThanSuc__atLeastAtMost]) ).

fof(i_0_10565,plain,
    ! [X22175,X22176] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X22176,X22175) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(X22176,X22175)),
    inference(variable_rename,[status(thm)],[fact_mod__int__def]) ).

fof(i_0_10566,plain,
    ! [X23903,X23904,X23905] :
      ( ~ class_Lattices_Osemilattice__inf(X23905)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23905),X23904),X23903) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23905),X23903),X23904) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf_Ocommute])]) ).

fof(i_0_10567,plain,
    ! [X23897,X23898,X23899] :
      ( ~ class_Lattices_Osemilattice__inf(X23899)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23899),X23898),X23897) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23899),X23897),X23898) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__commute])]) ).

fof(i_0_10568,plain,
    ! [X23900,X23901,X23902] :
      ( ~ class_Lattices_Olattice(X23902)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23902),X23901),X23900) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23902),X23900),X23901) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I1_J])]) ).

fof(i_0_10569,plain,
    ! [X22985,X22986,X22987] :
      ( ~ class_Lattices_Olattice(X22987)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X22987),X22986),X22985) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X22987),X22985),X22986) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I5_J])]) ).

fof(i_0_10570,plain,
    ! [X22988,X22989,X22990] :
      ( ~ class_Lattices_Osemilattice__sup(X22990)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X22990),X22989),X22988) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X22990),X22988),X22989) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__commute])]) ).

fof(i_0_10571,plain,
    ! [X22982,X22983,X22984] :
      ( ~ class_Lattices_Osemilattice__sup(X22984)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X22984),X22983),X22982) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X22984),X22982),X22983) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup_Ocommute])]) ).

fof(i_0_10572,plain,
    ! [X22639,X22640,X22641] :
      ( ~ class_Orderings_Olinorder(X22641)
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X22641),X22640),X22639) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X22641),X22639),X22640) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__commute])]) ).

fof(i_0_10573,plain,
    ! [X22636,X22637,X22638] :
      ( ~ class_Orderings_Olinorder(X22638)
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X22638),X22637),X22636) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X22638),X22636),X22637) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup_Ocommute])]) ).

fof(i_0_10574,plain,
    ! [X22418,X22419,X22420] :
      ( ~ class_Orderings_Olinorder(X22420)
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X22420),X22419),X22418) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X22420),X22418),X22419) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf_Ocommute])]) ).

fof(i_0_10575,plain,
    ! [X22415,X22416,X22417] :
      ( ~ class_Orderings_Olinorder(X22417)
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X22417),X22416),X22415) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X22417),X22415),X22416) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__commute])]) ).

fof(i_0_10576,plain,
    ! [X18176,X18177,X18178] :
      ( ~ class_Rings_Ocomm__semiring__1(X18178)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18178),X18177),X18176) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18178),X18176),X18177) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J])]) ).

fof(i_0_10577,plain,
    ! [X17827,X17828,X17829] :
      ( ~ class_Rings_Ocomm__semiring__1(X17829)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17829),X17828),X17827) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17829),X17827),X17828) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J])]) ).

fof(i_0_10578,plain,
    ! [X18219] : hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18219))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_nat__zminus__int]) ).

fof(i_0_10579,plain,
    ! [X17516] :
      ( X17516 = 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)),X17516)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gr0I])]) ).

fof(i_0_10580,plain,
    ! [X21295,X21296] :
      ( ~ c_Nat__Transfer_Ois__nat(X21296)
      | ~ c_Nat__Transfer_Ois__nat(X21295)
      | c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X21296),X21295)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__int__nat__function__closures_I1_J])]) ).

fof(i_0_10581,plain,
    ! [X21291,X21292] :
      ( ~ c_Nat__Transfer_Ois__nat(X21292)
      | ~ c_Nat__Transfer_Ois__nat(X21291)
      | c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21292),X21291)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J])]) ).

fof(i_0_10582,plain,
    ! [X21288,X21289] :
      ( ~ c_Nat__Transfer_Ois__nat(X21289)
      | ~ c_Nat__Transfer_Ois__nat(X21288)
      | c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21289),X21288)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J])]) ).

fof(i_0_10583,plain,
    ! [X18397,X18398] :
      ( ( X18398 = 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),X18398)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18397) )
      & ( X18397 = 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),X18398)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18397) )
      & ( X18398 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X18397 != 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),X18398)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18397) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_negative__eq__positive])])]) ).

fof(i_0_10584,plain,
    ! [X18003,X18004,X18005,X18006,X18007] : c_Com_Ocom_OLocal(X18007,X18006,X18005) != c_Com_Ocom_OWhile(X18004,X18003),
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I38_J]) ).

fof(i_0_10585,plain,
    ! [X17732,X17733,X17734,X17735,X17736] : c_Com_Ocom_OLocal(X17736,X17735,X17734) != c_Com_Ocom_OAss(X17733,X17732),
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I23_J]) ).

fof(i_0_10586,plain,
    ! [X17737,X17738,X17739,X17740,X17741] : c_Com_Ocom_OLocal(X17741,X17740,X17739) != c_Com_Ocom_OSemi(X17738,X17737),
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I34_J]) ).

fof(i_0_10587,plain,
    ! [X17967,X17968,X17969,X17970,X17971] : c_Com_Ocom_OCond(X17971,X17970,X17969) != c_Com_Ocom_OWhile(X17968,X17967),
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I52_J]) ).

fof(i_0_10588,plain,
    ! [X17770,X17771,X17772,X17773,X17774] : c_Com_Ocom_OCond(X17774,X17773,X17772) != c_Com_Ocom_OAss(X17771,X17770),
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I27_J]) ).

fof(i_0_10589,plain,
    ! [X17775,X17776,X17777,X17778,X17779] : c_Com_Ocom_OCond(X17779,X17778,X17777) != c_Com_Ocom_OSemi(X17776,X17775),
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I45_J]) ).

fof(i_0_10590,plain,
    ! [X17985,X17986,X17987,X17988,X17989] : c_Com_Ocom_OCall(X17989,X17988,X17987) != c_Com_Ocom_OWhile(X17986,X17985),
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I61_J]) ).

fof(i_0_10591,plain,
    ! [X17335,X17336,X17337,X17338,X17339] : c_Com_Ocom_OCall(X17339,X17338,X17337) != c_Com_Ocom_OAss(X17336,X17335),
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I33_J]) ).

fof(i_0_10592,plain,
    ! [X17571,X17572,X17573,X17574,X17575] : c_Com_Ocom_OCall(X17575,X17574,X17573) != c_Com_Ocom_OSemi(X17572,X17571),
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I51_J]) ).

fof(i_0_10593,plain,
    ! [X18008,X18009,X18010,X18011,X18012] : c_Com_Ocom_OWhile(X18012,X18011) != c_Com_Ocom_OLocal(X18010,X18009,X18008),
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I39_J]) ).

fof(i_0_10594,plain,
    ! [X17972,X17973,X17974,X17975,X17976] : c_Com_Ocom_OWhile(X17976,X17975) != c_Com_Ocom_OCond(X17974,X17973,X17972),
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I53_J]) ).

fof(i_0_10595,plain,
    ! [X17990,X17991,X17992,X17993,X17994] : c_Com_Ocom_OWhile(X17994,X17993) != c_Com_Ocom_OCall(X17992,X17991,X17990),
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I60_J]) ).

fof(i_0_10596,plain,
    ! [X17727,X17728,X17729,X17730,X17731] : c_Com_Ocom_OAss(X17731,X17730) != c_Com_Ocom_OLocal(X17729,X17728,X17727),
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I22_J]) ).

fof(i_0_10597,plain,
    ! [X17765,X17766,X17767,X17768,X17769] : c_Com_Ocom_OAss(X17769,X17768) != c_Com_Ocom_OCond(X17767,X17766,X17765),
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I26_J]) ).

fof(i_0_10598,plain,
    ! [X17340,X17341,X17342,X17343,X17344] : c_Com_Ocom_OAss(X17344,X17343) != c_Com_Ocom_OCall(X17342,X17341,X17340),
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I32_J]) ).

fof(i_0_10599,plain,
    ! [X17742,X17743,X17744,X17745,X17746] : c_Com_Ocom_OSemi(X17746,X17745) != c_Com_Ocom_OLocal(X17744,X17743,X17742),
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I35_J]) ).

fof(i_0_10600,plain,
    ! [X17780,X17781,X17782,X17783,X17784] : c_Com_Ocom_OSemi(X17784,X17783) != c_Com_Ocom_OCond(X17782,X17781,X17780),
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I44_J]) ).

fof(i_0_10601,plain,
    ! [X17566,X17567,X17568,X17569,X17570] : c_Com_Ocom_OSemi(X17570,X17569) != c_Com_Ocom_OCall(X17568,X17567,X17566),
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I50_J]) ).

cnf(i_0_10602,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_6038]) ).

fof(i_0_10603,plain,
    ! [X19088] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19088)),
    inference(variable_rename,[status(thm)],[fact_less__eq__nat_Osimps_I1_J]) ).

fof(i_0_10604,plain,
    ! [X19073] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19073)),
    inference(variable_rename,[status(thm)],[fact_le0]) ).

fof(i_0_10605,plain,
    ! [X23468,X23469] : c_Relation_Ototal__on(X23469,c_Orderings_Obot__class_Obot(tc_fun(X23469,tc_HOL_Obool)),X23468),
    inference(variable_rename,[status(thm)],[fact_total__on__empty]) ).

fof(i_0_10606,plain,
    ! [X18264,X18265,X18266] :
      ( ~ class_Rings_Ono__zero__divisors(X18266)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18266),X18265),X18264) != c_Groups_Ozero__class_Ozero(X18266)
      | X18265 = c_Groups_Ozero__class_Ozero(X18266)
      | X18264 = c_Groups_Ozero__class_Ozero(X18266) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divisors__zero])]) ).

fof(i_0_10607,plain,
    ! [X18261,X18262,X18263] :
      ( ~ class_Rings_Ono__zero__divisors(X18263)
      | X18262 = c_Groups_Ozero__class_Ozero(X18263)
      | X18261 = c_Groups_Ozero__class_Ozero(X18263)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18263),X18262),X18261) != c_Groups_Ozero__class_Ozero(X18263) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_no__zero__divisors])]) ).

fof(i_0_10608,plain,
    ! [X18258,X18259,X18260] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18260),X18259),X18258) != c_Groups_Ozero__class_Ozero(X18260)
        | X18259 = c_Groups_Ozero__class_Ozero(X18260)
        | X18258 = c_Groups_Ozero__class_Ozero(X18260)
        | ~ class_Rings_Oring__no__zero__divisors(X18260) )
      & ( X18259 != c_Groups_Ozero__class_Ozero(X18260)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18260),X18259),X18258) = c_Groups_Ozero__class_Ozero(X18260)
        | ~ class_Rings_Oring__no__zero__divisors(X18260) )
      & ( X18258 != c_Groups_Ozero__class_Ozero(X18260)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18260),X18259),X18258) = c_Groups_Ozero__class_Ozero(X18260)
        | ~ class_Rings_Oring__no__zero__divisors(X18260) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__eq__0__iff])])]) ).

fof(i_0_10609,plain,
    ! [X21818] : c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X21818) = 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_10610,plain,
    ! [X22255,X22256] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X22256),X22255) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(X22256,X22255)),
    inference(variable_rename,[status(thm)],[fact_div__int__def]) ).

fof(i_0_10611,plain,
    ! [X20563,X20564] :
      ( ~ class_Power_Opower(X20564)
      | ~ class_Rings_Osemiring__0(X20564)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X20564),c_Groups_Ozero__class_Ozero(X20564)),hAPP(c_Nat_OSuc,X20563)) = c_Groups_Ozero__class_Ozero(X20564) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__0__Suc])]) ).

fof(i_0_10612,plain,
    ! [X21525,X21526] :
      ( ~ class_Fields_Ofield__inverse__zero(X21526)
      | ~ class_Int_Onumber__ring(X21526)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21526),X21525),hAPP(c_Int_Onumber__class_Onumber__of(X21526),c_Int_OPls)) = c_Groups_Ozero__class_Ozero(X21526) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__Numeral0])]) ).

fof(i_0_10613,plain,
    ! [X20410,X20411] :
      ( ~ class_Rings_Olinordered__idom(X20411)
      | hAPP(c_Groups_Oabs__class_Oabs(X20411),X20410) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20411),X20410),c_Groups_Osgn__class_Osgn(X20411,X20410)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__sgn])]) ).

fof(i_0_10614,plain,
    ! [X17705,X17706,X17707,X17708] : c_Com_Ocom_OLocal(X17708,X17707,X17706) != hAPP(c_Com_Ocom_OBODY,X17705),
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I40_J]) ).

fof(i_0_10615,plain,
    ! [X17723,X17724,X17725,X17726] : c_Com_Ocom_OCond(X17726,X17725,X17724) != hAPP(c_Com_Ocom_OBODY,X17723),
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I54_J]) ).

fof(i_0_10616,plain,
    ! [X17546,X17547,X17548,X17549] : c_Com_Ocom_OCall(X17549,X17548,X17547) != hAPP(c_Com_Ocom_OBODY,X17546),
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I63_J]) ).

fof(i_0_10617,plain,
    ! [X17701,X17702,X17703,X17704] : hAPP(c_Com_Ocom_OBODY,X17704) != c_Com_Ocom_OLocal(X17703,X17702,X17701),
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I41_J]) ).

fof(i_0_10618,plain,
    ! [X17719,X17720,X17721,X17722] : hAPP(c_Com_Ocom_OBODY,X17722) != c_Com_Ocom_OCond(X17721,X17720,X17719),
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I55_J]) ).

fof(i_0_10619,plain,
    ! [X17550,X17551,X17552,X17553] : hAPP(c_Com_Ocom_OBODY,X17553) != c_Com_Ocom_OCall(X17552,X17551,X17550),
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I62_J]) ).

fof(i_0_10620,plain,
    ! [X28648] : c_List_Olists(X28648,c_Orderings_Otop__class_Otop(tc_fun(X28648,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X28648),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_lists__UNIV]) ).

fof(i_0_10621,plain,
    ! [X29978,X29979] : hAPP(hAPP(c_List_Omap(X29979,X29979),c_COMBI(X29979)),X29978) = X29978,
    inference(variable_rename,[status(thm)],[fact_map__ident]) ).

fof(i_0_10622,plain,
    ! [X31980,X31981,X31982] :
      ( ~ c_Wellfounded_OwfP(X31982,X31981)
      | hBOOL(hAPP(c_Wellfounded_Oaccp(X31982,X31981),X31980)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_accp__wfPD])]) ).

fof(i_0_10623,plain,
    ! [X27931,X27932,X27933] :
      ( ~ c_Predicate_Oreflp(X27933,X27932)
      | hBOOL(hAPP(hAPP(X27932,X27931),X27931)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_reflpE])]) ).

fof(i_0_10624,plain,
    ! [X26891,X26892,X26893] :
      ( ~ c_Equiv__Relations_Oequivp(X26893,X26892)
      | hBOOL(hAPP(hAPP(X26892,X26891),X26891)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equivp__reflp])]) ).

fof(i_0_10625,plain,
    ! [X28480,X28481] : c_List_Osublist(X28481,X28480,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = c_List_Olist_ONil(X28481),
    inference(variable_rename,[status(thm)],[fact_sublist__empty]) ).

fof(i_0_10626,plain,
    ! [X21376,X21377,X21378] :
      ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21378),X21376),X21377) != c_Groups_Oone__class_Oone(X21378)
        | X21376 = X21377
        | X21377 = c_Groups_Ozero__class_Ozero(X21378)
        | ~ class_Rings_Odivision__ring(X21378) )
      & ( X21376 != X21377
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21378),X21376),X21377) = c_Groups_Oone__class_Oone(X21378)
        | X21377 = c_Groups_Ozero__class_Ozero(X21378)
        | ~ class_Rings_Odivision__ring(X21378) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__inverse__eq])])]) ).

fof(i_0_10627,plain,
    ! [X31627,X31628] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31628)),hAPP(c_List_Orev(X31628),X31627)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31628)),X31627),
    inference(variable_rename,[status(thm)],[fact_length__rev]) ).

fof(i_0_10628,plain,
    ! [X29302,X29303] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29303)),hAPP(c_List_Orotate1(X29303),X29302)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29303)),X29302),
    inference(variable_rename,[status(thm)],[fact_length__rotate1]) ).

fof(i_0_10629,plain,
    ! [X30245,X30246,X30247,X30248] :
      ( ~ hBOOL(hAPP(X30247,X30248))
      | X30246 != c_Hilbert__Choice_OEps(X30245,X30247)
      | hBOOL(hAPP(X30247,X30246)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_exE__some])])]) ).

fof(i_0_10630,plain,
    ! [X27946,X27947] : hAPP(hAPP(c_Nat_Ocompow(X27947,X27947),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X27946) = c_Fun_Oid(X27947),
    inference(variable_rename,[status(thm)],[fact_funpow_Osimps_I1_J]) ).

fof(i_0_10631,plain,
    ! [X30090,X30091,X30092] : hAPP(hAPP(c_List_Omap(X30092,X30091),X30090),c_List_Olist_ONil(X30092)) = c_List_Olist_ONil(X30091),
    inference(variable_rename,[status(thm)],[fact_map_Osimps_I1_J]) ).

fof(i_0_10632,plain,
    ! [X24016,X24017] :
      ( ~ class_Lattices_Oboolean__algebra(X24017)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24017),X24016),hAPP(c_Groups_Ouminus__class_Ouminus(X24017),X24016)) = c_Orderings_Obot__class_Obot(X24017) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__compl__bot])]) ).

fof(i_0_10633,plain,
    ! [X26782,X26783] :
      ( ~ class_Lattices_Oboolean__algebra(X26783)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X26783),X26782),hAPP(c_Groups_Ouminus__class_Ouminus(X26783),X26782)) = c_Orderings_Otop__class_Otop(X26783) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__compl__top])]) ).

fof(i_0_10634,plain,
    ! [X18326,X18327] :
      ( ~ class_Groups_Ogroup__add(X18327)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18327),X18326),hAPP(c_Groups_Ouminus__class_Ouminus(X18327),X18326)) = c_Groups_Ozero__class_Ozero(X18327) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__minus])]) ).

fof(i_0_10635,plain,
    ! [X21297,X21298] :
      ( ~ c_Nat__Transfer_Ois__nat(X21298)
      | c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X21298),X21297)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J])]) ).

fof(i_0_10636,plain,
    ! [X20661,X20662] :
      ( ( X20662 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
        | X20662 = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20662),X20661) != c_Groups_Oone__class_Oone(tc_Int_Oint) )
      & ( X20661 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
        | X20662 = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20662),X20661) != c_Groups_Oone__class_Oone(tc_Int_Oint) )
      & ( X20662 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
        | X20661 = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20662),X20661) != c_Groups_Oone__class_Oone(tc_Int_Oint) )
      & ( X20661 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
        | X20661 = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20662),X20661) != c_Groups_Oone__class_Oone(tc_Int_Oint) )
      & ( X20662 != c_Groups_Oone__class_Oone(tc_Int_Oint)
        | X20661 != c_Groups_Oone__class_Oone(tc_Int_Oint)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20662),X20661) = c_Groups_Oone__class_Oone(tc_Int_Oint) )
      & ( X20662 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
        | X20661 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20662),X20661) = 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_10637,plain,
    ! [X26702,X26703,X26704] :
      ( ( X26703 = c_Orderings_Otop__class_Otop(X26704)
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X26704),X26703),X26702) != c_Orderings_Otop__class_Otop(X26704)
        | ~ class_Lattices_Obounded__lattice__top(X26704) )
      & ( X26702 = c_Orderings_Otop__class_Otop(X26704)
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X26704),X26703),X26702) != c_Orderings_Otop__class_Otop(X26704)
        | ~ class_Lattices_Obounded__lattice__top(X26704) )
      & ( X26703 != c_Orderings_Otop__class_Otop(X26704)
        | X26702 != c_Orderings_Otop__class_Otop(X26704)
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X26704),X26703),X26702) = c_Orderings_Otop__class_Otop(X26704)
        | ~ class_Lattices_Obounded__lattice__top(X26704) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__eq__top__iff])])]) ).

fof(i_0_10638,plain,
    ! [X22828,X22829,X22830] :
      ( ( X22829 = c_Orderings_Obot__class_Obot(X22830)
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X22830),X22829),X22828) != c_Orderings_Obot__class_Obot(X22830)
        | ~ class_Lattices_Obounded__lattice__bot(X22830) )
      & ( X22828 = c_Orderings_Obot__class_Obot(X22830)
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X22830),X22829),X22828) != c_Orderings_Obot__class_Obot(X22830)
        | ~ class_Lattices_Obounded__lattice__bot(X22830) )
      & ( X22829 != c_Orderings_Obot__class_Obot(X22830)
        | X22828 != c_Orderings_Obot__class_Obot(X22830)
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X22830),X22829),X22828) = c_Orderings_Obot__class_Obot(X22830)
        | ~ class_Lattices_Obounded__lattice__bot(X22830) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__eq__bot__iff])])]) ).

fof(i_0_10639,plain,
    ! [X20522,X20523,X20524] :
      ( ~ class_Rings_Oring__1__no__zero__divisors(X20524)
      | X20523 = c_Groups_Ozero__class_Ozero(X20524)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X20524),X20523),X20522) != c_Groups_Ozero__class_Ozero(X20524) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_field__power__not__zero])]) ).

fof(i_0_10640,plain,
    ! [X17619,X17620] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17620),X17619),X17619) != c_Groups_Ozero__class_Ozero(X17620)
        | X17619 = c_Groups_Ozero__class_Ozero(X17620)
        | ~ class_Groups_Olinordered__ab__group__add(X17620) )
      & ( X17619 != c_Groups_Ozero__class_Ozero(X17620)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17620),X17619),X17619) = c_Groups_Ozero__class_Ozero(X17620)
        | ~ class_Groups_Olinordered__ab__group__add(X17620) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__eq__0__iff])])]) ).

fof(i_0_10641,plain,
    ! [X17493,X17494] :
      ( ( c_Groups_Ozero__class_Ozero(X17494) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17494),X17493),X17493)
        | X17493 = c_Groups_Ozero__class_Ozero(X17494)
        | ~ class_Groups_Olinordered__ab__group__add(X17494) )
      & ( X17493 != c_Groups_Ozero__class_Ozero(X17494)
        | c_Groups_Ozero__class_Ozero(X17494) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17494),X17493),X17493)
        | ~ class_Groups_Olinordered__ab__group__add(X17494) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__zero__sym])])]) ).

fof(i_0_10642,plain,
    ! [X26102] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X26102))),
    inference(variable_rename,[status(thm)],[fact_finite__lessThan]) ).

fof(i_0_10643,plain,
    ! [X25666] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X25666))),
    inference(variable_rename,[status(thm)],[fact_finite__atMost]) ).

cnf(i_0_10644,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_5815]) ).

fof(i_0_10645,plain,
    ! [X20492] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20492)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X20492)),
    inference(variable_rename,[status(thm)],[fact_minus__numeral__code_I5_J]) ).

fof(i_0_10646,plain,
    ! [X19840,X19841,X19842] :
      ( ( X19841 != X19840
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19842),X19841),X19840) = c_Groups_Ozero__class_Ozero(X19842)
        | ~ class_Groups_Oab__group__add(X19842) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19842),X19841),X19840) != c_Groups_Ozero__class_Ozero(X19842)
        | X19841 = X19840
        | ~ class_Groups_Oab__group__add(X19842) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__iff__diff__eq__0])])]) ).

fof(i_0_10647,plain,
    ! [X19837,X19838,X19839] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19839),X19838),X19837) != c_Groups_Ozero__class_Ozero(X19839)
        | X19838 = X19837
        | ~ class_Groups_Ogroup__add(X19839) )
      & ( X19838 != X19837
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19839),X19838),X19837) = c_Groups_Ozero__class_Ozero(X19839)
        | ~ class_Groups_Ogroup__add(X19839) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__minus__eq])])]) ).

fof(i_0_10648,plain,
    ! [X19077,X19078] :
      ( X19078 != X19077
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19078),X19077)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__imp__le])]) ).

fof(i_0_10649,plain,
    ! [X28775,X28776,X28777] :
      ( ( hAPP(hAPP(c_List_Otake(X28777),X28776),X28775) != c_List_Olist_ONil(X28777)
        | X28776 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X28775 = c_List_Olist_ONil(X28777) )
      & ( X28776 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Otake(X28777),X28776),X28775) = c_List_Olist_ONil(X28777) )
      & ( X28775 != c_List_Olist_ONil(X28777)
        | hAPP(hAPP(c_List_Otake(X28777),X28776),X28775) = c_List_Olist_ONil(X28777) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__eq__Nil])])]) ).

fof(i_0_10650,plain,
    ! [X20663,X20664] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20664),X20663) != c_Groups_Oone__class_Oone(tc_Int_Oint)
      | X20664 = c_Groups_Oone__class_Oone(tc_Int_Oint)
      | X20664 = 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_10651,plain,
    ! [X17616,X17617,X17618] :
      ( ( X17617 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17618),X17617),X17616)
        | X17616 = c_Groups_Ozero__class_Ozero(X17618)
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X17618) )
      & ( X17616 != c_Groups_Ozero__class_Ozero(X17618)
        | X17617 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17618),X17617),X17616)
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X17618) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__iff])])]) ).

fof(i_0_10652,plain,
    ! [X33392,X33393,X33394] :
      ( ( c_List_Oreplicate(X33394,X33393,X33392) != c_List_Olist_ONil(X33394)
        | X33393 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X33393 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_List_Oreplicate(X33394,X33393,X33392) = c_List_Olist_ONil(X33394) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_replicate__empty])]) ).

fof(i_0_10653,plain,
    ! [X33389,X33390,X33391] :
      ( ( c_List_Olist_ONil(X33391) != c_List_Oreplicate(X33391,X33390,X33389)
        | X33390 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X33390 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_List_Olist_ONil(X33391) = c_List_Oreplicate(X33391,X33390,X33389) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_empty__replicate])]) ).

fof(i_0_10654,plain,
    ! [X20050] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X20050)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X20050,
    inference(variable_rename,[status(thm)],[fact_diff__Suc__1]) ).

fof(i_0_10655,plain,
    ! [X29503,X29504] : hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X29504,X29503)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X29504,X29503),
    inference(variable_rename,[status(thm)],[fact_set__upto]) ).

fof(i_0_10656,plain,
    ! [X29501,X29502] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X29502,X29501) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X29502,X29501)),
    inference(variable_rename,[status(thm)],[fact_atLeastAtMost__upto]) ).

fof(i_0_10657,plain,
    ! [X33209,X33210] : ~ c_List_Olist__ex1(X33210,X33209,c_List_Olist_ONil(X33210)),
    inference(variable_rename,[status(thm)],[i_0_6039]) ).

fof(i_0_10658,plain,
    ! [X32747,X32748] : ~ c_List_Olist__ex(X32748,X32747,c_List_Olist_ONil(X32748)),
    inference(variable_rename,[status(thm)],[i_0_6040]) ).

fof(i_0_10659,plain,
    ! [X20898,X20899] :
      ( ~ class_Int_Onumber__ring(X20899)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20899),X20898),hAPP(c_Int_Onumber__class_Onumber__of(X20899),c_Int_OPls)) = X20898 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__numeral__0__right])]) ).

fof(i_0_10660,plain,
    ! [X18518] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X18518),X18518)),
    inference(variable_rename,[status(thm)],[fact_zle__refl]) ).

fof(i_0_10661,plain,
    ! [X19074] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19074),X19074)),
    inference(variable_rename,[status(thm)],[fact_le__refl]) ).

fof(i_0_10662,plain,
    ! [X17103] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X17103),X17103)),
    inference(variable_rename,[status(thm)],[fact_evalc_Oequations_I1_J]) ).

fof(i_0_10663,plain,
    ! [X17085] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X17085),X17085)),
    inference(variable_rename,[status(thm)],[fact_evalc_OSkip]) ).

fof(i_0_10664,plain,
    ! [X30562,X30563] : hBOOL(hAPP(c_List_Olistsp(X30563,X30562),c_List_Olist_ONil(X30563))),
    inference(variable_rename,[status(thm)],[fact_listsp_Oequations_I1_J]) ).

fof(i_0_10665,plain,
    ! [X30498,X30499] : hBOOL(hAPP(c_List_Olistsp(X30499,X30498),c_List_Olist_ONil(X30499))),
    inference(variable_rename,[status(thm)],[fact_listsp_ONil]) ).

fof(i_0_10666,plain,
    ! [X31451,X31452] : hBOOL(hAPP(c_List_Odistinct(X31452),c_List_Oremdups(X31452,X31451))),
    inference(variable_rename,[status(thm)],[fact_distinct__remdups]) ).

fof(i_0_10667,plain,
    ! [X28430,X28431,X28432] :
      ( ( X28431 = c_List_Olist_ONil(X28432)
        | hAPP(hAPP(c_List_Oappend(X28432),X28431),X28430) != c_List_Olist_ONil(X28432) )
      & ( X28430 = c_List_Olist_ONil(X28432)
        | hAPP(hAPP(c_List_Oappend(X28432),X28431),X28430) != c_List_Olist_ONil(X28432) )
      & ( X28431 != c_List_Olist_ONil(X28432)
        | X28430 != c_List_Olist_ONil(X28432)
        | hAPP(hAPP(c_List_Oappend(X28432),X28431),X28430) = c_List_Olist_ONil(X28432) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__is__Nil__conv])])]) ).

fof(i_0_10668,plain,
    ! [X28441,X28442,X28443] :
      ( ( X28442 = c_List_Olist_ONil(X28443)
        | c_List_Olist_ONil(X28443) != hAPP(hAPP(c_List_Oappend(X28443),X28442),X28441) )
      & ( X28441 = c_List_Olist_ONil(X28443)
        | c_List_Olist_ONil(X28443) != hAPP(hAPP(c_List_Oappend(X28443),X28442),X28441) )
      & ( X28442 != c_List_Olist_ONil(X28443)
        | X28441 != c_List_Olist_ONil(X28443)
        | c_List_Olist_ONil(X28443) = hAPP(hAPP(c_List_Oappend(X28443),X28442),X28441) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nil__is__append__conv])])]) ).

cnf(i_0_10669,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_6041]) ).

cnf(i_0_10670,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_6042]) ).

cnf(i_0_10671,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_6043]) ).

fof(i_0_10672,plain,
    ! [X32213,X32214] : hAPP(c_Relation_ODomain(X32214,X32214),c_Transitive__Closure_Ortrancl(X32214,X32213)) = c_Orderings_Otop__class_Otop(tc_fun(X32214,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Domain__rtrancl]) ).

fof(i_0_10673,plain,
    ! [X32176,X32177] : hAPP(c_Relation_ORange(X32177,X32177),c_Transitive__Closure_Ortrancl(X32177,X32176)) = c_Orderings_Otop__class_Otop(tc_fun(X32177,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Range__rtrancl]) ).

fof(i_0_10674,plain,
    ! [X34264,X34265,X34266,X34267] : hAPP(hAPP(c_COMBK(X34267,X34266),X34265),X34264) = X34265,
    inference(variable_rename,[status(thm)],[help_c__COMBK__1]) ).

cnf(i_0_10675,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_5975]) ).

fof(i_0_10676,plain,
    ! [X33638,X33639,X33640] : c_Lazy__Sequence_Olazy__sequence_OInsert(X33640,X33639,X33638) != c_Lazy__Sequence_Olazy__sequence_OEmpty(X33640),
    inference(variable_rename,[status(thm)],[fact_lazy__sequence_Osimps_I3_J]) ).

fof(i_0_10677,plain,
    ! [X33641,X33642,X33643] : c_Lazy__Sequence_Olazy__sequence_OEmpty(X33643) != c_Lazy__Sequence_Olazy__sequence_OInsert(X33643,X33642,X33641),
    inference(variable_rename,[status(thm)],[fact_lazy__sequence_Osimps_I2_J]) ).

fof(i_0_10678,plain,
    ! [X20675] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20675),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X20675),
    inference(variable_rename,[status(thm)],[fact_zdiv__minus1__right]) ).

fof(i_0_10679,plain,
    ! [X18174,X18175] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X18175),X18174) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X18174),X18175),
    inference(variable_rename,[status(thm)],[fact_zmult__commute]) ).

fof(i_0_10680,plain,
    ! [X18453,X18454] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18454),X18453) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18453),X18454),
    inference(variable_rename,[status(thm)],[fact_nat__mult__commute]) ).

fof(i_0_10681,plain,
    ! [X18096,X18097] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18097),X18096) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18096),X18097),
    inference(variable_rename,[status(thm)],[fact_zadd__commute]) ).

fof(i_0_10682,plain,
    ! [X17458,X17459] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17459),X17458) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17458),X17459),
    inference(variable_rename,[status(thm)],[fact_nat__add__commute]) ).

fof(i_0_10683,plain,
    ! [X26989,X26990,X26991] : hAPP(hAPP(c_Nitpick_Ofrac(X26991),X26990),X26989) = c_Nitpick_OAbs__Frac(X26991,c_Nitpick_Onorm__frac(X26990,X26989)),
    inference(variable_rename,[status(thm)],[fact_Nitpick_Ofrac__def]) ).

fof(i_0_10684,plain,
    ! [X19974,X19975] :
      ( ~ class_Groups_Ogroup__add(X19975)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19975),c_Groups_Ozero__class_Ozero(X19975)),X19974) = hAPP(c_Groups_Ouminus__class_Ouminus(X19975),X19974) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__0])]) ).

fof(i_0_10685,plain,
    ! [X34292,X34293] :
      ( ~ hBOOL(X34293)
      | ~ hBOOL(X34292)
      | hBOOL(hAPP(hAPP(c_fconj,X34293),X34292)) ),
    inference(variable_rename,[status(thm)],[i_0_6044]) ).

fof(i_0_10686,plain,
    ! [X28424,X28425,X28426] :
      ( ( hAPP(hAPP(c_List_Oappend(X28426),X28425),X28424) != X28424
        | X28425 = c_List_Olist_ONil(X28426) )
      & ( X28425 != c_List_Olist_ONil(X28426)
        | hAPP(hAPP(c_List_Oappend(X28426),X28425),X28424) = X28424 ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__self__conv2])]) ).

fof(i_0_10687,plain,
    ! [X28427,X28428,X28429] :
      ( ( hAPP(hAPP(c_List_Oappend(X28429),X28428),X28427) != X28428
        | X28427 = c_List_Olist_ONil(X28429) )
      & ( X28427 != c_List_Olist_ONil(X28429)
        | hAPP(hAPP(c_List_Oappend(X28429),X28428),X28427) = X28428 ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__self__conv])]) ).

fof(i_0_10688,plain,
    ! [X28436,X28437,X28438] :
      ( ( X28438 != hAPP(hAPP(c_List_Oappend(X28437),X28438),X28436)
        | X28436 = c_List_Olist_ONil(X28437) )
      & ( X28436 != c_List_Olist_ONil(X28437)
        | X28438 = hAPP(hAPP(c_List_Oappend(X28437),X28438),X28436) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_self__append__conv])]) ).

fof(i_0_10689,plain,
    ! [X28433,X28434,X28435] :
      ( ( X28435 != hAPP(hAPP(c_List_Oappend(X28434),X28433),X28435)
        | X28433 = c_List_Olist_ONil(X28434) )
      & ( X28433 != c_List_Olist_ONil(X28434)
        | X28435 = hAPP(hAPP(c_List_Oappend(X28434),X28433),X28435) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_self__append__conv2])]) ).

fof(i_0_10690,plain,
    ! [X20602,X20603] :
      ( ( X20602 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X20603),c_Groups_Ozero__class_Ozero(X20603)),X20602) = c_Groups_Oone__class_Oone(X20603)
        | ~ class_Power_Opower(X20603)
        | ~ class_Rings_Osemiring__0(X20603) )
      & ( X20602 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X20603),c_Groups_Ozero__class_Ozero(X20603)),X20602) = c_Groups_Ozero__class_Ozero(X20603)
        | ~ class_Power_Opower(X20603)
        | ~ class_Rings_Osemiring__0(X20603) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__0__left])])]) ).

fof(i_0_10691,plain,
    ! [X28413,X28414,X28415] : hAPP(hAPP(c_List_Olist_OCons(X28415),X28414),X28413) != c_List_Olist_ONil(X28415),
    inference(variable_rename,[status(thm)],[fact_list_Osimps_I3_J]) ).

fof(i_0_10692,plain,
    ! [X28416,X28417,X28418] : c_List_Olist_ONil(X28418) != hAPP(hAPP(c_List_Olist_OCons(X28418),X28417),X28416),
    inference(variable_rename,[status(thm)],[fact_list_Osimps_I2_J]) ).

fof(i_0_10693,plain,
    ! [X29497,X29498] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(X29498,X29497))),
    inference(variable_rename,[status(thm)],[fact_distinct__upto]) ).

cnf(i_0_10694,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_6045]) ).

fof(i_0_10695,plain,
    ! [X17759,X17760,X17761] : c_Com_Ocom_OLocal(X17761,X17760,X17759) != c_Com_Ocom_OSKIP,
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I11_J]) ).

fof(i_0_10696,plain,
    ! [X17797,X17798,X17799] : c_Com_Ocom_OCond(X17799,X17798,X17797) != c_Com_Ocom_OSKIP,
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I15_J]) ).

fof(i_0_10697,plain,
    ! [X17579,X17580,X17581] : c_Com_Ocom_OCall(X17581,X17580,X17579) != c_Com_Ocom_OSKIP,
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I21_J]) ).

fof(i_0_10698,plain,
    ! [X17762,X17763,X17764] : c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(X17764,X17763,X17762),
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I10_J]) ).

fof(i_0_10699,plain,
    ! [X17800,X17801,X17802] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(X17802,X17801,X17800),
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I14_J]) ).

fof(i_0_10700,plain,
    ! [X17576,X17577,X17578] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCall(X17578,X17577,X17576),
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I20_J]) ).

fof(i_0_10701,plain,
    ! [X32158,X32159] : c_List_Olistrel(X32159,c_Transitive__Closure_Ortrancl(X32159,X32158)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(X32159),c_List_Olistrel1(X32159,X32158)),
    inference(variable_rename,[status(thm)],[fact_listrel__rtrancl__eq__rtrancl__listrel1]) ).

fof(i_0_10702,plain,
    ! [X28131,X28132] :
      ( ~ c_Wellfounded_Owf(X28132,X28131)
      | c_Wellfounded_Owf(tc_fun(X28132,tc_HOL_Obool),c_Wellfounded_Omax__ext(X28132,X28131)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__ext__wf])]) ).

fof(i_0_10703,plain,
    ! [X28149,X28150] :
      ( ~ c_Wellfounded_Owf(X28150,X28149)
      | c_Wellfounded_Owf(tc_fun(X28150,tc_HOL_Obool),c_Wellfounded_Omin__ext(X28150,X28149)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__ext__wf])]) ).

fof(i_0_10704,plain,
    ! [X31617,X31618] :
      ( ~ class_Groups_Ocomm__monoid__add(X31618)
      | hAPP(c_List_Omonoid__add__class_Olistsum(X31618),hAPP(c_List_Orev(X31618),X31617)) = hAPP(c_List_Omonoid__add__class_Olistsum(X31618),X31617) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__rev])]) ).

fof(i_0_10705,plain,
    ! [X20209,X20210] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X20210)
      | hAPP(c_Groups_Oabs__class_Oabs(X20210),hAPP(c_Groups_Oabs__class_Oabs(X20210),X20209)) = hAPP(c_Groups_Oabs__class_Oabs(X20210),X20209) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__idempotent])]) ).

fof(i_0_10706,plain,
    ! [X20235,X20236] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X20236)
      | hAPP(c_Groups_Oabs__class_Oabs(X20236),hAPP(c_Groups_Ouminus__class_Ouminus(X20236),X20235)) = hAPP(c_Groups_Oabs__class_Oabs(X20236),X20235) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__minus__cancel])]) ).

fof(i_0_10707,plain,
    ! [X20241,X20242] :
      ( ~ class_Rings_Olinordered__idom(X20242)
      | hAPP(c_Groups_Oabs__class_Oabs(X20242),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20242),X20241)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20242),X20241) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__nat])]) ).

fof(i_0_10708,plain,
    ! [X20868] :
      ( ~ class_Int_Onumber__ring(X20868)
      | ~ c_Int_Oiszero(X20868,hAPP(c_Int_Onumber__class_Onumber__of(X20868),c_Int_OMin)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6046])]) ).

fof(i_0_10709,plain,
    ! [X26673] : c_Orderings_Otop__class_Otop(tc_fun(X26673,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(X26673,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_UNIV__not__empty]) ).

fof(i_0_10710,plain,
    ! [X20660] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X20660,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_10711,plain,
    ! [X19608] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19608,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_10712,plain,
    ! [X18667,X18668] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18668),X18667) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X18668 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X18667 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X18668 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18668),X18667) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X18667 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18668),X18667) = 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_10713,plain,
    ! [X28361,X28362,X28363] : hAPP(hAPP(c_List_Olist_OCons(X28363),X28362),X28361) != X28361,
    inference(variable_rename,[status(thm)],[fact_not__Cons__self2]) ).

fof(i_0_10714,plain,
    ! [X28364,X28365,X28366] : X28366 != hAPP(hAPP(c_List_Olist_OCons(X28365),X28364),X28366),
    inference(variable_rename,[status(thm)],[fact_not__Cons__self]) ).

fof(i_0_10715,plain,
    ! [X27666] : c_Finite__Set_Ofun__left__comm__idem(X27666,tc_fun(X27666,tc_HOL_Obool),c_Set_Oinsert(X27666)),
    inference(variable_rename,[status(thm)],[fact_fun__left__comm__idem__insert]) ).

fof(i_0_10716,plain,
    ! [X34298,X34299] :
      ( ~ hBOOL(X34299)
      | hBOOL(hAPP(hAPP(c_fdisj,X34299),X34298)) ),
    inference(variable_rename,[status(thm)],[i_0_6047]) ).

fof(i_0_10717,plain,
    ! [X34300,X34301] :
      ( ~ hBOOL(X34301)
      | hBOOL(hAPP(hAPP(c_fdisj,X34300),X34301)) ),
    inference(variable_rename,[status(thm)],[i_0_6048]) ).

fof(i_0_10718,plain,
    ! [X34306,X34307] :
      ( ~ hBOOL(X34307)
      | hBOOL(hAPP(hAPP(c_fimplies,X34306),X34307)) ),
    inference(variable_rename,[status(thm)],[i_0_6049]) ).

fof(i_0_10719,plain,
    ! [X26655,X26656,X26657] :
      ( ~ class_Orderings_Otop(X26657)
      | hAPP(c_Orderings_Otop__class_Otop(tc_fun(X26656,X26657)),X26655) = c_Orderings_Otop__class_Otop(X26657) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_top__apply])]) ).

fof(i_0_10720,plain,
    ! [X21723,X21724,X21725] :
      ( ~ class_Orderings_Obot(X21725)
      | hAPP(c_Orderings_Obot__class_Obot(tc_fun(X21724,X21725)),X21723) = c_Orderings_Obot__class_Obot(X21725) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bot__fun__def])]) ).

fof(i_0_10721,plain,
    ! [X17004,X17005,X17006] :
      ( ~ class_Orderings_Obot(X17006)
      | hAPP(c_Orderings_Obot__class_Obot(tc_fun(X17005,X17006)),X17004) = c_Orderings_Obot__class_Obot(X17006) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bot__apply])]) ).

fof(i_0_10722,plain,
    ! [X21681,X21682] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X21682),X21681) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,X21682),X21681),
    inference(variable_rename,[status(thm)],[fact_minus__code__numeral__code]) ).

fof(i_0_10723,plain,
    ! [X33863,X33864] :
      ( ( c_Predicate_Oreflp(X33864,X33863)
        | ~ c_Equiv__Relations_Oequivp(X33864,X33863) )
      & ( c_Predicate_Osymp(X33864,X33863)
        | ~ c_Equiv__Relations_Oequivp(X33864,X33863) )
      & ( c_Predicate_Otransp(X33864,X33863)
        | ~ c_Equiv__Relations_Oequivp(X33864,X33863) )
      & ( ~ c_Predicate_Oreflp(X33864,X33863)
        | ~ c_Predicate_Osymp(X33864,X33863)
        | ~ c_Predicate_Otransp(X33864,X33863)
        | c_Equiv__Relations_Oequivp(X33864,X33863) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equivp__reflp__symp__transp])])]) ).

fof(i_0_10724,plain,
    ! [X33857,X33858] :
      ( ~ c_Predicate_Oreflp(X33858,X33857)
      | ~ c_Predicate_Osymp(X33858,X33857)
      | ~ c_Predicate_Otransp(X33858,X33857)
      | c_Equiv__Relations_Oequivp(X33858,X33857) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equivpI])]) ).

fof(i_0_10725,plain,
    ! [X31533,X31534] :
      ( ~ class_Orderings_Olinorder(X31534)
      | ~ c_List_Olinorder__class_Osorted(X31534,X31533)
      | c_List_Olinorder__class_Osorted(X31534,hAPP(c_List_Otl(X31534),X31533)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__tl])]) ).

fof(i_0_10726,plain,
    ! [X31481,X31482] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X31482),X31481))
      | c_List_Oremdups(X31482,X31481) = X31481 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__remdups__id])]) ).

fof(i_0_10727,plain,
    ! [X31479,X31480] :
      ( ( c_List_Oremdups(X31480,X31479) != X31479
        | hBOOL(hAPP(c_List_Odistinct(X31480),X31479)) )
      & ( ~ hBOOL(hAPP(c_List_Odistinct(X31480),X31479))
        | c_List_Oremdups(X31480,X31479) = X31479 ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_remdups__id__iff__distinct])]) ).

cnf(i_0_10728,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_10729,plain,
    ! [X19244,X19245] :
      ( X19245 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19245),X19244)
      | X19244 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
      | X19245 = 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_10730,plain,
    ! [X29011,X29012] :
      ( X29012 = c_List_Olist_ONil(X29011)
      | hAPP(c_List_Ohd(X29011),X29012) = hAPP(hAPP(c_List_Onth(X29011),X29012),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_10731,plain,
    ! [X34304,X34305] :
      ( hBOOL(X34305)
      | hBOOL(hAPP(hAPP(c_fimplies,X34305),X34304)) ),
    inference(variable_rename,[status(thm)],[help_c__fimplies__1]) ).

fof(i_0_10732,plain,
    ! [X32536,X32537] : c_Relation_Osingle__valued(X32537,X32537,c_Relation_OId__on(X32537,X32536)),
    inference(variable_rename,[status(thm)],[fact_single__valued__Id__on]) ).

fof(i_0_10733,plain,
    ! [X27612,X27613] : c_Relation_Orefl__on(X27613,X27612,c_Relation_OId__on(X27613,X27612)),
    inference(variable_rename,[status(thm)],[fact_refl__on__Id__on]) ).

fof(i_0_10734,plain,
    ! [X19183,X19184] :
      ( ( X19184 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19184),X19183) != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( X19183 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19184),X19183) != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( X19184 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | X19183 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19184),X19183) = 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_10735,plain,
    ! [X17501,X17502] :
      ( ( X17502 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17502),X17501) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X17501 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17502),X17501) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X17502 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X17501 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17502),X17501) = 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_10736,plain,
    ! [X19180,X19181] :
      ( ( X19181 = 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),X19181),X19180) )
      & ( X19180 = 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),X19181),X19180) )
      & ( X19181 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | X19180 != 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),X19181),X19180) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__1__eq__mult__iff])])]) ).

fof(i_0_10737,plain,
    ! [X20203,X20204,X20205] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(X20205),X20204) != hAPP(c_Int_Onumber__class_Onumber__of(X20205),X20203)
        | X20204 = X20203
        | ~ class_Int_Onumber__ring(X20205)
        | ~ class_Int_Oring__char__0(X20205) )
      & ( X20204 != X20203
        | hAPP(c_Int_Onumber__class_Onumber__of(X20205),X20204) = hAPP(c_Int_Onumber__class_Onumber__of(X20205),X20203)
        | ~ class_Int_Onumber__ring(X20205)
        | ~ class_Int_Oring__char__0(X20205) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__number__of])])]) ).

fof(i_0_10738,plain,
    ! [X32447,X32448] : hAPP(c_Relation_Oconverse(X32448,X32448),c_Relation_OId__on(X32448,X32447)) = c_Relation_OId__on(X32448,X32447),
    inference(variable_rename,[status(thm)],[fact_converse__Id__on]) ).

fof(i_0_10739,plain,
    ! [X34288,X34289] :
      ( X34289 != X34288
      | hBOOL(hAPP(hAPP(c_fequal,X34289),X34288)) ),
    inference(variable_rename,[status(thm)],[help_c__fequal__2]) ).

fof(i_0_10740,plain,
    ! [X20211,X20212] :
      ( ~ class_Int_Onumber__ring(X20212)
      | hAPP(c_Int_Oring__1__class_Oof__int(X20212),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20211)) = hAPP(c_Int_Onumber__class_Onumber__of(X20212),X20211) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__number__of__eq])]) ).

fof(i_0_10741,plain,
    ! [X18415,X18416] :
      ( ~ class_Rings_Oring__1(X18416)
      | hAPP(c_Int_Oring__1__class_Oof__int(X18416),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18415)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18416),X18415) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__of__nat__eq])]) ).

fof(i_0_10742,plain,
    ! [X28825,X28826] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(X28826,tc_HOL_Obool)) != hAPP(c_List_Oset(X28826),X28825)
        | X28825 = c_List_Olist_ONil(X28826) )
      & ( X28825 != c_List_Olist_ONil(X28826)
        | c_Orderings_Obot__class_Obot(tc_fun(X28826,tc_HOL_Obool)) = hAPP(c_List_Oset(X28826),X28825) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__empty2])]) ).

fof(i_0_10743,plain,
    ! [X28827,X28828] :
      ( ( hAPP(c_List_Oset(X28828),X28827) != c_Orderings_Obot__class_Obot(tc_fun(X28828,tc_HOL_Obool))
        | X28827 = c_List_Olist_ONil(X28828) )
      & ( X28827 != c_List_Olist_ONil(X28828)
        | hAPP(c_List_Oset(X28828),X28827) = c_Orderings_Obot__class_Obot(tc_fun(X28828,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__empty])]) ).

fof(i_0_10744,plain,
    ! [X33884,X33885] :
      ( ( ~ c_Relation_Osym(X33885,X33884)
        | hAPP(c_Relation_Oconverse(X33885,X33885),X33884) = X33884 )
      & ( hAPP(c_Relation_Oconverse(X33885,X33885),X33884) != X33884
        | c_Relation_Osym(X33885,X33884) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sym__conv__converse__eq])]) ).

fof(i_0_10745,plain,
    ! [X31633,X31634] : hAPP(c_List_Oset(X31634),hAPP(c_List_Orev(X31634),X31633)) = hAPP(c_List_Oset(X31634),X31633),
    inference(variable_rename,[status(thm)],[fact_set__rev]) ).

fof(i_0_10746,plain,
    ! [X29298,X29299] : hAPP(c_List_Oset(X29299),hAPP(c_List_Orotate1(X29299),X29298)) = hAPP(c_List_Oset(X29299),X29298),
    inference(variable_rename,[status(thm)],[fact_set__rotate1]) ).

fof(i_0_10747,plain,
    ! [X20637] :
      ( ~ class_Power_Opower(X20637)
      | c_Power_Opower__class_Opower(X20637) = c_Power_Opower_Opower(X20637,c_Groups_Oone__class_Oone(X20637),c_Groups_Otimes__class_Otimes(X20637)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__power__power])]) ).

fof(i_0_10748,plain,
    ! [X17503,X17504] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17504),X17503) != X17504
      | X17503 = 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_10749,plain,
    ! [X31679,X31680] :
      ( X31680 = c_List_Olist_ONil(X31679)
      | hAPP(c_List_Ohd(X31679),hAPP(c_List_Orev(X31679),X31680)) = c_List_Olast(X31679,X31680) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hd__rev])]) ).

fof(i_0_10750,plain,
    ! [X31677,X31678] :
      ( X31678 = c_List_Olist_ONil(X31677)
      | c_List_Olast(X31677,hAPP(c_List_Orev(X31677),X31678)) = hAPP(c_List_Ohd(X31677),X31678) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__rev])]) ).

fof(i_0_10751,plain,
    ! [X31039] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X31039)
      | c_Complete__Lattice_OInf__class_OInf(X31039,c_Orderings_Otop__class_Otop(tc_fun(X31039,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(X31039) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__UNIV])]) ).

fof(i_0_10752,plain,
    ! [X31038] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X31038)
      | c_Complete__Lattice_OInf__class_OInf(X31038,c_Orderings_Obot__class_Obot(tc_fun(X31038,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(X31038) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__empty])]) ).

fof(i_0_10753,plain,
    ! [X30911] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X30911)
      | c_Complete__Lattice_OSup__class_OSup(X30911,c_Orderings_Otop__class_Otop(tc_fun(X30911,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(X30911) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__UNIV])]) ).

fof(i_0_10754,plain,
    ! [X30905] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X30905)
      | c_Complete__Lattice_OSup__class_OSup(X30905,c_Orderings_Obot__class_Obot(tc_fun(X30905,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(X30905) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__empty])]) ).

fof(i_0_10755,plain,
    ! [X30477] :
      ( ~ class_Orderings_Olinorder(X30477)
      | c_List_Olinorder__class_Osorted__list__of__set(X30477,c_Orderings_Obot__class_Obot(tc_fun(X30477,tc_HOL_Obool))) = c_List_Olist_ONil(X30477) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__list__of__set__empty])]) ).

fof(i_0_10756,plain,
    ! [X19600] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X19600),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = X19600,
    inference(variable_rename,[status(thm)],[fact_div__1]) ).

fof(i_0_10757,plain,
    ! [X30838,X30839] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X30839,tc_HOL_Obool),hAPP(c_Set_OPow(X30839),X30838)) = X30838,
    inference(variable_rename,[status(thm)],[fact_Union__Pow__eq]) ).

fof(i_0_10758,plain,
    ! [X23835,X23836] :
      ( ~ class_Lattices_Obounded__lattice__bot(X23836)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23836),c_Orderings_Obot__class_Obot(X23836)),X23835) = c_Orderings_Obot__class_Obot(X23836) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__bot__left])]) ).

fof(i_0_10759,plain,
    ! [X26711,X26712] :
      ( ~ class_Lattices_Obounded__lattice__top(X26712)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X26712),c_Orderings_Otop__class_Otop(X26712)),X26711) = c_Orderings_Otop__class_Otop(X26712) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__top__left])]) ).

fof(i_0_10760,plain,
    ! [X21251,X21252] :
      ( ~ class_Rings_Odivision__ring(X21252)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21252),c_Groups_Ozero__class_Ozero(X21252)),X21251) = c_Groups_Ozero__class_Ozero(X21252) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__zero__left])]) ).

fof(i_0_10761,plain,
    ! [X20532,X20533] :
      ( ~ class_Groups_Omonoid__mult(X20533)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X20533),c_Groups_Oone__class_Oone(X20533)),X20532) = c_Groups_Oone__class_Oone(X20533) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__one])]) ).

fof(i_0_10762,plain,
    ! [X19590,X19591] :
      ( ~ class_Divides_Osemiring__div(X19591)
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X19591),c_Groups_Ozero__class_Ozero(X19591)),X19590) = c_Groups_Ozero__class_Ozero(X19591) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__0])]) ).

fof(i_0_10763,plain,
    ! [X18250,X18251] :
      ( ~ class_Rings_Omult__zero(X18251)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18251),c_Groups_Ozero__class_Ozero(X18251)),X18250) = c_Groups_Ozero__class_Ozero(X18251) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__zero__left])]) ).

fof(i_0_10764,plain,
    ! [X18252,X18253] :
      ( ~ class_Rings_Ocomm__semiring__1(X18253)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18253),c_Groups_Ozero__class_Ozero(X18253)),X18252) = c_Groups_Ozero__class_Ozero(X18253) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J])]) ).

fof(i_0_10765,plain,
    ! [X31457,X31458] :
      ( ~ class_Orderings_Olinorder(X31458)
      | X31457 = c_List_Olist_ONil(X31458)
      | ~ c_List_Olinorder__class_Osorted(X31458,X31457)
      | c_List_Olinorder__class_Osorted(X31458,c_List_Obutlast(X31458,X31457)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__butlast])]) ).

fof(i_0_10766,plain,
    ! [X20674] :
      ( ~ class_Int_Onumber__ring(X20674)
      | hAPP(c_Int_Oring__1__class_Oof__int(X20674),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(X20674),c_Int_OMin) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__m1])]) ).

fof(i_0_10767,plain,
    ! [X24526] : hAPP(c_Finite__Set_Ocard(X24526),c_Orderings_Obot__class_Obot(tc_fun(X24526,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_card_Oempty]) ).

cnf(i_0_10768,plain,
    ( c_Int_OPls = X1
    | c_Int_OPls != c_Int_OBit0(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6050]) ).

cnf(i_0_10769,plain,
    ( X1 = c_Int_OPls
    | c_Int_OBit0(X1) != c_Int_OPls ),
    inference(split_conjunct,[status(thm)],[i_0_6051]) ).

fof(i_0_10770,plain,
    ! [X20659] :
      ( ~ class_Int_Onumber__ring(X20659)
      | ~ class_Rings_Olinordered__idom(X20659)
      | hAPP(c_Groups_Oabs__class_Oabs(X20659),hAPP(c_Int_Onumber__class_Onumber__of(X20659),c_Int_OMin)) = c_Groups_Oone__class_Oone(X20659) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__minus__one])]) ).

fof(i_0_10771,plain,
    ! [X25831] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X25831) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X25831),
    inference(variable_rename,[status(thm)],[fact_atLeast0AtMost]) ).

cnf(i_0_10772,plain,
    c_Int_OBit0(X1) != c_Int_OMin,
    inference(split_conjunct,[status(thm)],[i_0_6052]) ).

cnf(i_0_10773,plain,
    c_Int_OMin != c_Int_OBit0(X1),
    inference(split_conjunct,[status(thm)],[i_0_6053]) ).

fof(i_0_10774,plain,
    ! [X26533,X26534,X26535] :
      ( ( hAPP(c_SetInterval_Oord__class_OgreaterThan(X26535),X26534) != hAPP(c_SetInterval_Oord__class_OgreaterThan(X26535),X26533)
        | X26534 = X26533
        | ~ class_Orderings_Olinorder(X26535) )
      & ( X26534 != X26533
        | hAPP(c_SetInterval_Oord__class_OgreaterThan(X26535),X26534) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X26535),X26533)
        | ~ class_Orderings_Olinorder(X26535) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_greaterThan__eq__iff])])]) ).

fof(i_0_10775,plain,
    ! [X26175,X26176,X26177] :
      ( ( hAPP(c_SetInterval_Oord__class_OatLeast(X26177),X26176) != hAPP(c_SetInterval_Oord__class_OatLeast(X26177),X26175)
        | X26176 = X26175
        | ~ class_Orderings_Olinorder(X26177) )
      & ( X26176 != X26175
        | hAPP(c_SetInterval_Oord__class_OatLeast(X26177),X26176) = hAPP(c_SetInterval_Oord__class_OatLeast(X26177),X26175)
        | ~ class_Orderings_Olinorder(X26177) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeast__eq__iff])])]) ).

fof(i_0_10776,plain,
    ! [X26108,X26109,X26110] :
      ( ( hAPP(c_SetInterval_Oord__class_OlessThan(X26110),X26109) != hAPP(c_SetInterval_Oord__class_OlessThan(X26110),X26108)
        | X26109 = X26108
        | ~ class_Orderings_Olinorder(X26110) )
      & ( X26109 != X26108
        | hAPP(c_SetInterval_Oord__class_OlessThan(X26110),X26109) = hAPP(c_SetInterval_Oord__class_OlessThan(X26110),X26108)
        | ~ class_Orderings_Olinorder(X26110) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lessThan__eq__iff])])]) ).

fof(i_0_10777,plain,
    ! [X25720,X25721,X25722] :
      ( ( hAPP(c_SetInterval_Oord__class_OatMost(X25722),X25721) != hAPP(c_SetInterval_Oord__class_OatMost(X25722),X25720)
        | X25721 = X25720
        | ~ class_Orderings_Olinorder(X25722) )
      & ( X25721 != X25720
        | hAPP(c_SetInterval_Oord__class_OatMost(X25722),X25721) = hAPP(c_SetInterval_Oord__class_OatMost(X25722),X25720)
        | ~ class_Orderings_Olinorder(X25722) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atMost__eq__iff])])]) ).

fof(i_0_10778,plain,
    ! [X19482,X19483,X19484] :
      ( ( hAPP(c_Groups_Ouminus__class_Ouminus(X19484),X19483) != hAPP(c_Groups_Ouminus__class_Ouminus(X19484),X19482)
        | X19483 = X19482
        | ~ class_Lattices_Oboolean__algebra(X19484) )
      & ( X19483 != X19482
        | hAPP(c_Groups_Ouminus__class_Ouminus(X19484),X19483) = hAPP(c_Groups_Ouminus__class_Ouminus(X19484),X19482)
        | ~ class_Lattices_Oboolean__algebra(X19484) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__eq__compl__iff])])]) ).

fof(i_0_10779,plain,
    ! [X18195,X18196,X18197] :
      ( ( hAPP(c_Groups_Ouminus__class_Ouminus(X18197),X18196) != hAPP(c_Groups_Ouminus__class_Ouminus(X18197),X18195)
        | X18196 = X18195
        | ~ class_Groups_Ogroup__add(X18197) )
      & ( X18196 != X18195
        | hAPP(c_Groups_Ouminus__class_Ouminus(X18197),X18196) = hAPP(c_Groups_Ouminus__class_Ouminus(X18197),X18195)
        | ~ class_Groups_Ogroup__add(X18197) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__equal__iff__equal])])]) ).

fof(i_0_10780,plain,
    ! [X18158,X18159,X18160] :
      ( ( hAPP(c_Int_Oring__1__class_Oof__int(X18160),X18159) != hAPP(c_Int_Oring__1__class_Oof__int(X18160),X18158)
        | X18159 = X18158
        | ~ class_Int_Oring__char__0(X18160) )
      & ( X18159 != X18158
        | hAPP(c_Int_Oring__1__class_Oof__int(X18160),X18159) = hAPP(c_Int_Oring__1__class_Oof__int(X18160),X18158)
        | ~ class_Int_Oring__char__0(X18160) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__eq__iff])])]) ).

fof(i_0_10781,plain,
    ! [X17904,X17905,X17906] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X17906),X17905) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(X17906),X17904)
        | X17905 = X17904
        | ~ class_Nat_Osemiring__char__0(X17906) )
      & ( X17905 != X17904
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X17906),X17905) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X17906),X17904)
        | ~ class_Nat_Osemiring__char__0(X17906) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__eq__iff])])]) ).

fof(i_0_10782,plain,
    ! [X26707,X26708] :
      ( ~ class_Lattices_Obounded__lattice__top(X26708)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X26708),c_Orderings_Otop__class_Otop(X26708)),X26707) = X26707 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__top__left])]) ).

fof(i_0_10783,plain,
    ! [X22824,X22825] :
      ( ~ class_Lattices_Obounded__lattice__bot(X22825)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X22825),c_Orderings_Obot__class_Obot(X22825)),X22824) = X22824 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__bot__left])]) ).

fof(i_0_10784,plain,
    ! [X18620,X18621] :
      ( ~ class_Groups_Ocomm__monoid__mult(X18621)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18621),c_Groups_Oone__class_Oone(X18621)),X18620) = X18620 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__1])]) ).

fof(i_0_10785,plain,
    ! [X18618,X18619] :
      ( ~ class_Groups_Omonoid__mult(X18619)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18619),c_Groups_Oone__class_Oone(X18619)),X18618) = X18618 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__1__left])]) ).

fof(i_0_10786,plain,
    ! [X18626,X18627] :
      ( ~ class_Rings_Ocomm__semiring__1(X18627)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18627),c_Groups_Oone__class_Oone(X18627)),X18626) = X18626 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J])]) ).

fof(i_0_10787,plain,
    ! [X17612,X17613] :
      ( ~ class_Rings_Ocomm__semiring__1(X17613)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17613),c_Groups_Ozero__class_Ozero(X17613)),X17612) = X17612 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J])]) ).

fof(i_0_10788,plain,
    ! [X17491,X17492] :
      ( ~ class_Groups_Ocomm__monoid__add(X17492)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17492),c_Groups_Ozero__class_Ozero(X17492)),X17491) = X17491 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0])]) ).

fof(i_0_10789,plain,
    ! [X17489,X17490] :
      ( ~ class_Groups_Omonoid__add(X17490)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17490),c_Groups_Ozero__class_Ozero(X17490)),X17489) = X17489 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__left])]) ).

fof(i_0_10790,plain,
    ! [X21381,X21382] :
      ( ( X21381 != c_Groups_Ozero__class_Ozero(X21382)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21382),X21381),X21381) = c_Groups_Ozero__class_Ozero(X21382)
        | ~ class_Rings_Odivision__ring__inverse__zero(X21382) )
      & ( X21381 = c_Groups_Ozero__class_Ozero(X21382)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21382),X21381),X21381) = c_Groups_Oone__class_Oone(X21382)
        | ~ class_Rings_Odivision__ring__inverse__zero(X21382) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__self__if])])]) ).

fof(i_0_10791,plain,
    ! [X19330,X19331] :
      ( ~ class_Divides_Osemiring__div(X19331)
      | c_Divides_Odiv__class_Omod(X19331,c_Groups_Ozero__class_Ozero(X19331),X19330) = c_Groups_Ozero__class_Ozero(X19331) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__0])]) ).

fof(i_0_10792,plain,
    ! [X19439,X19440] :
      ( ~ class_Divides_Osemiring__div(X19440)
      | c_Divides_Odiv__class_Omod(X19440,X19439,c_Groups_Oone__class_Oone(X19440)) = c_Groups_Ozero__class_Ozero(X19440) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__by__1])]) ).

fof(i_0_10793,plain,
    ! [X31537,X31538] :
      ( ~ class_Orderings_Olinorder(X31538)
      | ~ c_List_Olinorder__class_Osorted(X31538,X31537)
      | c_List_Olinorder__class_Osorted(X31538,c_List_Oremdups(X31538,X31537)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__remdups])]) ).

fof(i_0_10794,plain,
    ! [X23833,X23834] :
      ( ~ class_Lattices_Obounded__lattice__bot(X23834)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23834),X23833),c_Orderings_Obot__class_Obot(X23834)) = c_Orderings_Obot__class_Obot(X23834) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__bot__right])]) ).

fof(i_0_10795,plain,
    ! [X26709,X26710] :
      ( ~ class_Lattices_Obounded__lattice__top(X26710)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X26710),X26709),c_Orderings_Otop__class_Otop(X26710)) = c_Orderings_Otop__class_Otop(X26710) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__top__right])]) ).

fof(i_0_10796,plain,
    ! [X21249,X21250] :
      ( ~ class_Rings_Odivision__ring__inverse__zero(X21250)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21250),X21249),c_Groups_Ozero__class_Ozero(X21250)) = c_Groups_Ozero__class_Ozero(X21250) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__zero])]) ).

fof(i_0_10797,plain,
    ! [X19592,X19593] :
      ( ~ class_Divides_Osemiring__div(X19593)
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X19593),X19592),c_Groups_Ozero__class_Ozero(X19593)) = c_Groups_Ozero__class_Ozero(X19593) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__by__0])]) ).

fof(i_0_10798,plain,
    ! [X18254,X18255] :
      ( ~ class_Rings_Omult__zero(X18255)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18255),X18254),c_Groups_Ozero__class_Ozero(X18255)) = c_Groups_Ozero__class_Ozero(X18255) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__zero__right])]) ).

fof(i_0_10799,plain,
    ! [X18256,X18257] :
      ( ~ class_Rings_Ocomm__semiring__1(X18257)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18257),X18256),c_Groups_Ozero__class_Ozero(X18257)) = c_Groups_Ozero__class_Ozero(X18257) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J])]) ).

fof(i_0_10800,plain,
    ! [X33894,X33895] :
      ( ~ c_Relation_Osym(X33895,X33894)
      | c_Relation_Osym(tc_List_Olist(X33895),c_List_Olistrel(X33895,X33894)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__sym])]) ).

fof(i_0_10801,plain,
    ! [X33796,X33797] :
      ( ~ c_Relation_Otrans(X33797,X33796)
      | c_Relation_Otrans(tc_List_Olist(X33797),c_List_Olistrel(X33797,X33796)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__trans])]) ).

fof(i_0_10802,plain,
    ! [X33791,X33792] :
      ( ~ c_Relation_Otrans(X33792,X33791)
      | c_Relation_Otrans(tc_List_Olist(X33792),c_List_Olexord(X33792,X33791)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__transI])]) ).

fof(i_0_10803,plain,
    ! [X28312,X28313] :
      ( ~ c_Wellfounded_Owf(X28313,X28312)
      | c_Wellfounded_Owf(tc_List_Olist(X28313),c_List_Olex(X28313,X28312)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__lex])]) ).

fof(i_0_10804,plain,
    ! [X28245,X28246] :
      ( ~ c_Wellfounded_Owf(X28246,X28245)
      | c_Wellfounded_Owf(tc_List_Olist(X28246),c_List_Olenlex(X28246,X28245)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__lenlex])]) ).

fof(i_0_10805,plain,
    ! [X28421,X28422,X28423] :
      ( X28423 != X28422
      | X28423 = hAPP(hAPP(c_List_Oappend(X28421),c_List_Olist_ONil(X28421)),X28422) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__Nil__appendI])]) ).

fof(i_0_10806,plain,
    ! [X21379,X21380] :
      ( ~ class_Rings_Odivision__ring(X21380)
      | X21379 = c_Groups_Ozero__class_Ozero(X21380)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21380),X21379),X21379) = c_Groups_Oone__class_Oone(X21380) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__self])]) ).

fof(i_0_10807,plain,
    ! [X19657,X19658] :
      ( ~ class_Divides_Osemiring__div(X19658)
      | X19657 = c_Groups_Ozero__class_Ozero(X19658)
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X19658),X19657),X19657) = c_Groups_Oone__class_Oone(X19658) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__self])]) ).

fof(i_0_10808,plain,
    ! [X19332,X19333] :
      ( ~ class_Divides_Osemiring__div(X19333)
      | c_Divides_Odiv__class_Omod(X19333,X19332,c_Groups_Ozero__class_Ozero(X19333)) = X19332 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__by__0])]) ).

fof(i_0_10809,plain,
    ! [X20652] :
      ( hBOOL(hAPP(c_Nat__Numeral_Oneg,X20652))
      | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X20652)) = X20652 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6054])]) ).

fof(i_0_10810,plain,
    ! [X32980] :
      ( ~ class_Groups_Oab__semigroup__mult(X32980)
      | c_Finite__Set_Ofun__left__comm(X32980,X32980,c_Groups_Otimes__class_Otimes(X32980)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm])]) ).

fof(i_0_10811,plain,
    ! [X27669] :
      ( ~ class_Lattices_Osemilattice__inf(X27669)
      | c_Finite__Set_Ofun__left__comm__idem(X27669,X27669,c_Lattices_Osemilattice__inf__class_Oinf(X27669)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem__inf])]) ).

fof(i_0_10812,plain,
    ! [X27668] :
      ( ~ class_Lattices_Osemilattice__sup(X27668)
      | c_Finite__Set_Ofun__left__comm__idem(X27668,X27668,c_Lattices_Osemilattice__sup__class_Osup(X27668)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem__sup])]) ).

fof(i_0_10813,plain,
    ! [X27675] :
      ( ~ class_Orderings_Olinorder(X27675)
      | c_Finite__Set_Ofun__left__comm__idem(X27675,X27675,c_Orderings_Oord__class_Omax(X27675)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ofun__left__comm__idem__sup])]) ).

fof(i_0_10814,plain,
    ! [X27674] :
      ( ~ class_Orderings_Olinorder(X27674)
      | c_Finite__Set_Ofun__left__comm__idem(X27674,X27674,c_Orderings_Oord__class_Omin(X27674)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ofun__left__comm__idem__inf])]) ).

fof(i_0_10815,plain,
    ! [X27667] :
      ( ~ class_Lattices_Oab__semigroup__idem__mult(X27667)
      | c_Finite__Set_Ofun__left__comm__idem(X27667,X27667,c_Groups_Otimes__class_Otimes(X27667)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem])]) ).

fof(i_0_10816,plain,
    ! [X30831,X30832] : hAPP(c_Relation_ODomain(X30832,X30832),c_Relation_OId__on(X30832,X30831)) = X30831,
    inference(variable_rename,[status(thm)],[fact_Domain__Id__on]) ).

fof(i_0_10817,plain,
    ! [X28260,X28261] : hAPP(c_Relation_ORange(X28261,X28261),c_Relation_OId__on(X28261,X28260)) = X28260,
    inference(variable_rename,[status(thm)],[fact_Range__Id__on]) ).

fof(i_0_10818,plain,
    ! [X20575,X20576] :
      ( ~ class_Power_Opower(X20576)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X20576),X20575),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X20576) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__0])]) ).

fof(i_0_10819,plain,
    ! [X20356,X20357] :
      ( ~ class_Rings_Ocomm__semiring__1(X20357)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X20357),X20356),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X20357) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J])]) ).

fof(i_0_10820,plain,
    ! [X26705,X26706] :
      ( ~ class_Lattices_Obounded__lattice__top(X26706)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X26706),X26705),c_Orderings_Otop__class_Otop(X26706)) = X26705 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__top__right])]) ).

fof(i_0_10821,plain,
    ! [X22826,X22827] :
      ( ~ class_Lattices_Obounded__lattice__bot(X22827)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X22827),X22826),c_Orderings_Obot__class_Obot(X22827)) = X22826 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__bot__right])]) ).

fof(i_0_10822,plain,
    ! [X21270,X21271] :
      ( ~ class_Rings_Odivision__ring(X21271)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X21271),X21270),c_Groups_Oone__class_Oone(X21271)) = X21270 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__1])]) ).

fof(i_0_10823,plain,
    ! [X19845,X19846] :
      ( ~ class_Groups_Ogroup__add(X19846)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19846),X19845),c_Groups_Ozero__class_Ozero(X19846)) = X19845 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__0__right])]) ).

fof(i_0_10824,plain,
    ! [X19594,X19595] :
      ( ~ class_Divides_Osemiring__div(X19595)
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X19595),X19594),c_Groups_Oone__class_Oone(X19595)) = X19594 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__by__1])]) ).

fof(i_0_10825,plain,
    ! [X18624,X18625] :
      ( ~ class_Groups_Ocomm__monoid__mult(X18625)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18625),X18624),c_Groups_Oone__class_Oone(X18625)) = X18624 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Ocomm__neutral])]) ).

fof(i_0_10826,plain,
    ! [X18622,X18623] :
      ( ~ class_Groups_Omonoid__mult(X18623)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18623),X18622),c_Groups_Oone__class_Oone(X18623)) = X18622 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__1__right])]) ).

fof(i_0_10827,plain,
    ! [X18628,X18629] :
      ( ~ class_Rings_Ocomm__semiring__1(X18629)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18629),X18628),c_Groups_Oone__class_Oone(X18629)) = X18628 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J])]) ).

fof(i_0_10828,plain,
    ! [X17614,X17615] :
      ( ~ class_Rings_Ocomm__semiring__1(X17615)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17615),X17614),c_Groups_Ozero__class_Ozero(X17615)) = X17614 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J])]) ).

fof(i_0_10829,plain,
    ! [X17497,X17498] :
      ( ~ class_Groups_Ocomm__monoid__add(X17498)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17498),X17497),c_Groups_Ozero__class_Ozero(X17498)) = X17497 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add_Ocomm__neutral])]) ).

fof(i_0_10830,plain,
    ! [X17495,X17496] :
      ( ~ class_Groups_Omonoid__add(X17496)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17496),X17495),c_Groups_Ozero__class_Ozero(X17496)) = X17495 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__right])]) ).

fof(i_0_10831,plain,
    ! [X19489,X19490] :
      ( ~ class_Lattices_Oboolean__algebra(X19490)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X19490),hAPP(c_Groups_Ouminus__class_Ouminus(X19490),X19489)) = X19489 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__compl])]) ).

fof(i_0_10832,plain,
    ! [X18204,X18205] :
      ( ~ class_Groups_Ogroup__add(X18205)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X18205),hAPP(c_Groups_Ouminus__class_Ouminus(X18205),X18204)) = X18204 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__minus])]) ).

fof(i_0_10833,plain,
    ! [X20249] : hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20249)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20249),
    inference(variable_rename,[status(thm)],[fact_abs__int__eq]) ).

fof(i_0_10834,plain,
    ! [X18307] : hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18307)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18307),
    inference(variable_rename,[status(thm)],[fact_of__int__int__eq]) ).

fof(i_0_10835,plain,
    ! [X31521,X31522] : hAPP(c_List_Oset(X31522),c_List_Oremdups(X31522,X31521)) = hAPP(c_List_Oset(X31522),X31521),
    inference(variable_rename,[status(thm)],[fact_set__remdups]) ).

fof(i_0_10836,plain,
    ! [X19334,X19335] :
      ( ~ class_Divides_Osemiring__div(X19335)
      | c_Divides_Odiv__class_Omod(X19335,X19334,X19334) = c_Groups_Ozero__class_Ozero(X19335) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__self])]) ).

fof(i_0_10837,plain,
    ! [X31619,X31620,X31621] :
      ( ( hAPP(c_List_Orev(X31621),X31620) != hAPP(c_List_Orev(X31621),X31619)
        | X31620 = X31619 )
      & ( X31620 != X31619
        | hAPP(c_List_Orev(X31621),X31620) = hAPP(c_List_Orev(X31621),X31619) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__is__rev__conv])]) ).

fof(i_0_10838,plain,
    ! [X24527,X24528] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X24528),X24527))
      | hAPP(c_Finite__Set_Ocard(X24528),X24527) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6055])]) ).

fof(i_0_10839,plain,
    ! [X21631,X21632] :
      ( ( X21632 != X21631
        | c_Random_Oinc__shift(X21632,X21631) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
      & ( X21632 = X21631
        | c_Random_Oinc__shift(X21632,X21631) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X21631),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_10840,plain,
    ! [X28444,X28445] : hAPP(hAPP(c_List_Oappend(X28445),c_List_Olist_ONil(X28445)),X28444) = X28444,
    inference(variable_rename,[status(thm)],[fact_append__Nil]) ).

fof(i_0_10841,plain,
    ! [X19243] : hAPP(c_Nat_OSuc,X19243) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X19243),
    inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1__left]) ).

fof(i_0_10842,plain,
    ! [X28446,X28447] : c_List_Osublist(X28447,c_List_Olist_ONil(X28447),X28446) = c_List_Olist_ONil(X28447),
    inference(variable_rename,[status(thm)],[fact_sublist__nil]) ).

fof(i_0_10843,plain,
    ! [X31732,X31733] : c_List_OtakeWhile(X31733,X31732,c_List_Olist_ONil(X31733)) = c_List_Olist_ONil(X31733),
    inference(variable_rename,[status(thm)],[fact_takeWhile_Osimps_I1_J]) ).

fof(i_0_10844,plain,
    ! [X30446,X30447] : c_List_Oremove1(X30447,X30446,c_List_Olist_ONil(X30447)) = c_List_Olist_ONil(X30447),
    inference(variable_rename,[status(thm)],[fact_remove1_Osimps_I1_J]) ).

fof(i_0_10845,plain,
    ! [X25792] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X25792),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_10846,plain,
    ! [X20545,X20546] :
      ( ~ class_Groups_Omonoid__mult(X20546)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X20546),X20545),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X20545 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__one__right])]) ).

fof(i_0_10847,plain,
    ! [X20269,X20270] :
      ( ~ class_Rings_Ocomm__semiring__1(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_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J])]) ).

fof(i_0_10848,plain,
    ! [X19843,X19844] :
      ( ~ class_Groups_Ogroup__add(X19844)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19844),X19843),X19843) = c_Groups_Ozero__class_Ozero(X19844) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__self])]) ).

fof(i_0_10849,plain,
    ! [X28662,X28663] : c_List_Olist_Olist__size(X28663,X28662,c_List_Olist_ONil(X28663)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_list_Osize_I1_J]) ).

fof(i_0_10850,plain,
    ! [X33888,X33889] :
      ( ~ c_Relation_Osym(X33889,X33888)
      | c_Relation_Osym(X33889,c_Transitive__Closure_Ortrancl(X33889,X33888)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sym__rtrancl])]) ).

fof(i_0_10851,plain,
    ! [X33853,X33854] :
      ( ~ c_Wellfounded_Oacyclic(X33854,X33853)
      | c_Relation_Oantisym(X33854,c_Transitive__Closure_Ortrancl(X33854,X33853)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acyclic__impl__antisym__rtrancl])]) ).

fof(i_0_10852,plain,
    ! [X28773,X28774] : hAPP(hAPP(c_List_Otake(X28774),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X28773) = c_List_Olist_ONil(X28774),
    inference(variable_rename,[status(thm)],[fact_take__0]) ).

fof(i_0_10853,plain,
    ! [X28829,X28830] : hAPP(hAPP(c_List_Odrop(X28830),X28829),c_List_Olist_ONil(X28830)) = c_List_Olist_ONil(X28830),
    inference(variable_rename,[status(thm)],[fact_drop__Nil]) ).

fof(i_0_10854,plain,
    ! [X28778,X28779] : hAPP(hAPP(c_List_Otake(X28779),X28778),c_List_Olist_ONil(X28779)) = c_List_Olist_ONil(X28779),
    inference(variable_rename,[status(thm)],[fact_take__Nil]) ).

fof(i_0_10855,plain,
    ! [X18198,X18199,X18200] :
      ( ( hAPP(c_Groups_Ouminus__class_Ouminus(X18200),X18199) != X18198
        | hAPP(c_Groups_Ouminus__class_Ouminus(X18200),X18198) = X18199
        | ~ class_Groups_Ogroup__add(X18200) )
      & ( hAPP(c_Groups_Ouminus__class_Ouminus(X18200),X18198) != X18199
        | hAPP(c_Groups_Ouminus__class_Ouminus(X18200),X18199) = X18198
        | ~ class_Groups_Ogroup__add(X18200) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__equation__iff])])]) ).

fof(i_0_10856,plain,
    ! [X18201,X18202,X18203] :
      ( ( X18202 != hAPP(c_Groups_Ouminus__class_Ouminus(X18203),X18201)
        | X18201 = hAPP(c_Groups_Ouminus__class_Ouminus(X18203),X18202)
        | ~ class_Groups_Ogroup__add(X18203) )
      & ( X18201 != hAPP(c_Groups_Ouminus__class_Ouminus(X18203),X18202)
        | X18202 = hAPP(c_Groups_Ouminus__class_Ouminus(X18203),X18201)
        | ~ class_Groups_Ogroup__add(X18203) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equation__minus__iff])])]) ).

fof(i_0_10857,plain,
    ! [X29543] :
      ( ( ~ c_List_Onat__list(X29543)
        | c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X29543)) )
      & ( ~ c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X29543))
        | c_List_Onat__list(X29543) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__list__def])]) ).

fof(i_0_10858,plain,
    ! [X25879] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X25879)) = hAPP(c_Nat_OSuc,X25879),
    inference(variable_rename,[status(thm)],[fact_card__atMost]) ).

fof(i_0_10859,plain,
    ! [X30386] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),X30386)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X30386),
    inference(variable_rename,[status(thm)],[fact_nat__of__number]) ).

fof(i_0_10860,plain,
    ! [X20504] : hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20504)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20504),
    inference(variable_rename,[status(thm)],[fact_nat__number__of]) ).

fof(i_0_10861,plain,
    ! [X20505] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20505) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20505)),
    inference(variable_rename,[status(thm)],[fact_nat__number__of__def]) ).

fof(i_0_10862,plain,
    ! [X19242] : hAPP(c_Nat_OSuc,X19242) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19242),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1]) ).

fof(i_0_10863,plain,
    ! [X33387,X33388] : c_List_Oreplicate(X33388,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X33387) = c_List_Olist_ONil(X33388),
    inference(variable_rename,[status(thm)],[fact_replicate__0]) ).

fof(i_0_10864,plain,
    ! [X33636,X33637] : c_Lazy__Sequence_Oappend(X33637,c_Lazy__Sequence_Olazy__sequence_OEmpty(X33637),X33636) = X33636,
    inference(variable_rename,[status(thm)],[fact__02]) ).

fof(i_0_10865,plain,
    ! [X33318,X33319] : c_List_Osplice(X33319,c_List_Olist_ONil(X33319),X33318) = X33318,
    inference(variable_rename,[status(thm)],[fact_splice_Osimps_I1_J]) ).

fof(i_0_10866,plain,
    ! [X33320,X33321] : c_List_Osplice(X33321,X33320,c_List_Olist_ONil(X33321)) = X33320,
    inference(variable_rename,[status(thm)],[fact_splice__Nil2]) ).

fof(i_0_10867,plain,
    ! [X19323,X19324] :
      ( ~ class_Rings_Olinordered__idom(X19324)
      | c_Groups_Osgn__class_Osgn(X19324,c_Groups_Osgn__class_Osgn(X19324,X19323)) = c_Groups_Osgn__class_Osgn(X19324,X19323) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__sgn])]) ).

fof(i_0_10868,plain,
    ! [X33184,X33185] : c_List_Olist__all(X33185,X33184,c_List_Olist_ONil(X33185)),
    inference(variable_rename,[status(thm)],[fact_list__all__simps_I2_J]) ).

fof(i_0_10869,plain,
    ! [X23908,X23909] :
      ( ~ class_Lattices_Osemilattice__inf(X23909)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23909),X23908),X23908) = X23908 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf_Oidem])]) ).

fof(i_0_10870,plain,
    ! [X23906,X23907] :
      ( ~ class_Lattices_Osemilattice__inf(X23907)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23907),X23906),X23906) = X23906 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__idem])]) ).

fof(i_0_10871,plain,
    ! [X23934,X23935] :
      ( ~ class_Lattices_Olattice(X23935)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23935),X23934),X23934) = X23934 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oidem])]) ).

fof(i_0_10872,plain,
    ! [X22832,X22833] :
      ( ~ class_Lattices_Olattice(X22833)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X22833),X22832),X22832) = X22832 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oidem])]) ).

fof(i_0_10873,plain,
    ! [X22980,X22981] :
      ( ~ class_Lattices_Osemilattice__sup(X22981)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X22981),X22980),X22980) = X22980 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__idem])]) ).

fof(i_0_10874,plain,
    ! [X22978,X22979] :
      ( ~ class_Lattices_Osemilattice__sup(X22979)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X22979),X22978),X22978) = X22978 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup_Oidem])]) ).

fof(i_0_10875,plain,
    ! [X22752,X22753] :
      ( ~ class_Orderings_Olinorder(X22753)
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X22753),X22752),X22752) = X22752 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Oidem])]) ).

fof(i_0_10876,plain,
    ! [X22634,X22635] :
      ( ~ class_Orderings_Olinorder(X22635)
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X22635),X22634),X22634) = X22634 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup_Oidem])]) ).

fof(i_0_10877,plain,
    ! [X22750,X22751] :
      ( ~ class_Orderings_Olinorder(X22751)
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X22751),X22750),X22750) = X22750 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Oidem])]) ).

fof(i_0_10878,plain,
    ! [X22421,X22422] :
      ( ~ class_Orderings_Olinorder(X22422)
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X22422),X22421),X22421) = X22421 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf_Oidem])]) ).

fof(i_0_10879,plain,
    ! [X19480,X19481] :
      ( ~ class_Lattices_Oab__semigroup__idem__mult(X19481)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19481),X19480),X19480) = X19480 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_times_Oidem])]) ).

fof(i_0_10880,plain,
    ! [X19478,X19479] :
      ( ~ class_Lattices_Oab__semigroup__idem__mult(X19479)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19479),X19478),X19478) = X19478 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__idem])]) ).

fof(i_0_10881,plain,
    ! [X28449,X28450] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28450)),X28449) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X28449 = c_List_Olist_ONil(X28450) )
      & ( X28449 != c_List_Olist_ONil(X28450)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28450)),X28449) = 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_10882,plain,
    ! [X20648] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),X20648) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X20648),
    inference(variable_rename,[status(thm)],[fact_mult__Min]) ).

fof(i_0_10883,plain,
    ! [X26111] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X26111) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X26111),
    inference(variable_rename,[status(thm)],[fact_atLeast0LessThan]) ).

fof(i_0_10884,plain,
    ! [X33330,X33331,X33332] : hAPP(c_New__DSequence_Opos__single(X33332,X33331),X33330) = hAPP(c_Lazy__Sequence_Osingle(X33332),X33331),
    inference(variable_rename,[status(thm)],[fact_New__DSequence_Opos__single__def]) ).

fof(i_0_10885,plain,
    ! [X28845,X28846] : hAPP(hAPP(c_List_Odrop(X28846),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X28845) = X28845,
    inference(variable_rename,[status(thm)],[fact_drop__0]) ).

fof(i_0_10886,plain,
    ! [X28439,X28440] : hAPP(hAPP(c_List_Oappend(X28440),X28439),c_List_Olist_ONil(X28440)) = X28439,
    inference(variable_rename,[status(thm)],[fact_append__Nil2]) ).

fof(i_0_10887,plain,
    ! [X31625,X31626] : hAPP(c_List_Orev(X31626),hAPP(c_List_Orev(X31626),X31625)) = X31625,
    inference(variable_rename,[status(thm)],[fact_rev__rev__ident]) ).

fof(i_0_10888,plain,
    ! [X33539] : c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint,X33539) = c_Lazy__Sequence_Osmall__lazy_H(X33539,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X33539)),
    inference(variable_rename,[status(thm)],[fact_small__lazy__int__def]) ).

fof(i_0_10889,plain,
    ! [X19406] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X19406) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[fact_zmod__zero]) ).

fof(i_0_10890,plain,
    ! [X20651] :
      ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X20651))
      | hAPP(c_Int_Onat,X20651) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__nat])]) ).

fof(i_0_10891,plain,
    ! [X26546] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,X26546)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),X26546),
    inference(variable_rename,[status(thm)],[fact_atLeast__Suc__greaterThan]) ).

fof(i_0_10892,plain,
    ! [X26112] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X26112)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X26112),
    inference(variable_rename,[status(thm)],[fact_lessThan__Suc__atMost]) ).

fof(i_0_10893,plain,
    ! [X21737] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21737) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21737)),
    inference(variable_rename,[status(thm)],[fact_less__eq__Suc__le__raw]) ).

fof(i_0_10894,plain,
    ! [X19626] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19626),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      & c_Divides_Odiv__class_Omod(tc_Int_Oint,X19626,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X19626 ),
    inference(variable_rename,[status(thm)],[fact_DIVISION__BY__ZERO]) ).

fof(i_0_10895,plain,
    ! [X20902] :
      ( ~ class_Int_Onumber__ring(X20902)
      | c_Int_Oiszero(X20902,hAPP(c_Int_Onumber__class_Onumber__of(X20902),c_Int_OPls)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_iszero__Numeral0])]) ).

fof(i_0_10896,plain,
    ! [X30115] : hAPP(c_List_Omap(X30115,X30115),c_Fun_Oid(X30115)) = c_Fun_Oid(tc_List_Olist(X30115)),
    inference(variable_rename,[status(thm)],[fact_List_Omap_Oid]) ).

fof(i_0_10897,plain,
    ! [X29741] : hAPP(c_List_Omap(X29741,X29741),c_COMBI(X29741)) = c_Fun_Oid(tc_List_Olist(X29741)),
    inference(variable_rename,[status(thm)],[fact_List_Omap_Oidentity]) ).

fof(i_0_10898,plain,
    ! [X18088,X18089] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18089) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18088)
        | X18089 = X18088 )
      & ( X18089 != X18088
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18089) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18088) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__relations_I1_J])]) ).

fof(i_0_10899,plain,
    ! [X18086,X18087] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18087) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18086)
        | X18087 = X18086 )
      & ( X18087 != X18086
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18087) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18086) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__int__eq])]) ).

fof(i_0_10900,plain,
    ! [X19405] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X19405,X19405) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[fact_zmod__self]) ).

fof(i_0_10901,plain,
    ! [X31622,X31623,X31624] :
      ( ( hAPP(c_List_Orev(X31624),X31623) != X31622
        | X31623 = hAPP(c_List_Orev(X31624),X31622) )
      & ( X31623 != hAPP(c_List_Orev(X31624),X31622)
        | hAPP(c_List_Orev(X31624),X31623) = X31622 ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__swap])]) ).

fof(i_0_10902,plain,
    ! [X22444] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22444) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_min__0L]) ).

fof(i_0_10903,plain,
    ! [X19883] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19883) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_diff__0__eq__0]) ).

fof(i_0_10904,plain,
    ! [X19570] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19570) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[fact_zdiv__zero]) ).

fof(i_0_10905,plain,
    ! [X18670] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18670) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_mult__0]) ).

fof(i_0_10906,plain,
    ! [X29331] : hBOOL(hAPP(c_List_Odistinct(X29331),c_List_Olist_ONil(X29331))),
    inference(variable_rename,[status(thm)],[fact_distinct_Osimps_I1_J]) ).

fof(i_0_10907,plain,
    ! [X33303,X33304,X33305] : hAPP(c_New__DSequence_Oneg__single(X33305,X33304),X33303) = c_Lazy__Sequence_Ohb__single(X33305,X33304),
    inference(variable_rename,[status(thm)],[fact_New__DSequence_Oneg__single__def]) ).

fof(i_0_10908,plain,
    ! [X32164,X32165] : c_Transitive__Closure_Ortrancl(X32165,c_Transitive__Closure_Ortrancl(X32165,X32164)) = c_Transitive__Closure_Ortrancl(X32165,X32164),
    inference(variable_rename,[status(thm)],[fact_rtrancl__idemp]) ).

fof(i_0_10909,plain,
    ! [X31535,X31536] : c_List_Oremdups(X31536,c_List_Oremdups(X31536,X31535)) = c_List_Oremdups(X31536,X31535),
    inference(variable_rename,[status(thm)],[fact_remdups__remdups]) ).

fof(i_0_10910,plain,
    ! [X28824] : hAPP(c_List_Oset(X28824),c_List_Olist_ONil(X28824)) = c_Orderings_Obot__class_Obot(tc_fun(X28824,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_List_Oset_Osimps_I1_J]) ).

fof(i_0_10911,plain,
    ! [X22610] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22610) = X22610,
    inference(variable_rename,[status(thm)],[fact_max__0L]) ).

fof(i_0_10912,plain,
    ! [X18697] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X18697) = X18697,
    inference(variable_rename,[status(thm)],[fact_zmult__1]) ).

fof(i_0_10913,plain,
    ! [X19179] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X19179) = X19179,
    inference(variable_rename,[status(thm)],[fact_nat__mult__1]) ).

fof(i_0_10914,plain,
    ! [X18099] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18099) = X18099,
    inference(variable_rename,[status(thm)],[fact_zadd__0]) ).

fof(i_0_10915,plain,
    ! [X17499] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17499) = X17499,
    inference(variable_rename,[status(thm)],[fact_plus__nat_Oadd__0]) ).

fof(i_0_10916,plain,
    ! [X33348] : c_Predicate_Oconversep(X33348,X33348,c_fequal) = c_fequal,
    inference(variable_rename,[status(thm)],[fact_conversep__eq]) ).

fof(i_0_10917,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_10918,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_10919,plain,
    ! [X19619] :
      ( X19619 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19619),X19619) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__self])]) ).

fof(i_0_10920,plain,
    ! [X20657] :
      ( ~ class_Int_Onumber__ring(X20657)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X20657),c_Groups_Oone__class_Oone(X20657)) = hAPP(c_Int_Onumber__class_Onumber__of(X20657),c_Int_OMin) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_arith__simps_I31_J])]) ).

fof(i_0_10921,plain,
    ! [X20658] :
      ( ~ class_Int_Onumber__ring(X20658)
      | hAPP(c_Int_Onumber__class_Onumber__of(X20658),c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(X20658),c_Groups_Oone__class_Oone(X20658)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__Min])]) ).

fof(i_0_10922,plain,
    ! [X22443] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X22443),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_10923,plain,
    ! [X18669] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18669),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_10924,plain,
    ! [X18221,X18222] :
      ( ( c_Groups_Ozero__class_Ozero(X18222) != hAPP(c_Groups_Ouminus__class_Ouminus(X18222),X18221)
        | c_Groups_Ozero__class_Ozero(X18222) = X18221
        | ~ class_Groups_Ogroup__add(X18222) )
      & ( c_Groups_Ozero__class_Ozero(X18222) != X18221
        | c_Groups_Ozero__class_Ozero(X18222) = hAPP(c_Groups_Ouminus__class_Ouminus(X18222),X18221)
        | ~ class_Groups_Ogroup__add(X18222) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__0__equal__iff__equal])])]) ).

fof(i_0_10925,plain,
    ! [X20221,X20222] :
      ( ( hAPP(c_Groups_Oabs__class_Oabs(X20222),X20221) != c_Groups_Ozero__class_Ozero(X20222)
        | X20221 = c_Groups_Ozero__class_Ozero(X20222)
        | ~ class_Groups_Oordered__ab__group__add__abs(X20222) )
      & ( X20221 != c_Groups_Ozero__class_Ozero(X20222)
        | hAPP(c_Groups_Oabs__class_Oabs(X20222),X20221) = c_Groups_Ozero__class_Ozero(X20222)
        | ~ class_Groups_Oordered__ab__group__add__abs(X20222) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__eq__0])])]) ).

fof(i_0_10926,plain,
    ! [X18225,X18226] :
      ( ( hAPP(c_Groups_Ouminus__class_Ouminus(X18226),X18225) != c_Groups_Ozero__class_Ozero(X18226)
        | X18225 = c_Groups_Ozero__class_Ozero(X18226)
        | ~ class_Groups_Ogroup__add(X18226) )
      & ( X18225 != c_Groups_Ozero__class_Ozero(X18226)
        | hAPP(c_Groups_Ouminus__class_Ouminus(X18226),X18225) = c_Groups_Ozero__class_Ozero(X18226)
        | ~ class_Groups_Ogroup__add(X18226) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__equal__0__iff__equal])])]) ).

fof(i_0_10927,plain,
    ! [X34290] :
      ( ~ hBOOL(hAPP(c_fNot,X34290))
      | ~ hBOOL(X34290) ),
    inference(variable_rename,[status(thm)],[i_0_6056]) ).

fof(i_0_10928,plain,
    ! [X22611] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X22611),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X22611,
    inference(variable_rename,[status(thm)],[fact_max__0R]) ).

fof(i_0_10929,plain,
    ! [X19882] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19882),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X19882,
    inference(variable_rename,[status(thm)],[fact_minus__nat_Odiff__0]) ).

fof(i_0_10930,plain,
    ! [X18698] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X18698),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X18698,
    inference(variable_rename,[status(thm)],[fact_zmult__1__right]) ).

fof(i_0_10931,plain,
    ! [X19182] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19182),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X19182,
    inference(variable_rename,[status(thm)],[fact_nat__mult__1__right]) ).

fof(i_0_10932,plain,
    ! [X18098] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X18098),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X18098,
    inference(variable_rename,[status(thm)],[fact_zadd__0__right]) ).

fof(i_0_10933,plain,
    ! [X17500] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17500),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X17500,
    inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).

fof(i_0_10934,plain,
    ! [X26103] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X26103)) = X26103,
    inference(variable_rename,[status(thm)],[fact_card__lessThan]) ).

fof(i_0_10935,plain,
    ! [X18190] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X18190)) = X18190,
    inference(variable_rename,[status(thm)],[fact_zminus__zminus]) ).

fof(i_0_10936,plain,
    ! [X31189,X31190] : hAPP(c_List_Ofilter(X31190,X31189),c_List_Olist_ONil(X31190)) = c_List_Olist_ONil(X31190),
    inference(variable_rename,[status(thm)],[fact_filter_Osimps_I1_J]) ).

fof(i_0_10937,plain,
    ! [X23540,X23541] :
      ( ~ class_Finite__Set_Ofinite(X23541)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X23541),X23540)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__code])]) ).

fof(i_0_10938,plain,
    ! [X23538,X23539] :
      ( ~ class_Finite__Set_Ofinite(X23539)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X23539),X23538)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite])]) ).

fof(i_0_10939,plain,
    ! [X18407,X18408] :
      ( ( hAPP(c_Int_Oring__1__class_Oof__int(X18408),X18407) != c_Groups_Ozero__class_Ozero(X18408)
        | X18407 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ class_Int_Oring__char__0(X18408) )
      & ( X18407 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(c_Int_Oring__1__class_Oof__int(X18408),X18407) = c_Groups_Ozero__class_Ozero(X18408)
        | ~ class_Int_Oring__char__0(X18408) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__eq__0__iff])])]) ).

fof(i_0_10940,plain,
    ! [X18405,X18406] :
      ( ( c_Groups_Ozero__class_Ozero(X18406) != hAPP(c_Int_Oring__1__class_Oof__int(X18406),X18405)
        | X18405 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ class_Int_Oring__char__0(X18406) )
      & ( X18405 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Groups_Ozero__class_Ozero(X18406) = hAPP(c_Int_Oring__1__class_Oof__int(X18406),X18405)
        | ~ class_Int_Oring__char__0(X18406) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__0__eq__iff])])]) ).

cnf(i_0_10941,plain,
    ( c_Int_OBit0(X1) = c_Int_OPls
    | X1 != c_Int_OPls ),
    inference(split_conjunct,[status(thm)],[i_0_6051]) ).

cnf(i_0_10942,plain,
    ( c_Int_OPls = c_Int_OBit0(X1)
    | c_Int_OPls != X1 ),
    inference(split_conjunct,[status(thm)],[i_0_6050]) ).

fof(i_0_10943,plain,
    ! [X19881] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19881),X19881) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_diff__self__eq__0]) ).

fof(i_0_10944,plain,
    ! [X33630,X33631] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X33631,X33630),c_Lazy__Sequence_Olazy__sequence_OEmpty(X33631)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_lazy__sequence_Osize_I1_J]) ).

fof(i_0_10945,plain,
    ! [X20276,X20277] :
      ( ~ class_Int_Onumber__ring(X20277)
      | hAPP(c_Int_Onumber__class_Onumber__of(X20277),X20276) = hAPP(c_Int_Oring__1__class_Oof__int(X20277),X20276) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__eq])]) ).

fof(i_0_10946,plain,
    ! [X17900,X17901,X17902,X17903] :
      ( ( X17903 = X17901
        | c_Com_Ocom_OWhile(X17903,X17902) != c_Com_Ocom_OWhile(X17901,X17900) )
      & ( X17902 = X17900
        | c_Com_Ocom_OWhile(X17903,X17902) != c_Com_Ocom_OWhile(X17901,X17900) )
      & ( X17903 != X17901
        | X17902 != X17900
        | c_Com_Ocom_OWhile(X17903,X17902) = c_Com_Ocom_OWhile(X17901,X17900) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_com_Osimps_I5_J])])]) ).

fof(i_0_10947,plain,
    ! [X17331,X17332,X17333,X17334] :
      ( ( X17334 = X17332
        | c_Com_Ocom_OAss(X17334,X17333) != c_Com_Ocom_OAss(X17332,X17331) )
      & ( X17333 = X17331
        | c_Com_Ocom_OAss(X17334,X17333) != c_Com_Ocom_OAss(X17332,X17331) )
      & ( X17334 != X17332
        | X17333 != X17331
        | c_Com_Ocom_OAss(X17334,X17333) = c_Com_Ocom_OAss(X17332,X17331) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_com_Osimps_I1_J])])]) ).

fof(i_0_10948,plain,
    ! [X17061,X17062,X17063,X17064] :
      ( ( X17064 = X17062
        | c_Com_Ocom_OSemi(X17064,X17063) != c_Com_Ocom_OSemi(X17062,X17061) )
      & ( X17063 = X17061
        | c_Com_Ocom_OSemi(X17064,X17063) != c_Com_Ocom_OSemi(X17062,X17061) )
      & ( X17064 != X17062
        | X17063 != X17061
        | c_Com_Ocom_OSemi(X17064,X17063) = c_Com_Ocom_OSemi(X17062,X17061) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_com_Osimps_I3_J])])]) ).

fof(i_0_10949,plain,
    ! [X18227,X18228] :
      ( ( hAPP(c_Groups_Ouminus__class_Ouminus(X18228),X18227) != X18227
        | X18227 = c_Groups_Ozero__class_Ozero(X18228)
        | ~ class_Groups_Olinordered__ab__group__add(X18228) )
      & ( X18227 != c_Groups_Ozero__class_Ozero(X18228)
        | hAPP(c_Groups_Ouminus__class_Ouminus(X18228),X18227) = X18227
        | ~ class_Groups_Olinordered__ab__group__add(X18228) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__equal__zero])])]) ).

fof(i_0_10950,plain,
    ! [X18223,X18224] :
      ( ( X18223 != hAPP(c_Groups_Ouminus__class_Ouminus(X18224),X18223)
        | X18223 = c_Groups_Ozero__class_Ozero(X18224)
        | ~ class_Groups_Olinordered__ab__group__add(X18224) )
      & ( X18223 != c_Groups_Ozero__class_Ozero(X18224)
        | X18223 = hAPP(c_Groups_Ouminus__class_Ouminus(X18224),X18223)
        | ~ class_Groups_Olinordered__ab__group__add(X18224) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equal__neg__zero])])]) ).

fof(i_0_10951,plain,
    ! [X17249,X17250] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OAss(X17250,X17249)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_com_Osize_I10_J]) ).

fof(i_0_10952,plain,
    ! [X20895] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20895),c_Int_OPls) = X20895,
    inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I1_J]) ).

fof(i_0_10953,plain,
    ! [X20893] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20893),c_Int_OPls) = X20893,
    inference(variable_rename,[status(thm)],[fact_add__Pls__right]) ).

fof(i_0_10954,plain,
    ! [X18267] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18267)) = X18267,
    inference(variable_rename,[status(thm)],[fact_nat__int]) ).

fof(i_0_10955,plain,
    ! [X34252,X34253] :
      ( ~ class_Lazy__Sequence_Osmall__lazy(X34253)
      | ~ class_Lazy__Sequence_Osmall__lazy(X34252)
      | class_Lazy__Sequence_Osmall__lazy(tc_prod(X34253,X34252)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_prod__Lazy__Sequence_Osmall__lazy])]) ).

fof(i_0_10956,plain,
    ! [X34243,X34244] :
      ( ~ class_Enum_Oenum(X34244)
      | ~ class_Enum_Oenum(X34243)
      | class_Enum_Oenum(tc_sum(X34244,X34243)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_sum__Enum_Oenum])]) ).

fof(i_0_10957,plain,
    ! [X34256,X34257] :
      ( ~ class_Enum_Oenum(X34257)
      | ~ class_Enum_Oenum(X34256)
      | class_Enum_Oenum(tc_prod(X34257,X34256)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_prod__Enum_Oenum])]) ).

fof(i_0_10958,plain,
    ! [X34237,X34238] :
      ( ~ class_Enum_Oenum(X34238)
      | ~ class_Enum_Oenum(X34237)
      | class_Enum_Oenum(tc_fun(X34238,X34237)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Enum_Oenum])]) ).

fof(i_0_10959,plain,
    ! [X34241,X34242] :
      ( ~ class_Finite__Set_Ofinite(X34242)
      | ~ class_Finite__Set_Ofinite(X34241)
      | class_Finite__Set_Ofinite(tc_sum(X34242,X34241)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_sum__Finite__Set_Ofinite])]) ).

fof(i_0_10960,plain,
    ! [X34254,X34255] :
      ( ~ class_Finite__Set_Ofinite(X34255)
      | ~ class_Finite__Set_Ofinite(X34254)
      | class_Finite__Set_Ofinite(tc_prod(X34255,X34254)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_prod__Finite__Set_Ofinite])]) ).

fof(i_0_10961,plain,
    ! [X34221,X34222] :
      ( ~ class_Finite__Set_Ofinite(X34222)
      | ~ class_Finite__Set_Ofinite(X34221)
      | class_Finite__Set_Ofinite(tc_fun(X34222,X34221)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Finite__Set_Ofinite])]) ).

fof(i_0_10962,plain,
    ! [X21399,X21400] :
      ( ~ c_Nat__Transfer_Ois__nat(X21400)
      | ~ c_Nat__Transfer_Ois__nat(X21399)
      | c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(X21400,X21399)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J])]) ).

fof(i_0_10963,plain,
    ! [X17977,X17978,X17979,X17980] : c_Com_Ocom_OWhile(X17980,X17979) != c_Com_Ocom_OAss(X17978,X17977),
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I29_J]) ).

fof(i_0_10964,plain,
    ! [X17999,X18000,X18001,X18002] : c_Com_Ocom_OWhile(X18002,X18001) != c_Com_Ocom_OSemi(X18000,X17999),
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I47_J]) ).

fof(i_0_10965,plain,
    ! [X17981,X17982,X17983,X17984] : c_Com_Ocom_OAss(X17984,X17983) != c_Com_Ocom_OWhile(X17982,X17981),
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I28_J]) ).

fof(i_0_10966,plain,
    ! [X17995,X17996,X17997,X17998] : c_Com_Ocom_OSemi(X17998,X17997) != c_Com_Ocom_OWhile(X17996,X17995),
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I46_J]) ).

fof(i_0_10967,plain,
    ! [X17554,X17555,X17556,X17557] : c_Com_Ocom_OAss(X17557,X17556) != c_Com_Ocom_OSemi(X17555,X17554),
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I24_J]) ).

fof(i_0_10968,plain,
    ! [X17558,X17559,X17560,X17561] : c_Com_Ocom_OSemi(X17561,X17560) != c_Com_Ocom_OAss(X17559,X17558),
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I25_J]) ).

fof(i_0_10969,plain,
    ! [X20892] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X20892) = X20892,
    inference(variable_rename,[status(thm)],[fact_add__Pls]) ).

fof(i_0_10970,plain,
    ! [X31646,X31647] :
      ( ( hAPP(c_List_Orev(X31647),X31646) != c_List_Olist_ONil(X31647)
        | X31646 = c_List_Olist_ONil(X31647) )
      & ( X31646 != c_List_Olist_ONil(X31647)
        | hAPP(c_List_Orev(X31647),X31646) = c_List_Olist_ONil(X31647) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__is__Nil__conv])]) ).

fof(i_0_10971,plain,
    ! [X29300,X29301] :
      ( ( hAPP(c_List_Orotate1(X29301),X29300) != c_List_Olist_ONil(X29301)
        | X29300 = c_List_Olist_ONil(X29301) )
      & ( X29300 != c_List_Olist_ONil(X29301)
        | hAPP(c_List_Orotate1(X29301),X29300) = c_List_Olist_ONil(X29301) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rotate1__is__Nil__conv])]) ).

fof(i_0_10972,plain,
    ! [X31648,X31649] :
      ( ( c_List_Olist_ONil(X31649) != hAPP(c_List_Orev(X31649),X31648)
        | X31648 = c_List_Olist_ONil(X31649) )
      & ( X31648 != c_List_Olist_ONil(X31649)
        | c_List_Olist_ONil(X31649) = hAPP(c_List_Orev(X31649),X31648) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nil__is__rev__conv])]) ).

fof(i_0_10973,plain,
    ! [X20894] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),X20894) = c_Int_OPls,
    inference(variable_rename,[status(thm)],[fact_mult__Pls]) ).

fof(i_0_10974,plain,
    ! [X33790] : c_Relation_Otrans(tc_fun(X33790,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(X33790)),
    inference(variable_rename,[status(thm)],[fact_trans__finite__psubset]) ).

fof(i_0_10975,plain,
    ! [X28183] : c_Wellfounded_Owf(tc_fun(X28183,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(X28183)),
    inference(variable_rename,[status(thm)],[fact_wf__finite__psubset]) ).

fof(i_0_10976,plain,
    ! [X17225] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),hAPP(c_Com_Ocom_OBODY,X17225)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_com_Osize_I15_J]) ).

fof(i_0_10977,plain,
    ! [X31306] : c_List_Otranspose(X31306,c_List_Olist_ONil(tc_List_Olist(X31306))) = c_List_Olist_ONil(tc_List_Olist(X31306)),
    inference(variable_rename,[status(thm)],[fact_transpose_Osimps_I1_J]) ).

fof(i_0_10978,plain,
    ! [X17964,X17965,X17966] : hAPP(c_Com_Ocom_OBODY,X17966) != c_Com_Ocom_OWhile(X17965,X17964),
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I59_J]) ).

fof(i_0_10979,plain,
    ! [X17543,X17544,X17545] : hAPP(c_Com_Ocom_OBODY,X17545) != c_Com_Ocom_OAss(X17544,X17543),
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I31_J]) ).

fof(i_0_10980,plain,
    ! [X17058,X17059,X17060] : hAPP(c_Com_Ocom_OBODY,X17060) != c_Com_Ocom_OSemi(X17059,X17058),
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I49_J]) ).

fof(i_0_10981,plain,
    ! [X17961,X17962,X17963] : c_Com_Ocom_OWhile(X17963,X17962) != hAPP(c_Com_Ocom_OBODY,X17961),
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I58_J]) ).

fof(i_0_10982,plain,
    ! [X17540,X17541,X17542] : c_Com_Ocom_OAss(X17542,X17541) != hAPP(c_Com_Ocom_OBODY,X17540),
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I30_J]) ).

fof(i_0_10983,plain,
    ! [X17055,X17056,X17057] : c_Com_Ocom_OSemi(X17057,X17056) != hAPP(c_Com_Ocom_OBODY,X17055),
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I48_J]) ).

cnf(i_0_10984,plain,
    c_Int_Osucc(c_Int_OMin) = c_Int_OPls,
    inference(split_conjunct,[status(thm)],[fact_succ__Min]) ).

cnf(i_0_10985,plain,
    c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
    inference(split_conjunct,[status(thm)],[fact_Bit0__Pls]) ).

cnf(i_0_10986,plain,
    c_Int_Opred(c_Int_OPls) = c_Int_OMin,
    inference(split_conjunct,[status(thm)],[fact_pred__Pls]) ).

fof(i_0_10987,plain,
    ! [X30378,X30379] :
      ( ( hAPP(c_Code__Numeral_Onat__of,X30379) != hAPP(c_Code__Numeral_Onat__of,X30378)
        | X30379 = X30378 )
      & ( X30379 != X30378
        | hAPP(c_Code__Numeral_Onat__of,X30379) = hAPP(c_Code__Numeral_Onat__of,X30378) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Code__Numeral_Onat__of__inject])]) ).

fof(i_0_10988,plain,
    ! [X30376,X30377] :
      ( ( hAPP(c_Code__Numeral_Onat__of,X30377) != hAPP(c_Code__Numeral_Onat__of,X30376)
        | X30377 = X30376 )
      & ( X30377 != X30376
        | hAPP(c_Code__Numeral_Onat__of,X30377) = hAPP(c_Code__Numeral_Onat__of,X30376) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_code__numeral_Onat__of__inject])]) ).

fof(i_0_10989,plain,
    ! [X30270,X30271] :
      ( ( hAPP(c_Code__Numeral_Oof__nat,X30271) != hAPP(c_Code__Numeral_Oof__nat,X30270)
        | X30271 = X30270 )
      & ( X30271 != X30270
        | hAPP(c_Code__Numeral_Oof__nat,X30271) = hAPP(c_Code__Numeral_Oof__nat,X30270) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Code__Numeral_Oof__nat__inject])]) ).

fof(i_0_10990,plain,
    ! [X25267,X25268] :
      ( ( hAPP(c_Int_ORep__Integ,X25268) != hAPP(c_Int_ORep__Integ,X25267)
        | X25268 = X25267 )
      & ( X25268 != X25267
        | hAPP(c_Int_ORep__Integ,X25268) = hAPP(c_Int_ORep__Integ,X25267) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Rep__Integ__inject])]) ).

fof(i_0_10991,plain,
    ! [X17126,X17127] :
      ( ( hAPP(c_Nat_OSuc,X17127) != hAPP(c_Nat_OSuc,X17126)
        | X17127 = X17126 )
      & ( X17127 != X17126
        | hAPP(c_Nat_OSuc,X17127) = hAPP(c_Nat_OSuc,X17126) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat_Oinject])]) ).

fof(i_0_10992,plain,
    ! [X17124,X17125] :
      ( hAPP(c_Nat_OSuc,X17125) != hAPP(c_Nat_OSuc,X17124)
      | X17125 = X17124 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__inject])]) ).

fof(i_0_10993,plain,
    ! [X17065,X17066] :
      ( ( hAPP(c_Com_Ocom_OBODY,X17066) != hAPP(c_Com_Ocom_OBODY,X17065)
        | X17066 = X17065 )
      & ( X17066 != X17065
        | hAPP(c_Com_Ocom_OBODY,X17066) = hAPP(c_Com_Ocom_OBODY,X17065) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_com_Osimps_I6_J])]) ).

fof(i_0_10994,plain,
    ! [X19419,X19420] :
      ( ( c_Groups_Osgn__class_Osgn(X19420,X19419) != c_Groups_Ozero__class_Ozero(X19420)
        | X19419 = c_Groups_Ozero__class_Ozero(X19420)
        | ~ class_Rings_Olinordered__idom(X19420) )
      & ( X19419 != c_Groups_Ozero__class_Ozero(X19420)
        | c_Groups_Osgn__class_Osgn(X19420,X19419) = c_Groups_Ozero__class_Ozero(X19420)
        | ~ class_Rings_Olinordered__idom(X19420) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__0__0])])]) ).

fof(i_0_10995,plain,
    ! [X33629] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X33629)),c_Lazy__Sequence_Olazy__sequence_OEmpty(X33629)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_lazy__sequence_Osize_I3_J]) ).

fof(i_0_10996,plain,
    ! [X28448] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X28448)),c_List_Olist_ONil(X28448)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_list_Osize_I3_J]) ).

fof(i_0_10997,plain,
    ! [X33918,X33919] : c_Relation_Osym(X33919,c_Relation_OId__on(X33919,X33918)),
    inference(variable_rename,[status(thm)],[fact_sym__Id__on]) ).

fof(i_0_10998,plain,
    ! [X33827,X33828] : c_Relation_Oantisym(X33828,c_Relation_OId__on(X33828,X33827)),
    inference(variable_rename,[status(thm)],[fact_antisym__Id__on]) ).

fof(i_0_10999,plain,
    ! [X33802,X33803] : c_Relation_Otrans(X33803,c_Transitive__Closure_Ortrancl(X33803,X33802)),
    inference(variable_rename,[status(thm)],[fact_trans__rtrancl]) ).

fof(i_0_11000,plain,
    ! [X33793,X33794] : c_Relation_Otrans(X33794,c_Relation_OId__on(X33794,X33793)),
    inference(variable_rename,[status(thm)],[fact_trans__Id__on]) ).

fof(i_0_11001,plain,
    ! [X31939,X31940] : c_Wellfounded_Owf(X31940,c_List_Omeasures(X31940,X31939)),
    inference(variable_rename,[status(thm)],[fact_wf__measures]) ).

fof(i_0_11002,plain,
    ! [X20832] :
      ( ~ class_Rings_Osemiring__1(X20832)
      | ~ c_Int_Oiszero(X20832,c_Groups_Oone__class_Oone(X20832)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6057])]) ).

fof(i_0_11003,plain,
    ! [X31531,X31532] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(X31532,X31531)),
    inference(variable_rename,[status(thm)],[fact_sorted__upto]) ).

fof(i_0_11004,plain,
    ! [X30266,X30267] : c_Hilbert__Choice_OEps(X30267,hAPP(c_fequal,X30266)) = X30266,
    inference(variable_rename,[status(thm)],[fact_some__sym__eq__trivial]) ).

fof(i_0_11005,plain,
    ! [X32033,X32034] : c_HOL_OThe(X32034,hAPP(c_fequal,X32033)) = X32033,
    inference(variable_rename,[status(thm)],[fact_the__sym__eq__trivial]) ).

fof(i_0_11006,plain,
    ! [X29567] :
      ( ~ class_Groups_Omonoid__add(X29567)
      | hAPP(c_List_Omonoid__add__class_Olistsum(X29567),c_List_Olist_ONil(X29567)) = c_Groups_Ozero__class_Ozero(X29567) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__simps_I1_J])]) ).

fof(i_0_11007,plain,
    ! [X20234] :
      ( ~ class_Rings_Olinordered__idom(X20234)
      | hAPP(c_Groups_Oabs__class_Oabs(X20234),c_Groups_Oone__class_Oone(X20234)) = c_Groups_Oone__class_Oone(X20234) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__one])]) ).

fof(i_0_11008,plain,
    ! [X20220] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X20220)
      | hAPP(c_Groups_Oabs__class_Oabs(X20220),c_Groups_Ozero__class_Ozero(X20220)) = c_Groups_Ozero__class_Ozero(X20220) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__zero])]) ).

fof(i_0_11009,plain,
    ! [X26778] :
      ( ~ class_Lattices_Oboolean__algebra(X26778)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X26778),c_Orderings_Otop__class_Otop(X26778)) = c_Orderings_Obot__class_Obot(X26778) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__top__eq])]) ).

fof(i_0_11010,plain,
    ! [X18220] :
      ( ~ class_Groups_Ogroup__add(X18220)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X18220),c_Groups_Ozero__class_Ozero(X18220)) = c_Groups_Ozero__class_Ozero(X18220) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__zero])]) ).

fof(i_0_11011,plain,
    ! [X26779] :
      ( ~ class_Lattices_Oboolean__algebra(X26779)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X26779),c_Orderings_Obot__class_Obot(X26779)) = c_Orderings_Otop__class_Otop(X26779) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__bot__eq])]) ).

fof(i_0_11012,plain,
    ! [X34203,X34204] :
      ( ~ class_Lattices_Obounded__lattice(X34204)
      | class_Lattices_Obounded__lattice(tc_fun(X34203,X34204)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Obounded__lattice])]) ).

fof(i_0_11013,plain,
    ! [X34207,X34208] :
      ( ~ class_Lattices_Obounded__lattice(X34208)
      | class_Lattices_Obounded__lattice__top(tc_fun(X34207,X34208)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Obounded__lattice__top])]) ).

fof(i_0_11014,plain,
    ! [X34227,X34228] :
      ( ~ class_Orderings_Otop(X34228)
      | class_Orderings_Otop(tc_fun(X34227,X34228)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Otop])]) ).

fof(i_0_11015,plain,
    ! [X34205,X34206] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X34206)
      | class_Complete__Lattice_Ocomplete__lattice(tc_fun(X34205,X34206)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Complete__Lattice_Ocomplete__lattice])]) ).

fof(i_0_11016,plain,
    ! [X34215,X34216] :
      ( ~ class_Lattices_Odistrib__lattice(X34216)
      | class_Lattices_Odistrib__lattice(tc_fun(X34215,X34216)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Odistrib__lattice])]) ).

fof(i_0_11017,plain,
    ! [X34213,X34214] :
      ( ~ class_Lattices_Olattice(X34214)
      | class_Lattices_Osemilattice__inf(tc_fun(X34213,X34214)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Osemilattice__inf])]) ).

fof(i_0_11018,plain,
    ! [X34223,X34224] :
      ( ~ class_Lattices_Olattice(X34224)
      | class_Lattices_Olattice(tc_fun(X34223,X34224)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Olattice])]) ).

fof(i_0_11019,plain,
    ! [X34211,X34212] :
      ( ~ class_Lattices_Olattice(X34212)
      | class_Lattices_Osemilattice__sup(tc_fun(X34211,X34212)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Osemilattice__sup])]) ).

fof(i_0_11020,plain,
    ! [X34209,X34210] :
      ( ~ class_Lattices_Obounded__lattice(X34210)
      | class_Lattices_Obounded__lattice__bot(tc_fun(X34209,X34210)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Obounded__lattice__bot])]) ).

fof(i_0_11021,plain,
    ! [X34235,X34236] :
      ( ~ class_Groups_Ominus(X34236)
      | class_Groups_Ominus(tc_fun(X34235,X34236)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Groups_Ominus])]) ).

fof(i_0_11022,plain,
    ! [X34233,X34234] :
      ( ~ class_Groups_Ouminus(X34234)
      | class_Groups_Ouminus(tc_fun(X34233,X34234)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Groups_Ouminus])]) ).

fof(i_0_11023,plain,
    ! [X34217,X34218] :
      ( ~ class_Lattices_Oboolean__algebra(X34218)
      | class_Lattices_Oboolean__algebra(tc_fun(X34217,X34218)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Oboolean__algebra])]) ).

fof(i_0_11024,plain,
    ! [X34229,X34230] :
      ( ~ class_Orderings_Oord(X34230)
      | class_Orderings_Oord(tc_fun(X34229,X34230)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oord])]) ).

fof(i_0_11025,plain,
    ! [X34225,X34226] :
      ( ~ class_Orderings_Oorder(X34226)
      | class_Orderings_Oorder(tc_fun(X34225,X34226)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oorder])]) ).

fof(i_0_11026,plain,
    ! [X34219,X34220] :
      ( ~ class_Orderings_Opreorder(X34220)
      | class_Orderings_Opreorder(tc_fun(X34219,X34220)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Opreorder])]) ).

fof(i_0_11027,plain,
    ! [X34231,X34232] :
      ( ~ class_Orderings_Obot(X34232)
      | class_Orderings_Obot(tc_fun(X34231,X34232)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Obot])]) ).

fof(i_0_11028,plain,
    ! [X33926,X33927] :
      ( ~ c_Equiv__Relations_Oequivp(X33927,X33926)
      | c_Equiv__Relations_Opart__equivp(X33927,X33926) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equivp__implies__part__equivp])]) ).

fof(i_0_11029,plain,
    ! [X33855,X33856] :
      ( ( c_Predicate_Oreflp(X33856,X33855)
        | ~ c_Equiv__Relations_Oequivp(X33856,X33855) )
      & ( c_Predicate_Osymp(X33856,X33855)
        | ~ c_Equiv__Relations_Oequivp(X33856,X33855) )
      & ( c_Predicate_Otransp(X33856,X33855)
        | ~ c_Equiv__Relations_Oequivp(X33856,X33855) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6058])])]) ).

fof(i_0_11030,plain,
    ! [X32002,X32003] :
      ( ~ c_Wellfounded_Owf(X32003,X32002)
      | c_Wellfounded_Oacyclic(X32003,X32002) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__acyclic])]) ).

fof(i_0_11031,plain,
    ! [X21290] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X21290)),
    inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J]) ).

fof(i_0_11032,plain,
    ! [X30380] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,X30380)) = X30380,
    inference(variable_rename,[status(thm)],[fact_nat__of__of__nat]) ).

fof(i_0_11033,plain,
    ! [X30382] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X30382)) = X30382,
    inference(variable_rename,[status(thm)],[fact_nat__of__inverse]) ).

fof(i_0_11034,plain,
    ! [X30381] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X30381)) = X30381,
    inference(variable_rename,[status(thm)],[fact_of__nat__nat__of]) ).

fof(i_0_11035,plain,
    ! [X25269] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,X25269)) = X25269,
    inference(variable_rename,[status(thm)],[fact_Rep__Integ__inverse]) ).

fof(i_0_11036,plain,
    ! [X20829,X20830] :
      ( ( ~ c_Int_Oiszero(X20830,X20829)
        | X20829 = c_Groups_Ozero__class_Ozero(X20830)
        | ~ class_Rings_Osemiring__1(X20830) )
      & ( X20829 != c_Groups_Ozero__class_Ozero(X20830)
        | c_Int_Oiszero(X20830,X20829)
        | ~ class_Rings_Osemiring__1(X20830) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_iszero__def])])]) ).

fof(i_0_11037,plain,
    ! [X17907] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X17907) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | X17907 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X17907 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X17907) = 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_11038,plain,
    ! [X18535] :
      ( ~ class_Rings_Oring__1(X18535)
      | hAPP(c_Int_Oring__1__class_Oof__int(X18535),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(X18535) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__1])]) ).

fof(i_0_11039,plain,
    ! [X18404] :
      ( ~ class_Rings_Oring__1(X18404)
      | hAPP(c_Int_Oring__1__class_Oof__int(X18404),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(X18404) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__0])]) ).

fof(i_0_11040,plain,
    ! [X18528] :
      ( ~ class_Rings_Osemiring__1(X18528)
      | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18528),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X18528) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__1])]) ).

fof(i_0_11041,plain,
    ! [X18025] :
      ( ~ class_Rings_Osemiring__1(X18025)
      | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X18025),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(X18025) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__0])]) ).

fof(i_0_11042,plain,
    ! [X20501] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20501) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X20501),
    inference(variable_rename,[status(thm)],[fact_int__number__of__def]) ).

fof(i_0_11043,plain,
    ! [X31471,X31472] :
      ( ( c_List_Oremdups(X31472,X31471) != c_List_Olist_ONil(X31472)
        | X31471 = c_List_Olist_ONil(X31472) )
      & ( X31471 != c_List_Olist_ONil(X31472)
        | c_List_Oremdups(X31472,X31471) = c_List_Olist_ONil(X31472) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_remdups__eq__nil__iff])]) ).

fof(i_0_11044,plain,
    ! [X31469,X31470] :
      ( ( c_List_Olist_ONil(X31470) != c_List_Oremdups(X31470,X31469)
        | X31469 = c_List_Olist_ONil(X31470) )
      & ( X31469 != c_List_Olist_ONil(X31470)
        | c_List_Olist_ONil(X31470) = c_List_Oremdups(X31470,X31469) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_remdups__eq__nil__right__iff])]) ).

fof(i_0_11045,plain,
    ! [X17251,X17252] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OAss(X17252,X17251)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_com_Osize_I2_J]) ).

fof(i_0_11046,plain,
    ! [X34291] :
      ( hBOOL(X34291)
      | hBOOL(hAPP(c_fNot,X34291)) ),
    inference(variable_rename,[status(thm)],[i_0_6059]) ).

fof(i_0_11047,plain,
    ! [X19421] :
      ( ~ class_Groups_Osgn__if(X19421)
      | c_Groups_Osgn__class_Osgn(X19421,c_Groups_Ozero__class_Ozero(X19421)) = c_Groups_Ozero__class_Ozero(X19421) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn0])]) ).

fof(i_0_11048,plain,
    ! [X22738] :
      ( ~ class_Orderings_Oord(X22738)
      | c_Orderings_Oord__class_Omax(X22738) = c_Orderings_Oord_Omax(X22738,c_Orderings_Oord__class_Oless__eq(X22738)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__ord__max])]) ).

fof(i_0_11049,plain,
    ! [X22516] :
      ( ~ class_Orderings_Oord(X22516)
      | c_Orderings_Oord__class_Omin(X22516) = c_Orderings_Oord_Omin(X22516,c_Orderings_Oord__class_Oless__eq(X22516)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__ord__min])]) ).

fof(i_0_11050,plain,
    ! [X31650] : hAPP(c_List_Orev(X31650),c_List_Olist_ONil(X31650)) = c_List_Olist_ONil(X31650),
    inference(variable_rename,[status(thm)],[fact_rev_Osimps_I1_J]) ).

fof(i_0_11051,plain,
    ! [X29330] : hAPP(c_List_Otl(X29330),c_List_Olist_ONil(X29330)) = c_List_Olist_ONil(X29330),
    inference(variable_rename,[status(thm)],[fact_tl_Osimps_I1_J]) ).

fof(i_0_11052,plain,
    ! [X34245,X34246] : class_Nat_Osize(tc_sum(X34246,X34245)),
    inference(variable_rename,[status(thm)],[arity_sum__Nat_Osize]) ).

fof(i_0_11053,plain,
    ! [X34258,X34259] : class_Nat_Osize(tc_prod(X34259,X34258)),
    inference(variable_rename,[status(thm)],[arity_prod__Nat_Osize]) ).

fof(i_0_11054,plain,
    ! [X34250,X34251] : class_Nat_Osize(tc_Nitpick_Opair__box(X34251,X34250)),
    inference(variable_rename,[status(thm)],[arity_Nitpick__Opair____box__Nat_Osize]) ).

fof(i_0_11055,plain,
    ! [X20897] :
      ( ~ class_Int_Onumber__ring(X20897)
      | hAPP(c_Int_Onumber__class_Onumber__of(X20897),c_Int_OPls) = c_Groups_Ozero__class_Ozero(X20897) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__Pls])]) ).

fof(i_0_11056,plain,
    ! [X20896] :
      ( ~ class_Int_Onumber__ring(X20896)
      | c_Groups_Ozero__class_Ozero(X20896) = hAPP(c_Int_Onumber__class_Onumber__of(X20896),c_Int_OPls) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_semiring__norm_I112_J])]) ).

fof(i_0_11057,plain,
    ! [X17224] : c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY,X17224)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_com_Osize_I7_J]) ).

fof(i_0_11058,plain,
    ! [X31468] :
      ( ~ class_Orderings_Olinorder(X31468)
      | c_List_Olinorder__class_Osorted(X31468,c_List_Olist_ONil(X31468)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted_Oequations_I1_J])]) ).

fof(i_0_11059,plain,
    ! [X31450] :
      ( ~ class_Orderings_Olinorder(X31450)
      | c_List_Olinorder__class_Osorted(X31450,c_List_Olist_ONil(X31450)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted_ONil])]) ).

fof(i_0_11060,plain,
    ! [X20831] :
      ( ~ class_Rings_Osemiring__1(X20831)
      | c_Int_Oiszero(X20831,c_Groups_Ozero__class_Ozero(X20831)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_iszero__0])]) ).

fof(i_0_11061,plain,
    ! [X33269,X33270] : hAPP(c_New__DSequence_Opos__empty(X33270),X33269) = c_Lazy__Sequence_Oempty(X33270),
    inference(variable_rename,[status(thm)],[fact_New__DSequence_Opos__empty__def]) ).

fof(i_0_11062,plain,
    ! [X31467] : c_List_Oremdups(X31467,c_List_Olist_ONil(X31467)) = c_List_Olist_ONil(X31467),
    inference(variable_rename,[status(thm)],[fact_remdups_Osimps_I1_J]) ).

fof(i_0_11063,plain,
    ! [X29594] : c_List_Obutlast(X29594,c_List_Olist_ONil(X29594)) = c_List_Olist_ONil(X29594),
    inference(variable_rename,[status(thm)],[fact_butlast_Osimps_I1_J]) ).

fof(i_0_11064,plain,
    ! [X17178] : hAPP(c_Nat_OSuc,X17178) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_Suc__neq__Zero]) ).

fof(i_0_11065,plain,
    ! [X17176] : hAPP(c_Nat_OSuc,X17176) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_nat_Osimps_I3_J]) ).

fof(i_0_11066,plain,
    ! [X17175] : hAPP(c_Nat_OSuc,X17175) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_Suc__not__Zero]) ).

fof(i_0_11067,plain,
    ! [X17177] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X17177),
    inference(variable_rename,[status(thm)],[fact_Zero__neq__Suc]) ).

fof(i_0_11068,plain,
    ! [X17174] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X17174),
    inference(variable_rename,[status(thm)],[fact_nat_Osimps_I2_J]) ).

fof(i_0_11069,plain,
    ! [X17173] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X17173),
    inference(variable_rename,[status(thm)],[fact_Zero__not__Suc]) ).

fof(i_0_11070,plain,
    ! [X17262] :
      ( X17262 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | X17262 = hAPP(c_Nat_OSuc,esk22_1(X17262)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat_Oexhaust])])]) ).

fof(i_0_11071,plain,
    ! [X17254] :
      ( X17254 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | X17254 = hAPP(c_Nat_OSuc,esk19_1(X17254)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_not0__implies__Suc])])]) ).

fof(i_0_11072,plain,
    ! [X18015,X18016] : c_Com_Ocom_OWhile(X18016,X18015) != c_Com_Ocom_OSKIP,
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I17_J]) ).

fof(i_0_11073,plain,
    ! [X17564,X17565] : c_Com_Ocom_OAss(X17565,X17564) != c_Com_Ocom_OSKIP,
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I9_J]) ).

fof(i_0_11074,plain,
    ! [X17051,X17052] : c_Com_Ocom_OSemi(X17052,X17051) != c_Com_Ocom_OSKIP,
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I13_J]) ).

fof(i_0_11075,plain,
    ! [X18013,X18014] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(X18014,X18013),
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I16_J]) ).

fof(i_0_11076,plain,
    ! [X17562,X17563] : c_Com_Ocom_OSKIP != c_Com_Ocom_OAss(X17563,X17562),
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I8_J]) ).

fof(i_0_11077,plain,
    ! [X17049,X17050] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(X17050,X17049),
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I12_J]) ).

fof(i_0_11078,plain,
    ! [X23853] :
      ( ~ class_Lattices_Osemilattice__inf(X23853)
      | ~ class_Orderings_Olinorder(X23853)
      | c_Lattices_Osemilattice__inf__class_Oinf(X23853) = c_Orderings_Oord__class_Omin(X23853) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__min])]) ).

fof(i_0_11079,plain,
    ! [X22831] :
      ( ~ class_Lattices_Osemilattice__sup(X22831)
      | ~ class_Orderings_Olinorder(X22831)
      | c_Lattices_Osemilattice__sup__class_Osup(X22831) = c_Orderings_Oord__class_Omax(X22831) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__max])]) ).

fof(i_0_11080,plain,
    ! [X17128] : hAPP(c_Nat_OSuc,X17128) != X17128,
    inference(variable_rename,[status(thm)],[fact_Suc__n__not__n]) ).

fof(i_0_11081,plain,
    ! [X17129] : X17129 != hAPP(c_Nat_OSuc,X17129),
    inference(variable_rename,[status(thm)],[fact_n__not__Suc__n]) ).

fof(i_0_11082,plain,
    ! [X27927,X27928] : hAPP(c_Fun_Oid(X27928),X27927) = X27927,
    inference(variable_rename,[status(thm)],[fact_id__apply]) ).

fof(i_0_11083,plain,
    ! [X27925,X27926] : hAPP(c_Fun_Oid(X27926),X27925) = X27925,
    inference(variable_rename,[status(thm)],[fact_id__def]) ).

fof(i_0_11084,plain,
    ! [X27719,X27720] : hAPP(c_Set_OCollect(X27720),X27719) = X27719,
    inference(variable_rename,[status(thm)],[fact_Collect__def]) ).

fof(i_0_11085,plain,
    ! [X34262,X34263] : hAPP(c_COMBI(X34263),X34262) = X34262,
    inference(variable_rename,[status(thm)],[help_c__COMBI__1]) ).

fof(i_0_11086,plain,
    ! [X18550] :
      ( ~ class_Rings_Ozero__neq__one(X18550)
      | c_Groups_Oone__class_Oone(X18550) != c_Groups_Ozero__class_Ozero(X18550) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__neq__zero])]) ).

fof(i_0_11087,plain,
    ! [X18549] :
      ( ~ class_Rings_Ozero__neq__one(X18549)
      | c_Groups_Ozero__class_Ozero(X18549) != c_Groups_Oone__class_Oone(X18549) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__neq__one])]) ).

fof(i_0_11088,plain,
    ! [X17053] : hAPP(c_Com_Ocom_OBODY,X17053) != c_Com_Ocom_OSKIP,
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I19_J]) ).

fof(i_0_11089,plain,
    ! [X17054] : c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,X17054),
    inference(variable_rename,[status(thm)],[fact_com_Osimps_I18_J]) ).

fof(i_0_11090,plain,
    ! [X34099] : c_Quickcheck_Obeyond(X34099,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_11091,plain,
    ! [X28204] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(X28204)),
    inference(variable_rename,[status(thm)],[fact_wf__int__ge__less__than2]) ).

fof(i_0_11092,plain,
    ! [X28205] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(X28205)),
    inference(variable_rename,[status(thm)],[fact_wf__int__ge__less__than]) ).

fof(i_0_11093,plain,
    ! [X20483] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20483) = X20483,
    inference(variable_rename,[status(thm)],[fact_number__of__is__id]) ).

fof(i_0_11094,plain,
    ! [X17899] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X17899) = X17899,
    inference(variable_rename,[status(thm)],[fact_nat__size]) ).

fof(i_0_11095,plain,
    ! [X34239] :
      ( ~ class_Lazy__Sequence_Osmall__lazy(X34239)
      | class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(X34239)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_List__Olist__Lazy__Sequence_Osmall__lazy])]) ).

fof(i_0_11096,plain,
    ! [X34248] :
      ( ~ class_Enum_Oenum(X34248)
      | class_Enum_Oenum(tc_Option_Ooption(X34248)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Option__Ooption__Enum_Oenum])]) ).

fof(i_0_11097,plain,
    ! [X34247] :
      ( ~ class_Finite__Set_Ofinite(X34247)
      | class_Finite__Set_Ofinite(tc_Option_Ooption(X34247)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Option__Ooption__Finite__Set_Ofinite])]) ).

fof(i_0_11098,plain,
    ! [X26880] : c_Equiv__Relations_Oequivp(X26880,c_fequal),
    inference(variable_rename,[status(thm)],[fact_identity__equivp]) ).

fof(i_0_11099,plain,
    ! [X34261] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(X34261)),
    inference(variable_rename,[status(thm)],[arity_Lazy____Sequence__Olazy____sequence__Nat_Osize]) ).

fof(i_0_11100,plain,
    ! [X34240] : class_Nat_Osize(tc_List_Olist(X34240)),
    inference(variable_rename,[status(thm)],[arity_List__Olist__Nat_Osize]) ).

fof(i_0_11101,plain,
    ! [X34249] : class_Nat_Osize(tc_Option_Ooption(X34249)),
    inference(variable_rename,[status(thm)],[arity_Option__Ooption__Nat_Osize]) ).

fof(i_0_11102,plain,
    ! [X34260] : class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(X34260)),
    inference(variable_rename,[status(thm)],[arity_Hoare____Mirabelle__Otriple__Nat_Osize]) ).

fof(i_0_11103,plain,
    ~ hBOOL(c_fFalse),
    inference(fof_simplification,[status(thm)],[help_c__fFalse__1]) ).

cnf(i_0_11104,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,esk161_11(X3,X4,X5,X2,X1,X6,X7,X8,X9,X10,X11)),esk162_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_6060]),
    [final] ).

cnf(i_0_11105,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk162_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_6060]),
    [final] ).

cnf(i_0_11106,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk161_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_6060]),
    [final] ).

cnf(i_0_11107,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_6061,c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11108,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_6065]),
    [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_6066]),
    [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_6067]),
    [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_6068]),
    [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_6069]),
    [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_6070]),
    [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_6071]),
    [final] ).

cnf(i_0_11115,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk283_8(X3,X4,X5,X2,X1,X6,X7,X8)),esk284_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_6072]),
    [final] ).

cnf(i_0_11116,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_6073,c_0_6074]),
    [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_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_6075,c_0_6074]),
    [final] ).

cnf(i_0_11118,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,esk361_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_6076]),
    [final] ).

cnf(i_0_11119,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_6077]),
    [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__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_6078]),
    [final] ).

cnf(i_0_11121,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_6079]),
    [final] ).

cnf(i_0_11122,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,esk413_8(X4,X5,X6,X3,X2,X1,X7,X8))),X6) != hAPP(c_Fun_Ocomp(X2,X1,X2,X6),hAPP(X5,esk413_8(X4,X5,X6,X3,X2,X1,X7,X8))) ),
    inference(split_conjunct,[status(thm)],[i_0_6080]),
    [final] ).

cnf(i_0_11123,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_6081,c_0_6082]),c_0_6082]),c_0_6082]),c_0_6082]),c_0_6083]),c_0_6083]),
    [final] ).

cnf(i_0_11124,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_6084]),
    [final] ).

cnf(i_0_11125,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_6085]),
    [final] ).

cnf(i_0_11126,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_6086]),
    [final] ).

cnf(i_0_11127,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_6087,c_0_6088]),
    [final] ).

cnf(i_0_11128,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_6077]),
    [final] ).

cnf(i_0_11129,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_6078]),
    [final] ).

cnf(i_0_11130,plain,
    ( X3 = X2
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk159_7(X2,X3,X4,X5,X6,X7,X1)),esk160_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_6089]),
    [final] ).

cnf(i_0_11131,plain,
    ( X1 = hAPP(hAPP(c_Product__Type_OPair(X2,X3),hAPP(X4,esk283_8(X5,X6,X4,X7,X8,X1,X3,X2))),hAPP(X6,esk284_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_6072]),
    [final] ).

cnf(i_0_11132,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X1),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(X1)),X3)),c_Com_Ocom_OBODY)),X4)),X5))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool)),X2),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X1),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(X1)),X3)),c_Com_Ocom_OBODY)),X4)),X5)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X1),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(X1)),X3)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),X4)),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6090]),
    [final] ).

cnf(i_0_11133,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_6084]),
    [final] ).

cnf(i_0_11134,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_6085]),
    [final] ).

cnf(i_0_11135,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_6086]),
    [final] ).

cnf(i_0_11136,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_6091,c_0_6088]),
    [final] ).

cnf(i_0_11137,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_6092,c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11138,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_6093]),
    [final] ).

cnf(i_0_11139,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,esk477_8(X2,X1,X3,X4,X5,X6,X7,X8)) != hAPP(X2,hAPP(X5,esk477_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_6094]),
    [final] ).

cnf(i_0_11140,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),hAPP(X3,X6)),hAPP(c_Com_Ocom_OBODY,X6)),hAPP(X4,X6))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool)),X2),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X1),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(X1)),X3)),c_Com_Ocom_OBODY)),X4)),X5)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X1),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(X1))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(X1)),X3)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),X4)),X5))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X6),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6095]),
    [final] ).

cnf(i_0_11141,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_6096,c_0_6097]),c_0_6097]),
    [final] ).

cnf(i_0_11142,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_6098,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11143,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_6099]),
    [final] ).

cnf(i_0_11144,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk413_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_6080]),
    [final] ).

cnf(i_0_11145,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk361_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_6076]),
    [final] ).

cnf(i_0_11146,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk477_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_6094]),
    [final] ).

cnf(i_0_11147,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk224_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_6100]),
    [final] ).

cnf(i_0_11148,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),esk480_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_6101]),
    [final] ).

cnf(i_0_11149,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_6102]),
    [final] ).

cnf(i_0_11150,plain,
    ( hBOOL(hAPP(X1,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X6,X5,X3),X2),X4)))
    | ~ hBOOL(hAPP(X1,hAPP(hAPP(X2,esk533_7(X3,X2,X1,X4,X5,X6,X7)),esk534_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_6103]),
    [final] ).

cnf(i_0_11151,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_6104]),
    [final] ).

cnf(i_0_11152,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_6105]),
    [final] ).

cnf(i_0_11153,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_6106]),
    [final] ).

cnf(i_0_11154,plain,
    c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),X1),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X1),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj)),X3))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate),c_fNot),X4))),c_Com_Ocom_OWhile(X4,X5)),X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool)))),
    inference(split_conjunct,[status(thm)],[i_0_6107]),
    [final] ).

cnf(i_0_11155,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,esk224_8(X2,X1,X3,X4,X5,X6,X7,X8)) != hAPP(hAPP(c_Fun_Ocomp(X6,X8,X7,X2),X5),esk224_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_6100]),
    [final] ).

cnf(i_0_11156,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,esk480_8(X2,X1,X3,X4,X5,X6,X7,X8)) != hAPP(X2,esk480_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_6101]),
    [final] ).

cnf(i_0_11157,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_6108]),
    [final] ).

cnf(i_0_11158,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_6109]),
    [final] ).

cnf(i_0_11159,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_6099]),
    [final] ).

cnf(i_0_11160,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,esk163_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_6110]),
    [final] ).

cnf(i_0_11161,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,esk529_7(X2,X3,X4,X5,X1,X6,X7)),X5),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6111]),
    [final] ).

cnf(i_0_11162,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,esk358_7(X2,X3,X1,X4,X5,X6,X7)),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6112]),
    [final] ).

cnf(i_0_11163,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_6113]),
    [final] ).

cnf(i_0_11164,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_6114]),
    [final] ).

cnf(i_0_11165,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_6115]),
    [final] ).

cnf(i_0_11166,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_6116]),
    [final] ).

cnf(i_0_11167,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_6117]),
    [final] ).

cnf(i_0_11168,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_6118]),
    [final] ).

cnf(i_0_11169,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X5),X4),X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),X1),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),esk105_5(X3,X4,X2,X1,X5)))),X4),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),X1),hAPP(X3,esk104_5(X3,X4,X2,X1,X5))))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6119]),
    [final] ).

cnf(i_0_11170,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)),esk329_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_6120]),
    [final] ).

cnf(i_0_11171,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_6121]),
    [final] ).

cnf(i_0_11172,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_6122]),
    [final] ).

cnf(i_0_11173,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_6123]),
    [final] ).

cnf(i_0_11174,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),esk480_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_6101]),
    [final] ).

cnf(i_0_11175,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_6124]),
    [final] ).

cnf(i_0_11176,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_6108]),
    [final] ).

cnf(i_0_11177,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X7,X6,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X7)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X7),X2),X4),X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X7),tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(X1,esk9_7(X1,X2,X3,X4,X5,X6,X7)),esk11_7(X1,X2,X3,X4,X5,X6,X7)))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X7,X6,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X7)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X7),X5),X4),X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X7),tc_HOL_Obool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6125]),
    [final] ).

cnf(i_0_11178,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),esk78_7(X6,X7,X5,X4,X3,X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),esk79_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_6126]),
    [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),esk78_7(X6,X7,X5,X4,X3,X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),esk79_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_6126]),
    [final] ).

cnf(i_0_11180,plain,
    ( hBOOL(hAPP(hAPP(hAPP(X1,esk530_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_6127]),
    [final] ).

cnf(i_0_11181,plain,
    ( hBOOL(hAPP(hAPP(hAPP(X1,esk165_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_6128]),
    [final] ).

cnf(i_0_11182,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_6129]),
    [final] ).

cnf(i_0_11183,plain,
    c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),X1),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),X3)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),X4)),X5))),c_Com_Ocom_OAss(X4,X5)),X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool)))),
    inference(split_conjunct,[status(thm)],[i_0_6130]),
    [final] ).

cnf(i_0_11184,plain,
    c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),X1),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),X3)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),X4)),X5))),c_Com_Ocom_OAss(X4,X5)),X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool)))),
    inference(split_conjunct,[status(thm)],[i_0_6131]),
    [final] ).

cnf(i_0_11185,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_6132]),
    [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),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_6133,c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11187,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_6134,c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11188,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_6135,c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11189,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_6120]),
    [final] ).

cnf(i_0_11190,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_6121]),
    [final] ).

cnf(i_0_11191,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_6122]),
    [final] ).

cnf(i_0_11192,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_6123]),
    [final] ).

cnf(i_0_11193,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_6136]),
    [final] ).

cnf(i_0_11194,plain,
    ( hBOOL(hAPP(hAPP(X1,esk9_7(X2,X1,X3,X4,X5,X6,X7)),esk10_7(X2,X1,X3,X4,X5,X6,X7)))
    | c_Hoare__Mirabelle_Ohoare__derivs(X7,X6,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X7)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X7),X1),X4),X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X7),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X7,X6,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X7)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X7),X5),X4),X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X7),tc_HOL_Obool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6125]),
    [final] ).

cnf(i_0_11195,plain,
    ( hBOOL(hAPP(hAPP(X1,esk534_7(X2,X3,X4,X5,X6,X7,X1)),esk533_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_6103]),
    [final] ).

cnf(i_0_11196,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_6137,c_0_6138]),c_0_6138]),
    [final] ).

cnf(i_0_11197,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_6139,c_0_6138]),c_0_6138]),
    [final] ).

cnf(i_0_11198,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),esk293_6(X5,X4,X6,X3,X2,X1))))) != hAPP(X5,esk293_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_6140]),
    [final] ).

cnf(i_0_11199,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_6141]),
    [final] ).

cnf(i_0_11200,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_6142]),
    [final] ).

cnf(i_0_11201,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_6143,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11202,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),esk291_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_6144]),
    [final] ).

cnf(i_0_11203,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_6145]),
    [final] ).

cnf(i_0_11204,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_6146]),
    [final] ).

cnf(i_0_11205,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,esk441_5(X3,X4,X5,X2,X1)))),hAPP(X2,esk441_5(X3,X4,X5,X2,X1)))),c_Transitive__Closure_Ortrancl(X1,X5))) ),
    inference(split_conjunct,[status(thm)],[i_0_6147]),
    [final] ).

cnf(i_0_11206,plain,
    ( hBOOL(hAPP(hAPP(X5,X2),esk11_7(X3,X4,X5,X6,X1,X7,X8)))
    | c_Hoare__Mirabelle_Ohoare__derivs(X8,X7,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X8)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X8),X4),X6),X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X8),tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(X1,X2),esk10_7(X3,X4,X5,X6,X1,X7,X8)))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X8,X7,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X8)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X8),X1),X6),X5)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X8),tc_HOL_Obool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6125]),
    [final] ).

cnf(i_0_11207,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_6148]),
    [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_6149]),
    [final] ).

cnf(i_0_11209,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_6150]),
    [final] ).

cnf(i_0_11210,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_11211,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_6152]),
    [final] ).

cnf(i_0_11212,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk503_6(X3,X4,X1,X5,X2,X6)),esk504_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_6153]),
    [final] ).

cnf(i_0_11213,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk502_6(X3,X4,X2,X5,X6,X1)),esk503_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_6153]),
    [final] ).

cnf(i_0_11214,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_6154]),
    [final] ).

cnf(i_0_11215,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_6155]),
    [final] ).

cnf(i_0_11216,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,esk276_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_6156]),
    [final] ).

cnf(i_0_11217,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_6157,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [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_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_6158]),
    [final] ).

cnf(i_0_11219,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_6159]),
    [final] ).

cnf(i_0_11220,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_6160,c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11221,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk288_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_6161]),
    [final] ).

cnf(i_0_11222,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk78_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_6126]),
    [final] ).

cnf(i_0_11223,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk78_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_6126]),
    [final] ).

cnf(i_0_11224,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_6162]),
    [final] ).

cnf(i_0_11225,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk530_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_6127]),
    [final] ).

cnf(i_0_11226,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk165_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_6128]),
    [final] ).

cnf(i_0_11227,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk529_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_6111]),
    [final] ).

cnf(i_0_11228,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk358_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_6112]),
    [final] ).

cnf(i_0_11229,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk163_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_6110]),
    [final] ).

cnf(i_0_11230,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk160_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_6089]),
    [final] ).

cnf(i_0_11231,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk159_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_6089]),
    [final] ).

cnf(i_0_11232,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk454_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_6163]),
    [final] ).

cnf(i_0_11233,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk439_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_6164]),
    [final] ).

cnf(i_0_11234,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk77_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),esk76_4(X1,X2,X3,X4)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X2,esk76_4(X1,X2,X3,X4))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_6165]),
    [final] ).

cnf(i_0_11235,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),esk77_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),esk76_4(X2,X3,X4,X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X3,esk76_4(X2,X3,X4,X1))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_6165]),
    [final] ).

cnf(i_0_11236,plain,
    ( hAPP(X1,esk77_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),esk76_4(X2,X1,X3,X4)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X1,esk76_4(X2,X1,X3,X4))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_6165]),
    [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_6166]),
    [final] ).

cnf(i_0_11238,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk276_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_6156]),
    [final] ).

cnf(i_0_11239,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,esk458_6(X3,X2,X1,X4,X5,X6))),hAPP(X3,esk458_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_6167]),
    [final] ).

cnf(i_0_11240,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,esk428_6(X3,X2,X1,X4,X5,X6)),esk429_6(X3,X2,X1,X4,X5,X6)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6168]),
    [final] ).

cnf(i_0_11241,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_6169,c_0_6062]),c_0_6062]),c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),c_0_6064]),c_0_6064]),c_0_6064]),c_0_6064]),c_0_6064]),c_0_6064]),
    [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_6170,c_0_6062]),c_0_6062]),c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),c_0_6064]),c_0_6064]),c_0_6064]),c_0_6064]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11243,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_6171]),
    [final] ).

cnf(i_0_11244,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_6172]),
    [final] ).

cnf(i_0_11245,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,esk559_6(X3,X2,X1,X4,X5,X6))),hAPP(X2,esk560_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,esk558_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_6173]),
    [final] ).

cnf(i_0_11246,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_6174]),
    [final] ).

cnf(i_0_11247,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_6175]),
    [final] ).

cnf(i_0_11248,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk293_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_6140]),
    [final] ).

cnf(i_0_11249,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk291_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_6144]),
    [final] ).

cnf(i_0_11250,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_6176,c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11251,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_6177,c_0_6178]),c_0_6178]),
    [final] ).

cnf(i_0_11252,plain,
    ( hAPP(hAPP(X1,X2),X3) = hAPP(hAPP(X1,esk78_7(X3,X2,X4,X5,X1,X6,X7)),esk79_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_6126]),
    [final] ).

cnf(i_0_11253,plain,
    ( hAPP(hAPP(X1,X2),X3) = hAPP(hAPP(X1,esk78_7(X3,X2,X4,X5,X1,X6,X7)),esk79_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_6126]),
    [final] ).

cnf(i_0_11254,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk555_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_6179]),
    [final] ).

cnf(i_0_11255,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_6180,c_0_6181]),c_0_6181]),
    [final] ).

cnf(i_0_11256,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_6182]),
    [final] ).

cnf(i_0_11257,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_6183]),
    [final] ).

cnf(i_0_11258,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),esk334_3(X2,X3,X1)),esk334_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))),esk333_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_6184]),
    [final] ).

cnf(i_0_11259,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),esk558_6(X3,X2,X1,X4,X5,X6)),X4))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(X2,esk559_6(X3,X2,X1,X4,X5,X6))),hAPP(X2,esk560_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_6173]),
    [final] ).

cnf(i_0_11260,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_6185]),
    [final] ).

cnf(i_0_11261,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk334_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))),esk333_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_6184]),
    [final] ).

cnf(i_0_11262,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_6186,c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11263,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_6187,c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11264,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_6188,c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11265,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_6189]),
    [final] ).

cnf(i_0_11266,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),esk539_4(X3,X1,X4,X2)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6166]),
    [final] ).

cnf(i_0_11267,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_6190]),
    [final] ).

cnf(i_0_11268,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_6191]),
    [final] ).

cnf(i_0_11269,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_6192]),
    [final] ).

cnf(i_0_11270,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_6193]),
    [final] ).

cnf(i_0_11271,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_6194]),
    [final] ).

cnf(i_0_11272,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_6195]),
    [final] ).

cnf(i_0_11273,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk539_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_6166]),
    [final] ).

cnf(i_0_11274,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(X3,esk430_6(X4,X3,X5,X6,X2,X1)),esk431_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_6196]),
    [final] ).

cnf(i_0_11275,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_6197]),
    [final] ).

cnf(i_0_11276,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk560_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,esk558_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_6173]),
    [final] ).

cnf(i_0_11277,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk559_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,esk558_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_6173]),
    [final] ).

cnf(i_0_11278,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))))),esk487_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_6198]),
    [final] ).

cnf(i_0_11279,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X5),esk488_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_6199]),
    [final] ).

cnf(i_0_11280,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_6200]),
    [final] ).

cnf(i_0_11281,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_6201,c_0_6062]),c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),c_0_6064]),c_0_6064]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11282,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_6202,c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11283,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_6203,c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11284,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_6204,c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11285,plain,
    ( hAPP(X1,esk159_7(X2,X3,X1,X4,X5,X6,X7)) = hAPP(X1,esk160_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_6089]),
    [final] ).

cnf(i_0_11286,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,esk418_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_6205]),
    [final] ).

cnf(i_0_11287,plain,
    ( hBOOL(hAPP(X1,esk454_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_6163]),
    [final] ).

cnf(i_0_11288,plain,
    ( hBOOL(hAPP(X1,esk439_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_6164]),
    [final] ).

cnf(i_0_11289,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,esk302_4(X3,X2,X1,X4)))),hAPP(X1,esk302_4(X3,X2,X1,X4)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6206]),
    [final] ).

cnf(i_0_11290,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_6207]),
    [final] ).

cnf(i_0_11291,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_6208]),
    [final] ).

cnf(i_0_11292,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),c_Com_Ocom_OCond(X4,X5,X7)),X6)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),c_Hoare__Mirabelle_Opeek__and(X1,X3,X4)),X5),X6)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),c_Hoare__Mirabelle_Opeek__and(X1,X3,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),X4))),X7),X6)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6209]),
    [final] ).

cnf(i_0_11293,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X6,X5,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X6)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X6),X2),X4),X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X6),tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(X1,esk4_6(X2,X3,X4,X1,X5,X6)),esk5_6(X2,X3,X4,X1,X5,X6)))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X6,X5,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X6)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X6),X1),X4),X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X6),tc_HOL_Obool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6210]),
    [final] ).

cnf(i_0_11294,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X6,X5,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X6)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X6),X4),X3),X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X6),tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(X1,esk2_6(X1,X2,X3,X4,X5,X6)),esk3_6(X1,X2,X3,X4,X5,X6)))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X6,X5,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X6)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X6),X4),X3),X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X6),tc_HOL_Obool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6211]),
    [final] ).

cnf(i_0_11295,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)))),esk388_3(X2,X3,X1))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6212,c_0_6138]),c_0_6138]),
    [final] ).

cnf(i_0_11296,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)))),esk387_3(X3,X2,X1))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6213,c_0_6138]),c_0_6138]),
    [final] ).

cnf(i_0_11297,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk560_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),esk558_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_6173]),
    [final] ).

cnf(i_0_11298,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk559_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),esk558_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_6173]),
    [final] ).

cnf(i_0_11299,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_6214]),
    [final] ).

cnf(i_0_11300,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_6184]),
    [final] ).

cnf(i_0_11301,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_6215,c_0_6216]),
    [final] ).

cnf(i_0_11302,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)
    | esk559_6(X1,X2,X3,X4,X5,X6) != esk560_6(X1,X2,X3,X4,X5,X6)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(X2,esk558_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_6173]),
    [final] ).

cnf(i_0_11303,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_6217,c_0_6062]),c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),c_0_6064]),c_0_6064]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11304,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_6218]),
    [final] ).

cnf(i_0_11305,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_6219,c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11306,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,esk288_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_6161]),
    [final] ).

cnf(i_0_11307,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_6220,c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11308,plain,
    ( hBOOL(hAPP(X1,esk302_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_6206]),
    [final] ).

cnf(i_0_11309,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_6221]),
    [final] ).

cnf(i_0_11310,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_6222,c_0_6216]),
    [final] ).

cnf(i_0_11311,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_6223,c_0_6216]),
    [final] ).

cnf(i_0_11312,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_6190]),
    [final] ).

cnf(i_0_11313,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_6224]),
    [final] ).

cnf(i_0_11314,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_6225]),
    [final] ).

cnf(i_0_11315,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_6226]),
    [final] ).

cnf(i_0_11316,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_6191]),
    [final] ).

cnf(i_0_11317,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_6227,c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11318,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_6228,c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11319,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_6229]),
    [final] ).

cnf(i_0_11320,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_6230]),
    [final] ).

cnf(i_0_11321,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_6193]),
    [final] ).

cnf(i_0_11322,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_6194]),
    [final] ).

cnf(i_0_11323,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)),esk331_4(X3,X4,X2,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_6231]),
    [final] ).

cnf(i_0_11324,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_6232]),
    [final] ).

cnf(i_0_11325,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,esk279_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_6233]),
    [final] ).

cnf(i_0_11326,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,esk278_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_6234]),
    [final] ).

cnf(i_0_11327,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_6235]),
    [final] ).

cnf(i_0_11328,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_6236]),
    [final] ).

cnf(i_0_11329,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_6236]),
    [final] ).

cnf(i_0_11330,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_6236]),
    [final] ).

cnf(i_0_11331,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_6236]),
    [final] ).

cnf(i_0_11332,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)),esk250_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),esk250_4(X2,X3,X4,X1)),X3))),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_6237]),
    [final] ).

cnf(i_0_11333,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_6238,c_0_6062]),c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),c_0_6064]),c_0_6064]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11334,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_6239]),
    [final] ).

cnf(i_0_11335,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_6240,c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11336,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_6241,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11337,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_6242,c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11338,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_6243,c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11339,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_6244,c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11340,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_6245]),
    [final] ).

cnf(i_0_11341,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_6246,c_0_6097]),c_0_6097]),
    [final] ).

cnf(i_0_11342,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),esk558_6(X1,X2,X3,X4,X5,X6)),X4))
    | esk559_6(X1,X2,X3,X4,X5,X6) != esk560_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_6173]),
    [final] ).

cnf(i_0_11343,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_6247]),
    [final] ).

cnf(i_0_11344,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_6248]),
    [final] ).

cnf(i_0_11345,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,esk241_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_6249]),
    [final] ).

cnf(i_0_11346,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_6250]),
    [final] ).

cnf(i_0_11347,plain,
    ( hBOOL(hAPP(hAPP(X1,esk4_6(X1,X2,X3,X4,X5,X6)),esk5_6(X1,X2,X3,X4,X5,X6)))
    | c_Hoare__Mirabelle_Ohoare__derivs(X6,X5,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X6)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X6),X1),X3),X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X6),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X6,X5,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X6)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X6),X4),X3),X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X6),tc_HOL_Obool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6210]),
    [final] ).

cnf(i_0_11348,plain,
    ( hBOOL(hAPP(hAPP(X1,esk2_6(X2,X1,X3,X4,X5,X6)),esk3_6(X2,X1,X3,X4,X5,X6)))
    | c_Hoare__Mirabelle_Ohoare__derivs(X6,X5,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X6)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X6),X4),X3),X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X6),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X6,X5,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X6)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X6),X4),X3),X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X6),tc_HOL_Obool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6211]),
    [final] ).

cnf(i_0_11349,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_6251]),
    [final] ).

cnf(i_0_11350,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_6252]),
    [final] ).

cnf(i_0_11351,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_6250]),
    [final] ).

cnf(i_0_11352,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_6251]),
    [final] ).

cnf(i_0_11353,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_6252]),
    [final] ).

cnf(i_0_11354,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_6253]),
    [final] ).

cnf(i_0_11355,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_6254]),
    [final] ).

cnf(i_0_11356,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_6255]),
    [final] ).

cnf(i_0_11357,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_6256,c_0_6216]),
    [final] ).

cnf(i_0_11358,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_6257,c_0_6216]),
    [final] ).

cnf(i_0_11359,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_6258,c_0_6259]),c_0_6259]),c_0_6074]),c_0_6074]),
    [final] ).

cnf(i_0_11360,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_6260]),
    [final] ).

cnf(i_0_11361,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),esk292_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_6232]),
    [final] ).

cnf(i_0_11362,plain,
    ( X1 = hAPP(hAPP(X2,X3),esk488_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_6199]),
    [final] ).

cnf(i_0_11363,plain,
    ( X1 = hAPP(hAPP(X2,X3),esk487_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_6198]),
    [final] ).

cnf(i_0_11364,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk308_5(X5,X4,X3,X2,X1)),esk308_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_6261]),
    [final] ).

cnf(i_0_11365,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_6262]),
    [final] ).

cnf(i_0_11366,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_6263]),
    [final] ).

cnf(i_0_11367,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk450_5(X2,X3,X4,X5,X1)),esk451_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_6264]),
    [final] ).

cnf(i_0_11368,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk449_5(X2,X3,X4,X5,X1)),esk448_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_6265]),
    [final] ).

cnf(i_0_11369,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_6266]),
    [final] ).

cnf(i_0_11370,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_6267,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11371,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_6268,c_0_6216]),
    [final] ).

cnf(i_0_11372,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_6269,c_0_6216]),
    [final] ).

cnf(i_0_11373,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk73_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),esk72_3(X1,X2,X3)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X2,esk72_3(X1,X2,X3))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_6270]),
    [final] ).

cnf(i_0_11374,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk71_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),esk70_3(X1,X2,X3)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X2,esk70_3(X1,X2,X3))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_6271]),
    [final] ).

cnf(i_0_11375,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk96_5(X2,X3,X4,X5,X1)),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk97_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_6272]),
    [final] ).

cnf(i_0_11376,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk96_5(X2,X3,X4,X5,X1)),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk97_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_6272]),
    [final] ).

cnf(i_0_11377,plain,
    ( hAPP(X1,esk73_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),esk72_3(X2,X1,X3)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X1,esk72_3(X2,X1,X3))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_6270]),
    [final] ).

cnf(i_0_11378,plain,
    ( hAPP(X1,esk71_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),esk70_3(X2,X1,X3)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X1,esk70_3(X2,X1,X3))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_6271]),
    [final] ).

cnf(i_0_11379,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_11380,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk279_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_6233]),
    [final] ).

cnf(i_0_11381,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk278_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_6234]),
    [final] ).

cnf(i_0_11382,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_6231]),
    [final] ).

cnf(i_0_11383,plain,
    ( hBOOL(hAPP(X1,esk292_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_6232]),
    [final] ).

cnf(i_0_11384,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_6273]),
    [final] ).

cnf(i_0_11385,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_6274]),
    [final] ).

cnf(i_0_11386,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_6275]),
    [final] ).

cnf(i_0_11387,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_6276,c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11388,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_6277]),
    [final] ).

cnf(i_0_11389,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_6278]),
    [final] ).

cnf(i_0_11390,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_6279]),
    [final] ).

cnf(i_0_11391,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_6280,c_0_6281]),
    [final] ).

cnf(i_0_11392,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk239_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_6282]),
    [final] ).

cnf(i_0_11393,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk238_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_6282]),
    [final] ).

cnf(i_0_11394,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk458_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_6167]),
    [final] ).

cnf(i_0_11395,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_6283]),
    [final] ).

cnf(i_0_11396,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_6284,c_0_6074]),c_0_6074]),c_0_6074]),
    [final] ).

cnf(i_0_11397,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_6285,c_0_6259]),c_0_6259]),c_0_6259]),
    [final] ).

cnf(i_0_11398,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_6286]),
    [final] ).

cnf(i_0_11399,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk472_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_6287]),
    [final] ).

cnf(i_0_11400,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_6288,c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11401,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_6289,c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11402,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_6290]),
    [final] ).

cnf(i_0_11403,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk417_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_6291]),
    [final] ).

cnf(i_0_11404,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk241_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_6249]),
    [final] ).

cnf(i_0_11405,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,esk360_5(X3,X2,X4,X5,X1))),hAPP(X3,esk360_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_6292]),
    [final] ).

cnf(i_0_11406,plain,
    ( c_List_Olist__all2(X2,X5,X1,X3,X4)
    | ~ hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),esk427_5(X1,X4,X5,X3,X2))),hAPP(hAPP(c_List_Onth(X5),X4),esk427_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_6293]),
    [final] ).

cnf(i_0_11407,plain,
    ( c_List_Olist__all2(X2,X5,X1,X3,X4)
    | ~ hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),esk365_5(X4,X3,X1,X5,X2))),hAPP(hAPP(c_List_Onth(X5),X4),esk365_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_6294]),
    [final] ).

cnf(i_0_11408,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,esk245_5(X3,X2,X4,X5,X1))),hAPP(X3,esk245_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_6295]),
    [final] ).

cnf(i_0_11409,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_6296]),
    [final] ).

cnf(i_0_11410,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk448_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_6265]),
    [final] ).

cnf(i_0_11411,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_6297,c_0_6216]),
    [final] ).

cnf(i_0_11412,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_6298,c_0_6216]),
    [final] ).

cnf(i_0_11413,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,esk272_5(X5,X4,X3,X2,X1)),esk273_5(X5,X4,X3,X2,X1))) != hAPP(hAPP(X2,hAPP(X4,esk272_5(X5,X4,X3,X2,X1))),hAPP(X4,esk273_5(X5,X4,X3,X2,X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6299]),
    [final] ).

cnf(i_0_11414,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),esk390_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_6300,c_0_6181]),c_0_6181]),
    [final] ).

cnf(i_0_11415,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),esk390_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_6301,c_0_6181]),c_0_6181]),
    [final] ).

cnf(i_0_11416,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),esk390_3(X3,X1,X2))) != X3 ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6302,c_0_6181]),c_0_6181]),
    [final] ).

cnf(i_0_11417,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),esk390_3(X3,X1,X2))) != X3 ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6303,c_0_6181]),c_0_6181]),
    [final] ).

cnf(i_0_11418,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_6304,c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11419,plain,
    ( hBOOL(hAPP(hAPP(X1,X3),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk87_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),esk86_3(X1,X2,X3)),esk87_3(X1,X2,X3))))
    | hBOOL(hAPP(hAPP(X1,esk86_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)))),esk87_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_6305,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11420,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_6306]),
    [final] ).

cnf(i_0_11421,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_6307]),
    [final] ).

cnf(i_0_11422,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_6306]),
    [final] ).

cnf(i_0_11423,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_6307]),
    [final] ).

cnf(i_0_11424,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_6308]),
    [final] ).

cnf(i_0_11425,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_6309]),
    [final] ).

cnf(i_0_11426,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_6310]),
    [final] ).

cnf(i_0_11427,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),esk319_4(X3,X4,X2,X1))),hAPP(hAPP(c_List_Onth(X1),X4),esk319_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_6311]),
    [final] ).

cnf(i_0_11428,plain,
    ( hBOOL(hAPP(hAPP(X1,X3),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk89_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk88_3(X1,X2,X3)),esk89_3(X1,X2,X3)))
    | hBOOL(hAPP(hAPP(X1,esk88_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)))),esk89_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_6312,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11429,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)),esk316_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_6313]),
    [final] ).

cnf(i_0_11430,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_6314,c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11431,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk315_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_6313]),
    [final] ).

cnf(i_0_11432,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk457_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_6315]),
    [final] ).

cnf(i_0_11433,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk455_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_6316]),
    [final] ).

cnf(i_0_11434,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_6317,c_0_6082]),c_0_6082]),c_0_6083]),c_0_6083]),
    [final] ).

cnf(i_0_11435,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk94_5(X3,X4,X5,X2,X1))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk95_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_6318]),
    [final] ).

cnf(i_0_11436,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk94_5(X3,X4,X5,X2,X1))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk95_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_6318]),
    [final] ).

cnf(i_0_11437,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk456_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_6319]),
    [final] ).

cnf(i_0_11438,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_6320,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11439,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_6321,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11440,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk94_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_6318]),
    [final] ).

cnf(i_0_11441,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk94_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_6318]),
    [final] ).

cnf(i_0_11442,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_6322,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11443,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_6323,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11444,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_6324,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11445,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_6325,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11446,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_6326,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11447,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_6327,c_0_6216]),
    [final] ).

cnf(i_0_11448,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_6328,c_0_6216]),
    [final] ).

cnf(i_0_11449,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_6329,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11450,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_6330]),
    [final] ).

cnf(i_0_11451,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_6331,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11452,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_6332,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11453,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_6333,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11454,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_6334,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11455,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_6335,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11456,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_6336,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11457,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_6337,c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11458,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_6338,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11459,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_6339,c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11460,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_6340,c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11461,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk112_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_6341]),
    [final] ).

cnf(i_0_11462,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk109_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_6342]),
    [final] ).

cnf(i_0_11463,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,esk238_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_6282]),
    [final] ).

cnf(i_0_11464,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,esk134_4(X4,X3,X2,X1)),esk135_4(X4,X3,X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk134_4(X4,X3,X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk135_4(X4,X3,X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))) ),
    inference(split_conjunct,[status(thm)],[i_0_6343]),
    [final] ).

cnf(i_0_11465,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_6344,c_0_6138]),
    [final] ).

cnf(i_0_11466,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_6345,c_0_6216]),
    [final] ).

cnf(i_0_11467,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_6346]),
    [final] ).

cnf(i_0_11468,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_6347,c_0_6062]),c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),c_0_6064]),c_0_6064]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11469,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_6348]),
    [final] ).

cnf(i_0_11470,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,esk472_6(X2,X3,X1,X4,X5,X6)) != hAPP(X3,esk472_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_6287]),
    [final] ).

cnf(i_0_11471,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,esk417_6(X4,X3,X2,X1,X5,X6))) ),
    inference(split_conjunct,[status(thm)],[i_0_6291]),
    [final] ).

cnf(i_0_11472,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_6349]),
    [final] ).

cnf(i_0_11473,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_6350]),
    [final] ).

cnf(i_0_11474,plain,
    ( X1 = hAPP(hAPP(c_Product__Type_OPair(X2,X3),esk430_6(X1,X4,X3,X2,X5,X6)),esk431_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_6196]),
    [final] ).

cnf(i_0_11475,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_6351]),
    [final] ).

cnf(i_0_11476,plain,
    ( X1 = hAPP(hAPP(c_Product__Type_OPair(X2,X3),esk502_6(X4,X5,X6,X1,X3,X2)),esk504_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_6153]),
    [final] ).

cnf(i_0_11477,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_6352,c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11478,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_6353,c_0_6074]),c_0_6074]),
    [final] ).

cnf(i_0_11479,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_6354,c_0_6259]),c_0_6259]),
    [final] ).

cnf(i_0_11480,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_6355,c_0_6088]),
    [final] ).

cnf(i_0_11481,plain,
    ( X1 = hAPP(hAPP(c_Product__Type_OPair(X2,X3),esk428_6(X4,X5,X6,X3,X2,X1)),esk429_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_6168]),
    [final] ).

cnf(i_0_11482,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_6356,c_0_6259]),c_0_6074]),
    [final] ).

cnf(i_0_11483,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_6357,c_0_6259]),c_0_6074]),
    [final] ).

cnf(i_0_11484,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_6358]),
    [final] ).

cnf(i_0_11485,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_6359]),
    [final] ).

cnf(i_0_11486,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_6278]),
    [final] ).

cnf(i_0_11487,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_6279]),
    [final] ).

cnf(i_0_11488,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)))))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6360,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11489,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_6361]),
    [final] ).

cnf(i_0_11490,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_6362,c_0_6216]),
    [final] ).

cnf(i_0_11491,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_6363,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11492,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_6364,c_0_6216]),
    [final] ).

cnf(i_0_11493,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,esk158_5(X3,X2,X4,X5,X1))),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6365]),
    [final] ).

cnf(i_0_11494,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,esk228_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_6366]),
    [final] ).

cnf(i_0_11495,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_6367,c_0_6216]),
    [final] ).

cnf(i_0_11496,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_6368]),
    [final] ).

cnf(i_0_11497,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_6369]),
    [final] ).

cnf(i_0_11498,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,esk153_5(X3,X2,X4,X5,X1))),X3))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6370]),
    [final] ).

cnf(i_0_11499,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_6371,c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11500,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_6372,c_0_6062]),c_0_6062]),c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),c_0_6064]),c_0_6064]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11501,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_6373,c_0_6062]),c_0_6062]),c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),c_0_6064]),c_0_6064]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11502,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),esk321_4(X3,X4,X2,X1))),hAPP(hAPP(c_List_Onth(X1),X4),esk321_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_6374]),
    [final] ).

cnf(i_0_11503,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),esk321_4(X3,X4,X2,X1))),hAPP(hAPP(c_List_Onth(X1),X4),esk321_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_6374]),
    [final] ).

cnf(i_0_11504,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_6375,c_0_6138]),
    [final] ).

cnf(i_0_11505,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_6376]),
    [final] ).

cnf(i_0_11506,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_6377]),
    [final] ).

cnf(i_0_11507,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_6378]),
    [final] ).

cnf(i_0_11508,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_6379]),
    [final] ).

cnf(i_0_11509,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_6380,c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11510,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_6381]),
    [final] ).

cnf(i_0_11511,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_6382]),
    [final] ).

cnf(i_0_11512,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_6383]),
    [final] ).

cnf(i_0_11513,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_6384,c_0_6138]),
    [final] ).

cnf(i_0_11514,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_6385]),
    [final] ).

cnf(i_0_11515,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_6386,c_0_6088]),
    [final] ).

cnf(i_0_11516,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_6387]),
    [final] ).

cnf(i_0_11517,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_6388]),
    [final] ).

cnf(i_0_11518,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_6389]),
    [final] ).

cnf(i_0_11519,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk450_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_6264]),
    [final] ).

cnf(i_0_11520,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_6390]),
    [final] ).

cnf(i_0_11521,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_6391]),
    [final] ).

cnf(i_0_11522,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_6392,c_0_6216]),
    [final] ).

cnf(i_0_11523,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_6393,c_0_6216]),
    [final] ).

cnf(i_0_11524,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_6394]),
    [final] ).

cnf(i_0_11525,plain,
    ( hAPP(X1,esk238_6(X2,X3,X1,X4,X5,X6)) = hAPP(X1,esk239_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_6282]),
    [final] ).

cnf(i_0_11526,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),esk314_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_6395]),
    [final] ).

cnf(i_0_11527,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_6396,c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11528,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),c_Com_Ocom_OWhile(X4,X5)),c_Hoare__Mirabelle_Opeek__and(X1,X3,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),X4)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),c_Hoare__Mirabelle_Opeek__and(X1,X3,X4)),X5),X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6397]),
    [final] ).

cnf(i_0_11529,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_6398,c_0_6181]),
    [final] ).

cnf(i_0_11530,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk467_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_6399]),
    [final] ).

cnf(i_0_11531,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk313_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_6395]),
    [final] ).

cnf(i_0_11532,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_6400]),
    [final] ).

cnf(i_0_11533,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_6401]),
    [final] ).

cnf(i_0_11534,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_6402]),
    [final] ).

cnf(i_0_11535,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_6403]),
    [final] ).

cnf(i_0_11536,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X1,X2,esk260_5(X3,X4,X5,X2,X1),esk261_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_6404]),
    [final] ).

cnf(i_0_11537,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X1,X2,esk258_5(X3,X4,X5,X2,X1),esk259_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_6405]),
    [final] ).

cnf(i_0_11538,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),esk328_4(X3,X4,X2,X1))),esk327_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_6406]),
    [final] ).

cnf(i_0_11539,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_6407]),
    [final] ).

cnf(i_0_11540,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_6408]),
    [final] ).

cnf(i_0_11541,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_6409,c_0_6074]),c_0_6074]),
    [final] ).

cnf(i_0_11542,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_6410,c_0_6259]),c_0_6259]),
    [final] ).

cnf(i_0_11543,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk456_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_6319]),
    [final] ).

cnf(i_0_11544,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_6411,c_0_6082]),c_0_6083]),
    [final] ).

cnf(i_0_11545,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_6412,c_0_6074]),
    [final] ).

cnf(i_0_11546,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_6413,c_0_6259]),
    [final] ).

cnf(i_0_11547,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_6414]),
    [final] ).

cnf(i_0_11548,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_6415]),
    [final] ).

cnf(i_0_11549,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_6416,c_0_6074]),
    [final] ).

cnf(i_0_11550,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_6417,c_0_6259]),
    [final] ).

cnf(i_0_11551,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),esk260_5(X2,X3,X4,X5,X1)),esk261_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_6404]),
    [final] ).

cnf(i_0_11552,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),esk258_5(X2,X3,X4,X5,X1)),esk259_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_6405]),
    [final] ).

cnf(i_0_11553,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),esk345_4(X2,X3,X4,X1)),esk344_4(X2,X3,X4,X1))),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6418]),
    [final] ).

cnf(i_0_11554,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),esk344_4(X2,X3,X4,X1)),esk345_4(X2,X3,X4,X1))),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6418]),
    [final] ).

cnf(i_0_11555,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk457_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_6315]),
    [final] ).

cnf(i_0_11556,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk455_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_6316]),
    [final] ).

cnf(i_0_11557,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_6419]),
    [final] ).

cnf(i_0_11558,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_6420]),
    [final] ).

cnf(i_0_11559,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk96_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_6272]),
    [final] ).

cnf(i_0_11560,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk96_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_6272]),
    [final] ).

cnf(i_0_11561,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_6421,c_0_6216]),
    [final] ).

cnf(i_0_11562,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_6422]),
    [final] ).

cnf(i_0_11563,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_6423,c_0_6216]),
    [final] ).

cnf(i_0_11564,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_6424,c_0_6216]),
    [final] ).

cnf(i_0_11565,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_6425]),
    [final] ).

cnf(i_0_11566,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_6426]),
    [final] ).

cnf(i_0_11567,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_6427]),
    [final] ).

cnf(i_0_11568,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_6428,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11569,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)
    | esk238_6(X1,X2,X3,X4,X5,X6) != esk239_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_6282]),
    [final] ).

cnf(i_0_11570,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_6429]),
    [final] ).

cnf(i_0_11571,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6430,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11572,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin))))))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6431,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11573,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_6432,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11574,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_6433,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11575,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_6434,c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11576,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_6435,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11577,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_6436,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11578,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_6437,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11579,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_6438,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11580,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(X2,esk355_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_6439]),
    [final] ).

cnf(i_0_11581,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk152_5(X2,X3,X4,X5,X1)),hAPP(X3,esk151_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_6440]),
    [final] ).

cnf(i_0_11582,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_6441,c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11583,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_6442]),
    [final] ).

cnf(i_0_11584,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk282_5(X2,X3,X4,X1,X5)),hAPP(X2,esk281_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_6443]),
    [final] ).

cnf(i_0_11585,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_6444]),
    [final] ).

cnf(i_0_11586,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_6445]),
    [final] ).

cnf(i_0_11587,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_6361]),
    [final] ).

cnf(i_0_11588,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_6446]),
    [final] ).

cnf(i_0_11589,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_6447,c_0_6281]),c_0_6281]),
    [final] ).

cnf(i_0_11590,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_6448]),
    [final] ).

cnf(i_0_11591,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_6448]),
    [final] ).

cnf(i_0_11592,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),esk557_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_6449]),
    [final] ).

cnf(i_0_11593,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_6450]),
    [final] ).

cnf(i_0_11594,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_6451]),
    [final] ).

cnf(i_0_11595,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_6452]),
    [final] ).

cnf(i_0_11596,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_6452]),
    [final] ).

cnf(i_0_11597,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_6453]),
    [final] ).

cnf(i_0_11598,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_6454,c_0_6281]),
    [final] ).

cnf(i_0_11599,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_6455]),
    [final] ).

cnf(i_0_11600,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_6456]),
    [final] ).

cnf(i_0_11601,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_6457]),
    [final] ).

cnf(i_0_11602,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_6458]),
    [final] ).

cnf(i_0_11603,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_6459,c_0_6138]),
    [final] ).

cnf(i_0_11604,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_6460]),
    [final] ).

cnf(i_0_11605,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_6461]),
    [final] ).

cnf(i_0_11606,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_6462]),
    [final] ).

cnf(i_0_11607,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_6463]),
    [final] ).

cnf(i_0_11608,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)),esk251_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),esk251_4(X2,X3,X4,X1)),X3))),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6464]),
    [final] ).

cnf(i_0_11609,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),esk468_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_6399]),
    [final] ).

cnf(i_0_11610,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),esk257_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_6465]),
    [final] ).

cnf(i_0_11611,plain,
    ( hBOOL(hAPP(hAPP(X1,esk296_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_6466]),
    [final] ).

cnf(i_0_11612,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,esk475_3(X3,X2,X1)))),hAPP(X3,esk475_3(X3,X2,X1)))),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6467]),
    [final] ).

cnf(i_0_11613,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,esk300_3(X2,X1,X3)))),hAPP(X3,esk300_3(X2,X1,X3)))),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6468]),
    [final] ).

cnf(i_0_11614,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_6469]),
    [final] ).

cnf(i_0_11615,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_6470,c_0_6083]),
    [final] ).

cnf(i_0_11616,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_6471,c_0_6083]),
    [final] ).

cnf(i_0_11617,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_6472]),
    [final] ).

cnf(i_0_11618,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,esk237_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_6473]),
    [final] ).

cnf(i_0_11619,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,esk227_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_6474]),
    [final] ).

cnf(i_0_11620,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_6475]),
    [final] ).

cnf(i_0_11621,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_6476]),
    [final] ).

cnf(i_0_11622,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_6477]),
    [final] ).

cnf(i_0_11623,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_6478]),
    [final] ).

cnf(i_0_11624,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_6126]),
    [final] ).

cnf(i_0_11625,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_6462]),
    [final] ).

cnf(i_0_11626,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_6400]),
    [final] ).

cnf(i_0_11627,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_6479,c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11628,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_6480]),
    [final] ).

cnf(i_0_11629,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,esk351_5(X3,X4,X5,X2,X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6481]),
    [final] ).

cnf(i_0_11630,plain,
    ( c_Relation_Orefl__on(X1,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(X1,tc_HOL_Obool)),X4),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X5,tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X4),X3))
    | ~ c_Relation_Orefl__on(X1,hAPP(X2,esk520_5(X3,X2,X1,X4,X5)),hAPP(X3,esk520_5(X3,X2,X1,X4,X5))) ),
    inference(split_conjunct,[status(thm)],[i_0_6482]),
    [final] ).

cnf(i_0_11631,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_6483]),
    [final] ).

cnf(i_0_11632,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_6484,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11633,plain,
    ( hBOOL(hAPP(hAPP(X1,X2),esk296_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_6466]),
    [final] ).

cnf(i_0_11634,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,esk356_5(X3,X4,X5,X2,X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6485]),
    [final] ).

cnf(i_0_11635,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_6486]),
    [final] ).

cnf(i_0_11636,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_6462]),
    [final] ).

cnf(i_0_11637,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_6487]),
    [final] ).

cnf(i_0_11638,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_6488]),
    [final] ).

cnf(i_0_11639,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,esk357_5(X2,X1,X3,X4,X5)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6489]),
    [final] ).

cnf(i_0_11640,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_6490]),
    [final] ).

cnf(i_0_11641,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_6491]),
    [final] ).

cnf(i_0_11642,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,esk352_5(X3,X4,X5,X2,X1))))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6492]),
    [final] ).

cnf(i_0_11643,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,esk435_5(X3,X2,X4,X5,X1))))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6493]),
    [final] ).

cnf(i_0_11644,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,esk240_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_6494]),
    [final] ).

cnf(i_0_11645,plain,
    ( hBOOL(hAPP(hAPP(X1,esk104_5(X2,X3,X4,X5,X1)),esk105_5(X2,X3,X4,X5,X1)))
    | c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X5)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),X1),X3),X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6119]),
    [final] ).

cnf(i_0_11646,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_6495,c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11647,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_6496]),
    [final] ).

cnf(i_0_11648,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_6497]),
    [final] ).

cnf(i_0_11649,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),esk452_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_6163]),
    [final] ).

cnf(i_0_11650,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),esk437_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_6164]),
    [final] ).

cnf(i_0_11651,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_6498,c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11652,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk309_4(X2,X3,X4,X1)),esk310_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_6499]),
    [final] ).

cnf(i_0_11653,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_6500]),
    [final] ).

cnf(i_0_11654,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_6501]),
    [final] ).

cnf(i_0_11655,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_6502]),
    [final] ).

cnf(i_0_11656,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_6503]),
    [final] ).

cnf(i_0_11657,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_6462]),
    [final] ).

cnf(i_0_11658,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk467_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_6399]),
    [final] ).

cnf(i_0_11659,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_6488]),
    [final] ).

cnf(i_0_11660,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_11661,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_11662,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_6504]),
    [final] ).

cnf(i_0_11663,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_6505]),
    [final] ).

cnf(i_0_11664,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_6506]),
    [final] ).

cnf(i_0_11665,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_6507]),
    [final] ).

cnf(i_0_11666,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk164_5(X2,X3,X4,X1,X5)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X3)))
    | hAPP(hAPP(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_6508]),
    [final] ).

cnf(i_0_11667,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_6509]),
    [final] ).

cnf(i_0_11668,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_6510]),
    [final] ).

cnf(i_0_11669,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_6511]),
    [final] ).

cnf(i_0_11670,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_6422]),
    [final] ).

cnf(i_0_11671,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_6512,c_0_6082]),c_0_6083]),
    [final] ).

cnf(i_0_11672,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_6513]),
    [final] ).

cnf(i_0_11673,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_6426]),
    [final] ).

cnf(i_0_11674,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_6514]),
    [final] ).

cnf(i_0_11675,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_6515]),
    [final] ).

cnf(i_0_11676,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_6516]),
    [final] ).

cnf(i_0_11677,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk144_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_6517]),
    [final] ).

cnf(i_0_11678,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_6518]),
    [final] ).

cnf(i_0_11679,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_6519]),
    [final] ).

cnf(i_0_11680,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_6520]),
    [final] ).

cnf(i_0_11681,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_6477]),
    [final] ).

cnf(i_0_11682,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_6478]),
    [final] ).

cnf(i_0_11683,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk500_4(X3,X4,X1,X2)),esk501_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_6521]),
    [final] ).

cnf(i_0_11684,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_6522]),
    [final] ).

cnf(i_0_11685,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_6523]),
    [final] ).

cnf(i_0_11686,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(X2,X3)),hAPP(X2,X4)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(X2,esk30_4(X4,X3,X2,X1))),hAPP(X2,hAPP(c_Nat_OSuc,esk30_4(X4,X3,X2,X1)))))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6524]),
    [final] ).

cnf(i_0_11687,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(X2,X4)),hAPP(X2,X3)))
    | ~ class_Orderings_Oorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(X2,esk29_4(X3,X4,X2,X1))),hAPP(X2,hAPP(c_Nat_OSuc,esk29_4(X3,X4,X2,X1)))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6525]),
    [final] ).

cnf(i_0_11688,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(X4,X1)),hAPP(X4,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(X4,esk30_4(X2,X1,X4,X3))),hAPP(X4,hAPP(c_Nat_OSuc,esk30_4(X2,X1,X4,X3)))))
    | ~ class_Orderings_Oorder(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_6524]),
    [final] ).

cnf(i_0_11689,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_6526]),
    [final] ).

cnf(i_0_11690,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_6527]),
    [final] ).

cnf(i_0_11691,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_6528]),
    [final] ).

cnf(i_0_11692,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),esk275_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_6529]),
    [final] ).

cnf(i_0_11693,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_6530]),
    [final] ).

cnf(i_0_11694,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_6531]),
    [final] ).

cnf(i_0_11695,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_6532]),
    [final] ).

cnf(i_0_11696,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_6533]),
    [final] ).

cnf(i_0_11697,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_6534]),
    [final] ).

cnf(i_0_11698,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_6535]),
    [final] ).

cnf(i_0_11699,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_6536]),
    [final] ).

cnf(i_0_11700,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_6537]),
    [final] ).

cnf(i_0_11701,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_6538]),
    [final] ).

cnf(i_0_11702,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_6539]),
    [final] ).

cnf(i_0_11703,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),esk513_2(X1,X2)),hAPP(X2,esk513_2(X1,X2)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6540]),
    [final] ).

cnf(i_0_11704,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_6528]),
    [final] ).

cnf(i_0_11705,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_6448]),
    [final] ).

cnf(i_0_11706,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_6541]),
    [final] ).

cnf(i_0_11707,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_6463]),
    [final] ).

cnf(i_0_11708,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk498_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_6542]),
    [final] ).

cnf(i_0_11709,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_6452]),
    [final] ).

cnf(i_0_11710,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)),esk252_3(X2,X3,X1))),X3)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6543]),
    [final] ).

cnf(i_0_11711,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_6544]),
    [final] ).

cnf(i_0_11712,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_6545]),
    [final] ).

cnf(i_0_11713,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_6545]),
    [final] ).

cnf(i_0_11714,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_6450]),
    [final] ).

cnf(i_0_11715,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_6451]),
    [final] ).

cnf(i_0_11716,plain,
    ( X1 = hAPP(hAPP(c_List_Olist_OCons(X2),esk313_5(X3,X1,X4,X5,X2)),esk314_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_6395]),
    [final] ).

cnf(i_0_11717,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_6546]),
    [final] ).

cnf(i_0_11718,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk460_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_6547,c_0_6097]),
    [final] ).

cnf(i_0_11719,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk360_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_6292]),
    [final] ).

cnf(i_0_11720,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk459_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_6548,c_0_6097]),
    [final] ).

cnf(i_0_11721,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_6549]),
    [final] ).

cnf(i_0_11722,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_6550,c_0_6259]),
    [final] ).

cnf(i_0_11723,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_6551,c_0_6074]),
    [final] ).

cnf(i_0_11724,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_6462]),
    [final] ).

cnf(i_0_11725,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),esk366_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_6552]),
    [final] ).

cnf(i_0_11726,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),esk364_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_6553]),
    [final] ).

cnf(i_0_11727,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_6504]),
    [final] ).

cnf(i_0_11728,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_6505]),
    [final] ).

cnf(i_0_11729,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk237_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_6473]),
    [final] ).

cnf(i_0_11730,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk227_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_6474]),
    [final] ).

cnf(i_0_11731,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_6475]),
    [final] ).

cnf(i_0_11732,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_6476]),
    [final] ).

cnf(i_0_11733,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_6554]),
    [final] ).

cnf(i_0_11734,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk228_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_6366]),
    [final] ).

cnf(i_0_11735,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk158_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_6365]),
    [final] ).

cnf(i_0_11736,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_6555]),
    [final] ).

cnf(i_0_11737,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk236_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_6556]),
    [final] ).

cnf(i_0_11738,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk229_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_6557]),
    [final] ).

cnf(i_0_11739,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk146_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_6558]),
    [final] ).

cnf(i_0_11740,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk145_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_6559]),
    [final] ).

cnf(i_0_11741,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_6560]),
    [final] ).

cnf(i_0_11742,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_6462]),
    [final] ).

cnf(i_0_11743,plain,
    ( X1 = hAPP(hAPP(c_List_Olist_OCons(X2),esk315_5(X3,X4,X5,X1,X2)),esk316_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_6313]),
    [final] ).

cnf(i_0_11744,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_6561]),
    [final] ).

cnf(i_0_11745,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_6562,c_0_6178]),
    [final] ).

cnf(i_0_11746,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_6563]),
    [final] ).

cnf(i_0_11747,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk427_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_6293]),
    [final] ).

cnf(i_0_11748,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk365_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_6294]),
    [final] ).

cnf(i_0_11749,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_6561]),
    [final] ).

cnf(i_0_11750,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),esk107_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_6564]),
    [final] ).

cnf(i_0_11751,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_6565,c_0_6281]),c_0_6281]),
    [final] ).

cnf(i_0_11752,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(X3,esk155_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_6566]),
    [final] ).

cnf(i_0_11753,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_6567]),
    [final] ).

cnf(i_0_11754,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk151_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_6440]),
    [final] ).

cnf(i_0_11755,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_6568]),
    [final] ).

cnf(i_0_11756,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_6569]),
    [final] ).

cnf(i_0_11757,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk355_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_6439]),
    [final] ).

cnf(i_0_11758,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk155_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_6566]),
    [final] ).

cnf(i_0_11759,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk245_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_6295]),
    [final] ).

cnf(i_0_11760,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_6570,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11761,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk244_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_6571]),
    [final] ).

cnf(i_0_11762,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk243_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_6572]),
    [final] ).

cnf(i_0_11763,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk180_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_6573]),
    [final] ).

cnf(i_0_11764,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk179_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_6574]),
    [final] ).

cnf(i_0_11765,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)))
    | esk450_5(X1,X2,X3,X4,X5) != esk451_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_6264]),
    [final] ).

cnf(i_0_11766,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)))
    | esk449_5(X1,X2,X3,X4,X5) != esk448_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_6265]),
    [final] ).

cnf(i_0_11767,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_6575,c_0_6083]),
    [final] ).

cnf(i_0_11768,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_6576,c_0_6083]),
    [final] ).

cnf(i_0_11769,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk520_5(X2,X3,X4,X5,X1)),X5))
    | c_Relation_Orefl__on(X4,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X4,tc_HOL_Obool)),X5),X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X5),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6482]),
    [final] ).

cnf(i_0_11770,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk149_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_6577]),
    [final] ).

cnf(i_0_11771,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk557_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_6449]),
    [final] ).

cnf(i_0_11772,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_6578]),
    [final] ).

cnf(i_0_11773,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk150_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_6440]),
    [final] ).

cnf(i_0_11774,plain,
    ( hBOOL(hAPP(hAPP(X1,esk149_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_6577]),
    [final] ).

cnf(i_0_11775,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk281_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_6443]),
    [final] ).

cnf(i_0_11776,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk351_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_6481]),
    [final] ).

cnf(i_0_11777,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_6579]),
    [final] ).

cnf(i_0_11778,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_6580]),
    [final] ).

cnf(i_0_11779,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_6581]),
    [final] ).

cnf(i_0_11780,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_6582]),
    [final] ).

cnf(i_0_11781,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk112_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_6341]),
    [final] ).

cnf(i_0_11782,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk109_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_6342]),
    [final] ).

cnf(i_0_11783,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_6583]),
    [final] ).

cnf(i_0_11784,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_6584]),
    [final] ).

cnf(i_0_11785,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk153_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_6370]),
    [final] ).

cnf(i_0_11786,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk356_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_6485]),
    [final] ).

cnf(i_0_11787,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(X3,esk154_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_6585]),
    [final] ).

cnf(i_0_11788,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,esk498_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_6542]),
    [final] ).

cnf(i_0_11789,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_6488]),
    [final] ).

cnf(i_0_11790,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_6488]),
    [final] ).

cnf(i_0_11791,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk357_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_6489]),
    [final] ).

cnf(i_0_11792,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk154_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_6585]),
    [final] ).

cnf(i_0_11793,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_6586]),
    [final] ).

cnf(i_0_11794,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_6587,c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11795,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_6588,c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11796,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_6589,c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11797,plain,
    ( hBOOL(hAPP(X1,X4))
    | ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X2),esk225_4(X1,X3,X4,X2)),esk226_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_6590]),
    [final] ).

cnf(i_0_11798,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,esk349_4(X2,X1,X3,X4))),hAPP(X2,esk349_4(X2,X1,X3,X4)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6591]),
    [final] ).

cnf(i_0_11799,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_6592]),
    [final] ).

cnf(i_0_11800,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_6593,c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11801,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_6594,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11802,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_6595,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11803,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk399_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_6596]),
    [final] ).

cnf(i_0_11804,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_6597,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11805,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_6598,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11806,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk541_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_6599]),
    [final] ).

cnf(i_0_11807,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk255_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_6600]),
    [final] ).

cnf(i_0_11808,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_6601]),
    [final] ).

cnf(i_0_11809,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_6602]),
    [final] ).

cnf(i_0_11810,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_6603]),
    [final] ).

cnf(i_0_11811,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk352_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_6492]),
    [final] ).

cnf(i_0_11812,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk240_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_6494]),
    [final] ).

cnf(i_0_11813,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_6604,c_0_6281]),
    [final] ).

cnf(i_0_11814,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk435_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_6493]),
    [final] ).

cnf(i_0_11815,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_6605]),
    [final] ).

cnf(i_0_11816,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_6606]),
    [final] ).

cnf(i_0_11817,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_6607]),
    [final] ).

cnf(i_0_11818,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_6509]),
    [final] ).

cnf(i_0_11819,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_6510]),
    [final] ).

cnf(i_0_11820,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_6608]),
    [final] ).

cnf(i_0_11821,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,esk39_4(X3,X2,X4,X1))),hAPP(X3,esk39_4(X3,X2,X4,X1))))
    | ~ class_Orderings_Oord(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6609]),
    [final] ).

cnf(i_0_11822,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_6610]),
    [final] ).

cnf(i_0_11823,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk350_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_6611]),
    [final] ).

cnf(i_0_11824,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_6466]),
    [final] ).

cnf(i_0_11825,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_6612]),
    [final] ).

cnf(i_0_11826,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_6613]),
    [final] ).

cnf(i_0_11827,plain,
    ( X1 = hAPP(hAPP(c_List_Oappend(X2),esk452_5(X1,X3,X4,X5,X2)),hAPP(hAPP(c_List_Olist_OCons(X2),X5),esk453_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_6163]),
    [final] ).

cnf(i_0_11828,plain,
    ( X1 = hAPP(hAPP(c_List_Oappend(X2),esk437_5(X3,X4,X1,X5,X2)),hAPP(hAPP(c_List_Olist_OCons(X2),X4),esk438_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_6164]),
    [final] ).

cnf(i_0_11829,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_6614]),
    [final] ).

cnf(i_0_11830,plain,
    ( X1 = hAPP(hAPP(c_List_Oappend(X2),esk298_5(X3,X4,X1,X5,X2)),X3)
    | hAPP(hAPP(c_List_Oappend(X2),esk297_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_6615]),
    [final] ).

cnf(i_0_11831,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_6616]),
    [final] ).

cnf(i_0_11832,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,esk221_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_6617]),
    [final] ).

cnf(i_0_11833,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_6618]),
    [final] ).

cnf(i_0_11834,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_6619]),
    [final] ).

cnf(i_0_11835,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_6620]),
    [final] ).

cnf(i_0_11836,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),esk366_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_6552]),
    [final] ).

cnf(i_0_11837,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),esk364_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_6553]),
    [final] ).

cnf(i_0_11838,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_6621]),
    [final] ).

cnf(i_0_11839,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_6622]),
    [final] ).

cnf(i_0_11840,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_6623]),
    [final] ).

cnf(i_0_11841,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_11842,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_11843,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_6624]),
    [final] ).

cnf(i_0_11844,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_6625]),
    [final] ).

cnf(i_0_11845,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_6605]),
    [final] ).

cnf(i_0_11846,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_6606]),
    [final] ).

cnf(i_0_11847,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_6626]),
    [final] ).

cnf(i_0_11848,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,esk242_3(X2,X3,X1))),hAPP(X3,esk242_3(X2,X3,X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6627]),
    [final] ).

cnf(i_0_11849,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,esk223_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_6628]),
    [final] ).

cnf(i_0_11850,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X1)),hAPP(hAPP(c_Product__Type_OPair(X3,X1),esk305_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_6629]),
    [final] ).

cnf(i_0_11851,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X1)),hAPP(hAPP(c_Product__Type_OPair(X3,X1),esk303_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_6630]),
    [final] ).

cnf(i_0_11852,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_6631]),
    [final] ).

cnf(i_0_11853,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_6632]),
    [final] ).

cnf(i_0_11854,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_6633]),
    [final] ).

cnf(i_0_11855,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_6634]),
    [final] ).

cnf(i_0_11856,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_6635]),
    [final] ).

cnf(i_0_11857,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_6636]),
    [final] ).

cnf(i_0_11858,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_6637]),
    [final] ).

cnf(i_0_11859,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_6638]),
    [final] ).

cnf(i_0_11860,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_6639]),
    [final] ).

cnf(i_0_11861,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_6640]),
    [final] ).

cnf(i_0_11862,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_6641]),
    [final] ).

cnf(i_0_11863,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_6642]),
    [final] ).

cnf(i_0_11864,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_6643]),
    [final] ).

cnf(i_0_11865,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_6644]),
    [final] ).

cnf(i_0_11866,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_6645]),
    [final] ).

cnf(i_0_11867,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_6646]),
    [final] ).

cnf(i_0_11868,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_6647]),
    [final] ).

cnf(i_0_11869,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_6648]),
    [final] ).

cnf(i_0_11870,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_6649]),
    [final] ).

cnf(i_0_11871,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_6650]),
    [final] ).

cnf(i_0_11872,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_6651]),
    [final] ).

cnf(i_0_11873,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_6652]),
    [final] ).

cnf(i_0_11874,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_6653]),
    [final] ).

cnf(i_0_11875,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_6654]),
    [final] ).

cnf(i_0_11876,plain,
    ( hBOOL(hAPP(X1,X6))
    | ~ hBOOL(hAPP(X1,esk152_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_6440]),
    [final] ).

cnf(i_0_11877,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_6374]),
    [final] ).

cnf(i_0_11878,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_6655,c_0_6097]),c_0_6097]),c_0_6097]),
    [final] ).

cnf(i_0_11879,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_6656]),
    [final] ).

cnf(i_0_11880,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_6657]),
    [final] ).

cnf(i_0_11881,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_6658]),
    [final] ).

cnf(i_0_11882,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_6659]),
    [final] ).

cnf(i_0_11883,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_6660]),
    [final] ).

cnf(i_0_11884,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_6661,c_0_6097]),c_0_6097]),
    [final] ).

cnf(i_0_11885,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_6662,c_0_6097]),c_0_6097]),
    [final] ).

cnf(i_0_11886,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_6663]),
    [final] ).

cnf(i_0_11887,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_6664]),
    [final] ).

cnf(i_0_11888,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_6405]),
    [final] ).

cnf(i_0_11889,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_6632]),
    [final] ).

cnf(i_0_11890,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_6633]),
    [final] ).

cnf(i_0_11891,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_6634]),
    [final] ).

cnf(i_0_11892,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),esk287_3(X2,X3,X1)),esk287_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_6665]),
    [final] ).

cnf(i_0_11893,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),esk285_3(X2,X3,X1)),esk285_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_6666]),
    [final] ).

cnf(i_0_11894,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_6667]),
    [final] ).

cnf(i_0_11895,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_6668]),
    [final] ).

cnf(i_0_11896,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk459_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_6669,c_0_6097]),
    [final] ).

cnf(i_0_11897,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_6652]),
    [final] ).

cnf(i_0_11898,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_6653]),
    [final] ).

cnf(i_0_11899,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_6670]),
    [final] ).

cnf(i_0_11900,plain,
    ( X1 = hAPP(hAPP(c_Product__Type_OPair(X2,X3),esk281_5(X4,X5,X1,X3,X2)),esk282_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_6443]),
    [final] ).

cnf(i_0_11901,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk460_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_6671,c_0_6097]),
    [final] ).

cnf(i_0_11902,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_6672]),
    [final] ).

cnf(i_0_11903,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_6673,c_0_6281]),c_0_6281]),
    [final] ).

cnf(i_0_11904,plain,
    ( hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) = hAPP(hAPP(c_Set_Oinsert(X1),esk260_5(X4,X3,X2,X5,X1)),esk261_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_6404]),
    [final] ).

cnf(i_0_11905,plain,
    ( hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) = hAPP(hAPP(c_Set_Oinsert(X1),esk258_5(X4,X3,X2,X5,X1)),esk259_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_6405]),
    [final] ).

cnf(i_0_11906,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,esk164_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_6508]),
    [final] ).

cnf(i_0_11907,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_6647]),
    [final] ).

cnf(i_0_11908,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_6674,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11909,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_6675,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11910,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_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_6645]),
    [final] ).

cnf(i_0_11911,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,esk399_5(X2,X1,X3,X4,X5)))
    | ~ class_Groups_Omonoid__add(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_6596]),
    [final] ).

cnf(i_0_11912,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_6676]),
    [final] ).

cnf(i_0_11913,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_6677]),
    [final] ).

cnf(i_0_11914,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_6678]),
    [final] ).

cnf(i_0_11915,plain,
    ( hBOOL(hAPP(X1,X7))
    | ~ hBOOL(hAPP(X1,esk150_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_6440]),
    [final] ).

cnf(i_0_11916,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_6679]),
    [final] ).

cnf(i_0_11917,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_6680]),
    [final] ).

cnf(i_0_11918,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_6681]),
    [final] ).

cnf(i_0_11919,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,X5,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X2),hAPP(c_Com_Ocom_OBODY,X3)),X4)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X2),hAPP(c_Com_Ocom_OBODY,X3)),X4)),X5),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X3))),X4)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6682]),
    [final] ).

cnf(i_0_11920,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_6683]),
    [final] ).

cnf(i_0_11921,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_6684]),
    [final] ).

cnf(i_0_11922,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_6683]),
    [final] ).

cnf(i_0_11923,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_6684]),
    [final] ).

cnf(i_0_11924,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,esk247_5(X2,X1,X3,X4,X5)) != hAPP(X2,esk247_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_6685]),
    [final] ).

cnf(i_0_11925,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,esk246_5(X2,X1,X3,X4,X5)) != hAPP(X2,esk246_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_6686]),
    [final] ).

cnf(i_0_11926,plain,
    ( hAPP(hAPP(c_List_Omap(X5,X4),X1),X3) = hAPP(hAPP(c_List_Omap(X5,X4),X2),X3)
    | hAPP(X1,esk350_5(X2,X3,X1,X4,X5)) != hAPP(X2,esk350_5(X2,X3,X1,X4,X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6611]),
    [final] ).

cnf(i_0_11927,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_6687]),
    [final] ).

cnf(i_0_11928,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_6688]),
    [final] ).

cnf(i_0_11929,plain,
    ( hBOOL(hAPP(X1,esk498_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_6542]),
    [final] ).

cnf(i_0_11930,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_6689,c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11931,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_6690,c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_11932,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_6691]),
    [final] ).

cnf(i_0_11933,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_6692,c_0_6693]),c_0_6693]),c_0_6693]),
    [final] ).

cnf(i_0_11934,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_6694]),
    [final] ).

cnf(i_0_11935,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_6695]),
    [final] ).

cnf(i_0_11936,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_6696]),
    [final] ).

cnf(i_0_11937,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_6697]),
    [final] ).

cnf(i_0_11938,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_6698]),
    [final] ).

cnf(i_0_11939,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_6699]),
    [final] ).

cnf(i_0_11940,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_6700]),
    [final] ).

cnf(i_0_11941,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_6701]),
    [final] ).

cnf(i_0_11942,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_6702]),
    [final] ).

cnf(i_0_11943,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_6703]),
    [final] ).

cnf(i_0_11944,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_6704]),
    [final] ).

cnf(i_0_11945,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_6705]),
    [final] ).

cnf(i_0_11946,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_6645]),
    [final] ).

cnf(i_0_11947,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_6646]),
    [final] ).

cnf(i_0_11948,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_6647]),
    [final] ).

cnf(i_0_11949,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_6706]),
    [final] ).

cnf(i_0_11950,plain,
    ( hAPP(hAPP(c_List_Oappend(X1),X2),esk298_5(X3,X4,X5,X2,X1)) = X4
    | hAPP(hAPP(c_List_Oappend(X1),esk297_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_6615]),
    [final] ).

cnf(i_0_11951,plain,
    ( X1 = hAPP(hAPP(c_List_Oappend(X2),esk298_5(X3,X4,X1,X5,X2)),X3)
    | X5 = hAPP(hAPP(c_List_Oappend(X2),X4),esk297_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_6615]),
    [final] ).

cnf(i_0_11952,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_6707]),
    [final] ).

cnf(i_0_11953,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_6708]),
    [final] ).

cnf(i_0_11954,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_6709]),
    [final] ).

cnf(i_0_11955,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_6710]),
    [final] ).

cnf(i_0_11956,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_6711]),
    [final] ).

cnf(i_0_11957,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_6712,c_0_6713]),c_0_6713]),
    [final] ).

cnf(i_0_11958,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_6714]),
    [final] ).

cnf(i_0_11959,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_6715,c_0_6097]),c_0_6097]),
    [final] ).

cnf(i_0_11960,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_6716,c_0_6097]),c_0_6097]),
    [final] ).

cnf(i_0_11961,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_6561]),
    [final] ).

cnf(i_0_11962,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_6578]),
    [final] ).

cnf(i_0_11963,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_6717]),
    [final] ).

cnf(i_0_11964,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_6718]),
    [final] ).

cnf(i_0_11965,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_6719]),
    [final] ).

cnf(i_0_11966,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_6720]),
    [final] ).

cnf(i_0_11967,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_6721,c_0_6097]),c_0_6097]),
    [final] ).

cnf(i_0_11968,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_6722,c_0_6097]),c_0_6097]),
    [final] ).

cnf(i_0_11969,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_6723]),
    [final] ).

cnf(i_0_11970,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_6724]),
    [final] ).

cnf(i_0_11971,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_6725]),
    [final] ).

cnf(i_0_11972,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_6724]),
    [final] ).

cnf(i_0_11973,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_6726]),
    [final] ).

cnf(i_0_11974,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_6727]),
    [final] ).

cnf(i_0_11975,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_6728]),
    [final] ).

cnf(i_0_11976,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),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_6729]),
    [final] ).

cnf(i_0_11977,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_6730]),
    [final] ).

cnf(i_0_11978,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_6731]),
    [final] ).

cnf(i_0_11979,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,esk497_2(X2,X1)))
    | ~ hBOOL(hAPP(X2,esk497_2(X2,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_6732]),
    [final] ).

cnf(i_0_11980,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_6733,c_0_6178]),c_0_6178]),
    [final] ).

cnf(i_0_11981,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_6734]),
    [final] ).

cnf(i_0_11982,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_6735]),
    [final] ).

cnf(i_0_11983,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_6583]),
    [final] ).

cnf(i_0_11984,plain,
    ( hBOOL(hAPP(X1,esk497_2(X2,X1)))
    | hBOOL(hAPP(X2,esk497_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_6732]),
    [final] ).

cnf(i_0_11985,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk497_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_6732]),
    [final] ).

cnf(i_0_11986,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_6736]),
    [final] ).

cnf(i_0_11987,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_6737]),
    [final] ).

cnf(i_0_11988,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_6738]),
    [final] ).

cnf(i_0_11989,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_6645]),
    [final] ).

cnf(i_0_11990,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_6646]),
    [final] ).

cnf(i_0_11991,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_6647]),
    [final] ).

cnf(i_0_11992,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_6738]),
    [final] ).

cnf(i_0_11993,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_6739]),
    [final] ).

cnf(i_0_11994,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_6740]),
    [final] ).

cnf(i_0_11995,plain,
    ( X1 = hAPP(hAPP(c_List_Oappend(X2),esk311_4(X3,X1,X4,X2)),hAPP(hAPP(c_List_Olist_OCons(X2),esk310_4(X3,X1,X4,X2)),esk312_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_6499]),
    [final] ).

cnf(i_0_11996,plain,
    ( X1 = hAPP(hAPP(c_List_Oappend(X2),esk311_4(X3,X4,X1,X2)),hAPP(hAPP(c_List_Olist_OCons(X2),esk309_4(X3,X4,X1,X2)),esk312_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_6499]),
    [final] ).

cnf(i_0_11997,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_6741,c_0_6097]),
    [final] ).

cnf(i_0_11998,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_6742]),
    [final] ).

cnf(i_0_11999,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_6647]),
    [final] ).

cnf(i_0_12000,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_6743]),
    [final] ).

cnf(i_0_12001,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_6744]),
    [final] ).

cnf(i_0_12002,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)),esk182_3(X1,X3,X2)),hAPP(hAPP(c_Set_Oinsert(X2),esk181_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_6745]),
    [final] ).

cnf(i_0_12003,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_6645]),
    [final] ).

cnf(i_0_12004,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_6311]),
    [final] ).

cnf(i_0_12005,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_6746]),
    [final] ).

cnf(i_0_12006,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk333_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),esk334_3(X2,X3,X1)),esk334_3(X2,X3,X1))),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6184]),
    [final] ).

cnf(i_0_12007,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_6747,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_12008,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_6748]),
    [final] ).

cnf(i_0_12009,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_6749]),
    [final] ).

cnf(i_0_12010,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_6750]),
    [final] ).

cnf(i_0_12011,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_6406]),
    [final] ).

cnf(i_0_12012,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_6751]),
    [final] ).

cnf(i_0_12013,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_6752,c_0_6178]),c_0_6178]),c_0_6178]),
    [final] ).

cnf(i_0_12014,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_6753]),
    [final] ).

cnf(i_0_12015,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_6754]),
    [final] ).

cnf(i_0_12016,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_6755]),
    [final] ).

cnf(i_0_12017,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_6756]),
    [final] ).

cnf(i_0_12018,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_6757]),
    [final] ).

cnf(i_0_12019,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_6758]),
    [final] ).

cnf(i_0_12020,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_6759]),
    [final] ).

cnf(i_0_12021,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk322_3(X2,X3,X1)),esk322_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_6760]),
    [final] ).

cnf(i_0_12022,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_6761]),
    [final] ).

cnf(i_0_12023,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_6126]),
    [final] ).

cnf(i_0_12024,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_6762,c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6216]),c_0_6216]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_12025,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_6763]),
    [final] ).

cnf(i_0_12026,plain,
    ( hAPP(X1,esk144_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_6517]),
    [final] ).

cnf(i_0_12027,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_6764]),
    [final] ).

cnf(i_0_12028,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk321_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_6374]),
    [final] ).

cnf(i_0_12029,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_6765]),
    [final] ).

cnf(i_0_12030,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_6766]),
    [final] ).

cnf(i_0_12031,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_6767]),
    [final] ).

cnf(i_0_12032,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk526_4(X2,X3,X1,X4)),esk525_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)),esk523_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_6768]),
    [final] ).

cnf(i_0_12033,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk526_4(X2,X3,X1,X4)),esk524_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)),esk523_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_6768]),
    [final] ).

cnf(i_0_12034,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_6769]),
    [final] ).

cnf(i_0_12035,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_6770]),
    [final] ).

cnf(i_0_12036,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_6771]),
    [final] ).

cnf(i_0_12037,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_6772]),
    [final] ).

cnf(i_0_12038,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_6773,c_0_6259]),
    [final] ).

cnf(i_0_12039,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_6774]),
    [final] ).

cnf(i_0_12040,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_6775,c_0_6074]),
    [final] ).

cnf(i_0_12041,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_6776]),
    [final] ).

cnf(i_0_12042,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_6777,c_0_6074]),
    [final] ).

cnf(i_0_12043,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_6778]),
    [final] ).

cnf(i_0_12044,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_6759]),
    [final] ).

cnf(i_0_12045,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_6779]),
    [final] ).

cnf(i_0_12046,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_6780]),
    [final] ).

cnf(i_0_12047,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_6781]),
    [final] ).

cnf(i_0_12048,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_6782]),
    [final] ).

cnf(i_0_12049,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_6783]),
    [final] ).

cnf(i_0_12050,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_6759]),
    [final] ).

cnf(i_0_12051,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_6784]),
    [final] ).

cnf(i_0_12052,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_6785]),
    [final] ).

cnf(i_0_12053,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_6786]),
    [final] ).

cnf(i_0_12054,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_6647]),
    [final] ).

cnf(i_0_12055,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),esk492_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_6787]),
    [final] ).

cnf(i_0_12056,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),esk489_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_6788]),
    [final] ).

cnf(i_0_12057,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_6789]),
    [final] ).

cnf(i_0_12058,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk321_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_6374]),
    [final] ).

cnf(i_0_12059,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_6790,c_0_6088]),c_0_6097]),
    [final] ).

cnf(i_0_12060,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_6791]),
    [final] ).

cnf(i_0_12061,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_6645]),
    [final] ).

cnf(i_0_12062,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_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_6792]),
    [final] ).

cnf(i_0_12063,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),hAPP(hAPP(c_List_Olist_OCons(X1),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_6646]),
    [final] ).

cnf(i_0_12064,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_6793,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_12065,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_6794,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_12066,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_6720]),
    [final] ).

cnf(i_0_12067,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_6795]),
    [final] ).

cnf(i_0_12068,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_6796]),
    [final] ).

cnf(i_0_12069,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_6797]),
    [final] ).

cnf(i_0_12070,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),c_Com_Ocom_OSemi(X4,X6)),X7)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),X4),X5)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X5),X6),X7)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6798]),
    [final] ).

cnf(i_0_12071,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),esk116_3(X2,X3,X1)),esk115_3(X2,X3,X1))),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6799]),
    [final] ).

cnf(i_0_12072,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),esk115_3(X2,X3,X1)),esk116_3(X2,X3,X1))),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6799]),
    [final] ).

cnf(i_0_12073,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_6800]),
    [final] ).

cnf(i_0_12074,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_6801]),
    [final] ).

cnf(i_0_12075,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_6802]),
    [final] ).

cnf(i_0_12076,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_6803]),
    [final] ).

cnf(i_0_12077,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_6804]),
    [final] ).

cnf(i_0_12078,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_6805]),
    [final] ).

cnf(i_0_12079,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_6806]),
    [final] ).

cnf(i_0_12080,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_6759]),
    [final] ).

cnf(i_0_12081,plain,
    ( hBOOL(hAPP(X2,X4))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),esk225_4(X2,X3,X4,X1)),esk226_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_6590]),
    [final] ).

cnf(i_0_12082,plain,
    ( c_List_OtakeWhile(X1,X3,X2) = hAPP(c_List_Ofilter(X1,X3),X2)
    | hBOOL(hAPP(hAPP(c_member(X1),esk402_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_6807,c_0_6281]),
    [final] ).

cnf(i_0_12083,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk468_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_6399]),
    [final] ).

cnf(i_0_12084,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk257_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_6465]),
    [final] ).

cnf(i_0_12085,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_6808,c_0_6097]),
    [final] ).

cnf(i_0_12086,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_6809,c_0_6097]),
    [final] ).

cnf(i_0_12087,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_6810]),
    [final] ).

cnf(i_0_12088,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_6791]),
    [final] ).

cnf(i_0_12089,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_6811]),
    [final] ).

cnf(i_0_12090,plain,
    ( hBOOL(hAPP(hAPP(X1,X2),esk541_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_6599]),
    [final] ).

cnf(i_0_12091,plain,
    ( hBOOL(hAPP(hAPP(X1,X2),esk255_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_6600]),
    [final] ).

cnf(i_0_12092,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_6812,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_12093,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_6813,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_12094,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_6814,c_0_6097]),
    [final] ).

cnf(i_0_12095,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk526_4(X2,X3,X1,X4)),esk525_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),esk523_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_6768]),
    [final] ).

cnf(i_0_12096,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk526_4(X2,X3,X1,X4)),esk524_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),esk523_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_6768]),
    [final] ).

cnf(i_0_12097,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_6815]),
    [final] ).

cnf(i_0_12098,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_6816]),
    [final] ).

cnf(i_0_12099,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X3)),hAPP(hAPP(c_Product__Type_OPair(X1,X3),X2),esk375_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_6817]),
    [final] ).

cnf(i_0_12100,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X3)),hAPP(hAPP(c_Product__Type_OPair(X1,X3),X2),esk370_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_6818]),
    [final] ).

cnf(i_0_12101,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_6819]),
    [final] ).

cnf(i_0_12102,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_6820]),
    [final] ).

cnf(i_0_12103,negated_conjecture,
    ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),v_G),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
    inference(split_conjunct,[status(thm)],[i_0_6821]),
    [final] ).

cnf(i_0_12104,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_6822]),
    [final] ).

cnf(i_0_12105,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_6823,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_12106,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_6824]),
    [final] ).

cnf(i_0_12107,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_6825]),
    [final] ).

cnf(i_0_12108,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_6826]),
    [final] ).

cnf(i_0_12109,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_6827]),
    [final] ).

cnf(i_0_12110,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk99_4(X2,X3,X4,X1)),X3))
    | hBOOL(hAPP(hAPP(c_member(X1),esk98_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_6828]),
    [final] ).

cnf(i_0_12111,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_6829,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_12112,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk103_4(X2,X3,X4,X1)),X3))
    | hBOOL(hAPP(hAPP(c_member(X1),esk102_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_6830]),
    [final] ).

cnf(i_0_12113,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_6831,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_12114,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_6832,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_12115,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_6833,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_12116,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk525_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)),esk523_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_6768]),
    [final] ).

cnf(i_0_12117,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk524_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)),esk523_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_6768]),
    [final] ).

cnf(i_0_12118,plain,
    ( X1 = hAPP(c_Nat_OSuc,esk97_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_6272]),
    [final] ).

cnf(i_0_12119,plain,
    ( X1 = hAPP(c_Nat_OSuc,esk95_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_6318]),
    [final] ).

cnf(i_0_12120,plain,
    ( X1 = hAPP(c_Nat_OSuc,esk97_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_6272]),
    [final] ).

cnf(i_0_12121,plain,
    ( X1 = hAPP(c_Nat_OSuc,esk95_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_6318]),
    [final] ).

cnf(i_0_12122,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_6112]),
    [final] ).

cnf(i_0_12123,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_6834]),
    [final] ).

cnf(i_0_12124,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_6835]),
    [final] ).

cnf(i_0_12125,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_6836,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_12126,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_6837,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_12127,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_6399]),
    [final] ).

cnf(i_0_12128,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_6838,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_12129,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_6839,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_12130,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_6399]),
    [final] ).

cnf(i_0_12131,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_6399]),
    [final] ).

cnf(i_0_12132,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_6840,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_12133,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_6841,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_12134,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_6767]),
    [final] ).

cnf(i_0_12135,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_6842]),
    [final] ).

cnf(i_0_12136,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_6843,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_12137,plain,
    ( hAPP(hAPP(c_List_Otake(X1),esk321_4(X2,X3,X4,X1)),X4) = hAPP(hAPP(c_List_Otake(X1),esk321_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_6374]),
    [final] ).

cnf(i_0_12138,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_6844]),
    [final] ).

cnf(i_0_12139,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_6683]),
    [final] ).

cnf(i_0_12140,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_6684]),
    [final] ).

cnf(i_0_12141,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_6737]),
    [final] ).

cnf(i_0_12142,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_6845]),
    [final] ).

cnf(i_0_12143,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_6816]),
    [final] ).

cnf(i_0_12144,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_6846,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_12145,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_6847]),
    [final] ).

cnf(i_0_12146,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_6848]),
    [final] ).

cnf(i_0_12147,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk247_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_6685]),
    [final] ).

cnf(i_0_12148,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk246_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_6686]),
    [final] ).

cnf(i_0_12149,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_6849]),
    [final] ).

cnf(i_0_12150,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_6849]),
    [final] ).

cnf(i_0_12151,plain,
    ( hAPP(hAPP(c_List_Oappend(X1),X2),esk298_5(X3,X4,X5,X2,X1)) = X4
    | X2 = hAPP(hAPP(c_List_Oappend(X1),X4),esk297_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_6615]),
    [final] ).

cnf(i_0_12152,plain,
    ( X1 = hAPP(hAPP(c_List_Oappend(X2),esk306_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_6850]),
    [final] ).

cnf(i_0_12153,plain,
    ( hAPP(hAPP(c_List_Oappend(X1),esk307_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_6851]),
    [final] ).

cnf(i_0_12154,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk329_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_6120]),
    [final] ).

cnf(i_0_12155,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_6852]),
    [final] ).

cnf(i_0_12156,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),esk136_2(X2,X1)),esk137_2(X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk136_2(X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk137_2(X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))) ),
    inference(split_conjunct,[status(thm)],[i_0_6853]),
    [final] ).

cnf(i_0_12157,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),esk132_2(X2,X1)),esk133_2(X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk132_2(X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk133_2(X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))) ),
    inference(split_conjunct,[status(thm)],[i_0_6854]),
    [final] ).

cnf(i_0_12158,plain,
    ( c_Hoare__Mirabelle_Otriple__valid(X5,X4,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),X3),X2),X1))
    | ~ hBOOL(hAPP(hAPP(X1,esk12_4(X1,X2,X3,X4)),esk14_4(X1,X2,X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6855]),
    [final] ).

cnf(i_0_12159,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,esk280_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6856]),
    [final] ).

cnf(i_0_12160,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_6857]),
    [final] ).

cnf(i_0_12161,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_6858]),
    [final] ).

cnf(i_0_12162,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_6859]),
    [final] ).

cnf(i_0_12163,plain,
    ( hAPP(hAPP(c_List_Oappend(X1),esk307_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_6851]),
    [final] ).

cnf(i_0_12164,plain,
    ( X1 = hAPP(hAPP(c_List_Oappend(X2),esk306_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_6850]),
    [final] ).

cnf(i_0_12165,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),esk267_2(X2,X1)),esk268_2(X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk267_2(X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk268_2(X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))) ),
    inference(split_conjunct,[status(thm)],[i_0_6860]),
    [final] ).

cnf(i_0_12166,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_6861,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_12167,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_6862]),
    [final] ).

cnf(i_0_12168,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_6714]),
    [final] ).

cnf(i_0_12169,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_6863]),
    [final] ).

cnf(i_0_12170,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_6864]),
    [final] ).

cnf(i_0_12171,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,esk236_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_6556]),
    [final] ).

cnf(i_0_12172,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,esk229_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_6557]),
    [final] ).

cnf(i_0_12173,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,esk146_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_6558]),
    [final] ).

cnf(i_0_12174,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,esk145_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_6559]),
    [final] ).

cnf(i_0_12175,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_6865]),
    [final] ).

cnf(i_0_12176,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_6866]),
    [final] ).

cnf(i_0_12177,plain,
    ( hAPP(hAPP(c_List_Otake(X1),esk321_4(X2,X3,X4,X1)),X4) = hAPP(hAPP(c_List_Otake(X1),esk321_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_6374]),
    [final] ).

cnf(i_0_12178,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_6867]),
    [final] ).

cnf(i_0_12179,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_6868]),
    [final] ).

cnf(i_0_12180,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_6869]),
    [final] ).

cnf(i_0_12181,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_6870]),
    [final] ).

cnf(i_0_12182,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_6871]),
    [final] ).

cnf(i_0_12183,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk328_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_6406]),
    [final] ).

cnf(i_0_12184,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk77_4(X1,X2,X3,X4)),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk76_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_6165]),
    [final] ).

cnf(i_0_12185,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_6872]),
    [final] ).

cnf(i_0_12186,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_6873]),
    [final] ).

cnf(i_0_12187,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_6874,c_0_6097]),c_0_6097]),
    [final] ).

cnf(i_0_12188,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_6875]),
    [final] ).

cnf(i_0_12189,plain,
    ( hBOOL(hAPP(hAPP(c_member(X4),esk102_4(X1,X2,X3,X4)),X3))
    | hBOOL(hAPP(X1,X5))
    | ~ hBOOL(hAPP(X1,esk103_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_6830]),
    [final] ).

cnf(i_0_12190,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk103_4(X2,X3,X4,X1)),X3))
    | hBOOL(hAPP(X2,X5))
    | ~ hBOOL(hAPP(X2,esk102_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_6830]),
    [final] ).

cnf(i_0_12191,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_6876]),
    [final] ).

cnf(i_0_12192,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_6877]),
    [final] ).

cnf(i_0_12193,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_6878]),
    [final] ).

cnf(i_0_12194,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_6879]),
    [final] ).

cnf(i_0_12195,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_6880]),
    [final] ).

cnf(i_0_12196,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_6880]),
    [final] ).

cnf(i_0_12197,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),esk130_2(X2,X1)),esk131_2(X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk130_2(X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk131_2(X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))) ),
    inference(split_conjunct,[status(thm)],[i_0_6881]),
    [final] ).

cnf(i_0_12198,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),esk124_2(X2,X1)),esk125_2(X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk124_2(X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk125_2(X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))) ),
    inference(split_conjunct,[status(thm)],[i_0_6882]),
    [final] ).

cnf(i_0_12199,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),esk128_2(X2,X1)),esk129_2(X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk128_2(X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk129_2(X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))) ),
    inference(split_conjunct,[status(thm)],[i_0_6883]),
    [final] ).

cnf(i_0_12200,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),esk126_2(X2,X1)),esk127_2(X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk126_2(X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk127_2(X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))) ),
    inference(split_conjunct,[status(thm)],[i_0_6884]),
    [final] ).

cnf(i_0_12201,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_6885]),
    [final] ).

cnf(i_0_12202,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_6886]),
    [final] ).

cnf(i_0_12203,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk492_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_6787]),
    [final] ).

cnf(i_0_12204,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk489_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_6788]),
    [final] ).

cnf(i_0_12205,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_6887]),
    [final] ).

cnf(i_0_12206,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_6888]),
    [final] ).

cnf(i_0_12207,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_6889]),
    [final] ).

cnf(i_0_12208,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk525_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),esk523_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_6768]),
    [final] ).

cnf(i_0_12209,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk524_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),esk523_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_6768]),
    [final] ).

cnf(i_0_12210,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_6890,c_0_6097]),
    [final] ).

cnf(i_0_12211,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_6891]),
    [final] ).

cnf(i_0_12212,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_6892]),
    [final] ).

cnf(i_0_12213,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_6893]),
    [final] ).

cnf(i_0_12214,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_6894]),
    [final] ).

cnf(i_0_12215,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,esk244_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_6571]),
    [final] ).

cnf(i_0_12216,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,esk243_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_6572]),
    [final] ).

cnf(i_0_12217,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,esk180_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_6573]),
    [final] ).

cnf(i_0_12218,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,esk179_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_6574]),
    [final] ).

cnf(i_0_12219,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_6895,c_0_6097]),
    [final] ).

cnf(i_0_12220,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_6896,c_0_6097]),
    [final] ).

cnf(i_0_12221,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_6897]),
    [final] ).

cnf(i_0_12222,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_6898]),
    [final] ).

cnf(i_0_12223,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_6553]),
    [final] ).

cnf(i_0_12224,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_6899]),
    [final] ).

cnf(i_0_12225,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_6899]),
    [final] ).

cnf(i_0_12226,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_6900]),
    [final] ).

cnf(i_0_12227,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_6901]),
    [final] ).

cnf(i_0_12228,plain,
    ( X2 = X3
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),esk388_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_6902,c_0_6138]),c_0_6138]),
    [final] ).

cnf(i_0_12229,plain,
    ( X2 = X3
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),esk387_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_6903,c_0_6138]),c_0_6138]),
    [final] ).

cnf(i_0_12230,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),esk404_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_6904]),
    [final] ).

cnf(i_0_12231,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_6905,c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_12232,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_6906,c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_12233,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_6907,c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_12234,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_6908,c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_12235,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_6746]),
    [final] ).

cnf(i_0_12236,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_6909]),
    [final] ).

cnf(i_0_12237,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_6910]),
    [final] ).

cnf(i_0_12238,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_6911]),
    [final] ).

cnf(i_0_12239,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_6912]),
    [final] ).

cnf(i_0_12240,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_6913,c_0_6693]),
    [final] ).

cnf(i_0_12241,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_6914]),
    [final] ).

cnf(i_0_12242,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_6915]),
    [final] ).

cnf(i_0_12243,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_6916]),
    [final] ).

cnf(i_0_12244,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_6917]),
    [final] ).

cnf(i_0_12245,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_6918]),
    [final] ).

cnf(i_0_12246,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,esk424_3(X3,X2,X1)))),c_Predicate_ORangeP(X1,X1,hAPP(X2,esk425_3(X3,X2,X1)))) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ c_Wellfounded_OwfP(X1,hAPP(X2,esk423_3(X3,X2,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_6919]),
    [final] ).

cnf(i_0_12247,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_6920]),
    [final] ).

cnf(i_0_12248,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_6921,c_0_6693]),c_0_6693]),
    [final] ).

cnf(i_0_12249,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_6351]),
    [final] ).

cnf(i_0_12250,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,esk399_5(X1,X2,X3,X4,X5)) != c_Groups_Ozero__class_Ozero(X5)
    | ~ class_Groups_Omonoid__add(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_6596]),
    [final] ).

cnf(i_0_12251,plain,
    ( hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk342_3(X1,X2,X3)),c_Groups_Oone__class_Oone(tc_Int_Oint))),esk343_3(X1,X2,X3)))
    | hBOOL(hAPP(hAPP(X1,X3),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk342_3(X1,X2,X3)),esk343_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_6922]),
    [final] ).

cnf(i_0_12252,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_6923]),
    [final] ).

cnf(i_0_12253,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_6924,c_0_6097]),
    [final] ).

cnf(i_0_12254,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_6925]),
    [final] ).

cnf(i_0_12255,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_6926]),
    [final] ).

cnf(i_0_12256,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_6927]),
    [final] ).

cnf(i_0_12257,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_6928]),
    [final] ).

cnf(i_0_12258,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_6917]),
    [final] ).

cnf(i_0_12259,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_6929,c_0_6281]),c_0_6281]),
    [final] ).

cnf(i_0_12260,plain,
    ( hBOOL(hAPP(X1,X5))
    | ~ hBOOL(hAPP(X1,esk103_4(X1,X2,X3,X4)))
    | ~ hBOOL(hAPP(X1,esk102_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_6830]),
    [final] ).

cnf(i_0_12261,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_6930]),
    [final] ).

cnf(i_0_12262,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),esk426_4(X2,X3,X4,X1)),hAPP(c_List_Oset(X1),X4))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6931,c_0_6281]),c_0_6281]),
    [final] ).

cnf(i_0_12263,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_6771]),
    [final] ).

cnf(i_0_12264,plain,
    ( X1 = hAPP(hAPP(c_List_Olist__update(X2,X3),esk328_4(X4,X1,X3,X2)),esk327_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_6406]),
    [final] ).

cnf(i_0_12265,plain,
    ( hBOOL(hAPP(X1,esk99_4(X1,X2,X3,X4)))
    | hBOOL(hAPP(hAPP(c_member(X4),esk98_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_6828]),
    [final] ).

cnf(i_0_12266,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk99_4(X2,X3,X4,X1)),X3))
    | hBOOL(hAPP(X2,esk98_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_6828]),
    [final] ).

cnf(i_0_12267,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_6932,c_0_6693]),c_0_6693]),
    [final] ).

cnf(i_0_12268,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_6933]),
    [final] ).

cnf(i_0_12269,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_6934,c_0_6178]),
    [final] ).

cnf(i_0_12270,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk443_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_6935,c_0_6097]),
    [final] ).

cnf(i_0_12271,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)))
    | esk344_4(X1,X2,X3,X4) != esk345_4(X1,X2,X3,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6418]),
    [final] ).

cnf(i_0_12272,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_6759]),
    [final] ).

cnf(i_0_12273,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_6936]),
    [final] ).

cnf(i_0_12274,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_6937]),
    [final] ).

cnf(i_0_12275,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_6938,c_0_6138]),c_0_6138]),c_0_6138]),
    [final] ).

cnf(i_0_12276,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,esk421_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6939]),
    [final] ).

cnf(i_0_12277,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,esk148_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6940]),
    [final] ).

cnf(i_0_12278,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_6941]),
    [final] ).

cnf(i_0_12279,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_6923]),
    [final] ).

cnf(i_0_12280,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_6942]),
    [final] ).

cnf(i_0_12281,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_6943]),
    [final] ).

cnf(i_0_12282,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_6791]),
    [final] ).

cnf(i_0_12283,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_6944]),
    [final] ).

cnf(i_0_12284,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),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_6945]),
    [final] ).

cnf(i_0_12285,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_6946]),
    [final] ).

cnf(i_0_12286,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_6870]),
    [final] ).

cnf(i_0_12287,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_6947]),
    [final] ).

cnf(i_0_12288,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_6948]),
    [final] ).

cnf(i_0_12289,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_6949]),
    [final] ).

cnf(i_0_12290,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_6950]),
    [final] ).

cnf(i_0_12291,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk319_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_6311]),
    [final] ).

cnf(i_0_12292,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_6951]),
    [final] ).

cnf(i_0_12293,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_6952]),
    [final] ).

cnf(i_0_12294,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_6953]),
    [final] ).

cnf(i_0_12295,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_6954]),
    [final] ).

cnf(i_0_12296,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_6955]),
    [final] ).

cnf(i_0_12297,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_6956]),
    [final] ).

cnf(i_0_12298,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_6957]),
    [final] ).

cnf(i_0_12299,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,esk512_4(X2,X3,X4,X1))))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6958]),
    [final] ).

cnf(i_0_12300,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,esk505_4(X2,X3,X4,X1))))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6959]),
    [final] ).

cnf(i_0_12301,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk280_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_6856]),
    [final] ).

cnf(i_0_12302,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_6960]),
    [final] ).

cnf(i_0_12303,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_6961,c_0_6097]),
    [final] ).

cnf(i_0_12304,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_6962,c_0_6097]),
    [final] ).

cnf(i_0_12305,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_6963]),
    [final] ).

cnf(i_0_12306,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_6944]),
    [final] ).

cnf(i_0_12307,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_6964]),
    [final] ).

cnf(i_0_12308,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),esk77_4(X2,X3,X4,X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk76_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_6165]),
    [final] ).

cnf(i_0_12309,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk77_4(X1,X2,X3,X4)),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),esk76_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_6165]),
    [final] ).

cnf(i_0_12310,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,esk277_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6965]),
    [final] ).

cnf(i_0_12311,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_6966]),
    [final] ).

cnf(i_0_12312,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_6967]),
    [final] ).

cnf(i_0_12313,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk185_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_6968]),
    [final] ).

cnf(i_0_12314,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),esk403_4(X1,X3,X2,X4)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6969]),
    [final] ).

cnf(i_0_12315,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_6970]),
    [final] ).

cnf(i_0_12316,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,esk542_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_6599]),
    [final] ).

cnf(i_0_12317,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,esk540_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_6971]),
    [final] ).

cnf(i_0_12318,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,esk256_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_6600]),
    [final] ).

cnf(i_0_12319,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_6972]),
    [final] ).

cnf(i_0_12320,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_6973]),
    [final] ).

cnf(i_0_12321,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),esk403_4(X4,X3,X2,X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6969]),
    [final] ).

cnf(i_0_12322,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_6974,c_0_6097]),
    [final] ).

cnf(i_0_12323,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_6870]),
    [final] ).

cnf(i_0_12324,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)),esk523_4(X1,X2,X3,X4)),X2))
    | hAPP(X1,esk526_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_6768]),
    [final] ).

cnf(i_0_12325,plain,
    ( hBOOL(hAPP(X1,X4))
    | ~ hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),esk382_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_6975]),
    [final] ).

cnf(i_0_12326,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk491_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_6976]),
    [final] ).

cnf(i_0_12327,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk490_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_6977]),
    [final] ).

cnf(i_0_12328,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_6816]),
    [final] ).

cnf(i_0_12329,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)),esk523_4(X1,X2,X3,X4)),X2))
    | esk524_4(X1,X2,X3,X4) != esk525_4(X1,X2,X3,X4)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X3,tc_HOL_Obool)),X2))
    | ~ class_Groups_Ocomm__monoid__add(X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6768]),
    [final] ).

cnf(i_0_12330,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_6978]),
    [final] ).

cnf(i_0_12331,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_6979]),
    [final] ).

cnf(i_0_12332,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_6979]),
    [final] ).

cnf(i_0_12333,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_6980]),
    [final] ).

cnf(i_0_12334,plain,
    ( X1 = hAPP(c_Set_Oimage(X2,X3,X4),esk107_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_6564]),
    [final] ).

cnf(i_0_12335,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,esk426_4(X2,X1,X3,X4))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6981,c_0_6281]),c_0_6281]),
    [final] ).

cnf(i_0_12336,plain,
    ( X1 = hAPP(X2,esk249_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_6982]),
    [final] ).

cnf(i_0_12337,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_6983]),
    [final] ).

cnf(i_0_12338,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_6984]),
    [final] ).

cnf(i_0_12339,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_6985,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_12340,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_6986,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_12341,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_6987]),
    [final] ).

cnf(i_0_12342,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_6988]),
    [final] ).

cnf(i_0_12343,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_6989]),
    [final] ).

cnf(i_0_12344,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk445_3(X3,X2,X1)),esk447_3(X3,X2,X1))),X3))
    | c_Relation_Osingle__valued(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_6990]),
    [final] ).

cnf(i_0_12345,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk445_3(X3,X2,X1)),esk446_3(X3,X2,X1))),X3))
    | c_Relation_Osingle__valued(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_6990]),
    [final] ).

cnf(i_0_12346,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(esk301_2(X2,X1),hAPP(c_Nat_OSuc,X3))),hAPP(esk301_2(X2,X1),X3))),X2))
    | c_Wellfounded_Owf(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6468]),
    [final] ).

cnf(i_0_12347,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_6991]),
    [final] ).

cnf(i_0_12348,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_6992]),
    [final] ).

cnf(i_0_12349,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_6993]),
    [final] ).

cnf(i_0_12350,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_6994]),
    [final] ).

cnf(i_0_12351,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk183_4(X1,X2,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__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_6995]),
    [final] ).

cnf(i_0_12352,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_6996]),
    [final] ).

cnf(i_0_12353,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_6997]),
    [final] ).

cnf(i_0_12354,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_6998]),
    [final] ).

cnf(i_0_12355,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_6999]),
    [final] ).

cnf(i_0_12356,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),esk63_3(X2,X3,X1)),X3)),X2))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7000]),
    [final] ).

cnf(i_0_12357,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_7001]),
    [final] ).

cnf(i_0_12358,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_7002]),
    [final] ).

cnf(i_0_12359,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_7003]),
    [final] ).

cnf(i_0_12360,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk186_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_6968]),
    [final] ).

cnf(i_0_12361,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_7004]),
    [final] ).

cnf(i_0_12362,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_7005]),
    [final] ).

cnf(i_0_12363,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_7006]),
    [final] ).

cnf(i_0_12364,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_7007]),
    [final] ).

cnf(i_0_12365,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_7008]),
    [final] ).

cnf(i_0_12366,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_6128]),
    [final] ).

cnf(i_0_12367,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_7009]),
    [final] ).

cnf(i_0_12368,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_7010]),
    [final] ).

cnf(i_0_12369,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_6988]),
    [final] ).

cnf(i_0_12370,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_6989]),
    [final] ).

cnf(i_0_12371,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_7011]),
    [final] ).

cnf(i_0_12372,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_6827]),
    [final] ).

cnf(i_0_12373,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_6827]),
    [final] ).

cnf(i_0_12374,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_7012]),
    [final] ).

cnf(i_0_12375,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_7013]),
    [final] ).

cnf(i_0_12376,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_7014]),
    [final] ).

cnf(i_0_12377,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_7015]),
    [final] ).

cnf(i_0_12378,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_7016]),
    [final] ).

cnf(i_0_12379,plain,
    ( hAPP(c_Set_Oimage(X2,X1,esk222_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_6628]),
    [final] ).

cnf(i_0_12380,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_7017]),
    [final] ).

cnf(i_0_12381,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_7018]),
    [final] ).

cnf(i_0_12382,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_7019]),
    [final] ).

cnf(i_0_12383,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_6866]),
    [final] ).

cnf(i_0_12384,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk408_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),esk409_2(X2,X1))),hAPP(c_List_Oset(X1),esk410_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_7020,c_0_6138]),
    [final] ).

cnf(i_0_12385,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_6815]),
    [final] ).

cnf(i_0_12386,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_7021]),
    [final] ).

cnf(i_0_12387,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_7022]),
    [final] ).

cnf(i_0_12388,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_7023]),
    [final] ).

cnf(i_0_12389,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_7024]),
    [final] ).

cnf(i_0_12390,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_7025]),
    [final] ).

cnf(i_0_12391,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_7023]),
    [final] ).

cnf(i_0_12392,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),esk491_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_6976]),
    [final] ).

cnf(i_0_12393,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),esk490_4(X3,X2,X4,X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6977]),
    [final] ).

cnf(i_0_12394,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_7026,c_0_6713]),
    [final] ).

cnf(i_0_12395,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk184_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_6995]),
    [final] ).

cnf(i_0_12396,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_7027,c_0_6097]),
    [final] ).

cnf(i_0_12397,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_7028]),
    [final] ).

cnf(i_0_12398,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_7029]),
    [final] ).

cnf(i_0_12399,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_7029]),
    [final] ).

cnf(i_0_12400,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_7030]),
    [final] ).

cnf(i_0_12401,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_7031]),
    [final] ).

cnf(i_0_12402,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_7032]),
    [final] ).

cnf(i_0_12403,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_6991]),
    [final] ).

cnf(i_0_12404,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_6992]),
    [final] ).

cnf(i_0_12405,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_7033]),
    [final] ).

cnf(i_0_12406,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_7034,c_0_6693]),c_0_6693]),
    [final] ).

cnf(i_0_12407,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_7035]),
    [final] ).

cnf(i_0_12408,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_7036]),
    [final] ).

cnf(i_0_12409,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_7037]),
    [final] ).

cnf(i_0_12410,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_7038]),
    [final] ).

cnf(i_0_12411,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_7039]),
    [final] ).

cnf(i_0_12412,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_7040,c_0_6097]),c_0_6097]),
    [final] ).

cnf(i_0_12413,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_6990]),
    [final] ).

cnf(i_0_12414,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_7041]),
    [final] ).

cnf(i_0_12415,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_7042]),
    [final] ).

cnf(i_0_12416,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_7043]),
    [final] ).

cnf(i_0_12417,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk493_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_7044]),
    [final] ).

cnf(i_0_12418,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_7045,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_12419,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_7046,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_12420,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_7047,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_12421,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_7048,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_12422,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk287_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_6665]),
    [final] ).

cnf(i_0_12423,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk285_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_6666]),
    [final] ).

cnf(i_0_12424,plain,
    ( hBOOL(hAPP(hAPP(X1,esk12_4(X2,X3,X1,X4)),esk13_4(X2,X3,X1,X4)))
    | c_Hoare__Mirabelle_Otriple__valid(X5,X4,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),X1),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6855]),
    [final] ).

cnf(i_0_12425,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_7025]),
    [final] ).

cnf(i_0_12426,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_7049,c_0_7050]),
    [final] ).

cnf(i_0_12427,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_7051,c_0_6178]),c_0_6178]),
    [final] ).

cnf(i_0_12428,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_6365]),
    [final] ).

cnf(i_0_12429,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_7052]),
    [final] ).

cnf(i_0_12430,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_7053]),
    [final] ).

cnf(i_0_12431,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_12432,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_7054]),
    [final] ).

cnf(i_0_12433,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_7055]),
    [final] ).

cnf(i_0_12434,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_7056]),
    [final] ).

cnf(i_0_12435,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_7057]),
    [final] ).

cnf(i_0_12436,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_7058]),
    [final] ).

cnf(i_0_12437,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_7059]),
    [final] ).

cnf(i_0_12438,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_7060]),
    [final] ).

cnf(i_0_12439,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_7061]),
    [final] ).

cnf(i_0_12440,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_7062]),
    [final] ).

cnf(i_0_12441,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_7063]),
    [final] ).

cnf(i_0_12442,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_7064]),
    [final] ).

cnf(i_0_12443,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_7065,c_0_6097]),
    [final] ).

cnf(i_0_12444,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_7066]),
    [final] ).

cnf(i_0_12445,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_7067,c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6216]),c_0_6216]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_12446,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_7068]),
    [final] ).

cnf(i_0_12447,plain,
    ( hAPP(X1,esk77_4(X2,X1,X3,X4)) = X2
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk76_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_6165]),
    [final] ).

cnf(i_0_12448,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_7069]),
    [final] ).

cnf(i_0_12449,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_7061]),
    [final] ).

cnf(i_0_12450,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_7028]),
    [final] ).

cnf(i_0_12451,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_7070]),
    [final] ).

cnf(i_0_12452,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_6877]),
    [final] ).

cnf(i_0_12453,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),esk409_2(X2,X1))),hAPP(c_List_Oset(X1),esk410_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),esk408_2(X2,X1))) ),
    inference(rw,[status(thm)],[i_0_7071,c_0_6138]),
    [final] ).

cnf(i_0_12454,plain,
    ( hBOOL(hAPP(hAPP(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),esk90_3(X1,X2,X3))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),esk91_3(X1,X2,X3))))
    | hBOOL(hAPP(hAPP(X1,X3),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk91_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_7072]),
    [final] ).

cnf(i_0_12455,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk199_4(X1,X2,X3,X4)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_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_7073]),
    [final] ).

cnf(i_0_12456,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_7074]),
    [final] ).

cnf(i_0_12457,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_7075]),
    [final] ).

cnf(i_0_12458,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_7075]),
    [final] ).

cnf(i_0_12459,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)))))
    | esk249_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_6982]),
    [final] ).

cnf(i_0_12460,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_7070]),
    [final] ).

cnf(i_0_12461,plain,
    ( X2 = hAPP(hAPP(c_List_Olist_OCons(X1),esk317_3(X3,X2,X1)),esk318_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_7076]),
    [final] ).

cnf(i_0_12462,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_7077]),
    [final] ).

cnf(i_0_12463,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_7078]),
    [final] ).

cnf(i_0_12464,plain,
    ( c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X2),esk32_5(X3,X4,X5,X2,X1),X4,X3)
    | ~ hBOOL(hAPP(X1,X5))
    | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X2),X5,X4,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7079]),
    [final] ).

cnf(i_0_12465,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_7080]),
    [final] ).

cnf(i_0_12466,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_7081]),
    [final] ).

cnf(i_0_12467,plain,
    ( hBOOL(hAPP(X1,esk99_4(X1,X2,X3,X4)))
    | hBOOL(hAPP(X1,esk98_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_6828]),
    [final] ).

cnf(i_0_12468,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,esk526_4(X1,X2,X3,X4)) != c_Groups_Ozero__class_Ozero(X4)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),esk523_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_6768]),
    [final] ).

cnf(i_0_12469,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_7082]),
    [final] ).

cnf(i_0_12470,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk408_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))
    | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk410_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_7083,c_0_6138]),
    [final] ).

cnf(i_0_12471,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk408_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))
    | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk409_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_7084,c_0_6138]),
    [final] ).

cnf(i_0_12472,plain,
    ( c_Natural_Oevaln(X1,X2,X3,esk32_5(X4,X3,X2,X1,X5))
    | ~ hBOOL(hAPP(X5,X2))
    | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X5,X1),X2,X3,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_7079]),
    [final] ).

cnf(i_0_12473,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_7085]),
    [final] ).

cnf(i_0_12474,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)
    | esk524_4(X1,X2,X3,X4) != esk525_4(X1,X2,X3,X4)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),esk523_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_6768]),
    [final] ).

cnf(i_0_12475,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk518_3(X1,X2,X3)),esk519_3(X1,X2,X3)))
    | hBOOL(hAPP(hAPP(X1,esk518_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk519_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_7086]),
    [final] ).

cnf(i_0_12476,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_7087]),
    [final] ).

cnf(i_0_12477,plain,
    ( c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X2),esk32_5(X3,X4,X5,X2,X1),X4,X3)
    | X3 = X5
    | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X2),X5,X4,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7079]),
    [final] ).

cnf(i_0_12478,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_7088]),
    [final] ).

cnf(i_0_12479,plain,
    ( c_Natural_Oevaln(X1,X2,X3,esk32_5(X4,X3,X2,X1,X5))
    | X4 = X2
    | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X5,X1),X2,X3,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_7079]),
    [final] ).

cnf(i_0_12480,plain,
    ( c_Natural_Oevaln(X1,esk17_5(X2,X3,X4,X1,X5),X3,X2)
    | ~ c_Natural_Oevaln(c_Com_Ocom_OSemi(X5,X1),X4,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7089]),
    [final] ).

cnf(i_0_12481,plain,
    ( c_Natural_Oevaln(X1,esk16_5(X2,X3,X4,X1,X5),X3,X2)
    | ~ c_Natural_Oevaln(c_Com_Ocom_OSemi(X5,X1),X4,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7090]),
    [final] ).

cnf(i_0_12482,plain,
    ( c_Natural_Oevaln(X1,X2,X3,esk17_5(X4,X3,X2,X5,X1))
    | ~ c_Natural_Oevaln(c_Com_Ocom_OSemi(X1,X5),X2,X3,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_7089]),
    [final] ).

cnf(i_0_12483,plain,
    ( c_Natural_Oevaln(X1,X2,X3,esk16_5(X4,X3,X2,X5,X1))
    | ~ c_Natural_Oevaln(c_Com_Ocom_OSemi(X1,X5),X2,X3,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_7090]),
    [final] ).

cnf(i_0_12484,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_7091,c_0_6097]),
    [final] ).

cnf(i_0_12485,plain,
    ( X1 = hAPP(c_Relation_OImage(X2,X2,X3),hAPP(hAPP(c_Set_Oinsert(X2),esk123_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_7092]),
    [final] ).

cnf(i_0_12486,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_7093,c_0_7094]),c_0_7094]),
    [final] ).

cnf(i_0_12487,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_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_7095,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_12488,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_7096]),
    [final] ).

cnf(i_0_12489,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_7063]),
    [final] ).

cnf(i_0_12490,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_7064]),
    [final] ).

cnf(i_0_12491,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk404_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_6904]),
    [final] ).

cnf(i_0_12492,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk203_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_7097]),
    [final] ).

cnf(i_0_12493,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk211_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_7098]),
    [final] ).

cnf(i_0_12494,plain,
    ( X1 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk186_4(X2,X3,X4,X1)),esk185_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_6968]),
    [final] ).

cnf(i_0_12495,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_7099]),
    [final] ).

cnf(i_0_12496,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_7100]),
    [final] ).

cnf(i_0_12497,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_7101]),
    [final] ).

cnf(i_0_12498,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_7102]),
    [final] ).

cnf(i_0_12499,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_7103,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_12500,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_7104,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_12501,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_7105,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_12502,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_7106,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_12503,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_7107,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_12504,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_7108]),
    [final] ).

cnf(i_0_12505,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_7069]),
    [final] ).

cnf(i_0_12506,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_7109]),
    [final] ).

cnf(i_0_12507,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk197_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_7110]),
    [final] ).

cnf(i_0_12508,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_7111]),
    [final] ).

cnf(i_0_12509,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_6999]),
    [final] ).

cnf(i_0_12510,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_7112]),
    [final] ).

cnf(i_0_12511,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_7113]),
    [final] ).

cnf(i_0_12512,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk496_3(X2,X1,X3)),X3)),X2))
    | c_Wellfounded_Owf(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),esk494_2(X2,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_7044]),
    [final] ).

cnf(i_0_12513,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_6880]),
    [final] ).

cnf(i_0_12514,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),esk110_1(X1)),esk111_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_7114]),
    [final] ).

cnf(i_0_12515,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk108_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_7115]),
    [final] ).

cnf(i_0_12516,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk200_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_7073]),
    [final] ).

cnf(i_0_12517,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_7116]),
    [final] ).

cnf(i_0_12518,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_7117]),
    [final] ).

cnf(i_0_12519,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_7118]),
    [final] ).

cnf(i_0_12520,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_7119,c_0_6138]),
    [final] ).

cnf(i_0_12521,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_7120]),
    [final] ).

cnf(i_0_12522,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_7121]),
    [final] ).

cnf(i_0_12523,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_7122,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_12524,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_7123,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_12525,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_7124]),
    [final] ).

cnf(i_0_12526,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_7125]),
    [final] ).

cnf(i_0_12527,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk418_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_6205]),
    [final] ).

cnf(i_0_12528,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),esk169_3(X3,X2,X1)),esk170_3(X3,X2,X1))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(X2,esk169_3(X3,X2,X1))),hAPP(X2,esk170_3(X3,X2,X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7126]),
    [final] ).

cnf(i_0_12529,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),esk167_3(X3,X2,X1)),esk168_3(X3,X2,X1))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(X2,esk167_3(X3,X2,X1))),hAPP(X2,esk168_3(X3,X2,X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7127]),
    [final] ).

cnf(i_0_12530,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_6928]),
    [final] ).

cnf(i_0_12531,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_7128]),
    [final] ).

cnf(i_0_12532,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_7129]),
    [final] ).

cnf(i_0_12533,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_6294]),
    [final] ).

cnf(i_0_12534,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_7130]),
    [final] ).

cnf(i_0_12535,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_7131,c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_12536,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_7132,c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_12537,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_7133,c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_12538,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_7134,c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_12539,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_7135]),
    [final] ).

cnf(i_0_12540,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_7136]),
    [final] ).

cnf(i_0_12541,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_7116]),
    [final] ).

cnf(i_0_12542,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_7137]),
    [final] ).

cnf(i_0_12543,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_7138]),
    [final] ).

cnf(i_0_12544,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk421_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_6939]),
    [final] ).

cnf(i_0_12545,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk148_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_6940]),
    [final] ).

cnf(i_0_12546,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_7139]),
    [final] ).

cnf(i_0_12547,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_7140]),
    [final] ).

cnf(i_0_12548,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_7141]),
    [final] ).

cnf(i_0_12549,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_7140]),
    [final] ).

cnf(i_0_12550,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_7142]),
    [final] ).

cnf(i_0_12551,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_7143]),
    [final] ).

cnf(i_0_12552,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_7144]),
    [final] ).

cnf(i_0_12553,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),esk269_3(X3,X2,X1)),esk270_3(X3,X2,X1))) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(X2,esk269_3(X3,X2,X1))),hAPP(X2,esk270_3(X3,X2,X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7145]),
    [final] ).

cnf(i_0_12554,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_7146]),
    [final] ).

cnf(i_0_12555,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_7147]),
    [final] ).

cnf(i_0_12556,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk462_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_7148]),
    [final] ).

cnf(i_0_12557,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk461_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_7149]),
    [final] ).

cnf(i_0_12558,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk114_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_7150]),
    [final] ).

cnf(i_0_12559,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_7151]),
    [final] ).

cnf(i_0_12560,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk410_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),esk408_2(X2,X1))) ),
    inference(rw,[status(thm)],[i_0_7152,c_0_6138]),
    [final] ).

cnf(i_0_12561,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk409_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),esk408_2(X2,X1))) ),
    inference(rw,[status(thm)],[i_0_7153,c_0_6138]),
    [final] ).

cnf(i_0_12562,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_7154]),
    [final] ).

cnf(i_0_12563,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk349_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_6591]),
    [final] ).

cnf(i_0_12564,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_7155]),
    [final] ).

cnf(i_0_12565,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk205_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_7156]),
    [final] ).

cnf(i_0_12566,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk213_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_7157]),
    [final] ).

cnf(i_0_12567,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk184_4(X2,X3,X4,X1)),esk183_4(X2,X3,X4,X1))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__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_6995]),
    [final] ).

cnf(i_0_12568,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_7158]),
    [final] ).

cnf(i_0_12569,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk100_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_6828]),
    [final] ).

cnf(i_0_12570,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk100_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_6828]),
    [final] ).

cnf(i_0_12571,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk362_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_7159]),
    [final] ).

cnf(i_0_12572,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_7160]),
    [final] ).

cnf(i_0_12573,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_12574,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_12575,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_7161]),
    [final] ).

cnf(i_0_12576,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_7162]),
    [final] ).

cnf(i_0_12577,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk123_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_7092]),
    [final] ).

cnf(i_0_12578,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_7163]),
    [final] ).

cnf(i_0_12579,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),esk77_4(X2,X3,X4,X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),esk76_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_6165]),
    [final] ).

cnf(i_0_12580,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_7164]),
    [final] ).

cnf(i_0_12581,plain,
    ( hBOOL(hAPP(X4,X2))
    | hBOOL(hAPP(hAPP(c_member(X1),esk101_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_6830]),
    [final] ).

cnf(i_0_12582,plain,
    ( hBOOL(hAPP(X4,X2))
    | hBOOL(hAPP(hAPP(c_member(X1),esk101_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_6830]),
    [final] ).

cnf(i_0_12583,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_7165]),
    [final] ).

cnf(i_0_12584,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_7166]),
    [final] ).

cnf(i_0_12585,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_7167]),
    [final] ).

cnf(i_0_12586,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_7168]),
    [final] ).

cnf(i_0_12587,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk225_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_6590]),
    [final] ).

cnf(i_0_12588,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk212_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_7098]),
    [final] ).

cnf(i_0_12589,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk204_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_7097]),
    [final] ).

cnf(i_0_12590,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_7169]),
    [final] ).

cnf(i_0_12591,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_7169]),
    [final] ).

cnf(i_0_12592,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_6988]),
    [final] ).

cnf(i_0_12593,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_6989]),
    [final] ).

cnf(i_0_12594,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),hAPP(hAPP(c_Product__Type_OPair(X2,X1),X4),X3)),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_7137]),
    [final] ).

cnf(i_0_12595,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),hAPP(hAPP(c_Product__Type_OPair(X2,X1),X4),X3)),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_7170]),
    [final] ).

cnf(i_0_12596,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X2)),esk35_4(X3,X4,X2,X1)),X3))
    | ~ hBOOL(hAPP(X1,X4))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X2)),X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7171]),
    [final] ).

cnf(i_0_12597,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_7172]),
    [final] ).

cnf(i_0_12598,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_6617]),
    [final] ).

cnf(i_0_12599,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_7173,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_12600,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk198_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_7110]),
    [final] ).

cnf(i_0_12601,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_7174]),
    [final] ).

cnf(i_0_12602,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_7175]),
    [final] ).

cnf(i_0_12603,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),esk173_3(X3,X2,X1)),esk174_3(X3,X2,X1))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(X2,esk173_3(X3,X2,X1))),hAPP(X2,esk174_3(X3,X2,X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7176]),
    [final] ).

cnf(i_0_12604,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),esk171_3(X3,X2,X1)),esk172_3(X3,X2,X1))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(X2,esk171_3(X3,X2,X1))),hAPP(X2,esk172_3(X3,X2,X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7177]),
    [final] ).

cnf(i_0_12605,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),esk177_3(X3,X2,X1)),esk178_3(X3,X2,X1))) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(X2,esk177_3(X3,X2,X1))),hAPP(X2,esk178_3(X3,X2,X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7178]),
    [final] ).

cnf(i_0_12606,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),esk175_3(X3,X2,X1)),esk176_3(X3,X2,X1))) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(X2,esk175_3(X3,X2,X1))),hAPP(X2,esk176_3(X3,X2,X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7179]),
    [final] ).

cnf(i_0_12607,plain,
    ( hBOOL(hAPP(X3,esk210_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,esk207_2(X3,X2)))
    | ~ hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk207_2(X3,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk208_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_7180]),
    [final] ).

cnf(i_0_12608,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_7181]),
    [final] ).

cnf(i_0_12609,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2)),esk408_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)))
    | esk410_2(X1,X2) != esk409_2(X1,X2)
    | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X2)),X1)) ),
    inference(rw,[status(thm)],[i_0_7182,c_0_6138]),
    [final] ).

cnf(i_0_12610,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_7183]),
    [final] ).

cnf(i_0_12611,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_6991]),
    [final] ).

cnf(i_0_12612,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_6992]),
    [final] ).

cnf(i_0_12613,plain,
    ( c_Wellfounded_Oacyclic(X1,X2)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk444_2(X2,X1)),esk444_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_7184,c_0_6097]),
    [final] ).

cnf(i_0_12614,plain,
    ( c_Wellfounded_Oacyclic(X1,X2)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk442_2(X2,X1)),esk442_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_7185,c_0_6097]),
    [final] ).

cnf(i_0_12615,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_7186]),
    [final] ).

cnf(i_0_12616,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_7187]),
    [final] ).

cnf(i_0_12617,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_7088]),
    [final] ).

cnf(i_0_12618,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_7188]),
    [final] ).

cnf(i_0_12619,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_7189]),
    [final] ).

cnf(i_0_12620,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X2)),esk35_4(X3,X4,X2,X1)),X3))
    | X3 = X4
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X2)),X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7171]),
    [final] ).

cnf(i_0_12621,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_7190]),
    [final] ).

cnf(i_0_12622,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_7191]),
    [final] ).

cnf(i_0_12623,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_7192]),
    [final] ).

cnf(i_0_12624,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_7193]),
    [final] ).

cnf(i_0_12625,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_7194]),
    [final] ).

cnf(i_0_12626,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_7195]),
    [final] ).

cnf(i_0_12627,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_7063]),
    [final] ).

cnf(i_0_12628,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_7063]),
    [final] ).

cnf(i_0_12629,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_7064]),
    [final] ).

cnf(i_0_12630,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_7064]),
    [final] ).

cnf(i_0_12631,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_7196]),
    [final] ).

cnf(i_0_12632,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_7197]),
    [final] ).

cnf(i_0_12633,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_7198]),
    [final] ).

cnf(i_0_12634,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_7199]),
    [final] ).

cnf(i_0_12635,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_7200]),
    [final] ).

cnf(i_0_12636,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_7201]),
    [final] ).

cnf(i_0_12637,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_7202]),
    [final] ).

cnf(i_0_12638,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk463_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_7203]),
    [final] ).

cnf(i_0_12639,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk469_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_7204]),
    [final] ).

cnf(i_0_12640,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_7205]),
    [final] ).

cnf(i_0_12641,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_7206]),
    [final] ).

cnf(i_0_12642,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_7207]),
    [final] ).

cnf(i_0_12643,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_7208]),
    [final] ).

cnf(i_0_12644,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_7209]),
    [final] ).

cnf(i_0_12645,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_7210]),
    [final] ).

cnf(i_0_12646,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_7211]),
    [final] ).

cnf(i_0_12647,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk235_3(X2,X3,X1)),X3))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_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_7212]),
    [final] ).

cnf(i_0_12648,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk147_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_7213]),
    [final] ).

cnf(i_0_12649,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_6120]),
    [final] ).

cnf(i_0_12650,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_6311]),
    [final] ).

cnf(i_0_12651,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_7214]),
    [final] ).

cnf(i_0_12652,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_7215]),
    [final] ).

cnf(i_0_12653,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_6917]),
    [final] ).

cnf(i_0_12654,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_7216]),
    [final] ).

cnf(i_0_12655,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_7217]),
    [final] ).

cnf(i_0_12656,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_7218,c_0_6178]),
    [final] ).

cnf(i_0_12657,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_6374]),
    [final] ).

cnf(i_0_12658,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_7219,c_0_6088]),
    [final] ).

cnf(i_0_12659,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_6988]),
    [final] ).

cnf(i_0_12660,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_6989]),
    [final] ).

cnf(i_0_12661,plain,
    ( hBOOL(hAPP(X1,X3))
    | ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X2),esk514_3(X1,X3,X2)),esk515_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_7220]),
    [final] ).

cnf(i_0_12662,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_7221]),
    [final] ).

cnf(i_0_12663,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_7135]),
    [final] ).

cnf(i_0_12664,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_7136]),
    [final] ).

cnf(i_0_12665,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_7222]),
    [final] ).

cnf(i_0_12666,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk195_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_7223]),
    [final] ).

cnf(i_0_12667,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk187_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_7224]),
    [final] ).

cnf(i_0_12668,plain,
    ( hAPP(hAPP(c_List_Olist_OCons(X1),X2),esk306_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_6850]),
    [final] ).

cnf(i_0_12669,plain,
    ( X1 = hAPP(hAPP(c_List_Olist_OCons(X2),X3),esk307_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_6851]),
    [final] ).

cnf(i_0_12670,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_7225]),
    [final] ).

cnf(i_0_12671,plain,
    ( hBOOL(hAPP(X1,X4))
    | ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Product__Type_OPair(X2,X3),esk82_3(X3,X2,X1)),esk83_3(X3,X2,X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_7226]),
    [final] ).

cnf(i_0_12672,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_7227]),
    [final] ).

cnf(i_0_12673,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk214_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_7157]),
    [final] ).

cnf(i_0_12674,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk206_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_7156]),
    [final] ).

cnf(i_0_12675,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk277_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_6965]),
    [final] ).

cnf(i_0_12676,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_7228]),
    [final] ).

cnf(i_0_12677,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk411_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_7229]),
    [final] ).

cnf(i_0_12678,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_7019]),
    [final] ).

cnf(i_0_12679,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_7230,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_12680,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk209_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,esk207_2(X1,X2)))
    | ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk207_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk208_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_7180]),
    [final] ).

cnf(i_0_12681,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk517_4(X2,X3,X4,X1)),hAPP(c_List_Oset(X1),c_List_Oreplicate(X1,X4,X3))))
    | X4 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7231]),
    [final] ).

cnf(i_0_12682,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_7232,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_12683,plain,
    ( c_Relation_Osym(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk549_2(X2,X1)),esk548_2(X2,X1))),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7217]),
    [final] ).

cnf(i_0_12684,plain,
    ( c_Relation_Otrans(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk543_2(X2,X1)),esk545_2(X2,X1))),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6926]),
    [final] ).

cnf(i_0_12685,plain,
    ( c_Nitpick_Orefl_H(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk80_2(X2,X1)),esk80_2(X2,X1))),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7233]),
    [final] ).

cnf(i_0_12686,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),esk66_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_7234]),
    [final] ).

cnf(i_0_12687,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),esk62_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_7235]),
    [final] ).

cnf(i_0_12688,plain,
    ( hAPP(hAPP(c_List_Olist_OCons(X1),X2),esk306_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_6850]),
    [final] ).

cnf(i_0_12689,plain,
    ( X1 = hAPP(hAPP(c_List_Olist_OCons(X2),X3),esk307_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_6851]),
    [final] ).

cnf(i_0_12690,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_7236]),
    [final] ).

cnf(i_0_12691,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_6870]),
    [final] ).

cnf(i_0_12692,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_7237,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_12693,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_7238]),
    [final] ).

cnf(i_0_12694,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_7239]),
    [final] ).

cnf(i_0_12695,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk516_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_7240]),
    [final] ).

cnf(i_0_12696,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_7241]),
    [final] ).

cnf(i_0_12697,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_7242]),
    [final] ).

cnf(i_0_12698,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_7243,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_12699,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_7244,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_12700,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_7245,c_0_6693]),
    [final] ).

cnf(i_0_12701,plain,
    ( X1 = hAPP(c_List_Ofilter(X2,X3),esk453_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_6163]),
    [final] ).

cnf(i_0_12702,plain,
    ( X1 = hAPP(c_List_Ofilter(X2,X3),esk438_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_6164]),
    [final] ).

cnf(i_0_12703,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_7246,c_0_7094]),
    [final] ).

cnf(i_0_12704,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_7247]),
    [final] ).

cnf(i_0_12705,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk512_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_6958]),
    [final] ).

cnf(i_0_12706,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk505_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_6959]),
    [final] ).

cnf(i_0_12707,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_7248]),
    [final] ).

cnf(i_0_12708,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),esk518_3(X1,X2,X3)),esk519_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_7086]),
    [final] ).

cnf(i_0_12709,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),esk342_3(X1,X2,X3)),esk343_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_6922]),
    [final] ).

cnf(i_0_12710,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),esk90_3(X1,X2,X3)),esk91_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_7072]),
    [final] ).

cnf(i_0_12711,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),esk88_3(X1,X2,X3)),esk89_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_5312]),
    [final] ).

cnf(i_0_12712,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),esk86_3(X1,X2,X3)),esk87_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_5309]),
    [final] ).

cnf(i_0_12713,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),esk92_3(X1,X2,X3)),esk93_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_7249]),
    [final] ).

cnf(i_0_12714,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_7250]),
    [final] ).

cnf(i_0_12715,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),esk7_4(X2,X3,X1,X4)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(X4,X1)),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7251]),
    [final] ).

cnf(i_0_12716,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),esk6_4(X2,X3,X1,X4)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(X4,X1)),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7252]),
    [final] ).

cnf(i_0_12717,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_7253]),
    [final] ).

cnf(i_0_12718,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_7254]),
    [final] ).

cnf(i_0_12719,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_7255]),
    [final] ).

cnf(i_0_12720,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_7256,c_0_6178]),
    [final] ).

cnf(i_0_12721,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk443_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_7257,c_0_6097]),
    [final] ).

cnf(i_0_12722,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)))
    | esk410_2(X1,X2) != esk409_2(X1,X2)
    | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X2)),X1))
    | ~ hBOOL(hAPP(c_List_Odistinct(X2),esk408_2(X1,X2))) ),
    inference(rw,[status(thm)],[i_0_7258,c_0_6138]),
    [final] ).

cnf(i_0_12723,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),esk556_3(X1,X3,X2))) != esk556_3(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7259]),
    [final] ).

cnf(i_0_12724,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,esk235_3(X1,X2,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7212]),
    [final] ).

cnf(i_0_12725,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,esk147_3(X1,X2,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7213]),
    [final] ).

cnf(i_0_12726,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk522_4(X2,X3,X1,X4)),hAPP(c_List_Oset(X1),X2)))
    | c_List_Olist__ex1(X1,X3,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X2)))
    | ~ hBOOL(hAPP(X3,X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7260]),
    [final] ).

cnf(i_0_12727,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk511_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_7261]),
    [final] ).

cnf(i_0_12728,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_7262]),
    [final] ).

cnf(i_0_12729,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_7063]),
    [final] ).

cnf(i_0_12730,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_7064]),
    [final] ).

cnf(i_0_12731,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_7263]),
    [final] ).

cnf(i_0_12732,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_7264]),
    [final] ).

cnf(i_0_12733,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk331_4(X2,X3,X4,X1)),X3))
    | c_Equiv__Relations_Ocongruent(X1,X4,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6231]),
    [final] ).

cnf(i_0_12734,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),esk403_4(X1,X3,X2,X4)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_6969]),
    [final] ).

cnf(i_0_12735,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_7061]),
    [final] ).

cnf(i_0_12736,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_7265]),
    [final] ).

cnf(i_0_12737,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_7266,c_0_6281]),
    [final] ).

cnf(i_0_12738,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_7267,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_12739,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_7268]),
    [final] ).

cnf(i_0_12740,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_7269]),
    [final] ).

cnf(i_0_12741,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),esk403_4(X4,X3,X2,X1)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_6969]),
    [final] ).

cnf(i_0_12742,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_7270]),
    [final] ).

cnf(i_0_12743,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X1)),esk336_4(X2,X3,X1,X4)),X3))
    | c_Hoare__Mirabelle_Otriple__valid(X1,X4,X5)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X1)),X5),X2))
    | ~ c_Hoare__Mirabelle_Ohoare__valids(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7271]),
    [final] ).

cnf(i_0_12744,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk382_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_6975]),
    [final] ).

cnf(i_0_12745,plain,
    ( hAPP(hAPP(c_List_Otake(X1),X4),X2) = hAPP(hAPP(c_List_Otake(X1),X4),X3)
    | hAPP(hAPP(c_List_Onth(X1),X2),esk362_4(X3,X2,X1,X4)) != hAPP(hAPP(c_List_Onth(X1),X3),esk362_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_7159]),
    [final] ).

cnf(i_0_12746,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_6799]),
    [final] ).

cnf(i_0_12747,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_7272]),
    [final] ).

cnf(i_0_12748,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_7273]),
    [final] ).

cnf(i_0_12749,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk440_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_7274]),
    [final] ).

cnf(i_0_12750,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_7275]),
    [final] ).

cnf(i_0_12751,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_7211]),
    [final] ).

cnf(i_0_12752,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_7276]),
    [final] ).

cnf(i_0_12753,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk542_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_6599]),
    [final] ).

cnf(i_0_12754,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk256_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_6600]),
    [final] ).

cnf(i_0_12755,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk540_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_6971]),
    [final] ).

cnf(i_0_12756,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_7277]),
    [final] ).

cnf(i_0_12757,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_7278]),
    [final] ).

cnf(i_0_12758,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_7061]),
    [final] ).

cnf(i_0_12759,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk434_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_7279]),
    [final] ).

cnf(i_0_12760,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_7280]),
    [final] ).

cnf(i_0_12761,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk232_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_7281]),
    [final] ).

cnf(i_0_12762,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_7282]),
    [final] ).

cnf(i_0_12763,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk196_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_7223]),
    [final] ).

cnf(i_0_12764,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk188_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_7224]),
    [final] ).

cnf(i_0_12765,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_7283]),
    [final] ).

cnf(i_0_12766,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_7061]),
    [final] ).

cnf(i_0_12767,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_6991]),
    [final] ).

cnf(i_0_12768,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_6992]),
    [final] ).

cnf(i_0_12769,plain,
    ( esk93_3(X1,X2,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(hAPP(X1,esk93_3(X1,X2,X3)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,esk92_3(X1,X2,X3),esk93_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_7249]),
    [final] ).

cnf(i_0_12770,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_7284]),
    [final] ).

cnf(i_0_12771,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_7285]),
    [final] ).

cnf(i_0_12772,plain,
    ( X1 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk200_4(X2,X3,X4,X1)),esk199_4(X2,X3,X4,X1))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_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_7073]),
    [final] ).

cnf(i_0_12773,plain,
    ( X1 = X2
    | hAPP(c_Fun_Ofun__upd(X3,X4,X5,X2,X6),X1) = hAPP(X5,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7286]),
    [final] ).

cnf(i_0_12774,plain,
    ( X1 = X2
    | hAPP(c_Fun_Ofun__upd(X3,X4,X5,X2,X6),X1) = hAPP(X5,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7287]),
    [final] ).

cnf(i_0_12775,plain,
    ( X1 = X2
    | hAPP(c_Fun_Ofun__upd(X3,X4,X5,X2,X6),X1) = hAPP(X5,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7288]),
    [final] ).

cnf(i_0_12776,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_7015]),
    [final] ).

cnf(i_0_12777,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk234_4(X2,X3,X1,X4)),X3))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),X3) = 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_7289]),
    [final] ).

cnf(i_0_12778,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_7290]),
    [final] ).

cnf(i_0_12779,plain,
    ( hAPP(c_Fun_Ofun__upd(X3,X4,X5,X2,X6),X1) = X6
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_7286]),
    [final] ).

cnf(i_0_12780,plain,
    ( hAPP(c_Fun_Ofun__upd(X3,X4,X5,X2,X6),X1) = X6
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_7288]),
    [final] ).

cnf(i_0_12781,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_7174]),
    [final] ).

cnf(i_0_12782,plain,
    hAPP(c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X4) = X5,
    inference(split_conjunct,[status(thm)],[i_0_7291]),
    [final] ).

cnf(i_0_12783,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_7292]),
    [final] ).

cnf(i_0_12784,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_7162]),
    [final] ).

cnf(i_0_12785,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),esk403_4(X1,X3,X2,X4)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6969]),
    [final] ).

cnf(i_0_12786,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_7061]),
    [final] ).

cnf(i_0_12787,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_7293]),
    [final] ).

cnf(i_0_12788,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_7294,c_0_7295]),
    [final] ).

cnf(i_0_12789,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),esk403_4(X4,X3,X2,X1)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_6969]),
    [final] ).

cnf(i_0_12790,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_7296]),
    [final] ).

cnf(i_0_12791,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_6988]),
    [final] ).

cnf(i_0_12792,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_6989]),
    [final] ).

cnf(i_0_12793,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_7297]),
    [final] ).

cnf(i_0_12794,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_6342]),
    [final] ).

cnf(i_0_12795,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_7298]),
    [final] ).

cnf(i_0_12796,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_7299]),
    [final] ).

cnf(i_0_12797,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_7300]),
    [final] ).

cnf(i_0_12798,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_7301]),
    [final] ).

cnf(i_0_12799,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_7302]),
    [final] ).

cnf(i_0_12800,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_7276]),
    [final] ).

cnf(i_0_12801,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_7303]),
    [final] ).

cnf(i_0_12802,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_7304]),
    [final] ).

cnf(i_0_12803,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_7305]),
    [final] ).

cnf(i_0_12804,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_7306]),
    [final] ).

cnf(i_0_12805,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_7307]),
    [final] ).

cnf(i_0_12806,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_7308]),
    [final] ).

cnf(i_0_12807,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_7309]),
    [final] ).

cnf(i_0_12808,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_7310,c_0_6138]),c_0_6138]),
    [final] ).

cnf(i_0_12809,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_7311]),
    [final] ).

cnf(i_0_12810,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_7312]),
    [final] ).

cnf(i_0_12811,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_7313]),
    [final] ).

cnf(i_0_12812,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_7028]),
    [final] ).

cnf(i_0_12813,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_7314]),
    [final] ).

cnf(i_0_12814,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_7315]),
    [final] ).

cnf(i_0_12815,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_7316,c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_12816,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_7317,c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_12817,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_7318]),
    [final] ).

cnf(i_0_12818,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_7319]),
    [final] ).

cnf(i_0_12819,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_7320]),
    [final] ).

cnf(i_0_12820,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_7321]),
    [final] ).

cnf(i_0_12821,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk216_4(X2,X3,X4,X1)),X2))
    | c_Fun_Oinj__on(X1,X4,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7322]),
    [final] ).

cnf(i_0_12822,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk215_4(X2,X3,X4,X1)),X2))
    | c_Fun_Oinj__on(X1,X4,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7322]),
    [final] ).

cnf(i_0_12823,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_7323]),
    [final] ).

cnf(i_0_12824,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_7324]),
    [final] ).

cnf(i_0_12825,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_7099]),
    [final] ).

cnf(i_0_12826,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_7304]),
    [final] ).

cnf(i_0_12827,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_7305]),
    [final] ).

cnf(i_0_12828,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_7325]),
    [final] ).

cnf(i_0_12829,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk141_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_7326]),
    [final] ).

cnf(i_0_12830,plain,
    ( X1 = hAPP(hAPP(c_Product__Type_OPair(X2,X3),esk501_4(X4,X1,X3,X2)),esk500_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_6521]),
    [final] ).

cnf(i_0_12831,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_7327]),
    [final] ).

cnf(i_0_12832,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_7328]),
    [final] ).

cnf(i_0_12833,plain,
    ( hBOOL(hAPP(X1,esk209_2(X1,X2)))
    | ~ hBOOL(hAPP(X1,X3))
    | ~ hBOOL(hAPP(X1,esk207_2(X1,X2)))
    | ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk207_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk208_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_7180]),
    [final] ).

cnf(i_0_12834,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_7329,c_0_6088]),
    [final] ).

cnf(i_0_12835,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk212_4(X2,X3,X4,X1)),esk211_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_7098]),
    [final] ).

cnf(i_0_12836,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk204_4(X2,X3,X4,X1)),esk203_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_7097]),
    [final] ).

cnf(i_0_12837,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_7023]),
    [final] ).

cnf(i_0_12838,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk353_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_7330]),
    [final] ).

cnf(i_0_12839,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk156_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_7331]),
    [final] ).

cnf(i_0_12840,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk354_4(X2,X3,X1,X4)),X3))
    | c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X4,tc_HOL_Obool)),X3),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7332]),
    [final] ).

cnf(i_0_12841,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk157_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_7333]),
    [final] ).

cnf(i_0_12842,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X1,esk433_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_7334]),
    [final] ).

cnf(i_0_12843,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_7335]),
    [final] ).

cnf(i_0_12844,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_7336]),
    [final] ).

cnf(i_0_12845,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_7337]),
    [final] ).

cnf(i_0_12846,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_7338]),
    [final] ).

cnf(i_0_12847,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk407_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_7339]),
    [final] ).

cnf(i_0_12848,plain,
    ( hAPP(X1,esk77_4(X2,X1,X3,X4)) = X2
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),esk76_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_6165]),
    [final] ).

cnf(i_0_12849,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_7340]),
    [final] ).

cnf(i_0_12850,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_7341]),
    [final] ).

cnf(i_0_12851,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_7342,c_0_6693]),c_0_6693]),
    [final] ).

cnf(i_0_12852,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_7343]),
    [final] ).

cnf(i_0_12853,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_7344]),
    [final] ).

cnf(i_0_12854,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk198_4(X2,X3,X4,X1)),esk197_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_7110]),
    [final] ).

cnf(i_0_12855,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_7345,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_12856,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_7346]),
    [final] ).

cnf(i_0_12857,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)),esk378_3(X2,X3,X1)),X3))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),esk379_3(X2,X3,X1)),esk380_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_7347]),
    [final] ).

cnf(i_0_12858,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_7035]),
    [final] ).

cnf(i_0_12859,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_7348]),
    [final] ).

cnf(i_0_12860,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_7349]),
    [final] ).

cnf(i_0_12861,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_7350]),
    [final] ).

cnf(i_0_12862,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_7351,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_12863,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_7352]),
    [final] ).

cnf(i_0_12864,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_7353]),
    [final] ).

cnf(i_0_12865,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_7354]),
    [final] ).

cnf(i_0_12866,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_7355]),
    [final] ).

cnf(i_0_12867,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk433_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_7334]),
    [final] ).

cnf(i_0_12868,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_7356]),
    [final] ).

cnf(i_0_12869,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_7357,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_12870,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_7358]),
    [final] ).

cnf(i_0_12871,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_7135]),
    [final] ).

cnf(i_0_12872,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_7136]),
    [final] ).

cnf(i_0_12873,plain,
    ( X1 = hAPP(X2,esk248_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_6982]),
    [final] ).

cnf(i_0_12874,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_7359,c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_12875,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_7360]),
    [final] ).

cnf(i_0_12876,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_7361]),
    [final] ).

cnf(i_0_12877,hypothesis,
    c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
    inference(split_conjunct,[status(thm)],[conj_0]),
    [final] ).

cnf(i_0_12878,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_7362,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_12879,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_7363,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_12880,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_7364,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_12881,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_7365,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_12882,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_7366,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_12883,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_7367,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_12884,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_7368,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_12885,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_7369,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_12886,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_7370]),
    [final] ).

cnf(i_0_12887,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_7371]),
    [final] ).

cnf(i_0_12888,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk380_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)),esk378_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_7347]),
    [final] ).

cnf(i_0_12889,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk379_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)),esk378_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_7347]),
    [final] ).

cnf(i_0_12890,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_7372]),
    [final] ).

cnf(i_0_12891,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_7373]),
    [final] ).

cnf(i_0_12892,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_7374,c_0_6088]),
    [final] ).

cnf(i_0_12893,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_7375]),
    [final] ).

cnf(i_0_12894,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_7376]),
    [final] ).

cnf(i_0_12895,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_7377]),
    [final] ).

cnf(i_0_12896,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_7378]),
    [final] ).

cnf(i_0_12897,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_7379]),
    [final] ).

cnf(i_0_12898,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_7380]),
    [final] ).

cnf(i_0_12899,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_7381]),
    [final] ).

cnf(i_0_12900,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_7382,c_0_6281]),c_0_6281]),
    [final] ).

cnf(i_0_12901,plain,
    ( hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X3),X2),X4)))
    | ~ hBOOL(hAPP(X1,esk469_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_7204]),
    [final] ).

cnf(i_0_12902,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_7383]),
    [final] ).

cnf(i_0_12903,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_7118]),
    [final] ).

cnf(i_0_12904,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_7384]),
    [final] ).

cnf(i_0_12905,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_7385]),
    [final] ).

cnf(i_0_12906,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_7386]),
    [final] ).

cnf(i_0_12907,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_7038]),
    [final] ).

cnf(i_0_12908,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_7039]),
    [final] ).

cnf(i_0_12909,plain,
    ( c_Wellfounded_Owf(tc_prod(X3,X1),c_Recdef_Osame__fst(X3,X1,X4,X2))
    | ~ c_Wellfounded_Owf(X1,hAPP(X2,esk381_4(X3,X2,X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_7387]),
    [final] ).

cnf(i_0_12910,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_7388]),
    [final] ).

cnf(i_0_12911,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_7389]),
    [final] ).

cnf(i_0_12912,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_7390,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_12913,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_7391]),
    [final] ).

cnf(i_0_12914,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_7392,c_0_6097]),
    [final] ).

cnf(i_0_12915,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_7393]),
    [final] ).

cnf(i_0_12916,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_7394]),
    [final] ).

cnf(i_0_12917,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_7124]),
    [final] ).

cnf(i_0_12918,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_7125]),
    [final] ).

cnf(i_0_12919,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_7395]),
    [final] ).

cnf(i_0_12920,plain,
    ( X1 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk214_4(X2,X3,X4,X1)),esk213_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_7157]),
    [final] ).

cnf(i_0_12921,plain,
    ( X1 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk206_4(X2,X3,X4,X1)),esk205_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_7156]),
    [final] ).

cnf(i_0_12922,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_7396,c_0_6138]),c_0_6138]),
    [final] ).

cnf(i_0_12923,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_6481]),
    [final] ).

cnf(i_0_12924,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_7397]),
    [final] ).

cnf(i_0_12925,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_7398]),
    [final] ).

cnf(i_0_12926,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_7399]),
    [final] ).

cnf(i_0_12927,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_7400]),
    [final] ).

cnf(i_0_12928,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_7401]),
    [final] ).

cnf(i_0_12929,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_7402]),
    [final] ).

cnf(i_0_12930,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_7403]),
    [final] ).

cnf(i_0_12931,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_7404]),
    [final] ).

cnf(i_0_12932,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_7405]),
    [final] ).

cnf(i_0_12933,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_7406]),
    [final] ).

cnf(i_0_12934,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_7407]),
    [final] ).

cnf(i_0_12935,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_7408]),
    [final] ).

cnf(i_0_12936,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_7409]),
    [final] ).

cnf(i_0_12937,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_7410]),
    [final] ).

cnf(i_0_12938,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_7135]),
    [final] ).

cnf(i_0_12939,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_7063]),
    [final] ).

cnf(i_0_12940,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_7136]),
    [final] ).

cnf(i_0_12941,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_7064]),
    [final] ).

cnf(i_0_12942,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,esk68_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_7411]),
    [final] ).

cnf(i_0_12943,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_7412]),
    [final] ).

cnf(i_0_12944,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_7413]),
    [final] ).

cnf(i_0_12945,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_7414]),
    [final] ).

cnf(i_0_12946,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_7415]),
    [final] ).

cnf(i_0_12947,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_7416]),
    [final] ).

cnf(i_0_12948,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_7417,c_0_6138]),c_0_6138]),
    [final] ).

cnf(i_0_12949,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_7418]),
    [final] ).

cnf(i_0_12950,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_7419]),
    [final] ).

cnf(i_0_12951,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_7420]),
    [final] ).

cnf(i_0_12952,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_7421]),
    [final] ).

cnf(i_0_12953,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_7422]),
    [final] ).

cnf(i_0_12954,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_7423]),
    [final] ).

cnf(i_0_12955,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_7424]),
    [final] ).

cnf(i_0_12956,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_7425]),
    [final] ).

cnf(i_0_12957,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_7426]),
    [final] ).

cnf(i_0_12958,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_7427]),
    [final] ).

cnf(i_0_12959,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_7428,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_12960,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_7429,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_12961,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_6991]),
    [final] ).

cnf(i_0_12962,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_6992]),
    [final] ).

cnf(i_0_12963,plain,
    ( hBOOL(hAPP(X3,esk210_2(X3,X2)))
    | hBOOL(hAPP(X3,esk207_2(X3,X2)))
    | hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk207_2(X3,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk208_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_7180]),
    [final] ).

cnf(i_0_12964,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_7430]),
    [final] ).

cnf(i_0_12965,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_7431]),
    [final] ).

cnf(i_0_12966,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_7432]),
    [final] ).

cnf(i_0_12967,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_7433]),
    [final] ).

cnf(i_0_12968,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_7434]),
    [final] ).

cnf(i_0_12969,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)),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_7435,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_12970,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_7436,c_0_6097]),
    [final] ).

cnf(i_0_12971,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_7099]),
    [final] ).

cnf(i_0_12972,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_7437]),
    [final] ).

cnf(i_0_12973,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_7274]),
    [final] ).

cnf(i_0_12974,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_7150]),
    [final] ).

cnf(i_0_12975,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_7438]),
    [final] ).

cnf(i_0_12976,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_7439]),
    [final] ).

cnf(i_0_12977,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_7063]),
    [final] ).

cnf(i_0_12978,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_7064]),
    [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))
    | 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_7440]),
    [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_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_7441]),
    [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,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_7442]),
    [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_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_7443]),
    [final] ).

cnf(i_0_12983,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_7444]),
    [final] ).

cnf(i_0_12984,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_7445]),
    [final] ).

cnf(i_0_12985,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_7341]),
    [final] ).

cnf(i_0_12986,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_7446]),
    [final] ).

cnf(i_0_12987,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_7447]),
    [final] ).

cnf(i_0_12988,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_7448]),
    [final] ).

cnf(i_0_12989,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_7449]),
    [final] ).

cnf(i_0_12990,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_7450]),
    [final] ).

cnf(i_0_12991,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_7188]),
    [final] ).

cnf(i_0_12992,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_7189]),
    [final] ).

cnf(i_0_12993,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_7451,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_12994,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_7452,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_12995,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_7453,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_12996,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_7454,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_12997,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_7455,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_12998,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_7456,c_0_6713]),
    [final] ).

cnf(i_0_12999,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_7457]),
    [final] ).

cnf(i_0_13000,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_7458]),
    [final] ).

cnf(i_0_13001,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_7459]),
    [final] ).

cnf(i_0_13002,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_6988]),
    [final] ).

cnf(i_0_13003,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_6989]),
    [final] ).

cnf(i_0_13004,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_7460]),
    [final] ).

cnf(i_0_13005,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_7461]),
    [final] ).

cnf(i_0_13006,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_7462]),
    [final] ).

cnf(i_0_13007,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_7463]),
    [final] ).

cnf(i_0_13008,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_7446]),
    [final] ).

cnf(i_0_13009,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_7447]),
    [final] ).

cnf(i_0_13010,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_7464]),
    [final] ).

cnf(i_0_13011,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_6991]),
    [final] ).

cnf(i_0_13012,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_6992]),
    [final] ).

cnf(i_0_13013,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_7465]),
    [final] ).

cnf(i_0_13014,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_7466]),
    [final] ).

cnf(i_0_13015,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_7467]),
    [final] ).

cnf(i_0_13016,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_7468]),
    [final] ).

cnf(i_0_13017,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_7469,c_0_6088]),
    [final] ).

cnf(i_0_13018,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_7470]),
    [final] ).

cnf(i_0_13019,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_7471]),
    [final] ).

cnf(i_0_13020,plain,
    ( X3 = esk248_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_6982]),
    [final] ).

cnf(i_0_13021,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_7360]),
    [final] ).

cnf(i_0_13022,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_7472]),
    [final] ).

cnf(i_0_13023,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_7473,c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_13024,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_7268]),
    [final] ).

cnf(i_0_13025,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_7474]),
    [final] ).

cnf(i_0_13026,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_7475]),
    [final] ).

cnf(i_0_13027,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_7476]),
    [final] ).

cnf(i_0_13028,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_7477]),
    [final] ).

cnf(i_0_13029,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_7478]),
    [final] ).

cnf(i_0_13030,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_7479]),
    [final] ).

cnf(i_0_13031,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_7480]),
    [final] ).

cnf(i_0_13032,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_7481]),
    [final] ).

cnf(i_0_13033,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_7482]),
    [final] ).

cnf(i_0_13034,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_7483]),
    [final] ).

cnf(i_0_13035,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_7484]),
    [final] ).

cnf(i_0_13036,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_7485,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_13037,plain,
    ( hBOOL(hAPP(hAPP(X1,X3),X2))
    | ~ hBOOL(hAPP(hAPP(X1,esk518_3(X1,X2,X3)),esk519_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_7086]),
    [final] ).

cnf(i_0_13038,plain,
    ( hBOOL(hAPP(hAPP(X1,X3),X2))
    | ~ hBOOL(hAPP(hAPP(X1,esk342_3(X1,X2,X3)),esk343_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_6922]),
    [final] ).

cnf(i_0_13039,plain,
    ( hBOOL(hAPP(hAPP(X1,X3),X2))
    | ~ hBOOL(hAPP(hAPP(X1,esk92_3(X1,X2,X3)),esk93_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_7249]),
    [final] ).

cnf(i_0_13040,plain,
    ( hBOOL(hAPP(hAPP(X1,X3),X2))
    | ~ hBOOL(hAPP(hAPP(X1,esk90_3(X1,X2,X3)),esk91_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_7072]),
    [final] ).

cnf(i_0_13041,plain,
    ( hBOOL(hAPP(hAPP(X1,X3),X2))
    | ~ hBOOL(hAPP(hAPP(X1,esk88_3(X1,X2,X3)),esk89_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_5312]),
    [final] ).

cnf(i_0_13042,plain,
    ( hBOOL(hAPP(hAPP(X1,X3),X2))
    | ~ hBOOL(hAPP(hAPP(X1,esk86_3(X1,X2,X3)),esk87_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_5309]),
    [final] ).

cnf(i_0_13043,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_6294]),
    [final] ).

cnf(i_0_13044,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_6553]),
    [final] ).

cnf(i_0_13045,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_7486]),
    [final] ).

cnf(i_0_13046,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_7487]),
    [final] ).

cnf(i_0_13047,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_7488]),
    [final] ).

cnf(i_0_13048,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,esk52_3(X2,X1,X3)),esk53_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_7489]),
    [final] ).

cnf(i_0_13049,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_7490]),
    [final] ).

cnf(i_0_13050,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_7491]),
    [final] ).

cnf(i_0_13051,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_7492]),
    [final] ).

cnf(i_0_13052,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_7493]),
    [final] ).

cnf(i_0_13053,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_7494]),
    [final] ).

cnf(i_0_13054,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_7495]),
    [final] ).

cnf(i_0_13055,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_7489]),
    [final] ).

cnf(i_0_13056,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,esk54_3(X2,X1,X3)),esk55_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_7496]),
    [final] ).

cnf(i_0_13057,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_7497]),
    [final] ).

cnf(i_0_13058,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_7498]),
    [final] ).

cnf(i_0_13059,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_7499]),
    [final] ).

cnf(i_0_13060,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_7500]),
    [final] ).

cnf(i_0_13061,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_7501]),
    [final] ).

cnf(i_0_13062,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_7502]),
    [final] ).

cnf(i_0_13063,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_7503]),
    [final] ).

cnf(i_0_13064,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_7504]),
    [final] ).

cnf(i_0_13065,plain,
    ( hAPP(X4,hAPP(X3,X6)) = X6
    | ~ c_Typedef_Otype__definition(X1,X2,X3,X4,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_7505]),
    [final] ).

cnf(i_0_13066,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_7506]),
    [final] ).

cnf(i_0_13067,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_7496]),
    [final] ).

cnf(i_0_13068,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_7507,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_13069,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_7508]),
    [final] ).

cnf(i_0_13070,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_7509]),
    [final] ).

cnf(i_0_13071,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_7510,c_0_6097]),
    [final] ).

cnf(i_0_13072,plain,
    ( X1 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk188_4(X2,X3,X4,X1)),esk187_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_7224]),
    [final] ).

cnf(i_0_13073,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk196_4(X2,X3,X4,X1)),esk195_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_7223]),
    [final] ).

cnf(i_0_13074,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_7063]),
    [final] ).

cnf(i_0_13075,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_7064]),
    [final] ).

cnf(i_0_13076,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,esk434_4(X2,X1,X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_7279]),
    [final] ).

cnf(i_0_13077,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_7511]),
    [final] ).

cnf(i_0_13078,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk209_2(X1,X2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2)))
    | hBOOL(hAPP(X1,esk207_2(X1,X2)))
    | hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk207_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk208_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_7180]),
    [final] ).

cnf(i_0_13079,plain,
    ( hAPP(X3,X4) = X5
    | c_Fun_Ofun__upd(X1,X2,X3,X4,X5) != X3 ),
    inference(split_conjunct,[status(thm)],[i_0_7512]),
    [final] ).

cnf(i_0_13080,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_7513]),
    [final] ).

cnf(i_0_13081,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_7514]),
    [final] ).

cnf(i_0_13082,plain,
    ( X2 = X3
    | ~ c_Fun_Obij__betw(X1,X1,c_Fun_Oid(X1),X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7515]),
    [final] ).

cnf(i_0_13083,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_6818]),
    [final] ).

cnf(i_0_13084,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_7516]),
    [final] ).

cnf(i_0_13085,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_6630]),
    [final] ).

cnf(i_0_13086,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_7517]),
    [final] ).

cnf(i_0_13087,plain,
    ( c_Fun_Obij__betw(X1,X3,esk565_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_7430]),
    [final] ).

cnf(i_0_13088,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_7518]),
    [final] ).

cnf(i_0_13089,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_7519]),
    [final] ).

cnf(i_0_13090,plain,
    ( X2 = X3
    | ~ c_List_Olist__all2(X1,X1,c_fequal,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7520]),
    [final] ).

cnf(i_0_13091,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_7063]),
    [final] ).

cnf(i_0_13092,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_7135]),
    [final] ).

cnf(i_0_13093,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_7064]),
    [final] ).

cnf(i_0_13094,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_7136]),
    [final] ).

cnf(i_0_13095,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_7370]),
    [final] ).

cnf(i_0_13096,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_7371]),
    [final] ).

cnf(i_0_13097,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_7521]),
    [final] ).

cnf(i_0_13098,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_7522]),
    [final] ).

cnf(i_0_13099,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_7523,c_0_6138]),c_0_6138]),
    [final] ).

cnf(i_0_13100,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_7524]),
    [final] ).

cnf(i_0_13101,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_7525]),
    [final] ).

cnf(i_0_13102,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_7526]),
    [final] ).

cnf(i_0_13103,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_7527]),
    [final] ).

cnf(i_0_13104,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_7528,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_13105,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_7076]),
    [final] ).

cnf(i_0_13106,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_7529]),
    [final] ).

cnf(i_0_13107,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk332_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_7248]),
    [final] ).

cnf(i_0_13108,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_7530]),
    [final] ).

cnf(i_0_13109,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_7531]),
    [final] ).

cnf(i_0_13110,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_7532]),
    [final] ).

cnf(i_0_13111,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_7533]),
    [final] ).

cnf(i_0_13112,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_7534]),
    [final] ).

cnf(i_0_13113,plain,
    ( c_List_Olinorder__class_Osorted(X1,X3)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),esk407_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_7339]),
    [final] ).

cnf(i_0_13114,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_7535]),
    [final] ).

cnf(i_0_13115,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_7135]),
    [final] ).

cnf(i_0_13116,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_7135]),
    [final] ).

cnf(i_0_13117,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_7136]),
    [final] ).

cnf(i_0_13118,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_7136]),
    [final] ).

cnf(i_0_13119,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_7388]),
    [final] ).

cnf(i_0_13120,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_7536]),
    [final] ).

cnf(i_0_13121,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_6666]),
    [final] ).

cnf(i_0_13122,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_7537]),
    [final] ).

cnf(i_0_13123,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_7538]),
    [final] ).

cnf(i_0_13124,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_7539]),
    [final] ).

cnf(i_0_13125,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_7276]),
    [final] ).

cnf(i_0_13126,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_7276]),
    [final] ).

cnf(i_0_13127,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_7540]),
    [final] ).

cnf(i_0_13128,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_7541]),
    [final] ).

cnf(i_0_13129,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_7542,c_0_6181]),c_0_6181]),
    [final] ).

cnf(i_0_13130,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_7543]),
    [final] ).

cnf(i_0_13131,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_7544]),
    [final] ).

cnf(i_0_13132,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_7545]),
    [final] ).

cnf(i_0_13133,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_7546]),
    [final] ).

cnf(i_0_13134,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_7546]),
    [final] ).

cnf(i_0_13135,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_7547]),
    [final] ).

cnf(i_0_13136,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_7548]),
    [final] ).

cnf(i_0_13137,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_5318]),
    [final] ).

cnf(i_0_13138,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_7305]),
    [final] ).

cnf(i_0_13139,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_7549]),
    [final] ).

cnf(i_0_13140,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk374_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_7550]),
    [final] ).

cnf(i_0_13141,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk373_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_7550]),
    [final] ).

cnf(i_0_13142,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_7551]),
    [final] ).

cnf(i_0_13143,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_7552]),
    [final] ).

cnf(i_0_13144,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_7553,c_0_6088]),c_0_6097]),
    [final] ).

cnf(i_0_13145,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_7554]),
    [final] ).

cnf(i_0_13146,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_7555]),
    [final] ).

cnf(i_0_13147,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_7556]),
    [final] ).

cnf(i_0_13148,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_7414]),
    [final] ).

cnf(i_0_13149,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_7415]),
    [final] ).

cnf(i_0_13150,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_7557]),
    [final] ).

cnf(i_0_13151,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_7557]),
    [final] ).

cnf(i_0_13152,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_7558]),
    [final] ).

cnf(i_0_13153,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_7558]),
    [final] ).

cnf(i_0_13154,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_7559]),
    [final] ).

cnf(i_0_13155,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_7560]),
    [final] ).

cnf(i_0_13156,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_7561]),
    [final] ).

cnf(i_0_13157,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_7560]),
    [final] ).

cnf(i_0_13158,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_7561]),
    [final] ).

cnf(i_0_13159,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_7562,c_0_7563]),
    [final] ).

cnf(i_0_13160,plain,
    ( hBOOL(hAPP(X4,X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(X4,esk101_4(X4,X3,X5,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_6830]),
    [final] ).

cnf(i_0_13161,plain,
    ( hBOOL(hAPP(X4,X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(X4,esk101_4(X4,X5,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_6830]),
    [final] ).

cnf(i_0_13162,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_7564]),
    [final] ).

cnf(i_0_13163,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),esk226_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_6590]),
    [final] ).

cnf(i_0_13164,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_7565]),
    [final] ).

cnf(i_0_13165,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_7566]),
    [final] ).

cnf(i_0_13166,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_7567]),
    [final] ).

cnf(i_0_13167,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_7568]),
    [final] ).

cnf(i_0_13168,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_7569]),
    [final] ).

cnf(i_0_13169,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_7570]),
    [final] ).

cnf(i_0_13170,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_7571]),
    [final] ).

cnf(i_0_13171,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_6988]),
    [final] ).

cnf(i_0_13172,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_6989]),
    [final] ).

cnf(i_0_13173,plain,
    ( hBOOL(hAPP(X1,esk226_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_6590]),
    [final] ).

cnf(i_0_13174,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_7572,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_13175,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)),esk412_3(X2,X3,X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7573]),
    [final] ).

cnf(i_0_13176,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_7574]),
    [final] ).

cnf(i_0_13177,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_7575]),
    [final] ).

cnf(i_0_13178,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_6988]),
    [final] ).

cnf(i_0_13179,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_6989]),
    [final] ).

cnf(i_0_13180,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_6991]),
    [final] ).

cnf(i_0_13181,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_6992]),
    [final] ).

cnf(i_0_13182,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_7576]),
    [final] ).

cnf(i_0_13183,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_7577]),
    [final] ).

cnf(i_0_13184,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_7578,c_0_7295]),
    [final] ).

cnf(i_0_13185,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,esk424_3(X2,X1,X3)) != hAPP(X1,esk425_3(X2,X1,X3))
    | ~ c_Wellfounded_OwfP(X3,hAPP(X1,esk423_3(X2,X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_6919]),
    [final] ).

cnf(i_0_13186,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_7579]),
    [final] ).

cnf(i_0_13187,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_7580]),
    [final] ).

cnf(i_0_13188,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_7581]),
    [final] ).

cnf(i_0_13189,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_7582]),
    [final] ).

cnf(i_0_13190,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_7583]),
    [final] ).

cnf(i_0_13191,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)),esk379_3(X2,X3,X1)),esk380_3(X2,X3,X1)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hAPP(c_Finite__Set_Ocard(X1),esk378_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_7347]),
    [final] ).

cnf(i_0_13192,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_7584,c_0_6713]),c_0_6713]),c_0_6713]),
    [final] ).

cnf(i_0_13193,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_7585]),
    [final] ).

cnf(i_0_13194,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_7532]),
    [final] ).

cnf(i_0_13195,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_7585]),
    [final] ).

cnf(i_0_13196,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_7532]),
    [final] ).

cnf(i_0_13197,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_7586]),
    [final] ).

cnf(i_0_13198,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_7587]),
    [final] ).

cnf(i_0_13199,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_7588]),
    [final] ).

cnf(i_0_13200,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_7589]),
    [final] ).

cnf(i_0_13201,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_7590]),
    [final] ).

cnf(i_0_13202,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_7591]),
    [final] ).

cnf(i_0_13203,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_7592]),
    [final] ).

cnf(i_0_13204,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_7593]),
    [final] ).

cnf(i_0_13205,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_7594]),
    [final] ).

cnf(i_0_13206,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_7595,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_13207,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_7596,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_13208,plain,
    ( X2 = hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk479_2(X2,X1)),esk479_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_7597,c_0_6088]),
    [final] ).

cnf(i_0_13209,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X3))
    | hBOOL(hAPP(hAPP(c_Natural_Oevalc(X4),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X5,X4,X1)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7598]),
    [final] ).

cnf(i_0_13210,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X3))
    | hBOOL(hAPP(hAPP(c_Natural_Oevalc(X4),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X5,X4,X1)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7599]),
    [final] ).

cnf(i_0_13211,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X3))
    | hBOOL(hAPP(hAPP(c_Natural_Oevalc(X4),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X5,X4,X1)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7600]),
    [final] ).

cnf(i_0_13212,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_7601,c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_13213,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_7602]),
    [final] ).

cnf(i_0_13214,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_7545]),
    [final] ).

cnf(i_0_13215,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_7603,c_0_6088]),
    [final] ).

cnf(i_0_13216,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_7604,c_0_6088]),
    [final] ).

cnf(i_0_13217,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_7605]),
    [final] ).

cnf(i_0_13218,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_7606]),
    [final] ).

cnf(i_0_13219,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_7607]),
    [final] ).

cnf(i_0_13220,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_7608]),
    [final] ).

cnf(i_0_13221,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_7609]),
    [final] ).

cnf(i_0_13222,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk193_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_7610]),
    [final] ).

cnf(i_0_13223,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk201_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_7611]),
    [final] ).

cnf(i_0_13224,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_7612]),
    [final] ).

cnf(i_0_13225,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk138_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_7613]),
    [final] ).

cnf(i_0_13226,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_7614,c_0_6138]),
    [final] ).

cnf(i_0_13227,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_7490]),
    [final] ).

cnf(i_0_13228,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_7615,c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_13229,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_7616]),
    [final] ).

cnf(i_0_13230,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_6370]),
    [final] ).

cnf(i_0_13231,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_7617]),
    [final] ).

cnf(i_0_13232,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_7618]),
    [final] ).

cnf(i_0_13233,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_7619]),
    [final] ).

cnf(i_0_13234,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_7620]),
    [final] ).

cnf(i_0_13235,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk380_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),esk378_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_7347]),
    [final] ).

cnf(i_0_13236,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk379_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),esk378_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_7347]),
    [final] ).

cnf(i_0_13237,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_7621]),
    [final] ).

cnf(i_0_13238,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_6991]),
    [final] ).

cnf(i_0_13239,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_6992]),
    [final] ).

cnf(i_0_13240,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_7622]),
    [final] ).

cnf(i_0_13241,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk548_2(X2,X1)),esk549_2(X2,X1))),X2))
    | c_Relation_Osym(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7217]),
    [final] ).

cnf(i_0_13242,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk547_2(X2,X1)),esk546_2(X2,X1))),X2))
    | c_Relation_Oantisym(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7056]),
    [final] ).

cnf(i_0_13243,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk546_2(X2,X1)),esk547_2(X2,X1))),X2))
    | c_Relation_Oantisym(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7056]),
    [final] ).

cnf(i_0_13244,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk544_2(X2,X1)),esk545_2(X2,X1))),X2))
    | c_Relation_Otrans(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6926]),
    [final] ).

cnf(i_0_13245,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk543_2(X2,X1)),esk544_2(X2,X1))),X2))
    | c_Relation_Otrans(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6926]),
    [final] ).

cnf(i_0_13246,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk106_2(X2,X1)),esk106_2(X2,X1))),X2))
    | c_Relation_Oirrefl(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7623]),
    [final] ).

cnf(i_0_13247,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_7624]),
    [final] ).

cnf(i_0_13248,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),esk56_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_7625]),
    [final] ).

cnf(i_0_13249,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_7626]),
    [final] ).

cnf(i_0_13250,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_7627]),
    [final] ).

cnf(i_0_13251,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_7628]),
    [final] ).

cnf(i_0_13252,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_7629]),
    [final] ).

cnf(i_0_13253,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_7446]),
    [final] ).

cnf(i_0_13254,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_7447]),
    [final] ).

cnf(i_0_13255,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_7630]),
    [final] ).

cnf(i_0_13256,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_7631]),
    [final] ).

cnf(i_0_13257,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X3),X2),X4))
    | ~ hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X1,X3,X5)),X2),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7598]),
    [final] ).

cnf(i_0_13258,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X3),X2),X4))
    | ~ hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X1,X3,X5)),X2),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7599]),
    [final] ).

cnf(i_0_13259,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X3),X2),X4))
    | ~ hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X1,X3,X5)),X2),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7600]),
    [final] ).

cnf(i_0_13260,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_7038]),
    [final] ).

cnf(i_0_13261,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_7039]),
    [final] ).

cnf(i_0_13262,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_7632]),
    [final] ).

cnf(i_0_13263,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_7633]),
    [final] ).

cnf(i_0_13264,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_7099]),
    [final] ).

cnf(i_0_13265,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)),esk378_3(X1,X2,X3)),X2))
    | esk379_3(X1,X2,X3) != esk380_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_7347]),
    [final] ).

cnf(i_0_13266,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_7634]),
    [final] ).

cnf(i_0_13267,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_7635]),
    [final] ).

cnf(i_0_13268,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_7636]),
    [final] ).

cnf(i_0_13269,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_7637]),
    [final] ).

cnf(i_0_13270,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_7623]),
    [final] ).

cnf(i_0_13271,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_7638]),
    [final] ).

cnf(i_0_13272,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_7639]),
    [final] ).

cnf(i_0_13273,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_7446]),
    [final] ).

cnf(i_0_13274,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_7446]),
    [final] ).

cnf(i_0_13275,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_7447]),
    [final] ).

cnf(i_0_13276,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_7447]),
    [final] ).

cnf(i_0_13277,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_7640,c_0_6088]),
    [final] ).

cnf(i_0_13278,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_7641]),
    [final] ).

cnf(i_0_13279,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X3))
    | hBOOL(hAPP(X4,X2))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X4,X5,X1)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7598]),
    [final] ).

cnf(i_0_13280,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X3))
    | hBOOL(hAPP(X4,X2))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X4,X5,X1)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7599]),
    [final] ).

cnf(i_0_13281,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X3))
    | hBOOL(hAPP(X4,X2))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X4,X5,X1)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7600]),
    [final] ).

cnf(i_0_13282,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_7642]),
    [final] ).

cnf(i_0_13283,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_7643]),
    [final] ).

cnf(i_0_13284,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_7397]),
    [final] ).

cnf(i_0_13285,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_7398]),
    [final] ).

cnf(i_0_13286,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_7399]),
    [final] ).

cnf(i_0_13287,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),esk56_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_7625]),
    [final] ).

cnf(i_0_13288,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),esk400_2(X2,X1))),hAPP(hAPP(c_List_Onth(X1),X2),esk401_2(X2,X1))))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7644]),
    [final] ).

cnf(i_0_13289,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),esk396_2(X2,X1))),hAPP(hAPP(c_List_Onth(X1),X2),esk395_2(X2,X1))))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7645]),
    [final] ).

cnf(i_0_13290,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_6485]),
    [final] ).

cnf(i_0_13291,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_7646]),
    [final] ).

cnf(i_0_13292,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_7647]),
    [final] ).

cnf(i_0_13293,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_7648]),
    [final] ).

cnf(i_0_13294,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_7649]),
    [final] ).

cnf(i_0_13295,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_7650]),
    [final] ).

cnf(i_0_13296,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk572_3(X2,X1,X3))),esk573_3(X2,X1,X3))
    | X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk570_3(X2,X1,X3))),esk571_3(X2,X1,X3))
    | epred2_3(X3,X1,X2)
    | ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7651]),
    [final] ).

cnf(i_0_13297,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_7652]),
    [final] ).

cnf(i_0_13298,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),esk35_4(X3,X2,X1,X4)))
    | ~ hBOOL(hAPP(X4,X2))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X4,X1)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7171]),
    [final] ).

cnf(i_0_13299,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_7653,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_13300,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_7654,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_13301,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_7655,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_13302,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_7656,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_13303,plain,
    ( hBOOL(hAPP(X1,X2))
    | X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(X1,esk516_4(X1,X2,X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_7240]),
    [final] ).

cnf(i_0_13304,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_7657]),
    [final] ).

cnf(i_0_13305,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_7658]),
    [final] ).

cnf(i_0_13306,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_7659]),
    [final] ).

cnf(i_0_13307,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_7660]),
    [final] ).

cnf(i_0_13308,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk568_3(X2,X1,X3))),esk569_3(X2,X1,X3))
    | X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk566_3(X2,X1,X3))),esk567_3(X2,X1,X3))
    | epred1_3(X3,X1,X2)
    | ~ hBOOL(hAPP(X3,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_7661]),
    [final] ).

cnf(i_0_13309,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_7662]),
    [final] ).

cnf(i_0_13310,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_7663]),
    [final] ).

cnf(i_0_13311,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk73_3(X1,X2,X3)),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk72_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_6270]),
    [final] ).

cnf(i_0_13312,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk71_3(X1,X2,X3)),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk70_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_6271]),
    [final] ).

cnf(i_0_13313,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_7664]),
    [final] ).

cnf(i_0_13314,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_7665]),
    [final] ).

cnf(i_0_13315,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_7666,c_0_6063]),
    [final] ).

cnf(i_0_13316,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_7667]),
    [final] ).

cnf(i_0_13317,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_7668]),
    [final] ).

cnf(i_0_13318,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_7669]),
    [final] ).

cnf(i_0_13319,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_7670]),
    [final] ).

cnf(i_0_13320,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_7671]),
    [final] ).

cnf(i_0_13321,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_7672]),
    [final] ).

cnf(i_0_13322,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_7673]),
    [final] ).

cnf(i_0_13323,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_7532]),
    [final] ).

cnf(i_0_13324,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_7532]),
    [final] ).

cnf(i_0_13325,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_7674]),
    [final] ).

cnf(i_0_13326,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_7675]),
    [final] ).

cnf(i_0_13327,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_7676,c_0_6281]),
    [final] ).

cnf(i_0_13328,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_7677]),
    [final] ).

cnf(i_0_13329,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_7135]),
    [final] ).

cnf(i_0_13330,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_7136]),
    [final] ).

cnf(i_0_13331,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_7678,c_0_6178]),
    [final] ).

cnf(i_0_13332,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_7418]),
    [final] ).

cnf(i_0_13333,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_7679]),
    [final] ).

cnf(i_0_13334,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_7680,c_0_6181]),
    [final] ).

cnf(i_0_13335,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),esk35_4(X3,X2,X1,X4)))
    | X3 = X2
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X4,X1)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7171]),
    [final] ).

cnf(i_0_13336,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,esk56_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_7625]),
    [final] ).

cnf(i_0_13337,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_7681]),
    [final] ).

cnf(i_0_13338,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),esk7_4(X3,X2,X4,X1)))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(X1,X4)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7251]),
    [final] ).

cnf(i_0_13339,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),esk6_4(X3,X2,X4,X1)))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(X1,X4)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7252]),
    [final] ).

cnf(i_0_13340,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_7682]),
    [final] ).

cnf(i_0_13341,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk572_3(X2,X1,X3))),esk573_3(X2,X1,X3))
    | X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk570_3(X2,X1,X3))),esk571_3(X2,X1,X3))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7651]),
    [final] ).

cnf(i_0_13342,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk568_3(X2,X1,X3))),esk569_3(X2,X1,X3))
    | X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk566_3(X2,X1,X3))),esk567_3(X2,X1,X3))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7661]),
    [final] ).

cnf(i_0_13343,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_7683,c_0_6713]),c_0_6713]),c_0_6713]),
    [final] ).

cnf(i_0_13344,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk52_3(X1,X3,X2))),esk53_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_7489]),
    [final] ).

cnf(i_0_13345,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_7532]),
    [final] ).

cnf(i_0_13346,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_7277]),
    [final] ).

cnf(i_0_13347,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_7277]),
    [final] ).

cnf(i_0_13348,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_7684,c_0_6178]),
    [final] ).

cnf(i_0_13349,plain,
    ( hBOOL(hAPP(X1,esk209_2(X1,X2)))
    | hBOOL(hAPP(X1,esk207_2(X1,X2)))
    | hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk207_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk208_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_7180]),
    [final] ).

cnf(i_0_13350,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_7685]),
    [final] ).

cnf(i_0_13351,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_7686]),
    [final] ).

cnf(i_0_13352,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk54_3(X1,X3,X2))),esk55_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_7496]),
    [final] ).

cnf(i_0_13353,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_7687]),
    [final] ).

cnf(i_0_13354,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_7688]),
    [final] ).

cnf(i_0_13355,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_7689]),
    [final] ).

cnf(i_0_13356,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_7690]),
    [final] ).

cnf(i_0_13357,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_7691]),
    [final] ).

cnf(i_0_13358,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_7692]),
    [final] ).

cnf(i_0_13359,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,esk411_4(X3,X2,X1,X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7229]),
    [final] ).

cnf(i_0_13360,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_7693,c_0_7563]),
    [final] ).

cnf(i_0_13361,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_7694]),
    [final] ).

cnf(i_0_13362,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_7694]),
    [final] ).

cnf(i_0_13363,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,esk56_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_7625]),
    [final] ).

cnf(i_0_13364,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_7695]),
    [final] ).

cnf(i_0_13365,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_7696]),
    [final] ).

cnf(i_0_13366,plain,
    ( hBOOL(hAPP(X1,esk381_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_7387]),
    [final] ).

cnf(i_0_13367,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_7625]),
    [final] ).

cnf(i_0_13368,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_7697]),
    [final] ).

cnf(i_0_13369,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_7259]),
    [final] ).

cnf(i_0_13370,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_6940]),
    [final] ).

cnf(i_0_13371,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_7698]),
    [final] ).

cnf(i_0_13372,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_7699]),
    [final] ).

cnf(i_0_13373,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_7700]),
    [final] ).

cnf(i_0_13374,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_7701]),
    [final] ).

cnf(i_0_13375,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_7702]),
    [final] ).

cnf(i_0_13376,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_7703]),
    [final] ).

cnf(i_0_13377,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_7704,c_0_6713]),c_0_6713]),
    [final] ).

cnf(i_0_13378,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_7475]),
    [final] ).

cnf(i_0_13379,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_7705]),
    [final] ).

cnf(i_0_13380,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_7706]),
    [final] ).

cnf(i_0_13381,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_7707]),
    [final] ).

cnf(i_0_13382,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_7708]),
    [final] ).

cnf(i_0_13383,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_7709]),
    [final] ).

cnf(i_0_13384,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_7410]),
    [final] ).

cnf(i_0_13385,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_7063]),
    [final] ).

cnf(i_0_13386,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_7064]),
    [final] ).

cnf(i_0_13387,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X4),X3)),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_7710]),
    [final] ).

cnf(i_0_13388,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_7710]),
    [final] ).

cnf(i_0_13389,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_7711]),
    [final] ).

cnf(i_0_13390,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_7711]),
    [final] ).

cnf(i_0_13391,plain,
    ( c_Natural_Oevaln(X1,esk13_4(X2,X1,X3,X4),X4,esk14_4(X2,X1,X3,X4))
    | c_Hoare__Mirabelle_Otriple__valid(X5,X4,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X5),X3),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6855]),
    [final] ).

cnf(i_0_13392,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_7712,c_0_6088]),
    [final] ).

cnf(i_0_13393,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_7713]),
    [final] ).

cnf(i_0_13394,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_6759]),
    [final] ).

cnf(i_0_13395,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_7714]),
    [final] ).

cnf(i_0_13396,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_7715]),
    [final] ).

cnf(i_0_13397,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_7716]),
    [final] ).

cnf(i_0_13398,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_7717]),
    [final] ).

cnf(i_0_13399,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_7718,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_13400,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_7719]),
    [final] ).

cnf(i_0_13401,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_7720,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_13402,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_7721,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_13403,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_7722,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_13404,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_7723,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_13405,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_7724]),
    [final] ).

cnf(i_0_13406,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin))),c_Int_OMin) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7725,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6216]),c_0_6216]),c_0_6216]),c_0_6064]),
    [final] ).

cnf(i_0_13407,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_7726]),
    [final] ).

cnf(i_0_13408,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_7727]),
    [final] ).

cnf(i_0_13409,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_7728,c_0_6097]),
    [final] ).

cnf(i_0_13410,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk194_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_7610]),
    [final] ).

cnf(i_0_13411,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk202_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_7611]),
    [final] ).

cnf(i_0_13412,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_7677]),
    [final] ).

cnf(i_0_13413,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_7729]),
    [final] ).

cnf(i_0_13414,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_7730]),
    [final] ).

cnf(i_0_13415,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_7731]),
    [final] ).

cnf(i_0_13416,plain,
    ( hBOOL(hAPP(X2,X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),esk514_3(X2,X3,X1)),esk515_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_7220]),
    [final] ).

cnf(i_0_13417,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_7732]),
    [final] ).

cnf(i_0_13418,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_7733,c_0_6088]),
    [final] ).

cnf(i_0_13419,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_7734]),
    [final] ).

cnf(i_0_13420,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_7735]),
    [final] ).

cnf(i_0_13421,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_7736]),
    [final] ).

cnf(i_0_13422,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_7737]),
    [final] ).

cnf(i_0_13423,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_7738]),
    [final] ).

cnf(i_0_13424,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_7739]),
    [final] ).

cnf(i_0_13425,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_7740]),
    [final] ).

cnf(i_0_13426,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_7741]),
    [final] ).

cnf(i_0_13427,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_7742]),
    [final] ).

cnf(i_0_13428,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_7743]),
    [final] ).

cnf(i_0_13429,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_7744,c_0_6281]),
    [final] ).

cnf(i_0_13430,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_7745]),
    [final] ).

cnf(i_0_13431,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_7746]),
    [final] ).

cnf(i_0_13432,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_7747]),
    [final] ).

cnf(i_0_13433,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_7748]),
    [final] ).

cnf(i_0_13434,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_7749,c_0_6138]),
    [final] ).

cnf(i_0_13435,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,esk463_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_7203]),
    [final] ).

cnf(i_0_13436,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_7731]),
    [final] ).

cnf(i_0_13437,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_7750]),
    [final] ).

cnf(i_0_13438,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_7751]),
    [final] ).

cnf(i_0_13439,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_7752]),
    [final] ).

cnf(i_0_13440,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_7753]),
    [final] ).

cnf(i_0_13441,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_7754]),
    [final] ).

cnf(i_0_13442,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_7755]),
    [final] ).

cnf(i_0_13443,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_7756]),
    [final] ).

cnf(i_0_13444,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_7757]),
    [final] ).

cnf(i_0_13445,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_7758]),
    [final] ).

cnf(i_0_13446,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_7759]),
    [final] ).

cnf(i_0_13447,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_7760]),
    [final] ).

cnf(i_0_13448,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_7761]),
    [final] ).

cnf(i_0_13449,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_7762,c_0_6138]),
    [final] ).

cnf(i_0_13450,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_7763]),
    [final] ).

cnf(i_0_13451,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_7731]),
    [final] ).

cnf(i_0_13452,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk265_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_7764]),
    [final] ).

cnf(i_0_13453,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk263_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_7765]),
    [final] ).

cnf(i_0_13454,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),esk263_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_7765]),
    [final] ).

cnf(i_0_13455,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),esk265_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_7764]),
    [final] ).

cnf(i_0_13456,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_6489]),
    [final] ).

cnf(i_0_13457,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_7766]),
    [final] ).

cnf(i_0_13458,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_7767]),
    [final] ).

cnf(i_0_13459,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_7768]),
    [final] ).

cnf(i_0_13460,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_7769]),
    [final] ).

cnf(i_0_13461,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_7770]),
    [final] ).

cnf(i_0_13462,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_7771]),
    [final] ).

cnf(i_0_13463,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_7772]),
    [final] ).

cnf(i_0_13464,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_7773]),
    [final] ).

cnf(i_0_13465,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X1)),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1))),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7774]),
    [final] ).

cnf(i_0_13466,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X1)),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1))),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7775]),
    [final] ).

cnf(i_0_13467,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_7557]),
    [final] ).

cnf(i_0_13468,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_7558]),
    [final] ).

cnf(i_0_13469,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_7776,c_0_6088]),
    [final] ).

cnf(i_0_13470,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_7777]),
    [final] ).

cnf(i_0_13471,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_7356]),
    [final] ).

cnf(i_0_13472,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_7778]),
    [final] ).

cnf(i_0_13473,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,esk271_3(X1,X2,X3))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7779]),
    [final] ).

cnf(i_0_13474,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,esk143_3(X1,X2,X3))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7780]),
    [final] ).

cnf(i_0_13475,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_7781]),
    [final] ).

cnf(i_0_13476,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_7782]),
    [final] ).

cnf(i_0_13477,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_7783]),
    [final] ).

cnf(i_0_13478,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_7784]),
    [final] ).

cnf(i_0_13479,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_7785]),
    [final] ).

cnf(i_0_13480,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_7786]),
    [final] ).

cnf(i_0_13481,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_7061]),
    [final] ).

cnf(i_0_13482,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_5319]),
    [final] ).

cnf(i_0_13483,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_7787]),
    [final] ).

cnf(i_0_13484,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_7788]),
    [final] ).

cnf(i_0_13485,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_7789]),
    [final] ).

cnf(i_0_13486,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_7790]),
    [final] ).

cnf(i_0_13487,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_7791]),
    [final] ).

cnf(i_0_13488,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_7792]),
    [final] ).

cnf(i_0_13489,plain,
    ( X1 = hAPP(X2,esk108_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_7115]),
    [final] ).

cnf(i_0_13490,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_7793]),
    [final] ).

cnf(i_0_13491,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_7500]),
    [final] ).

cnf(i_0_13492,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_7794]),
    [final] ).

cnf(i_0_13493,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_6564]),
    [final] ).

cnf(i_0_13494,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_7795]),
    [final] ).

cnf(i_0_13495,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_7796]),
    [final] ).

cnf(i_0_13496,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_7797,c_0_6178]),
    [final] ).

cnf(i_0_13497,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_7798,c_0_6088]),
    [final] ).

cnf(i_0_13498,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_7799,c_0_6088]),
    [final] ).

cnf(i_0_13499,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_7800]),
    [final] ).

cnf(i_0_13500,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_7801]),
    [final] ).

cnf(i_0_13501,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_7802]),
    [final] ).

cnf(i_0_13502,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_7802]),
    [final] ).

cnf(i_0_13503,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_7803]),
    [final] ).

cnf(i_0_13504,plain,
    ( hBOOL(hAPP(X1,esk522_4(X2,X1,X3,X4)))
    | c_List_Olist__ex1(X3,X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(X3),X4),hAPP(c_List_Oset(X3),X2)))
    | ~ hBOOL(hAPP(X1,X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7260]),
    [final] ).

cnf(i_0_13505,plain,
    ( hBOOL(hAPP(X1,esk511_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_7261]),
    [final] ).

cnf(i_0_13506,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_7804,c_0_6088]),
    [final] ).

cnf(i_0_13507,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_7805,c_0_6088]),
    [final] ).

cnf(i_0_13508,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_6988]),
    [final] ).

cnf(i_0_13509,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_6989]),
    [final] ).

cnf(i_0_13510,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk573_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk570_3(X1,X2,X3))),esk571_3(X1,X2,X3))
    | epred2_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7651]),
    [final] ).

cnf(i_0_13511,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_7806,c_0_6281]),
    [final] ).

cnf(i_0_13512,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_7807]),
    [final] ).

cnf(i_0_13513,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk572_3(X2,X1,X3))),esk573_3(X2,X1,X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk571_3(X2,X1,X3)),X2))
    | epred2_3(X3,X1,X2)
    | ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7651]),
    [final] ).

cnf(i_0_13514,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_7099]),
    [final] ).

cnf(i_0_13515,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk569_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk566_3(X1,X2,X3))),esk567_3(X1,X2,X3))
    | epred1_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7661]),
    [final] ).

cnf(i_0_13516,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_7808]),
    [final] ).

cnf(i_0_13517,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_7809]),
    [final] ).

cnf(i_0_13518,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_7810]),
    [final] ).

cnf(i_0_13519,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_7811]),
    [final] ).

cnf(i_0_13520,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_7812]),
    [final] ).

cnf(i_0_13521,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_7813,c_0_6088]),
    [final] ).

cnf(i_0_13522,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_7814]),
    [final] ).

cnf(i_0_13523,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_7815]),
    [final] ).

cnf(i_0_13524,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_7816]),
    [final] ).

cnf(i_0_13525,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_7817]),
    [final] ).

cnf(i_0_13526,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_7818]),
    [final] ).

cnf(i_0_13527,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk568_3(X2,X1,X3))),esk569_3(X2,X1,X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk567_3(X2,X1,X3)),X2))
    | epred1_3(X3,X1,X2)
    | ~ hBOOL(hAPP(X3,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_7661]),
    [final] ).

cnf(i_0_13528,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_7819]),
    [final] ).

cnf(i_0_13529,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_7820]),
    [final] ).

cnf(i_0_13530,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_7821]),
    [final] ).

cnf(i_0_13531,plain,
    ( c_Fun_Oinj__on(X1,X2,esk221_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_6617]),
    [final] ).

cnf(i_0_13532,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_7822]),
    [final] ).

cnf(i_0_13533,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_7823]),
    [final] ).

cnf(i_0_13534,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_7824,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_13535,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_7825]),
    [final] ).

cnf(i_0_13536,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_7826]),
    [final] ).

cnf(i_0_13537,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_7827]),
    [final] ).

cnf(i_0_13538,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_7815]),
    [final] ).

cnf(i_0_13539,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_7814]),
    [final] ).

cnf(i_0_13540,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_7828]),
    [final] ).

cnf(i_0_13541,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_7829]),
    [final] ).

cnf(i_0_13542,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_7830]),
    [final] ).

cnf(i_0_13543,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_7831]),
    [final] ).

cnf(i_0_13544,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_7832]),
    [final] ).

cnf(i_0_13545,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_7833]),
    [final] ).

cnf(i_0_13546,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk412_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_7573]),
    [final] ).

cnf(i_0_13547,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_7834,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_13548,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_7814]),
    [final] ).

cnf(i_0_13549,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_7815]),
    [final] ).

cnf(i_0_13550,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_7835]),
    [final] ).

cnf(i_0_13551,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_7836]),
    [final] ).

cnf(i_0_13552,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_7677]),
    [final] ).

cnf(i_0_13553,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_7837]),
    [final] ).

cnf(i_0_13554,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_7838]),
    [final] ).

cnf(i_0_13555,plain,
    ( hBOOL(hAPP(X1,X4))
    | ~ hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),esk324_3(X1,X3,X2))))
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7839]),
    [final] ).

cnf(i_0_13556,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_7840]),
    [final] ).

cnf(i_0_13557,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_7472]),
    [final] ).

cnf(i_0_13558,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_7841,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_13559,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_7842,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_13560,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_7815]),
    [final] ).

cnf(i_0_13561,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_7814]),
    [final] ).

cnf(i_0_13562,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_7560]),
    [final] ).

cnf(i_0_13563,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_7561]),
    [final] ).

cnf(i_0_13564,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_7843,c_0_6097]),
    [final] ).

cnf(i_0_13565,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk573_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk570_3(X1,X2,X3))),esk571_3(X1,X2,X3))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7651]),
    [final] ).

cnf(i_0_13566,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk569_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk566_3(X1,X2,X3))),esk567_3(X1,X2,X3))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7661]),
    [final] ).

cnf(i_0_13567,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_6439]),
    [final] ).

cnf(i_0_13568,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),esk392_3(X2,X3,X1)),esk393_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_7844]),
    [final] ).

cnf(i_0_13569,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_7845]),
    [final] ).

cnf(i_0_13570,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk572_3(X2,X1,X3))),esk573_3(X2,X1,X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk571_3(X2,X1,X3)),X2))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7651]),
    [final] ).

cnf(i_0_13571,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk568_3(X2,X1,X3))),esk569_3(X2,X1,X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk567_3(X2,X1,X3)),X2))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7661]),
    [final] ).

cnf(i_0_13572,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_7135]),
    [final] ).

cnf(i_0_13573,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_7136]),
    [final] ).

cnf(i_0_13574,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_7846]),
    [final] ).

cnf(i_0_13575,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_7847]),
    [final] ).

cnf(i_0_13576,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk53_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_7489]),
    [final] ).

cnf(i_0_13577,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_7848]),
    [final] ).

cnf(i_0_13578,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_7446]),
    [final] ).

cnf(i_0_13579,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_7447]),
    [final] ).

cnf(i_0_13580,plain,
    ( c_Hoare__Mirabelle_Otriple__valid(X1,hAPP(c_Nat_OSuc,X2),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),hAPP(c_Com_Ocom_OBODY,X4)),X5))
    | ~ c_Hoare__Mirabelle_Otriple__valid(X1,X2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X4))),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_7849]),
    [final] ).

cnf(i_0_13581,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_7850]),
    [final] ).

cnf(i_0_13582,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_7851]),
    [final] ).

cnf(i_0_13583,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk55_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_7496]),
    [final] ).

cnf(i_0_13584,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk194_3(X2,X1,X3)),esk193_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_7610]),
    [final] ).

cnf(i_0_13585,plain,
    ( X1 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk202_3(X2,X1,X3)),esk201_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_7611]),
    [final] ).

cnf(i_0_13586,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_7852]),
    [final] ).

cnf(i_0_13587,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_7853]),
    [final] ).

cnf(i_0_13588,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_7854]),
    [final] ).

cnf(i_0_13589,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_7557]),
    [final] ).

cnf(i_0_13590,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_7446]),
    [final] ).

cnf(i_0_13591,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_7855]),
    [final] ).

cnf(i_0_13592,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_7856]),
    [final] ).

cnf(i_0_13593,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_7857]),
    [final] ).

cnf(i_0_13594,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_7558]),
    [final] ).

cnf(i_0_13595,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_7447]),
    [final] ).

cnf(i_0_13596,plain,
    ( X2 = hAPP(c_Set_Oimage(tc_Nat_Onat,X1,esk295_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)),esk294_2(X2,X1))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7567]),
    [final] ).

cnf(i_0_13597,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_7800]),
    [final] ).

cnf(i_0_13598,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_7858]),
    [final] ).

cnf(i_0_13599,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_7487]),
    [final] ).

cnf(i_0_13600,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_7488]),
    [final] ).

cnf(i_0_13601,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk334_3(X2,X3,X1)),X3))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk333_3(X2,X3,X1)),X2))
    | c_Relation_Orefl__on(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6184]),
    [final] ).

cnf(i_0_13602,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_7859]),
    [final] ).

cnf(i_0_13603,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_7860]),
    [final] ).

cnf(i_0_13604,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_7633]),
    [final] ).

cnf(i_0_13605,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_7861,c_0_6713]),
    [final] ).

cnf(i_0_13606,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_7862,c_0_6138]),
    [final] ).

cnf(i_0_13607,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_7863,c_0_6138]),
    [final] ).

cnf(i_0_13608,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_7864]),
    [final] ).

cnf(i_0_13609,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_7865]),
    [final] ).

cnf(i_0_13610,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_7866]),
    [final] ).

cnf(i_0_13611,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_7867]),
    [final] ).

cnf(i_0_13612,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_7868]),
    [final] ).

cnf(i_0_13613,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_7869]),
    [final] ).

cnf(i_0_13614,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_7816]),
    [final] ).

cnf(i_0_13615,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_7870]),
    [final] ).

cnf(i_0_13616,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_7871]),
    [final] ).

cnf(i_0_13617,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_7872]),
    [final] ).

cnf(i_0_13618,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_7873]),
    [final] ).

cnf(i_0_13619,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_7874,c_0_6181]),c_0_6181]),c_0_6181]),
    [final] ).

cnf(i_0_13620,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_7875]),
    [final] ).

cnf(i_0_13621,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_7876]),
    [final] ).

cnf(i_0_13622,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_5320]),
    [final] ).

cnf(i_0_13623,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_7490]),
    [final] ).

cnf(i_0_13624,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_7877]),
    [final] ).

cnf(i_0_13625,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_7878]),
    [final] ).

cnf(i_0_13626,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)),esk373_3(X2,X3,X1)),esk374_3(X2,X3,X1)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_7550]),
    [final] ).

cnf(i_0_13627,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_7879]),
    [final] ).

cnf(i_0_13628,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_7880]),
    [final] ).

cnf(i_0_13629,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_7881]),
    [final] ).

cnf(i_0_13630,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_6184]),
    [final] ).

cnf(i_0_13631,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_6666]),
    [final] ).

cnf(i_0_13632,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_7882]),
    [final] ).

cnf(i_0_13633,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_7883]),
    [final] ).

cnf(i_0_13634,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_7884]),
    [final] ).

cnf(i_0_13635,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X2)),esk34_3(X3,X2,X1)),X3))
    | ~ hBOOL(hAPP(X1,X3))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X2)),X3),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7885]),
    [final] ).

cnf(i_0_13636,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_7886]),
    [final] ).

cnf(i_0_13637,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_7887]),
    [final] ).

cnf(i_0_13638,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_6759]),
    [final] ).

cnf(i_0_13639,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_7638]),
    [final] ).

cnf(i_0_13640,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_7888]),
    [final] ).

cnf(i_0_13641,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_7889]),
    [final] ).

cnf(i_0_13642,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_7890]),
    [final] ).

cnf(i_0_13643,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_7891,c_0_6281]),
    [final] ).

cnf(i_0_13644,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),esk69_3(X3,X2,X1))))
    | ~ class_Fields_Olinordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7892]),
    [final] ).

cnf(i_0_13645,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_7585]),
    [final] ).

cnf(i_0_13646,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_7893]),
    [final] ).

cnf(i_0_13647,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_7894]),
    [final] ).

cnf(i_0_13648,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_7895]),
    [final] ).

cnf(i_0_13649,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_7896]),
    [final] ).

cnf(i_0_13650,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_7897]),
    [final] ).

cnf(i_0_13651,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_7898]),
    [final] ).

cnf(i_0_13652,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_7899]),
    [final] ).

cnf(i_0_13653,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_7900]),
    [final] ).

cnf(i_0_13654,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_7901]),
    [final] ).

cnf(i_0_13655,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_7902]),
    [final] ).

cnf(i_0_13656,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_7903]),
    [final] ).

cnf(i_0_13657,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_7904,c_0_6281]),
    [final] ).

cnf(i_0_13658,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_7905]),
    [final] ).

cnf(i_0_13659,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_7906]),
    [final] ).

cnf(i_0_13660,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_7546]),
    [final] ).

cnf(i_0_13661,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_7907]),
    [final] ).

cnf(i_0_13662,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_6991]),
    [final] ).

cnf(i_0_13663,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_6992]),
    [final] ).

cnf(i_0_13664,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_7908,c_0_6693]),
    [final] ).

cnf(i_0_13665,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_7909]),
    [final] ).

cnf(i_0_13666,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_7545]),
    [final] ).

cnf(i_0_13667,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_7910]),
    [final] ).

cnf(i_0_13668,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_7911]),
    [final] ).

cnf(i_0_13669,plain,
    ( hAPP(X1,esk215_4(X2,X1,X3,X4)) = hAPP(X1,esk216_4(X2,X1,X3,X4))
    | c_Fun_Oinj__on(X4,X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7322]),
    [final] ).

cnf(i_0_13670,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_7554]),
    [final] ).

cnf(i_0_13671,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_7912]),
    [final] ).

cnf(i_0_13672,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_13673,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_7913]),
    [final] ).

cnf(i_0_13674,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_7914]),
    [final] ).

cnf(i_0_13675,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_7915]),
    [final] ).

cnf(i_0_13676,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_7916]),
    [final] ).

cnf(i_0_13677,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_7917]),
    [final] ).

cnf(i_0_13678,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_7918]),
    [final] ).

cnf(i_0_13679,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_7919]),
    [final] ).

cnf(i_0_13680,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_7920]),
    [final] ).

cnf(i_0_13681,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk572_3(X2,X1,X3))),esk573_3(X2,X1,X3))
    | epred2_3(X3,X1,X2)
    | ~ hBOOL(hAPP(X3,esk570_3(X2,X1,X3)))
    | ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7651]),
    [final] ).

cnf(i_0_13682,plain,
    ( X3 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk570_3(X2,X3,X1))),esk571_3(X2,X3,X1))
    | epred2_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk572_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7651]),
    [final] ).

cnf(i_0_13683,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_7921]),
    [final] ).

cnf(i_0_13684,plain,
    c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),c_Com_Ocom_OSKIP),X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool)))),
    inference(split_conjunct,[status(thm)],[i_0_7922]),
    [final] ).

cnf(i_0_13685,plain,
    c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),c_Com_Ocom_OSKIP),X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool)))),
    inference(split_conjunct,[status(thm)],[i_0_7923]),
    [final] ).

cnf(i_0_13686,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_7924]),
    [final] ).

cnf(i_0_13687,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_6566]),
    [final] ).

cnf(i_0_13688,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_7925]),
    [final] ).

cnf(i_0_13689,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_7926]),
    [final] ).

cnf(i_0_13690,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_7927]),
    [final] ).

cnf(i_0_13691,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_7928]),
    [final] ).

cnf(i_0_13692,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_7929,c_0_6281]),
    [final] ).

cnf(i_0_13693,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_7930]),
    [final] ).

cnf(i_0_13694,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk568_3(X2,X1,X3))),esk569_3(X2,X1,X3))
    | epred1_3(X3,X1,X2)
    | ~ hBOOL(hAPP(X3,esk567_3(X2,X1,X3)))
    | ~ hBOOL(hAPP(X3,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_7661]),
    [final] ).

cnf(i_0_13695,plain,
    ( X3 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk566_3(X2,X3,X1))),esk567_3(X2,X3,X1))
    | epred1_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk569_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7661]),
    [final] ).

cnf(i_0_13696,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),esk484_3(X3,X2,X1))))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7931]),
    [final] ).

cnf(i_0_13697,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),esk481_3(X3,X2,X1))))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7932]),
    [final] ).

cnf(i_0_13698,plain,
    ( c_Hoare__Mirabelle_Otriple__valid(X1,X2,X5)
    | ~ c_Hoare__Mirabelle_Otriple__valid(X1,X2,esk336_4(X3,X4,X1,X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X1)),X5),X3))
    | ~ c_Hoare__Mirabelle_Ohoare__valids(X1,X4,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7271]),
    [final] ).

cnf(i_0_13699,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_7933,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_13700,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_7934]),
    [final] ).

cnf(i_0_13701,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_7935]),
    [final] ).

cnf(i_0_13702,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_7936]),
    [final] ).

cnf(i_0_13703,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_7937]),
    [final] ).

cnf(i_0_13704,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_7938]),
    [final] ).

cnf(i_0_13705,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_7939]),
    [final] ).

cnf(i_0_13706,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_7940]),
    [final] ).

cnf(i_0_13707,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_7941]),
    [final] ).

cnf(i_0_13708,plain,
    ( c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X2),esk33_4(X3,X4,X2,X1),X3,X4)
    | ~ hBOOL(hAPP(X1,X4))
    | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X2),X4,X3,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_7942]),
    [final] ).

cnf(i_0_13709,plain,
    ( c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1)),X2,esk8_4(X3,X4,X2,X1),X3)
    | ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X1),X2,X4,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7943]),
    [final] ).

cnf(i_0_13710,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_7944]),
    [final] ).

cnf(i_0_13711,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_7645]),
    [final] ).

cnf(i_0_13712,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_13713,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_7945]),
    [final] ).

cnf(i_0_13714,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_7946]),
    [final] ).

cnf(i_0_13715,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_7947]),
    [final] ).

cnf(i_0_13716,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_7948]),
    [final] ).

cnf(i_0_13717,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_7826]),
    [final] ).

cnf(i_0_13718,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_7949,c_0_6063]),
    [final] ).

cnf(i_0_13719,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_7950,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_13720,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_7951]),
    [final] ).

cnf(i_0_13721,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_6759]),
    [final] ).

cnf(i_0_13722,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_7952]),
    [final] ).

cnf(i_0_13723,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_7953]),
    [final] ).

cnf(i_0_13724,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_7954]),
    [final] ).

cnf(i_0_13725,plain,
    ( hBOOL(hAPP(X1,esk100_4(X1,X2,X3,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(X4),X5),X2))
    | ~ hBOOL(hAPP(X1,X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6828]),
    [final] ).

cnf(i_0_13726,plain,
    ( hBOOL(hAPP(X1,esk100_4(X1,X2,X3,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(X4),X5),X3))
    | ~ hBOOL(hAPP(X1,X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6828]),
    [final] ).

cnf(i_0_13727,plain,
    c_Fun_Ofun__upd(X1,X2,X3,X4,hAPP(X3,X4)) = X3,
    inference(split_conjunct,[status(thm)],[i_0_7955]),
    [final] ).

cnf(i_0_13728,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_7956,c_0_6693]),
    [final] ).

cnf(i_0_13729,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_7957,c_0_7958]),c_0_7959]),c_0_7959]),
    [final] ).

cnf(i_0_13730,plain,
    ( c_Fun_Ofun__upd(X4,X5,X1,X2,X3) = X1
    | hAPP(X1,X2) != X3 ),
    inference(split_conjunct,[status(thm)],[i_0_7960]),
    [final] ).

cnf(i_0_13731,plain,
    ( c_Fun_Ofun__upd(X4,X5,X1,X2,X3) = X1
    | hAPP(X1,X2) != X3 ),
    inference(split_conjunct,[status(thm)],[i_0_7512]),
    [final] ).

cnf(i_0_13732,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),esk139_3(X2,X3,X1)),esk140_3(X2,X3,X1)))
    | hAPP(c_Finite__Set_Ocard(X1),X3) != hAPP(c_Nat_OSuc,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7961]),
    [final] ).

cnf(i_0_13733,plain,
    ( c_Hoare__Mirabelle_Otriple__valid(X1,X2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X4))),X5))
    | ~ c_Hoare__Mirabelle_Otriple__valid(X1,hAPP(c_Nat_OSuc,X2),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),hAPP(c_Com_Ocom_OBODY,X4)),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_7849]),
    [final] ).

cnf(i_0_13734,plain,
    ( hAPP(X1,esk73_3(X2,X1,X3)) = X2
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk72_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_6270]),
    [final] ).

cnf(i_0_13735,plain,
    ( hAPP(X1,esk71_3(X2,X1,X3)) = X2
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk70_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_6271]),
    [final] ).

cnf(i_0_13736,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_7962]),
    [final] ).

cnf(i_0_13737,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_7963]),
    [final] ).

cnf(i_0_13738,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_7964]),
    [final] ).

cnf(i_0_13739,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_7965]),
    [final] ).

cnf(i_0_13740,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_7966]),
    [final] ).

cnf(i_0_13741,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_7967]),
    [final] ).

cnf(i_0_13742,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_7968]),
    [final] ).

cnf(i_0_13743,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_7969]),
    [final] ).

cnf(i_0_13744,plain,
    ( c_Natural_Oevaln(X1,X2,X3,esk33_4(X3,X2,X1,X4))
    | ~ hBOOL(hAPP(X4,X2))
    | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X4,X1),X2,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7942]),
    [final] ).

cnf(i_0_13745,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),esk398_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2))) ),
    inference(rw,[status(thm)],[i_0_7970,c_0_6281]),
    [final] ).

cnf(i_0_13746,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_7513]),
    [final] ).

cnf(i_0_13747,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_7514]),
    [final] ).

cnf(i_0_13748,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_7853]),
    [final] ).

cnf(i_0_13749,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_7971]),
    [final] ).

cnf(i_0_13750,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_7446]),
    [final] ).

cnf(i_0_13751,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_7852]),
    [final] ).

cnf(i_0_13752,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_7557]),
    [final] ).

cnf(i_0_13753,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_7856]),
    [final] ).

cnf(i_0_13754,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_7972]),
    [final] ).

cnf(i_0_13755,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_7447]),
    [final] ).

cnf(i_0_13756,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_7855]),
    [final] ).

cnf(i_0_13757,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_7558]),
    [final] ).

cnf(i_0_13758,plain,
    ( c_Fun_Obij__betw(X3,X3,c_Fun_Oid(X3),X1,X2)
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_7515]),
    [final] ).

cnf(i_0_13759,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_7973]),
    [final] ).

cnf(i_0_13760,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_7974]),
    [final] ).

cnf(i_0_13761,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_7532]),
    [final] ).

cnf(i_0_13762,plain,
    ( X3 = X2
    | ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),c_fequal),esk332_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_7248]),
    [final] ).

cnf(i_0_13763,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_7975]),
    [final] ).

cnf(i_0_13764,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_7976]),
    [final] ).

cnf(i_0_13765,plain,
    c_Fun_Obij__betw(X1,X1,c_Fun_Oid(X1),X2,X2),
    inference(split_conjunct,[status(thm)],[i_0_7977]),
    [final] ).

cnf(i_0_13766,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_7978]),
    [final] ).

cnf(i_0_13767,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_7979]),
    [final] ).

cnf(i_0_13768,plain,
    ( c_List_Olist__all2(X3,X3,c_fequal,X1,X2)
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_7520]),
    [final] ).

cnf(i_0_13769,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_7816]),
    [final] ).

cnf(i_0_13770,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk572_3(X2,X1,X3))),esk573_3(X2,X1,X3))
    | X2 = 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_7651]),
    [final] ).

cnf(i_0_13771,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk568_3(X2,X1,X3))),esk569_3(X2,X1,X3))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X3,X1,X2)
    | ~ hBOOL(hAPP(X3,esk567_3(X2,X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7661]),
    [final] ).

cnf(i_0_13772,plain,
    ( X3 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk570_3(X2,X3,X1))),esk571_3(X2,X3,X1))
    | X2 = 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_7651]),
    [final] ).

cnf(i_0_13773,plain,
    ( X3 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk566_3(X2,X3,X1))),esk567_3(X2,X3,X1))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk569_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_7661]),
    [final] ).

cnf(i_0_13774,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_7980,c_0_6693]),
    [final] ).

cnf(i_0_13775,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_7981]),
    [final] ).

cnf(i_0_13776,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_7982]),
    [final] ).

cnf(i_0_13777,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_7983]),
    [final] ).

cnf(i_0_13778,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_7984]),
    [final] ).

cnf(i_0_13779,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_7446]),
    [final] ).

cnf(i_0_13780,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_7447]),
    [final] ).

cnf(i_0_13781,plain,
    ( hBOOL(hAPP(X1,esk66_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_7234]),
    [final] ).

cnf(i_0_13782,plain,
    ( hBOOL(hAPP(X1,esk62_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_7235]),
    [final] ).

cnf(i_0_13783,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_7985]),
    [final] ).

cnf(i_0_13784,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_7986]),
    [final] ).

cnf(i_0_13785,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk572_3(X2,X1,X3))),esk573_3(X2,X1,X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk571_3(X2,X1,X3)))
    | epred2_3(X3,X1,X2)
    | ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7651]),
    [final] ).

cnf(i_0_13786,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_7987,c_0_6181]),c_0_6181]),
    [final] ).

cnf(i_0_13787,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk323_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_7839]),
    [final] ).

cnf(i_0_13788,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_7988]),
    [final] ).

cnf(i_0_13789,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_7989]),
    [final] ).

cnf(i_0_13790,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_7990]),
    [final] ).

cnf(i_0_13791,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_7991,c_0_6713]),c_0_6713]),
    [final] ).

cnf(i_0_13792,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_7992,c_0_6097]),c_0_6097]),
    [final] ).

cnf(i_0_13793,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1))),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X1)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7774]),
    [final] ).

cnf(i_0_13794,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1))),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X1)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7993]),
    [final] ).

cnf(i_0_13795,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk568_3(X2,X1,X3))),esk569_3(X2,X1,X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk567_3(X2,X1,X3)))
    | epred1_3(X3,X1,X2)
    | ~ hBOOL(hAPP(X3,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_7661]),
    [final] ).

cnf(i_0_13796,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,esk232_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_7281]),
    [final] ).

cnf(i_0_13797,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_7994]),
    [final] ).

cnf(i_0_13798,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_7995]),
    [final] ).

cnf(i_0_13799,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_7996]),
    [final] ).

cnf(i_0_13800,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_6988]),
    [final] ).

cnf(i_0_13801,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_6989]),
    [final] ).

cnf(i_0_13802,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk573_3(X1,X2,X3)))
    | X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk570_3(X1,X2,X3))),esk571_3(X1,X2,X3))
    | epred2_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7651]),
    [final] ).

cnf(i_0_13803,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_7997]),
    [final] ).

cnf(i_0_13804,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_7998]),
    [final] ).

cnf(i_0_13805,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_7999]),
    [final] ).

cnf(i_0_13806,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X1,X3,X5)),X2),X4))
    | ~ hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X3),X2),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7598]),
    [final] ).

cnf(i_0_13807,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X1,X3,X5)),X2),X4))
    | ~ hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X3),X2),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7599]),
    [final] ).

cnf(i_0_13808,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X1,X3,X5)),X2),X4))
    | ~ hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X3),X2),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8000]),
    [final] ).

cnf(i_0_13809,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_8001]),
    [final] ).

cnf(i_0_13810,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_8002]),
    [final] ).

cnf(i_0_13811,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_7903]),
    [final] ).

cnf(i_0_13812,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_7903]),
    [final] ).

cnf(i_0_13813,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_6791]),
    [final] ).

cnf(i_0_13814,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_8003]),
    [final] ).

cnf(i_0_13815,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk569_3(X1,X2,X3)))
    | X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk566_3(X1,X2,X3))),esk567_3(X1,X2,X3))
    | epred1_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7661]),
    [final] ).

cnf(i_0_13816,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_8004]),
    [final] ).

cnf(i_0_13817,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_8005]),
    [final] ).

cnf(i_0_13818,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_8006]),
    [final] ).

cnf(i_0_13819,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_8007]),
    [final] ).

cnf(i_0_13820,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_8005]),
    [final] ).

cnf(i_0_13821,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_8007]),
    [final] ).

cnf(i_0_13822,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_8008]),
    [final] ).

cnf(i_0_13823,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_7952]),
    [final] ).

cnf(i_0_13824,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_7953]),
    [final] ).

cnf(i_0_13825,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_8009]),
    [final] ).

cnf(i_0_13826,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_7826]),
    [final] ).

cnf(i_0_13827,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_8010]),
    [final] ).

cnf(i_0_13828,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_8011]),
    [final] ).

cnf(i_0_13829,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_6637]),
    [final] ).

cnf(i_0_13830,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_6759]),
    [final] ).

cnf(i_0_13831,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_8012]),
    [final] ).

cnf(i_0_13832,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk573_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk571_3(X1,X2,X3)),X1))
    | epred2_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7651]),
    [final] ).

cnf(i_0_13833,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_8013]),
    [final] ).

cnf(i_0_13834,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_8014,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_13835,plain,
    ( hBOOL(hAPP(X1,X2))
    | hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X1,X5,X3)),X2),X4))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X3),X2),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7598]),
    [final] ).

cnf(i_0_13836,plain,
    ( hBOOL(hAPP(X1,X2))
    | hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X1,X5,X3)),X2),X4))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X3),X2),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7599]),
    [final] ).

cnf(i_0_13837,plain,
    ( hBOOL(hAPP(X1,X2))
    | hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(X1,X5,X3)),X2),X4))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X3),X2),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8015]),
    [final] ).

cnf(i_0_13838,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_7158]),
    [final] ).

cnf(i_0_13839,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_8016]),
    [final] ).

cnf(i_0_13840,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_8017]),
    [final] ).

cnf(i_0_13841,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_6991]),
    [final] ).

cnf(i_0_13842,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_6992]),
    [final] ).

cnf(i_0_13843,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_8018]),
    [final] ).

cnf(i_0_13844,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_8019]),
    [final] ).

cnf(i_0_13845,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk569_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk567_3(X1,X2,X3)),X1))
    | epred1_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7661]),
    [final] ).

cnf(i_0_13846,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,esk234_4(X1,X2,X3,X4)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(X3),X4),X2))
    | hAPP(X1,X4) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7289]),
    [final] ).

cnf(i_0_13847,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_8020]),
    [final] ).

cnf(i_0_13848,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_8021,c_0_6178]),
    [final] ).

cnf(i_0_13849,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_8022]),
    [final] ).

cnf(i_0_13850,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_8023]),
    [final] ).

cnf(i_0_13851,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_8024,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_13852,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_8025]),
    [final] ).

cnf(i_0_13853,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_8026]),
    [final] ).

cnf(i_0_13854,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_8027]),
    [final] ).

cnf(i_0_13855,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_8028]),
    [final] ).

cnf(i_0_13856,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_7135]),
    [final] ).

cnf(i_0_13857,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_7136]),
    [final] ).

cnf(i_0_13858,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))
    | esk379_3(X1,X2,X3) != esk380_3(X1,X2,X3)
    | hAPP(c_Finite__Set_Ocard(X3),esk378_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_7347]),
    [final] ).

cnf(i_0_13859,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_8029]),
    [final] ).

cnf(i_0_13860,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_8030]),
    [final] ).

cnf(i_0_13861,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_8031]),
    [final] ).

cnf(i_0_13862,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_8032]),
    [final] ).

cnf(i_0_13863,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_8033]),
    [final] ).

cnf(i_0_13864,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_8034]),
    [final] ).

cnf(i_0_13865,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_8035]),
    [final] ).

cnf(i_0_13866,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_8036]),
    [final] ).

cnf(i_0_13867,plain,
    ( c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X3),X2,X4,X6)
    | ~ hBOOL(hAPP(X1,X2))
    | ~ c_Natural_Oevaln(X3,X2,X4,X5)
    | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X3),X5,X4,X6) ),
    inference(split_conjunct,[status(thm)],[i_0_7079]),
    [final] ).

cnf(i_0_13868,plain,
    ( c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X3),X2,X4,X6)
    | ~ hBOOL(hAPP(X1,X2))
    | ~ c_Natural_Oevaln(X3,X2,X4,X5)
    | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X3),X5,X4,X6) ),
    inference(split_conjunct,[status(thm)],[i_0_8037]),
    [final] ).

cnf(i_0_13869,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_8038]),
    [final] ).

cnf(i_0_13870,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk572_3(X2,X1,X3))),esk573_3(X2,X1,X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk571_3(X2,X1,X3)))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7651]),
    [final] ).

cnf(i_0_13871,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk568_3(X2,X1,X3))),esk569_3(X2,X1,X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk567_3(X2,X1,X3)))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7661]),
    [final] ).

cnf(i_0_13872,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_8039]),
    [final] ).

cnf(i_0_13873,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_8040]),
    [final] ).

cnf(i_0_13874,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_8041,c_0_6181]),
    [final] ).

cnf(i_0_13875,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_8042]),
    [final] ).

cnf(i_0_13876,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_5319]),
    [final] ).

cnf(i_0_13877,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk53_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_7489]),
    [final] ).

cnf(i_0_13878,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_8043]),
    [final] ).

cnf(i_0_13879,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_8044,c_0_6063]),
    [final] ).

cnf(i_0_13880,plain,
    ( hBOOL(hAPP(X1,esk527_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_8045]),
    [final] ).

cnf(i_0_13881,plain,
    c_Fun_Oinj__on(X1,tc_prod(X2,X1),esk275_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_6529]),
    [final] ).

cnf(i_0_13882,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_8046]),
    [final] ).

cnf(i_0_13883,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_8047]),
    [final] ).

cnf(i_0_13884,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_8048]),
    [final] ).

cnf(i_0_13885,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk573_3(X1,X2,X3)))
    | X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk570_3(X1,X2,X3))),esk571_3(X1,X2,X3))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7651]),
    [final] ).

cnf(i_0_13886,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk569_3(X1,X2,X3)))
    | X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk566_3(X1,X2,X3))),esk567_3(X1,X2,X3))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7661]),
    [final] ).

cnf(i_0_13887,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_7557]),
    [final] ).

cnf(i_0_13888,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_7557]),
    [final] ).

cnf(i_0_13889,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_7558]),
    [final] ).

cnf(i_0_13890,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_7558]),
    [final] ).

cnf(i_0_13891,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_7557]),
    [final] ).

cnf(i_0_13892,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_7558]),
    [final] ).

cnf(i_0_13893,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_8049]),
    [final] ).

cnf(i_0_13894,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_8050]),
    [final] ).

cnf(i_0_13895,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_8051]),
    [final] ).

cnf(i_0_13896,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_8052]),
    [final] ).

cnf(i_0_13897,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_8053,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_13898,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_8054,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_13899,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_8055,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_13900,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_8056,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_13901,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_7576]),
    [final] ).

cnf(i_0_13902,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_8057]),
    [final] ).

cnf(i_0_13903,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_8058]),
    [final] ).

cnf(i_0_13904,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_6759]),
    [final] ).

cnf(i_0_13905,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_8059]),
    [final] ).

cnf(i_0_13906,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_8060]),
    [final] ).

cnf(i_0_13907,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_8061]),
    [final] ).

cnf(i_0_13908,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk55_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_7496]),
    [final] ).

cnf(i_0_13909,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_8062]),
    [final] ).

cnf(i_0_13910,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_8063]),
    [final] ).

cnf(i_0_13911,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_8064]),
    [final] ).

cnf(i_0_13912,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_8065]),
    [final] ).

cnf(i_0_13913,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_8066]),
    [final] ).

cnf(i_0_13914,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_8002]),
    [final] ).

cnf(i_0_13915,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk499_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_8067]),
    [final] ).

cnf(i_0_13916,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_8068]),
    [final] ).

cnf(i_0_13917,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk166_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_8069]),
    [final] ).

cnf(i_0_13918,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_8070]),
    [final] ).

cnf(i_0_13919,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_8071]),
    [final] ).

cnf(i_0_13920,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk573_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk571_3(X1,X2,X3)),X1))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7651]),
    [final] ).

cnf(i_0_13921,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk569_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk567_3(X1,X2,X3)),X1))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7661]),
    [final] ).

cnf(i_0_13922,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_8072]),
    [final] ).

cnf(i_0_13923,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_8073]),
    [final] ).

cnf(i_0_13924,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_8074]),
    [final] ).

cnf(i_0_13925,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_8075]),
    [final] ).

cnf(i_0_13926,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_8076]),
    [final] ).

cnf(i_0_13927,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_8077]),
    [final] ).

cnf(i_0_13928,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_8078]),
    [final] ).

cnf(i_0_13929,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_7631]),
    [final] ).

cnf(i_0_13930,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_8079]),
    [final] ).

cnf(i_0_13931,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_8080]),
    [final] ).

cnf(i_0_13932,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_8081]),
    [final] ).

cnf(i_0_13933,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_8082]),
    [final] ).

cnf(i_0_13934,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_8083]),
    [final] ).

cnf(i_0_13935,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_7755]),
    [final] ).

cnf(i_0_13936,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_8084]),
    [final] ).

cnf(i_0_13937,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_7814]),
    [final] ).

cnf(i_0_13938,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_8085]),
    [final] ).

cnf(i_0_13939,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_7815]),
    [final] ).

cnf(i_0_13940,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_8086]),
    [final] ).

cnf(i_0_13941,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_8087]),
    [final] ).

cnf(i_0_13942,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_7761]),
    [final] ).

cnf(i_0_13943,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_8088]),
    [final] ).

cnf(i_0_13944,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_8089]),
    [final] ).

cnf(i_0_13945,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_8090]),
    [final] ).

cnf(i_0_13946,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_8091]),
    [final] ).

cnf(i_0_13947,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_8092]),
    [final] ).

cnf(i_0_13948,plain,
    ( c_Big__Operators_Olinorder__class_OMax(X1,X3) = X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),esk474_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_8093]),
    [final] ).

cnf(i_0_13949,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_5465]),
    [final] ).

cnf(i_0_13950,plain,
    ( c_List_Olist__all(X2,X1,X3)
    | ~ hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),esk506_3(X3,X1,X2)))) ),
    inference(split_conjunct,[status(thm)],[i_0_8094]),
    [final] ).

cnf(i_0_13951,plain,
    ( c_Natural_Oevaln(c_Com_Ocom_OWhile(X5,X1),X2,X3,X2)
    | ~ c_Natural_Oevaln(X1,X2,X3,X4)
    | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X5,X1),X4,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7942]),
    [final] ).

cnf(i_0_13952,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_7780]),
    [final] ).

cnf(i_0_13953,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_8095]),
    [final] ).

cnf(i_0_13954,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_8096]),
    [final] ).

cnf(i_0_13955,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_8097]),
    [final] ).

cnf(i_0_13956,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_8098]),
    [final] ).

cnf(i_0_13957,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_8099,c_0_6063]),c_0_6063]),
    [final] ).

cnf(i_0_13958,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_8100,c_0_6063]),c_0_6063]),
    [final] ).

cnf(i_0_13959,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_8101]),
    [final] ).

cnf(i_0_13960,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_8102,c_0_6063]),c_0_6063]),
    [final] ).

cnf(i_0_13961,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_8103,c_0_6063]),c_0_6063]),
    [final] ).

cnf(i_0_13962,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_8077]),
    [final] ).

cnf(i_0_13963,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_8076]),
    [final] ).

cnf(i_0_13964,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_8104]),
    [final] ).

cnf(i_0_13965,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_8105]),
    [final] ).

cnf(i_0_13966,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_8106]),
    [final] ).

cnf(i_0_13967,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_8107,c_0_6693]),
    [final] ).

cnf(i_0_13968,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_7894]),
    [final] ).

cnf(i_0_13969,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_8108]),
    [final] ).

cnf(i_0_13970,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_8109]),
    [final] ).

cnf(i_0_13971,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_8110]),
    [final] ).

cnf(i_0_13972,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_8111]),
    [final] ).

cnf(i_0_13973,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_8089]),
    [final] ).

cnf(i_0_13974,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_8089]),
    [final] ).

cnf(i_0_13975,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_8090]),
    [final] ).

cnf(i_0_13976,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_8090]),
    [final] ).

cnf(i_0_13977,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_8091]),
    [final] ).

cnf(i_0_13978,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_8091]),
    [final] ).

cnf(i_0_13979,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_6815]),
    [final] ).

cnf(i_0_13980,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_6815]),
    [final] ).

cnf(i_0_13981,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_7688]),
    [final] ).

cnf(i_0_13982,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_8112]),
    [final] ).

cnf(i_0_13983,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_7769]),
    [final] ).

cnf(i_0_13984,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_8113]),
    [final] ).

cnf(i_0_13985,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_7770]),
    [final] ).

cnf(i_0_13986,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_8114]),
    [final] ).

cnf(i_0_13987,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_8115]),
    [final] ).

cnf(i_0_13988,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_8116]),
    [final] ).

cnf(i_0_13989,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_7782]),
    [final] ).

cnf(i_0_13990,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_8117]),
    [final] ).

cnf(i_0_13991,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_7814]),
    [final] ).

cnf(i_0_13992,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_8118]),
    [final] ).

cnf(i_0_13993,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_7815]),
    [final] ).

cnf(i_0_13994,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_8119]),
    [final] ).

cnf(i_0_13995,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_7783]),
    [final] ).

cnf(i_0_13996,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_7099]),
    [final] ).

cnf(i_0_13997,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_7811]),
    [final] ).

cnf(i_0_13998,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_7812]),
    [final] ).

cnf(i_0_13999,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_7727]),
    [final] ).

cnf(i_0_14000,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_8120,c_0_6281]),
    [final] ).

cnf(i_0_14001,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),esk462_3(X2,X3,X1)),c_Wellfounded_Oacc(X1,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_7148]),
    [final] ).

cnf(i_0_14002,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),esk461_3(X2,X3,X1)),c_Wellfounded_Oacc(X1,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_7149]),
    [final] ).

cnf(i_0_14003,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),esk114_3(X2,X3,X1)),c_Wellfounded_Oacc(X1,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_7150]),
    [final] ).

cnf(i_0_14004,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_8121]),
    [final] ).

cnf(i_0_14005,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_8122]),
    [final] ).

cnf(i_0_14006,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_8002]),
    [final] ).

cnf(i_0_14007,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_8089]),
    [final] ).

cnf(i_0_14008,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_8090]),
    [final] ).

cnf(i_0_14009,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_8091]),
    [final] ).

cnf(i_0_14010,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_8123]),
    [final] ).

cnf(i_0_14011,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_8124,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_14012,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_6492]),
    [final] ).

cnf(i_0_14013,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_7621]),
    [final] ).

cnf(i_0_14014,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_8125]),
    [final] ).

cnf(i_0_14015,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_8126]),
    [final] ).

cnf(i_0_14016,plain,
    ( hBOOL(hAPP(X1,esk517_4(X1,X2,X3,X4)))
    | X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7231]),
    [final] ).

cnf(i_0_14017,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_8127]),
    [final] ).

cnf(i_0_14018,plain,
    hAPP(hAPP(c_Fun_Ocomp(X1,X2,X3,X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
    inference(split_conjunct,[status(thm)],[i_0_8128]),
    [final] ).

cnf(i_0_14019,plain,
    hAPP(hAPP(c_Fun_Ocomp(X1,X2,X3,X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
    inference(split_conjunct,[status(thm)],[i_0_8129]),
    [final] ).

cnf(i_0_14020,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_7233]),
    [final] ).

cnf(i_0_14021,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_8130]),
    [final] ).

cnf(i_0_14022,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_8131]),
    [final] ).

cnf(i_0_14023,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_8132]),
    [final] ).

cnf(i_0_14024,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_8133]),
    [final] ).

cnf(i_0_14025,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_8134]),
    [final] ).

cnf(i_0_14026,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_8135]),
    [final] ).

cnf(i_0_14027,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_8136]),
    [final] ).

cnf(i_0_14028,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_8137]),
    [final] ).

cnf(i_0_14029,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_7745]),
    [final] ).

cnf(i_0_14030,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_8138]),
    [final] ).

cnf(i_0_14031,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_8139]),
    [final] ).

cnf(i_0_14032,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_8140]),
    [final] ).

cnf(i_0_14033,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_8141]),
    [final] ).

cnf(i_0_14034,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_8142]),
    [final] ).

cnf(i_0_14035,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_8143]),
    [final] ).

cnf(i_0_14036,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_8144]),
    [final] ).

cnf(i_0_14037,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_8145]),
    [final] ).

cnf(i_0_14038,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_8146]),
    [final] ).

cnf(i_0_14039,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_8147]),
    [final] ).

cnf(i_0_14040,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_6577]),
    [final] ).

cnf(i_0_14041,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_8148]),
    [final] ).

cnf(i_0_14042,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),esk368_3(X2,X3,X1)),X2))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8149]),
    [final] ).

cnf(i_0_14043,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_6791]),
    [final] ).

cnf(i_0_14044,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_8003]),
    [final] ).

cnf(i_0_14045,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_8150]),
    [final] ).

cnf(i_0_14046,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_8151]),
    [final] ).

cnf(i_0_14047,plain,
    ( c_Natural_Oevaln(X1,X2,X3,X4)
    | c_Natural_Oevaln(X5,X2,X3,X4)
    | ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X6,X5,X1),X2,X3,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_8152]),
    [final] ).

cnf(i_0_14048,plain,
    ( c_Natural_Oevaln(X1,X2,X3,X4)
    | c_Natural_Oevaln(X5,X2,X3,X4)
    | ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X6,X5,X1),X2,X3,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_8153]),
    [final] ).

cnf(i_0_14049,plain,
    ( c_Natural_Oevaln(X1,X2,X3,X4)
    | c_Natural_Oevaln(X5,X2,X3,X4)
    | ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X6,X5,X1),X2,X3,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_8154]),
    [final] ).

cnf(i_0_14050,plain,
    ( c_Natural_Oevaln(c_Com_Ocom_OSemi(X1,X5),X2,X3,X6)
    | ~ c_Natural_Oevaln(X1,X2,X3,X4)
    | ~ c_Natural_Oevaln(X5,X4,X3,X6) ),
    inference(split_conjunct,[status(thm)],[i_0_7090]),
    [final] ).

cnf(i_0_14051,plain,
    ( c_Natural_Oevaln(c_Com_Ocom_OSemi(X1,X5),X2,X3,X6)
    | ~ c_Natural_Oevaln(X1,X2,X3,X4)
    | ~ c_Natural_Oevaln(X5,X4,X3,X6) ),
    inference(split_conjunct,[status(thm)],[i_0_8155]),
    [final] ).

cnf(i_0_14052,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_8156]),
    [final] ).

cnf(i_0_14053,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_8157]),
    [final] ).

cnf(i_0_14054,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_8158]),
    [final] ).

cnf(i_0_14055,plain,
    ( hBOOL(hAPP(hAPP(X5,X6),X8))
    | ~ c_Hoare__Mirabelle_Otriple__valid(X1,X2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),X4),X5))
    | ~ hBOOL(hAPP(hAPP(X3,X6),X7))
    | ~ c_Natural_Oevaln(X4,X7,X2,X8) ),
    inference(split_conjunct,[status(thm)],[i_0_6855]),
    [final] ).

cnf(i_0_14056,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,esk353_4(X1,X2,X3,X4)) != c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_7330]),
    [final] ).

cnf(i_0_14057,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,esk156_4(X1,X2,X3,X4)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_7331]),
    [final] ).

cnf(i_0_14058,plain,
    ( c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X3,tc_fun(X4,tc_HOL_Obool)),X2),X1)
    | hAPP(X1,esk354_4(X1,X2,X3,X4)) != c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_7332]),
    [final] ).

cnf(i_0_14059,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,esk157_4(X1,X2,X3,X4)) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_7333]),
    [final] ).

cnf(i_0_14060,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_8159]),
    [final] ).

cnf(i_0_14061,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_8160]),
    [final] ).

cnf(i_0_14062,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),esk60_3(X2,X1,X3))),esk61_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_8161]),
    [final] ).

cnf(i_0_14063,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk271_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_7779]),
    [final] ).

cnf(i_0_14064,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk143_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_7780]),
    [final] ).

cnf(i_0_14065,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),c_List_Olists(X1,X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),esk325_3(X2,X3,X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8162]),
    [final] ).

cnf(i_0_14066,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_8163]),
    [final] ).

cnf(i_0_14067,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_7800]),
    [final] ).

cnf(i_0_14068,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_7585]),
    [final] ).

cnf(i_0_14069,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_8164]),
    [final] ).

cnf(i_0_14070,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_7724]),
    [final] ).

cnf(i_0_14071,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_8165]),
    [final] ).

cnf(i_0_14072,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_8166]),
    [final] ).

cnf(i_0_14073,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_7231]),
    [final] ).

cnf(i_0_14074,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_7240]),
    [final] ).

cnf(i_0_14075,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_8167,c_0_6178]),
    [final] ).

cnf(i_0_14076,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_8043]),
    [final] ).

cnf(i_0_14077,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_8168]),
    [final] ).

cnf(i_0_14078,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_8169,c_0_6138]),
    [final] ).

cnf(i_0_14079,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_8170,c_0_6138]),
    [final] ).

cnf(i_0_14080,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_8171]),
    [final] ).

cnf(i_0_14081,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_8172]),
    [final] ).

cnf(i_0_14082,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_8173]),
    [final] ).

cnf(i_0_14083,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_8174]),
    [final] ).

cnf(i_0_14084,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk369_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_8057]),
    [final] ).

cnf(i_0_14085,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_8175]),
    [final] ).

cnf(i_0_14086,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_8176]),
    [final] ).

cnf(i_0_14087,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),esk58_3(X2,X1,X3))),esk59_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_8177]),
    [final] ).

cnf(i_0_14088,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_8178]),
    [final] ).

cnf(i_0_14089,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_8179]),
    [final] ).

cnf(i_0_14090,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_8180,c_0_6713]),c_0_6713]),
    [final] ).

cnf(i_0_14091,plain,
    ( c_Fun_Oinj__on(X4,X3,X2,X1)
    | esk215_4(X1,X2,X3,X4) != esk216_4(X1,X2,X3,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_7322]),
    [final] ).

cnf(i_0_14092,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_8181]),
    [final] ).

cnf(i_0_14093,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X3)),X2),X5))
    | ~ hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X3),X2),X4))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X3)),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_7171]),
    [final] ).

cnf(i_0_14094,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X3)),X2),X5))
    | ~ hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X3),X2),X4))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X3)),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_8182]),
    [final] ).

cnf(i_0_14095,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk573_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,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7651]),
    [final] ).

cnf(i_0_14096,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_8052]),
    [final] ).

cnf(i_0_14097,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_8183,c_0_6181]),c_0_6181]),
    [final] ).

cnf(i_0_14098,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_8184]),
    [final] ).

cnf(i_0_14099,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk571_3(X2,X3,X1)),X2))
    | epred2_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk572_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7651]),
    [final] ).

cnf(i_0_14100,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk569_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | epred1_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,esk567_3(X1,X2,X3)))
    | ~ hBOOL(hAPP(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7661]),
    [final] ).

cnf(i_0_14101,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_8005]),
    [final] ).

cnf(i_0_14102,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_8185]),
    [final] ).

cnf(i_0_14103,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_7231]),
    [final] ).

cnf(i_0_14104,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_8186]),
    [final] ).

cnf(i_0_14105,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk567_3(X2,X3,X1)),X2))
    | epred1_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk569_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7661]),
    [final] ).

cnf(i_0_14106,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_8187]),
    [final] ).

cnf(i_0_14107,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_8187]),
    [final] ).

cnf(i_0_14108,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_8188]),
    [final] ).

cnf(i_0_14109,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_8189]),
    [final] ).

cnf(i_0_14110,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_8190]),
    [final] ).

cnf(i_0_14111,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_8190]),
    [final] ).

cnf(i_0_14112,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_8191]),
    [final] ).

cnf(i_0_14113,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),esk60_3(X2,X1,X3))),esk61_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_8161]),
    [final] ).

cnf(i_0_14114,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_8192]),
    [final] ).

cnf(i_0_14115,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_8193]),
    [final] ).

cnf(i_0_14116,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_8194]),
    [final] ).

cnf(i_0_14117,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk181_3(X2,X3,X1)),esk182_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_6745]),
    [final] ).

cnf(i_0_14118,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_5321]),
    [final] ).

cnf(i_0_14119,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_7240]),
    [final] ).

cnf(i_0_14120,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_8048]),
    [final] ).

cnf(i_0_14121,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_8195]),
    [final] ).

cnf(i_0_14122,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_8195]),
    [final] ).

cnf(i_0_14123,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_8196]),
    [final] ).

cnf(i_0_14124,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_8196]),
    [final] ).

cnf(i_0_14125,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_8197]),
    [final] ).

cnf(i_0_14126,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_8198]),
    [final] ).

cnf(i_0_14127,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_8199]),
    [final] ).

cnf(i_0_14128,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_8200]),
    [final] ).

cnf(i_0_14129,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,esk398_3(X2,X1,X3))) ),
    inference(rw,[status(thm)],[i_0_8201,c_0_6281]),
    [final] ).

cnf(i_0_14130,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_8202]),
    [final] ).

cnf(i_0_14131,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_8203]),
    [final] ).

cnf(i_0_14132,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),esk436_2(X2,X1)),hAPP(c_Relation_OImage(X1,X1,X2),esk436_2(X2,X1))))
    | c_Wellfounded_Owf(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8204]),
    [final] ).

cnf(i_0_14133,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_8205]),
    [final] ).

cnf(i_0_14134,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_8206]),
    [final] ).

cnf(i_0_14135,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_8033]),
    [final] ).

cnf(i_0_14136,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_8207]),
    [final] ).

cnf(i_0_14137,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_8208]),
    [final] ).

cnf(i_0_14138,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_8209]),
    [final] ).

cnf(i_0_14139,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_6751]),
    [final] ).

cnf(i_0_14140,plain,
    ( X1 = hAPP(hAPP(c_Product__Type_OPair(X2,X2),esk166_3(X3,X1,X2)),esk166_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_8069]),
    [final] ).

cnf(i_0_14141,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_8210]),
    [final] ).

cnf(i_0_14142,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_8211]),
    [final] ).

cnf(i_0_14143,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_5321]),
    [final] ).

cnf(i_0_14144,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_8212,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6216]),c_0_6064]),
    [final] ).

cnf(i_0_14145,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_8213]),
    [final] ).

cnf(i_0_14146,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_8214,c_0_6097]),
    [final] ).

cnf(i_0_14147,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk572_3(X2,X1,X3))),esk573_3(X2,X1,X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
    | epred2_3(X3,X1,X2)
    | ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7651]),
    [final] ).

cnf(i_0_14148,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_8215,c_0_6181]),c_0_6181]),
    [final] ).

cnf(i_0_14149,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_8216,c_0_6181]),c_0_6181]),
    [final] ).

cnf(i_0_14150,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_7446]),
    [final] ).

cnf(i_0_14151,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_7447]),
    [final] ).

cnf(i_0_14152,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_8217]),
    [final] ).

cnf(i_0_14153,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_8218]),
    [final] ).

cnf(i_0_14154,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_8219]),
    [final] ).

cnf(i_0_14155,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X4,X1)),X2),X2))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X4,X1)),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7885]),
    [final] ).

cnf(i_0_14156,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),esk58_3(X2,X1,X3))),esk59_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_8177]),
    [final] ).

cnf(i_0_14157,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_7836]),
    [final] ).

cnf(i_0_14158,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_8220]),
    [final] ).

cnf(i_0_14159,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_8220]),
    [final] ).

cnf(i_0_14160,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_8221]),
    [final] ).

cnf(i_0_14161,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_8222]),
    [final] ).

cnf(i_0_14162,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),esk570_3(X1,X2,X3))),esk571_3(X1,X2,X3))
    | epred2_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7651]),
    [final] ).

cnf(i_0_14163,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_8223,c_0_6713]),c_0_6713]),
    [final] ).

cnf(i_0_14164,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_8224]),
    [final] ).

cnf(i_0_14165,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_8225]),
    [final] ).

cnf(i_0_14166,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk568_3(X2,X1,X3))),esk569_3(X2,X1,X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
    | epred1_3(X3,X1,X2)
    | ~ hBOOL(hAPP(X3,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_7661]),
    [final] ).

cnf(i_0_14167,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_8226,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_14168,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk573_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,esk570_3(X1,X2,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7651]),
    [final] ).

cnf(i_0_14169,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk569_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,esk567_3(X1,X2,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7661]),
    [final] ).

cnf(i_0_14170,plain,
    ( X1 = hAPP(c_Int_ORep__Integ,esk286_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_8227]),
    [final] ).

cnf(i_0_14171,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk471_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_8228]),
    [final] ).

cnf(i_0_14172,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk347_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_8229]),
    [final] ).

cnf(i_0_14173,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk324_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_7839]),
    [final] ).

cnf(i_0_14174,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_8230]),
    [final] ).

cnf(i_0_14175,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),esk566_3(X1,X2,X3))),esk567_3(X1,X2,X3))
    | epred1_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7661]),
    [final] ).

cnf(i_0_14176,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk571_3(X2,X3,X1)),X2))
    | X2 = 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_7651]),
    [final] ).

cnf(i_0_14177,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk567_3(X2,X3,X1)),X2))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk569_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_7661]),
    [final] ).

cnf(i_0_14178,plain,
    ( hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X3),X2),X4)))
    | ~ hBOOL(hAPP(X1,esk323_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_7839]),
    [final] ).

cnf(i_0_14179,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_8231]),
    [final] ).

cnf(i_0_14180,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_8232]),
    [final] ).

cnf(i_0_14181,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_8233]),
    [final] ).

cnf(i_0_14182,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_8234]),
    [final] ).

cnf(i_0_14183,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_8230]),
    [final] ).

cnf(i_0_14184,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk573_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)),esk571_3(X1,X2,X3)))
    | epred2_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7651]),
    [final] ).

cnf(i_0_14185,plain,
    ( c_Fun_Oinj__on(X1,X2,esk223_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_6628]),
    [final] ).

cnf(i_0_14186,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_8224]),
    [final] ).

cnf(i_0_14187,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)
    | ~ epred1_3(X5,X3,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7661]),
    [final] ).

cnf(i_0_14188,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)
    | ~ epred2_3(X5,X3,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7651]),
    [final] ).

cnf(i_0_14189,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_8235]),
    [final] ).

cnf(i_0_14190,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_8236]),
    [final] ).

cnf(i_0_14191,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_8237]),
    [final] ).

cnf(i_0_14192,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_8238]),
    [final] ).

cnf(i_0_14193,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),esk422_2(X1,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8239]),
    [final] ).

cnf(i_0_14194,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_8240]),
    [final] ).

cnf(i_0_14195,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_8241]),
    [final] ).

cnf(i_0_14196,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_7765]),
    [final] ).

cnf(i_0_14197,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_7764]),
    [final] ).

cnf(i_0_14198,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_8242]),
    [final] ).

cnf(i_0_14199,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_8243]),
    [final] ).

cnf(i_0_14200,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_8244]),
    [final] ).

cnf(i_0_14201,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_8245]),
    [final] ).

cnf(i_0_14202,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_7952]),
    [final] ).

cnf(i_0_14203,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_8246]),
    [final] ).

cnf(i_0_14204,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_8247]),
    [final] ).

cnf(i_0_14205,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_8248]),
    [final] ).

cnf(i_0_14206,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_7915]),
    [final] ).

cnf(i_0_14207,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_8249]),
    [final] ).

cnf(i_0_14208,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_8076]),
    [final] ).

cnf(i_0_14209,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_8250]),
    [final] ).

cnf(i_0_14210,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_8077]),
    [final] ).

cnf(i_0_14211,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_7917]),
    [final] ).

cnf(i_0_14212,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_8251]),
    [final] ).

cnf(i_0_14213,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk569_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)),esk567_3(X1,X2,X3)))
    | epred1_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7661]),
    [final] ).

cnf(i_0_14214,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_8252]),
    [final] ).

cnf(i_0_14215,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_8253]),
    [final] ).

cnf(i_0_14216,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_8254]),
    [final] ).

cnf(i_0_14217,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_8255]),
    [final] ).

cnf(i_0_14218,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_8256]),
    [final] ).

cnf(i_0_14219,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_8257]),
    [final] ).

cnf(i_0_14220,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_6751]),
    [final] ).

cnf(i_0_14221,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_6751]),
    [final] ).

cnf(i_0_14222,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk266_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_8258]),
    [final] ).

cnf(i_0_14223,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk264_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_8259]),
    [final] ).

cnf(i_0_14224,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk262_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_8260]),
    [final] ).

cnf(i_0_14225,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_7061]),
    [final] ).

cnf(i_0_14226,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_8261]),
    [final] ).

cnf(i_0_14227,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)),esk385_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2))) ),
    inference(rw,[status(thm)],[i_0_8262,c_0_6138]),
    [final] ).

cnf(i_0_14228,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)),esk386_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2))) ),
    inference(rw,[status(thm)],[i_0_8263,c_0_6138]),
    [final] ).

cnf(i_0_14229,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_8264]),
    [final] ).

cnf(i_0_14230,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_8265]),
    [final] ).

cnf(i_0_14231,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk573_3(X1,X2,X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk571_3(X1,X2,X3)),X1))
    | epred2_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7651]),
    [final] ).

cnf(i_0_14232,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_8266]),
    [final] ).

cnf(i_0_14233,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_8267,c_0_8268]),
    [final] ).

cnf(i_0_14234,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)
    | ~ epred1_3(X5,X3,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7661]),
    [final] ).

cnf(i_0_14235,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)
    | ~ epred2_3(X5,X3,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7651]),
    [final] ).

cnf(i_0_14236,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_8269]),
    [final] ).

cnf(i_0_14237,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_8270]),
    [final] ).

cnf(i_0_14238,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_8271]),
    [final] ).

cnf(i_0_14239,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_8272]),
    [final] ).

cnf(i_0_14240,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_8273]),
    [final] ).

cnf(i_0_14241,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_8274]),
    [final] ).

cnf(i_0_14242,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_8275]),
    [final] ).

cnf(i_0_14243,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_8276]),
    [final] ).

cnf(i_0_14244,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk326_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_8277]),
    [final] ).

cnf(i_0_14245,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk569_3(X1,X2,X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk567_3(X1,X2,X3)),X1))
    | epred1_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7661]),
    [final] ).

cnf(i_0_14246,plain,
    ( X1 = hAPP(c_Nat_OSuc,esk8_4(X2,X1,X3,X4))
    | ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X4),X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7943]),
    [final] ).

cnf(i_0_14247,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_8278]),
    [final] ).

cnf(i_0_14248,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_8279]),
    [final] ).

cnf(i_0_14249,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_8280]),
    [final] ).

cnf(i_0_14250,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_8281]),
    [final] ).

cnf(i_0_14251,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_8282]),
    [final] ).

cnf(i_0_14252,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_8283]),
    [final] ).

cnf(i_0_14253,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_7996]),
    [final] ).

cnf(i_0_14254,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_8284]),
    [final] ).

cnf(i_0_14255,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_8285]),
    [final] ).

cnf(i_0_14256,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_8286]),
    [final] ).

cnf(i_0_14257,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_8287]),
    [final] ).

cnf(i_0_14258,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_8288]),
    [final] ).

cnf(i_0_14259,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_8289]),
    [final] ).

cnf(i_0_14260,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_8290,c_0_6088]),
    [final] ).

cnf(i_0_14261,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_7384]),
    [final] ).

cnf(i_0_14262,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_8291]),
    [final] ).

cnf(i_0_14263,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_8292]),
    [final] ).

cnf(i_0_14264,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_8089]),
    [final] ).

cnf(i_0_14265,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_8089]),
    [final] ).

cnf(i_0_14266,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_8293]),
    [final] ).

cnf(i_0_14267,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_8294]),
    [final] ).

cnf(i_0_14268,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_8293]),
    [final] ).

cnf(i_0_14269,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_8295]),
    [final] ).

cnf(i_0_14270,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_8090]),
    [final] ).

cnf(i_0_14271,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_8090]),
    [final] ).

cnf(i_0_14272,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_8296]),
    [final] ).

cnf(i_0_14273,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_8297]),
    [final] ).

cnf(i_0_14274,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_8298]),
    [final] ).

cnf(i_0_14275,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_8091]),
    [final] ).

cnf(i_0_14276,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_8091]),
    [final] ).

cnf(i_0_14277,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_8299]),
    [final] ).

cnf(i_0_14278,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_8300]),
    [final] ).

cnf(i_0_14279,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_8301]),
    [final] ).

cnf(i_0_14280,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_8302]),
    [final] ).

cnf(i_0_14281,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk572_3(X2,X1,X3))),esk573_3(X2,X1,X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7651]),
    [final] ).

cnf(i_0_14282,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk568_3(X2,X1,X3))),esk569_3(X2,X1,X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7661]),
    [final] ).

cnf(i_0_14283,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_8303]),
    [final] ).

cnf(i_0_14284,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_8304,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_14285,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_8305,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_14286,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_8306]),
    [final] ).

cnf(i_0_14287,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_8307]),
    [final] ).

cnf(i_0_14288,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_8306]),
    [final] ).

cnf(i_0_14289,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_8307]),
    [final] ).

cnf(i_0_14290,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_8308]),
    [final] ).

cnf(i_0_14291,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_8309]),
    [final] ).

cnf(i_0_14292,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_8308]),
    [final] ).

cnf(i_0_14293,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_8309]),
    [final] ).

cnf(i_0_14294,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_8310]),
    [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(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X2)),X3))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8310]),
    [final] ).

cnf(i_0_14296,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_8311]),
    [final] ).

cnf(i_0_14297,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_8312]),
    [final] ).

cnf(i_0_14298,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_8313]),
    [final] ).

cnf(i_0_14299,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk422_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_8239]),
    [final] ).

cnf(i_0_14300,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_8314]),
    [final] ).

cnf(i_0_14301,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_8315]),
    [final] ).

cnf(i_0_14302,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_8313]),
    [final] ).

cnf(i_0_14303,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),esk570_3(X1,X2,X3))),esk571_3(X1,X2,X3))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7651]),
    [final] ).

cnf(i_0_14304,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),esk566_3(X1,X2,X3))),esk567_3(X1,X2,X3))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7661]),
    [final] ).

cnf(i_0_14305,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_8316]),
    [final] ).

cnf(i_0_14306,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_8317,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_14307,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_8318,c_0_8319]),c_0_8319]),
    [final] ).

cnf(i_0_14308,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_8320]),
    [final] ).

cnf(i_0_14309,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_6635]),
    [final] ).

cnf(i_0_14310,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_6636]),
    [final] ).

cnf(i_0_14311,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)),esk369_3(X2,X3,X1)),X2) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_8057]),
    [final] ).

cnf(i_0_14312,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_8321]),
    [final] ).

cnf(i_0_14313,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_8322]),
    [final] ).

cnf(i_0_14314,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_8323]),
    [final] ).

cnf(i_0_14315,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_8324]),
    [final] ).

cnf(i_0_14316,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),esk262_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ class_Lattices_Osemilattice__inf(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8260]),
    [final] ).

cnf(i_0_14317,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),esk264_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8259]),
    [final] ).

cnf(i_0_14318,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),esk266_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8258]),
    [final] ).

cnf(i_0_14319,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_8046]),
    [final] ).

cnf(i_0_14320,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_8325]),
    [final] ).

cnf(i_0_14321,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_8326,c_0_6713]),
    [final] ).

cnf(i_0_14322,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_5322]),
    [final] ).

cnf(i_0_14323,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_8327]),
    [final] ).

cnf(i_0_14324,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_8161]),
    [final] ).

cnf(i_0_14325,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_8328]),
    [final] ).

cnf(i_0_14326,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_8329]),
    [final] ).

cnf(i_0_14327,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_8330]),
    [final] ).

cnf(i_0_14328,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_8331]),
    [final] ).

cnf(i_0_14329,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_8122]),
    [final] ).

cnf(i_0_14330,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_8332]),
    [final] ).

cnf(i_0_14331,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_8333]),
    [final] ).

cnf(i_0_14332,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_8334]),
    [final] ).

cnf(i_0_14333,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_8335]),
    [final] ).

cnf(i_0_14334,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_8336]),
    [final] ).

cnf(i_0_14335,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_8337]),
    [final] ).

cnf(i_0_14336,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_8338]),
    [final] ).

cnf(i_0_14337,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_8339]),
    [final] ).

cnf(i_0_14338,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_8340]),
    [final] ).

cnf(i_0_14339,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_8341]),
    [final] ).

cnf(i_0_14340,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_8342]),
    [final] ).

cnf(i_0_14341,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_8343]),
    [final] ).

cnf(i_0_14342,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_8344]),
    [final] ).

cnf(i_0_14343,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk573_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)),esk571_3(X1,X2,X3)))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7651]),
    [final] ).

cnf(i_0_14344,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk569_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)),esk567_3(X1,X2,X3)))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7661]),
    [final] ).

cnf(i_0_14345,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_8345]),
    [final] ).

cnf(i_0_14346,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_8020]),
    [final] ).

cnf(i_0_14347,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_6585]),
    [final] ).

cnf(i_0_14348,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_8346]),
    [final] ).

cnf(i_0_14349,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_8028]),
    [final] ).

cnf(i_0_14350,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_7731]),
    [final] ).

cnf(i_0_14351,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_8165]),
    [final] ).

cnf(i_0_14352,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_8347]),
    [final] ).

cnf(i_0_14353,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_8348]),
    [final] ).

cnf(i_0_14354,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_8349]),
    [final] ).

cnf(i_0_14355,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_8350]),
    [final] ).

cnf(i_0_14356,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_8351]),
    [final] ).

cnf(i_0_14357,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_7352]),
    [final] ).

cnf(i_0_14358,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_7353]),
    [final] ).

cnf(i_0_14359,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_8352]),
    [final] ).

cnf(i_0_14360,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_8353]),
    [final] ).

cnf(i_0_14361,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_8354]),
    [final] ).

cnf(i_0_14362,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_8355]),
    [final] ).

cnf(i_0_14363,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_8356]),
    [final] ).

cnf(i_0_14364,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_7935]),
    [final] ).

cnf(i_0_14365,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_8357]),
    [final] ).

cnf(i_0_14366,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_7937]),
    [final] ).

cnf(i_0_14367,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_8358]),
    [final] ).

cnf(i_0_14368,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_7938]),
    [final] ).

cnf(i_0_14369,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_8359]),
    [final] ).

cnf(i_0_14370,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_7940]),
    [final] ).

cnf(i_0_14371,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_8360]),
    [final] ).

cnf(i_0_14372,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_8361]),
    [final] ).

cnf(i_0_14373,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_8362]),
    [final] ).

cnf(i_0_14374,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_8174]),
    [final] ).

cnf(i_0_14375,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_8363]),
    [final] ).

cnf(i_0_14376,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_8364]),
    [final] ).

cnf(i_0_14377,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_8365]),
    [final] ).

cnf(i_0_14378,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_8366]),
    [final] ).

cnf(i_0_14379,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_8367]),
    [final] ).

cnf(i_0_14380,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk573_3(X1,X2,X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk571_3(X1,X2,X3)),X1))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7651]),
    [final] ).

cnf(i_0_14381,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk569_3(X1,X2,X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk567_3(X1,X2,X3)),X1))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7661]),
    [final] ).

cnf(i_0_14382,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_8368]),
    [final] ).

cnf(i_0_14383,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_8369]),
    [final] ).

cnf(i_0_14384,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_8370]),
    [final] ).

cnf(i_0_14385,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_8208]),
    [final] ).

cnf(i_0_14386,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_8209]),
    [final] ).

cnf(i_0_14387,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_8371]),
    [final] ).

cnf(i_0_14388,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_8253]),
    [final] ).

cnf(i_0_14389,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_8372]),
    [final] ).

cnf(i_0_14390,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_8373]),
    [final] ).

cnf(i_0_14391,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_8374]),
    [final] ).

cnf(i_0_14392,plain,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(X4,X1,X5),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8375]),
    [final] ).

cnf(i_0_14393,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_8376]),
    [final] ).

cnf(i_0_14394,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_8377]),
    [final] ).

cnf(i_0_14395,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_8378]),
    [final] ).

cnf(i_0_14396,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_8379]),
    [final] ).

cnf(i_0_14397,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X1)),esk335_3(X2,X3,X1)),X3))
    | c_Hoare__Mirabelle_Otriple__valid(X1,X2,X4)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X1)),X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8380]),
    [final] ).

cnf(i_0_14398,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,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7651]),
    [final] ).

cnf(i_0_14399,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk377_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_8381]),
    [final] ).

cnf(i_0_14400,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),esk377_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_8381]),
    [final] ).

cnf(i_0_14401,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_8382]),
    [final] ).

cnf(i_0_14402,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_8383]),
    [final] ).

cnf(i_0_14403,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_8384]),
    [final] ).

cnf(i_0_14404,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_8385]),
    [final] ).

cnf(i_0_14405,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_8386]),
    [final] ).

cnf(i_0_14406,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_8387]),
    [final] ).

cnf(i_0_14407,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_8388]),
    [final] ).

cnf(i_0_14408,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_7844]),
    [final] ).

cnf(i_0_14409,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_8389]),
    [final] ).

cnf(i_0_14410,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_8390]),
    [final] ).

cnf(i_0_14411,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_8177]),
    [final] ).

cnf(i_0_14412,plain,
    ( X1 = hAPP(hAPP(c_List_Oappend(X2),esk483_3(X1,X3,X2)),hAPP(hAPP(c_List_Olist_OCons(X2),X3),esk484_3(X1,X3,X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_7931]),
    [final] ).

cnf(i_0_14413,plain,
    ( X1 = hAPP(hAPP(c_List_Oappend(X2),esk481_3(X1,X3,X2)),hAPP(hAPP(c_List_Olist_OCons(X2),X3),esk482_3(X1,X3,X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_7932]),
    [final] ).

cnf(i_0_14414,plain,
    ( X3 = hAPP(hAPP(c_List_Oappend(X1),esk485_3(X3,X2,X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),esk486_3(X3,X2,X1)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8391]),
    [final] ).

cnf(i_0_14415,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_8392]),
    [final] ).

cnf(i_0_14416,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_8393]),
    [final] ).

cnf(i_0_14417,plain,
    ( epred1_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk569_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,esk567_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7661]),
    [final] ).

cnf(i_0_14418,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_8394]),
    [final] ).

cnf(i_0_14419,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_8395]),
    [final] ).

cnf(i_0_14420,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_8260]),
    [final] ).

cnf(i_0_14421,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_8259]),
    [final] ).

cnf(i_0_14422,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_8258]),
    [final] ).

cnf(i_0_14423,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_8396]),
    [final] ).

cnf(i_0_14424,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_8322]),
    [final] ).

cnf(i_0_14425,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_8322]),
    [final] ).

cnf(i_0_14426,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_8397]),
    [final] ).

cnf(i_0_14427,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_7557]),
    [final] ).

cnf(i_0_14428,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_7558]),
    [final] ).

cnf(i_0_14429,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk346_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_8229]),
    [final] ).

cnf(i_0_14430,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_8398]),
    [final] ).

cnf(i_0_14431,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_8399]),
    [final] ).

cnf(i_0_14432,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_8400]),
    [final] ).

cnf(i_0_14433,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_8401]),
    [final] ).

cnf(i_0_14434,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_7403]),
    [final] ).

cnf(i_0_14435,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),esk34_3(X2,X1,X3)))
    | ~ hBOOL(hAPP(X3,X2))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X3,X1)),X2),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7885]),
    [final] ).

cnf(i_0_14436,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_8402]),
    [final] ).

cnf(i_0_14437,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_8403]),
    [final] ).

cnf(i_0_14438,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_8404]),
    [final] ).

cnf(i_0_14439,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_8405]),
    [final] ).

cnf(i_0_14440,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_8406]),
    [final] ).

cnf(i_0_14441,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_8407]),
    [final] ).

cnf(i_0_14442,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_5329]),
    [final] ).

cnf(i_0_14443,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_8408]),
    [final] ).

cnf(i_0_14444,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_8409]),
    [final] ).

cnf(i_0_14445,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_8410]),
    [final] ).

cnf(i_0_14446,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_8411]),
    [final] ).

cnf(i_0_14447,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_8412]),
    [final] ).

cnf(i_0_14448,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_8307]),
    [final] ).

cnf(i_0_14449,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_8413]),
    [final] ).

cnf(i_0_14450,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_8414]),
    [final] ).

cnf(i_0_14451,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_8309]),
    [final] ).

cnf(i_0_14452,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_8310]),
    [final] ).

cnf(i_0_14453,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_8415]),
    [final] ).

cnf(i_0_14454,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_8416]),
    [final] ).

cnf(i_0_14455,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_8417]),
    [final] ).

cnf(i_0_14456,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_8418]),
    [final] ).

cnf(i_0_14457,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_8419,c_0_6713]),
    [final] ).

cnf(i_0_14458,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_8420]),
    [final] ).

cnf(i_0_14459,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),X3),X4))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_8421]),
    [final] ).

cnf(i_0_14460,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_8422]),
    [final] ).

cnf(i_0_14461,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_8423]),
    [final] ).

cnf(i_0_14462,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_8424]),
    [final] ).

cnf(i_0_14463,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_8425]),
    [final] ).

cnf(i_0_14464,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_8426]),
    [final] ).

cnf(i_0_14465,plain,
    ( c_Natural_Oevaln(X3,X2,X4,X5)
    | ~ hBOOL(hAPP(X1,X2))
    | ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X1,X3,X6),X2,X4,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_8152]),
    [final] ).

cnf(i_0_14466,plain,
    ( c_Natural_Oevaln(X3,X2,X4,X5)
    | ~ hBOOL(hAPP(X1,X2))
    | ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X1,X3,X6),X2,X4,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_8153]),
    [final] ).

cnf(i_0_14467,plain,
    ( c_Natural_Oevaln(X3,X2,X4,X5)
    | ~ hBOOL(hAPP(X1,X2))
    | ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X1,X3,X6),X2,X4,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_8154]),
    [final] ).

cnf(i_0_14468,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_8427]),
    [final] ).

cnf(i_0_14469,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_8428]),
    [final] ).

cnf(i_0_14470,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_7985]),
    [final] ).

cnf(i_0_14471,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_8011]),
    [final] ).

cnf(i_0_14472,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk496_3(X2,X1,X3)),esk494_2(X2,X1)))
    | c_Wellfounded_Owf(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),esk494_2(X2,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_7044]),
    [final] ).

cnf(i_0_14473,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_7404]),
    [final] ).

cnf(i_0_14474,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_7405]),
    [final] ).

cnf(i_0_14475,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_7406]),
    [final] ).

cnf(i_0_14476,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_7407]),
    [final] ).

cnf(i_0_14477,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_8429]),
    [final] ).

cnf(i_0_14478,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_8147]),
    [final] ).

cnf(i_0_14479,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_8430]),
    [final] ).

cnf(i_0_14480,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_8431]),
    [final] ).

cnf(i_0_14481,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_8432]),
    [final] ).

cnf(i_0_14482,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_8433]),
    [final] ).

cnf(i_0_14483,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_8434]),
    [final] ).

cnf(i_0_14484,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_8435]),
    [final] ).

cnf(i_0_14485,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_8436]),
    [final] ).

cnf(i_0_14486,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_7889]),
    [final] ).

cnf(i_0_14487,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_8437]),
    [final] ).

cnf(i_0_14488,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_8438]),
    [final] ).

cnf(i_0_14489,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_7889]),
    [final] ).

cnf(i_0_14490,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_8437]),
    [final] ).

cnf(i_0_14491,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_8439]),
    [final] ).

cnf(i_0_14492,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_8440]),
    [final] ).

cnf(i_0_14493,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_8441]),
    [final] ).

cnf(i_0_14494,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_8442]),
    [final] ).

cnf(i_0_14495,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_8443]),
    [final] ).

cnf(i_0_14496,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_8444]),
    [final] ).

cnf(i_0_14497,plain,
    ( c_Natural_Oevaln(X1,X2,X3,X4)
    | hBOOL(hAPP(X5,X2))
    | ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X5,X6,X1),X2,X3,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_8152]),
    [final] ).

cnf(i_0_14498,plain,
    ( c_Natural_Oevaln(X1,X2,X3,X4)
    | hBOOL(hAPP(X5,X2))
    | ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X5,X6,X1),X2,X3,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_8153]),
    [final] ).

cnf(i_0_14499,plain,
    ( c_Natural_Oevaln(X1,X2,X3,X4)
    | hBOOL(hAPP(X5,X2))
    | ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X5,X6,X1),X2,X3,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_8154]),
    [final] ).

cnf(i_0_14500,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_8445]),
    [final] ).

cnf(i_0_14501,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_8446]),
    [final] ).

cnf(i_0_14502,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_8447]),
    [final] ).

cnf(i_0_14503,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_8448]),
    [final] ).

cnf(i_0_14504,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_8449]),
    [final] ).

cnf(i_0_14505,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_8450]),
    [final] ).

cnf(i_0_14506,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_8451]),
    [final] ).

cnf(i_0_14507,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(X3,X4,X1),X5),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8375]),
    [final] ).

cnf(i_0_14508,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_8452]),
    [final] ).

cnf(i_0_14509,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_8453]),
    [final] ).

cnf(i_0_14510,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_7379]),
    [final] ).

cnf(i_0_14511,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_7380]),
    [final] ).

cnf(i_0_14512,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_8454]),
    [final] ).

cnf(i_0_14513,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_8455]),
    [final] ).

cnf(i_0_14514,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_8456]),
    [final] ).

cnf(i_0_14515,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_8165]),
    [final] ).

cnf(i_0_14516,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_8457]),
    [final] ).

cnf(i_0_14517,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_8458]),
    [final] ).

cnf(i_0_14518,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_8459]),
    [final] ).

cnf(i_0_14519,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_8460]),
    [final] ).

cnf(i_0_14520,plain,
    ( X2 = 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_7651]),
    [final] ).

cnf(i_0_14521,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk569_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,esk567_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_7661]),
    [final] ).

cnf(i_0_14522,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_8461]),
    [final] ).

cnf(i_0_14523,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_8462]),
    [final] ).

cnf(i_0_14524,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_8463]),
    [final] ).

cnf(i_0_14525,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_8464,c_0_6063]),
    [final] ).

cnf(i_0_14526,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_8465,c_0_6063]),c_0_6063]),
    [final] ).

cnf(i_0_14527,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_8156]),
    [final] ).

cnf(i_0_14528,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_8156]),
    [final] ).

cnf(i_0_14529,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_8466]),
    [final] ).

cnf(i_0_14530,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_6426]),
    [final] ).

cnf(i_0_14531,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_8467]),
    [final] ).

cnf(i_0_14532,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_8174]),
    [final] ).

cnf(i_0_14533,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_8400]),
    [final] ).

cnf(i_0_14534,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_8468]),
    [final] ).

cnf(i_0_14535,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_8469]),
    [final] ).

cnf(i_0_14536,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_8470]),
    [final] ).

cnf(i_0_14537,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_8471]),
    [final] ).

cnf(i_0_14538,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_8472]),
    [final] ).

cnf(i_0_14539,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_8168]),
    [final] ).

cnf(i_0_14540,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk325_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_8162]),
    [final] ).

cnf(i_0_14541,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_8473]),
    [final] ).

cnf(i_0_14542,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_8474]),
    [final] ).

cnf(i_0_14543,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_8475]),
    [final] ).

cnf(i_0_14544,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk571_3(X2,X3,X1)))
    | epred2_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk572_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7651]),
    [final] ).

cnf(i_0_14545,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_8476]),
    [final] ).

cnf(i_0_14546,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_8477]),
    [final] ).

cnf(i_0_14547,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_8478]),
    [final] ).

cnf(i_0_14548,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_8478]),
    [final] ).

cnf(i_0_14549,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_8478]),
    [final] ).

cnf(i_0_14550,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_8478]),
    [final] ).

cnf(i_0_14551,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_8048]),
    [final] ).

cnf(i_0_14552,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_8479]),
    [final] ).

cnf(i_0_14553,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_7099]),
    [final] ).

cnf(i_0_14554,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_8480]),
    [final] ).

cnf(i_0_14555,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_8480]),
    [final] ).

cnf(i_0_14556,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_8481]),
    [final] ).

cnf(i_0_14557,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_8482]),
    [final] ).

cnf(i_0_14558,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_8483]),
    [final] ).

cnf(i_0_14559,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk61_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_8161]),
    [final] ).

cnf(i_0_14560,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk567_3(X2,X3,X1)))
    | epred1_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk569_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7661]),
    [final] ).

cnf(i_0_14561,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_8484]),
    [final] ).

cnf(i_0_14562,plain,
    ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X1),X2,hAPP(c_Nat_OSuc,X3),X4)
    | ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1)),X2,X3,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_8485]),
    [final] ).

cnf(i_0_14563,plain,
    ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X1),X2,hAPP(c_Nat_OSuc,X3),X4)
    | ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1)),X2,X3,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_8486]),
    [final] ).

cnf(i_0_14564,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_8151]),
    [final] ).

cnf(i_0_14565,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk573_3(X1,X2,X3)))
    | epred2_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,esk570_3(X1,X2,X3)))
    | ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7651]),
    [final] ).

cnf(i_0_14566,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_8487]),
    [final] ).

cnf(i_0_14567,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_8488]),
    [final] ).

cnf(i_0_14568,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_8489]),
    [final] ).

cnf(i_0_14569,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_8490,c_0_6063]),
    [final] ).

cnf(i_0_14570,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_8491,c_0_6063]),
    [final] ).

cnf(i_0_14571,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_8492,c_0_6063]),
    [final] ).

cnf(i_0_14572,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_8493,c_0_6063]),
    [final] ).

cnf(i_0_14573,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_8494,c_0_6063]),
    [final] ).

cnf(i_0_14574,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_8495,c_0_6063]),
    [final] ).

cnf(i_0_14575,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_8496]),
    [final] ).

cnf(i_0_14576,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_8497]),
    [final] ).

cnf(i_0_14577,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_6771]),
    [final] ).

cnf(i_0_14578,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk367_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_8498]),
    [final] ).

cnf(i_0_14579,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_8499]),
    [final] ).

cnf(i_0_14580,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_8500,c_0_6088]),
    [final] ).

cnf(i_0_14581,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_8501]),
    [final] ).

cnf(i_0_14582,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_8502]),
    [final] ).

cnf(i_0_14583,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk569_3(X1,X2,X3)))
    | epred1_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,esk567_3(X1,X2,X3)))
    | ~ hBOOL(hAPP(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7661]),
    [final] ).

cnf(i_0_14584,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_8224]),
    [final] ).

cnf(i_0_14585,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_8503]),
    [final] ).

cnf(i_0_14586,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_8504]),
    [final] ).

cnf(i_0_14587,plain,
    ( c_Natural_Oevaln(c_Com_Ocom_OCond(X1,X3,X6),X2,X4,X5)
    | ~ hBOOL(hAPP(X1,X2))
    | ~ c_Natural_Oevaln(X3,X2,X4,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_8152]),
    [final] ).

cnf(i_0_14588,plain,
    ( c_Natural_Oevaln(c_Com_Ocom_OCond(X1,X3,X6),X2,X4,X5)
    | ~ hBOOL(hAPP(X1,X2))
    | ~ c_Natural_Oevaln(X3,X2,X4,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_8153]),
    [final] ).

cnf(i_0_14589,plain,
    ( c_Natural_Oevaln(c_Com_Ocom_OCond(X1,X3,X6),X2,X4,X5)
    | ~ hBOOL(hAPP(X1,X2))
    | ~ c_Natural_Oevaln(X3,X2,X4,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_8505]),
    [final] ).

cnf(i_0_14590,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_8092]),
    [final] ).

cnf(i_0_14591,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk473_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_8506]),
    [final] ).

cnf(i_0_14592,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk474_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_8093]),
    [final] ).

cnf(i_0_14593,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_8507]),
    [final] ).

cnf(i_0_14594,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk371_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_8508]),
    [final] ).

cnf(i_0_14595,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_8509]),
    [final] ).

cnf(i_0_14596,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_8510]),
    [final] ).

cnf(i_0_14597,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_8511]),
    [final] ).

cnf(i_0_14598,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk59_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_8177]),
    [final] ).

cnf(i_0_14599,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_8512,c_0_6216]),
    [final] ).

cnf(i_0_14600,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_8513,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_14601,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_8514]),
    [final] ).

cnf(i_0_14602,plain,
    ( c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1)),X2,X3,X4)
    | ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X1),X2,hAPP(c_Nat_OSuc,X3),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_8485]),
    [final] ).

cnf(i_0_14603,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_8515]),
    [final] ).

cnf(i_0_14604,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_8516]),
    [final] ).

cnf(i_0_14605,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_8200]),
    [final] ).

cnf(i_0_14606,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_8517]),
    [final] ).

cnf(i_0_14607,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_8207]),
    [final] ).

cnf(i_0_14608,plain,
    ( c_Natural_Oevaln(X1,X2,X5,X4)
    | ~ c_Natural_Oevaln(X1,X2,X3,X4)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_8518]),
    [final] ).

cnf(i_0_14609,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_8229]),
    [final] ).

cnf(i_0_14610,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_8519]),
    [final] ).

cnf(i_0_14611,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_8520]),
    [final] ).

cnf(i_0_14612,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_8520]),
    [final] ).

cnf(i_0_14613,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_8521]),
    [final] ).

cnf(i_0_14614,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_8521]),
    [final] ).

cnf(i_0_14615,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_8520]),
    [final] ).

cnf(i_0_14616,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_8520]),
    [final] ).

cnf(i_0_14617,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_8521]),
    [final] ).

cnf(i_0_14618,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_8521]),
    [final] ).

cnf(i_0_14619,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_8522]),
    [final] ).

cnf(i_0_14620,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_8522]),
    [final] ).

cnf(i_0_14621,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_8522]),
    [final] ).

cnf(i_0_14622,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_8522]),
    [final] ).

cnf(i_0_14623,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk532_3(X1,X2,X3)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X2,X1)))
    | c_List_Oall__interval__int(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8523]),
    [final] ).

cnf(i_0_14624,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_7440]),
    [final] ).

cnf(i_0_14625,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_7441]),
    [final] ).

cnf(i_0_14626,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_7442]),
    [final] ).

cnf(i_0_14627,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_7443]),
    [final] ).

cnf(i_0_14628,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_8524,c_0_6063]),c_0_6063]),
    [final] ).

cnf(i_0_14629,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_8525,c_0_6063]),c_0_6063]),
    [final] ).

cnf(i_0_14630,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_8526]),
    [final] ).

cnf(i_0_14631,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_8527]),
    [final] ).

cnf(i_0_14632,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_8528]),
    [final] ).

cnf(i_0_14633,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_8529]),
    [final] ).

cnf(i_0_14634,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_7913]),
    [final] ).

cnf(i_0_14635,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_8530]),
    [final] ).

cnf(i_0_14636,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_7914]),
    [final] ).

cnf(i_0_14637,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_8531]),
    [final] ).

cnf(i_0_14638,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_8532]),
    [final] ).

cnf(i_0_14639,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_8101]),
    [final] ).

cnf(i_0_14640,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_8533,c_0_6063]),c_0_6063]),
    [final] ).

cnf(i_0_14641,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_8534,c_0_6063]),c_0_6063]),
    [final] ).

cnf(i_0_14642,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_8535]),
    [final] ).

cnf(i_0_14643,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_8536]),
    [final] ).

cnf(i_0_14644,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_8104]),
    [final] ).

cnf(i_0_14645,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_8537]),
    [final] ).

cnf(i_0_14646,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_8538]),
    [final] ).

cnf(i_0_14647,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_8539]),
    [final] ).

cnf(i_0_14648,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_8540]),
    [final] ).

cnf(i_0_14649,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_8541]),
    [final] ).

cnf(i_0_14650,plain,
    ( c_List_Olist__ex1(X3,X2,X1)
    | esk522_4(X1,X2,X3,X4) != X4
    | ~ hBOOL(hAPP(hAPP(c_member(X3),X4),hAPP(c_List_Oset(X3),X1)))
    | ~ hBOOL(hAPP(X2,X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7260]),
    [final] ).

cnf(i_0_14651,plain,
    ( c_List_Olist__ex1(X3,X2,X1)
    | esk511_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_7261]),
    [final] ).

cnf(i_0_14652,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_8542]),
    [final] ).

cnf(i_0_14653,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_8543,c_0_6064]),
    [final] ).

cnf(i_0_14654,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_8544]),
    [final] ).

cnf(i_0_14655,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_8545]),
    [final] ).

cnf(i_0_14656,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_8545]),
    [final] ).

cnf(i_0_14657,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk393_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_7844]),
    [final] ).

cnf(i_0_14658,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk392_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_7844]),
    [final] ).

cnf(i_0_14659,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk341_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_8151]),
    [final] ).

cnf(i_0_14660,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_8546]),
    [final] ).

cnf(i_0_14661,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_8547]),
    [final] ).

cnf(i_0_14662,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_7115]),
    [final] ).

cnf(i_0_14663,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_8548]),
    [final] ).

cnf(i_0_14664,plain,
    ( hBOOL(hAPP(X1,hAPP(hAPP(c_Product__Type_OPair(X3,X2),X4),X5)))
    | ~ hBOOL(hAPP(X1,esk81_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_7226]),
    [final] ).

cnf(i_0_14665,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_6185]),
    [final] ).

cnf(i_0_14666,plain,
    ( hBOOL(hAPP(X1,X2))
    | c_Natural_Oevaln(c_Com_Ocom_OCond(X1,X6,X3),X2,X4,X5)
    | ~ c_Natural_Oevaln(X3,X2,X4,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_8152]),
    [final] ).

cnf(i_0_14667,plain,
    ( hBOOL(hAPP(X1,X2))
    | c_Natural_Oevaln(c_Com_Ocom_OCond(X1,X6,X3),X2,X4,X5)
    | ~ c_Natural_Oevaln(X3,X2,X4,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_8153]),
    [final] ).

cnf(i_0_14668,plain,
    ( hBOOL(hAPP(X1,X2))
    | c_Natural_Oevaln(c_Com_Ocom_OCond(X1,X6,X3),X2,X4,X5)
    | ~ c_Natural_Oevaln(X3,X2,X4,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_8549]),
    [final] ).

cnf(i_0_14669,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_8476]),
    [final] ).

cnf(i_0_14670,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_8477]),
    [final] ).

cnf(i_0_14671,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 != esk232_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_7281]),
    [final] ).

cnf(i_0_14672,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_8550]),
    [final] ).

cnf(i_0_14673,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_7322]),
    [final] ).

cnf(i_0_14674,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_8551]),
    [final] ).

cnf(i_0_14675,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_8552]),
    [final] ).

cnf(i_0_14676,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_8553]),
    [final] ).

cnf(i_0_14677,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_8554]),
    [final] ).

cnf(i_0_14678,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_8555]),
    [final] ).

cnf(i_0_14679,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_8556]),
    [final] ).

cnf(i_0_14680,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_8557]),
    [final] ).

cnf(i_0_14681,plain,
    ( c_Equiv__Relations_Opart__equivp(X3,X1)
    | ~ hBOOL(hAPP(hAPP(X1,esk551_1(X1)),esk552_1(X1)))
    | ~ hBOOL(hAPP(hAPP(X1,esk551_1(X1)),esk551_1(X1)))
    | ~ hBOOL(hAPP(hAPP(X1,esk552_1(X1)),esk552_1(X1)))
    | hAPP(X1,esk551_1(X1)) != hAPP(X1,esk552_1(X1))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8558]),
    [final] ).

cnf(i_0_14682,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_8479]),
    [final] ).

cnf(i_0_14683,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_8559]),
    [final] ).

cnf(i_0_14684,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_8560]),
    [final] ).

cnf(i_0_14685,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk61_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_8161]),
    [final] ).

cnf(i_0_14686,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCond(X1,X2,X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X2)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X3))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(split_conjunct,[status(thm)],[i_0_8561]),
    [final] ).

cnf(i_0_14687,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_8562]),
    [final] ).

cnf(i_0_14688,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_8563]),
    [final] ).

cnf(i_0_14689,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_6609]),
    [final] ).

cnf(i_0_14690,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk571_3(X2,X3,X1)))
    | X2 = 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_7651]),
    [final] ).

cnf(i_0_14691,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk567_3(X2,X3,X1)))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk569_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_7661]),
    [final] ).

cnf(i_0_14692,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_8564]),
    [final] ).

cnf(i_0_14693,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_8565]),
    [final] ).

cnf(i_0_14694,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_8566]),
    [final] ).

cnf(i_0_14695,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_8567]),
    [final] ).

cnf(i_0_14696,plain,
    ( c_Big__Operators_Olinorder__class_OMin(X1,X3) = X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),esk473_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_8506]),
    [final] ).

cnf(i_0_14697,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk231_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_7281]),
    [final] ).

cnf(i_0_14698,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_8568]),
    [final] ).

cnf(i_0_14699,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_8569]),
    [final] ).

cnf(i_0_14700,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_8570]),
    [final] ).

cnf(i_0_14701,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_8571]),
    [final] ).

cnf(i_0_14702,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_8387]),
    [final] ).

cnf(i_0_14703,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_8572]),
    [final] ).

cnf(i_0_14704,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_8573]),
    [final] ).

cnf(i_0_14705,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_8574]),
    [final] ).

cnf(i_0_14706,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_8575]),
    [final] ).

cnf(i_0_14707,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk470_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_8576]),
    [final] ).

cnf(i_0_14708,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk394_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_8577]),
    [final] ).

cnf(i_0_14709,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk391_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_8578]),
    [final] ).

cnf(i_0_14710,plain,
    hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(X1,X2)),X3),hAPP(hAPP(hAPP(c_Natural_Oupdate,X3),X1),hAPP(X2,X3)))),
    inference(split_conjunct,[status(thm)],[i_0_8579]),
    [final] ).

cnf(i_0_14711,plain,
    hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(X1,X2)),X3),hAPP(hAPP(hAPP(c_Natural_Oupdate,X3),X1),hAPP(X2,X3)))),
    inference(split_conjunct,[status(thm)],[i_0_8580]),
    [final] ).

cnf(i_0_14712,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_8581]),
    [final] ).

cnf(i_0_14713,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_7557]),
    [final] ).

cnf(i_0_14714,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_7558]),
    [final] ).

cnf(i_0_14715,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_8582]),
    [final] ).

cnf(i_0_14716,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_8520]),
    [final] ).

cnf(i_0_14717,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_8583]),
    [final] ).

cnf(i_0_14718,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_8584]),
    [final] ).

cnf(i_0_14719,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_8521]),
    [final] ).

cnf(i_0_14720,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_8585]),
    [final] ).

cnf(i_0_14721,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_8586]),
    [final] ).

cnf(i_0_14722,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_8587]),
    [final] ).

cnf(i_0_14723,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_8522]),
    [final] ).

cnf(i_0_14724,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_8588]),
    [final] ).

cnf(i_0_14725,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_8589]),
    [final] ).

cnf(i_0_14726,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_8590]),
    [final] ).

cnf(i_0_14727,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_8591]),
    [final] ).

cnf(i_0_14728,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk68_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_7411]),
    [final] ).

cnf(i_0_14729,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_8592]),
    [final] ).

cnf(i_0_14730,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_8593]),
    [final] ).

cnf(i_0_14731,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_8594]),
    [final] ).

cnf(i_0_14732,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_8595,c_0_6088]),
    [final] ).

cnf(i_0_14733,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_8596]),
    [final] ).

cnf(i_0_14734,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),esk471_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8228]),
    [final] ).

cnf(i_0_14735,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_8597,c_0_6181]),c_0_6181]),
    [final] ).

cnf(i_0_14736,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_8598,c_0_6181]),c_0_6181]),
    [final] ).

cnf(i_0_14737,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_8599]),
    [final] ).

cnf(i_0_14738,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk368_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_8149]),
    [final] ).

cnf(i_0_14739,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_8600]),
    [final] ).

cnf(i_0_14740,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_8601]),
    [final] ).

cnf(i_0_14741,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk320_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_8602]),
    [final] ).

cnf(i_0_14742,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk573_3(X1,X2,X3)))
    | X1 = 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_7651]),
    [final] ).

cnf(i_0_14743,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk569_3(X1,X2,X3)))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,esk567_3(X1,X2,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7661]),
    [final] ).

cnf(i_0_14744,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_8603]),
    [final] ).

cnf(i_0_14745,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X4)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool)),X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8604]),
    [final] ).

cnf(i_0_14746,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X3)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool)),X2),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8605]),
    [final] ).

cnf(i_0_14747,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_8606]),
    [final] ).

cnf(i_0_14748,plain,
    ( hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),esk476_3(X3,X1,X2))))
    | ~ c_List_Olist__ex(X2,X1,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8556]),
    [final] ).

cnf(i_0_14749,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_8607]),
    [final] ).

cnf(i_0_14750,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_8608]),
    [final] ).

cnf(i_0_14751,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_8609]),
    [final] ).

cnf(i_0_14752,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_8610]),
    [final] ).

cnf(i_0_14753,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_8611]),
    [final] ).

cnf(i_0_14754,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_8612]),
    [final] ).

cnf(i_0_14755,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_8613]),
    [final] ).

cnf(i_0_14756,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_8190]),
    [final] ).

cnf(i_0_14757,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_8614]),
    [final] ).

cnf(i_0_14758,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_8123]),
    [final] ).

cnf(i_0_14759,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk573_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | epred2_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7651]),
    [final] ).

cnf(i_0_14760,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_8615]),
    [final] ).

cnf(i_0_14761,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),esk531_2(X2,X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8616]),
    [final] ).

cnf(i_0_14762,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_8617]),
    [final] ).

cnf(i_0_14763,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_8618]),
    [final] ).

cnf(i_0_14764,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_8619]),
    [final] ).

cnf(i_0_14765,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_8620]),
    [final] ).

cnf(i_0_14766,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_8612]),
    [final] ).

cnf(i_0_14767,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_8613]),
    [final] ).

cnf(i_0_14768,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_8621]),
    [final] ).

cnf(i_0_14769,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_8622]),
    [final] ).

cnf(i_0_14770,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_8623]),
    [final] ).

cnf(i_0_14771,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_8624]),
    [final] ).

cnf(i_0_14772,plain,
    ( hAPP(X1,esk141_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_7326]),
    [final] ).

cnf(i_0_14773,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_8625]),
    [final] ).

cnf(i_0_14774,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_8626]),
    [final] ).

cnf(i_0_14775,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_8627]),
    [final] ).

cnf(i_0_14776,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_7914]),
    [final] ).

cnf(i_0_14777,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_7913]),
    [final] ).

cnf(i_0_14778,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk573_3(X1,X2,X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk571_3(X1,X2,X3)))
    | epred2_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7651]),
    [final] ).

cnf(i_0_14779,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 != esk234_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_7289]),
    [final] ).

cnf(i_0_14780,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk190_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_8628]),
    [final] ).

cnf(i_0_14781,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk233_3(X2,X3,X1)),X3))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X2),X3) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7289]),
    [final] ).

cnf(i_0_14782,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_8629]),
    [final] ).

cnf(i_0_14783,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),esk419_2(X1,X2)),c_Int_OInteg))
    | hBOOL(hAPP(X2,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_8630]),
    [final] ).

cnf(i_0_14784,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_8042]),
    [final] ).

cnf(i_0_14785,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_8631,c_0_6063]),
    [final] ).

cnf(i_0_14786,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk569_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | epred1_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7661]),
    [final] ).

cnf(i_0_14787,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_8632]),
    [final] ).

cnf(i_0_14788,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_8633]),
    [final] ).

cnf(i_0_14789,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_8634]),
    [final] ).

cnf(i_0_14790,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_8593]),
    [final] ).

cnf(i_0_14791,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_8635]),
    [final] ).

cnf(i_0_14792,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk59_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_8177]),
    [final] ).

cnf(i_0_14793,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_8636]),
    [final] ).

cnf(i_0_14794,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_8637]),
    [final] ).

cnf(i_0_14795,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_8638]),
    [final] ).

cnf(i_0_14796,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),esk571_3(X1,X2,X3)),X1))
    | epred2_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7651]),
    [final] ).

cnf(i_0_14797,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_8639]),
    [final] ).

cnf(i_0_14798,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk476_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_8556]),
    [final] ).

cnf(i_0_14799,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_8640]),
    [final] ).

cnf(i_0_14800,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_8641]),
    [final] ).

cnf(i_0_14801,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk569_3(X1,X2,X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk567_3(X1,X2,X3)))
    | epred1_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7661]),
    [final] ).

cnf(i_0_14802,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_8642]),
    [final] ).

cnf(i_0_14803,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_8643]),
    [final] ).

cnf(i_0_14804,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_8644]),
    [final] ).

cnf(i_0_14805,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_8645]),
    [final] ).

cnf(i_0_14806,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_8646]),
    [final] ).

cnf(i_0_14807,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_8647]),
    [final] ).

cnf(i_0_14808,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_8648]),
    [final] ).

cnf(i_0_14809,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_8649]),
    [final] ).

cnf(i_0_14810,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_8650]),
    [final] ).

cnf(i_0_14811,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_8651]),
    [final] ).

cnf(i_0_14812,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_8652]),
    [final] ).

cnf(i_0_14813,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_8653]),
    [final] ).

cnf(i_0_14814,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_8040]),
    [final] ).

cnf(i_0_14815,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_8039]),
    [final] ).

cnf(i_0_14816,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_8654]),
    [final] ).

cnf(i_0_14817,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_8655]),
    [final] ).

cnf(i_0_14818,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_8656]),
    [final] ).

cnf(i_0_14819,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_8555]),
    [final] ).

cnf(i_0_14820,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),esk567_3(X1,X2,X3)),X1))
    | epred1_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7661]),
    [final] ).

cnf(i_0_14821,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_8657]),
    [final] ).

cnf(i_0_14822,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_8658]),
    [final] ).

cnf(i_0_14823,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_8659]),
    [final] ).

cnf(i_0_14824,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_8660]),
    [final] ).

cnf(i_0_14825,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_8661]),
    [final] ).

cnf(i_0_14826,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk493_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_7044]),
    [final] ).

cnf(i_0_14827,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_8662]),
    [final] ).

cnf(i_0_14828,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_8663]),
    [final] ).

cnf(i_0_14829,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk191_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_8664]),
    [final] ).

cnf(i_0_14830,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_8665]),
    [final] ).

cnf(i_0_14831,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_8236]),
    [final] ).

cnf(i_0_14832,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_8237]),
    [final] ).

cnf(i_0_14833,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_8238]),
    [final] ).

cnf(i_0_14834,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_8666]),
    [final] ).

cnf(i_0_14835,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_8667]),
    [final] ).

cnf(i_0_14836,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_8162]),
    [final] ).

cnf(i_0_14837,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_8668]),
    [final] ).

cnf(i_0_14838,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_8669]),
    [final] ).

cnf(i_0_14839,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_8520]),
    [final] ).

cnf(i_0_14840,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_8583]),
    [final] ).

cnf(i_0_14841,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_8670]),
    [final] ).

cnf(i_0_14842,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_8521]),
    [final] ).

cnf(i_0_14843,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_8671]),
    [final] ).

cnf(i_0_14844,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_8522]),
    [final] ).

cnf(i_0_14845,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_8672]),
    [final] ).

cnf(i_0_14846,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_8501]),
    [final] ).

cnf(i_0_14847,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_8502]),
    [final] ).

cnf(i_0_14848,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_8673]),
    [final] ).

cnf(i_0_14849,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_8674]),
    [final] ).

cnf(i_0_14850,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_8675]),
    [final] ).

cnf(i_0_14851,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),esk499_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_8067]),
    [final] ).

cnf(i_0_14852,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_8676]),
    [final] ).

cnf(i_0_14853,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_8555]),
    [final] ).

cnf(i_0_14854,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_8677]),
    [final] ).

cnf(i_0_14855,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_6361]),
    [final] ).

cnf(i_0_14856,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_8678]),
    [final] ).

cnf(i_0_14857,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_8679]),
    [final] ).

cnf(i_0_14858,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_8680,c_0_6216]),
    [final] ).

cnf(i_0_14859,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_8681]),
    [final] ).

cnf(i_0_14860,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_8682]),
    [final] ).

cnf(i_0_14861,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_8683]),
    [final] ).

cnf(i_0_14862,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_8684]),
    [final] ).

cnf(i_0_14863,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_8685]),
    [final] ).

cnf(i_0_14864,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_8686]),
    [final] ).

cnf(i_0_14865,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_8687]),
    [final] ).

cnf(i_0_14866,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_8688,c_0_6062]),c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_14867,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_8689]),
    [final] ).

cnf(i_0_14868,plain,
    ( X1 = hAPP(hAPP(c_List_Olist_OCons(X2),esk346_3(X3,X1,X2)),esk347_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_8229]),
    [final] ).

cnf(i_0_14869,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_8690]),
    [final] ).

cnf(i_0_14870,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk122_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_8691]),
    [final] ).

cnf(i_0_14871,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk121_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_8691]),
    [final] ).

cnf(i_0_14872,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))
    | esk373_3(X1,X2,X3) != esk374_3(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7550]),
    [final] ).

cnf(i_0_14873,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_8692]),
    [final] ).

cnf(i_0_14874,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_8693]),
    [final] ).

cnf(i_0_14875,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_8264]),
    [final] ).

cnf(i_0_14876,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_8265]),
    [final] ).

cnf(i_0_14877,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_8694]),
    [final] ).

cnf(i_0_14878,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_8695]),
    [final] ).

cnf(i_0_14879,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_8696]),
    [final] ).

cnf(i_0_14880,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_8697]),
    [final] ).

cnf(i_0_14881,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk506_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_8094]),
    [final] ).

cnf(i_0_14882,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_8698]),
    [final] ).

cnf(i_0_14883,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_8699]),
    [final] ).

cnf(i_0_14884,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk376_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_8700]),
    [final] ).

cnf(i_0_14885,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_8701]),
    [final] ).

cnf(i_0_14886,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_8702]),
    [final] ).

cnf(i_0_14887,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_7716]),
    [final] ).

cnf(i_0_14888,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),esk406_2(X3,X1)),X2))
    | X3 = c_List_Olist_ONil(X1)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),esk405_2(X3,X1))))
    | ~ c_List_Olinorder__class_Osorted(X1,X3)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7339]),
    [final] ).

cnf(i_0_14889,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk536_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))
    | ~ c_List_Olist__ex(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8703]),
    [final] ).

cnf(i_0_14890,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk535_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X3)))
    | ~ c_List_Olist__ex(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8704]),
    [final] ).

cnf(i_0_14891,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk521_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))
    | ~ c_List_Olist__ex1(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7260]),
    [final] ).

cnf(i_0_14892,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk510_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))
    | ~ c_List_Olist__ex1(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7261]),
    [final] ).

cnf(i_0_14893,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk478_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))
    | ~ c_List_Olist__ex(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8705]),
    [final] ).

cnf(i_0_14894,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_8706]),
    [final] ).

cnf(i_0_14895,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_8707]),
    [final] ).

cnf(i_0_14896,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_8288]),
    [final] ).

cnf(i_0_14897,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_8287]),
    [final] ).

cnf(i_0_14898,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_8286]),
    [final] ).

cnf(i_0_14899,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_8285]),
    [final] ).

cnf(i_0_14900,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_8289]),
    [final] ).

cnf(i_0_14901,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk573_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7651]),
    [final] ).

cnf(i_0_14902,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk569_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7661]),
    [final] ).

cnf(i_0_14903,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk363_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_8708]),
    [final] ).

cnf(i_0_14904,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_5330]),
    [final] ).

cnf(i_0_14905,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_8709]),
    [final] ).

cnf(i_0_14906,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_8710]),
    [final] ).

cnf(i_0_14907,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_8711]),
    [final] ).

cnf(i_0_14908,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_8712]),
    [final] ).

cnf(i_0_14909,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_8713]),
    [final] ).

cnf(i_0_14910,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_8714]),
    [final] ).

cnf(i_0_14911,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_8715,c_0_6138]),
    [final] ).

cnf(i_0_14912,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_8716]),
    [final] ).

cnf(i_0_14913,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_8717]),
    [final] ).

cnf(i_0_14914,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_8175]),
    [final] ).

cnf(i_0_14915,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_8718]),
    [final] ).

cnf(i_0_14916,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_8175]),
    [final] ).

cnf(i_0_14917,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_8719]),
    [final] ).

cnf(i_0_14918,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_8720]),
    [final] ).

cnf(i_0_14919,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_8721]),
    [final] ).

cnf(i_0_14920,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_8176]),
    [final] ).

cnf(i_0_14921,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_8722]),
    [final] ).

cnf(i_0_14922,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_8176]),
    [final] ).

cnf(i_0_14923,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_8723]),
    [final] ).

cnf(i_0_14924,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_8724]),
    [final] ).

cnf(i_0_14925,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk230_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_8725]),
    [final] ).

cnf(i_0_14926,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk142_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_8726]),
    [final] ).

cnf(i_0_14927,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_8687]),
    [final] ).

cnf(i_0_14928,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_8687]),
    [final] ).

cnf(i_0_14929,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,esk65_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8727]),
    [final] ).

cnf(i_0_14930,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,esk64_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8728]),
    [final] ).

cnf(i_0_14931,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_8729]),
    [final] ).

cnf(i_0_14932,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_8730]),
    [final] ).

cnf(i_0_14933,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk573_3(X1,X2,X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk571_3(X1,X2,X3)))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7651]),
    [final] ).

cnf(i_0_14934,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk569_3(X1,X2,X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk567_3(X1,X2,X3)))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7661]),
    [final] ).

cnf(i_0_14935,plain,
    ( hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(X5,X1,X4),X2),X3))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(X4,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8375]),
    [final] ).

cnf(i_0_14936,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_8731]),
    [final] ).

cnf(i_0_14937,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_8125]),
    [final] ).

cnf(i_0_14938,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_8732]),
    [final] ).

cnf(i_0_14939,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_8733,c_0_8319]),c_0_8319]),
    [final] ).

cnf(i_0_14940,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSemi(X1,X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X1)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(split_conjunct,[status(thm)],[i_0_8734]),
    [final] ).

cnf(i_0_14941,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_8735]),
    [final] ).

cnf(i_0_14942,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),esk571_3(X1,X2,X3)),X1))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7651]),
    [final] ).

cnf(i_0_14943,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),esk567_3(X1,X2,X3)),X1))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7661]),
    [final] ).

cnf(i_0_14944,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_8736]),
    [final] ).

cnf(i_0_14945,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_8737]),
    [final] ).

cnf(i_0_14946,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_8738]),
    [final] ).

cnf(i_0_14947,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_8738]),
    [final] ).

cnf(i_0_14948,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_8739]),
    [final] ).

cnf(i_0_14949,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_8313]),
    [final] ).

cnf(i_0_14950,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_8740]),
    [final] ).

cnf(i_0_14951,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_8741]),
    [final] ).

cnf(i_0_14952,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_8742]),
    [final] ).

cnf(i_0_14953,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_8743]),
    [final] ).

cnf(i_0_14954,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_8744]),
    [final] ).

cnf(i_0_14955,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_8745]),
    [final] ).

cnf(i_0_14956,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_8746]),
    [final] ).

cnf(i_0_14957,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_8747]),
    [final] ).

cnf(i_0_14958,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_8748]),
    [final] ).

cnf(i_0_14959,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_8749]),
    [final] ).

cnf(i_0_14960,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_8750]),
    [final] ).

cnf(i_0_14961,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_8751]),
    [final] ).

cnf(i_0_14962,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_8752]),
    [final] ).

cnf(i_0_14963,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_5327]),
    [final] ).

cnf(i_0_14964,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_8753,c_0_6181]),c_0_6181]),
    [final] ).

cnf(i_0_14965,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_8754]),
    [final] ).

cnf(i_0_14966,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_8755]),
    [final] ).

cnf(i_0_14967,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_8441]),
    [final] ).

cnf(i_0_14968,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_8756]),
    [final] ).

cnf(i_0_14969,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_8756]),
    [final] ).

cnf(i_0_14970,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_8442]),
    [final] ).

cnf(i_0_14971,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_8757]),
    [final] ).

cnf(i_0_14972,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_8757]),
    [final] ).

cnf(i_0_14973,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_8213]),
    [final] ).

cnf(i_0_14974,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_8758]),
    [final] ).

cnf(i_0_14975,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_8759]),
    [final] ).

cnf(i_0_14976,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_8454]),
    [final] ).

cnf(i_0_14977,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_8760,c_0_6713]),
    [final] ).

cnf(i_0_14978,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_8761]),
    [final] ).

cnf(i_0_14979,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_8762]),
    [final] ).

cnf(i_0_14980,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_8687]),
    [final] ).

cnf(i_0_14981,plain,
    ( hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,X2)))
    | ~ hBOOL(hAPP(X1,esk61_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8161]),
    [final] ).

cnf(i_0_14982,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_8763]),
    [final] ).

cnf(i_0_14983,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),esk376_3(X3,X2,X1)))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8700]),
    [final] ).

cnf(i_0_14984,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_8764]),
    [final] ).

cnf(i_0_14985,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_8765]),
    [final] ).

cnf(i_0_14986,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_8094]),
    [final] ).

cnf(i_0_14987,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),esk67_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_8766]),
    [final] ).

cnf(i_0_14988,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk397_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))
    | c_List_OtakeWhile(X1,X3,X2) = X2 ),
    inference(split_conjunct,[status(thm)],[i_0_8767]),
    [final] ).

cnf(i_0_14989,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_8768]),
    [final] ).

cnf(i_0_14990,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_8769]),
    [final] ).

cnf(i_0_14991,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk508_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X3)))
    | c_List_Olist__all(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8770]),
    [final] ).

cnf(i_0_14992,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk509_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))
    | c_List_Olist__all(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8771]),
    [final] ).

cnf(i_0_14993,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk507_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))
    | c_List_Olist__all(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8772]),
    [final] ).

cnf(i_0_14994,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_8773]),
    [final] ).

cnf(i_0_14995,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,X3,X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8774]),
    [final] ).

cnf(i_0_14996,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_8775,c_0_6281]),
    [final] ).

cnf(i_0_14997,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_8776]),
    [final] ).

cnf(i_0_14998,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_8777]),
    [final] ).

cnf(i_0_14999,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_8778]),
    [final] ).

cnf(i_0_15000,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_8779]),
    [final] ).

cnf(i_0_15001,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_8780]),
    [final] ).

cnf(i_0_15002,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_8781]),
    [final] ).

cnf(i_0_15003,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_8782]),
    [final] ).

cnf(i_0_15004,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_8783]),
    [final] ).

cnf(i_0_15005,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_8784]),
    [final] ).

cnf(i_0_15006,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_8785]),
    [final] ).

cnf(i_0_15007,plain,
    ( c_Natural_Oevaln(X1,X2,hAPP(c_Nat_OSuc,X3),X4)
    | ~ c_Natural_Oevaln(X1,X2,X3,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_8786]),
    [final] ).

cnf(i_0_15008,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),esk63_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_7000]),
    [final] ).

cnf(i_0_15009,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_8504]),
    [final] ).

cnf(i_0_15010,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_8787]),
    [final] ).

cnf(i_0_15011,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_8788]),
    [final] ).

cnf(i_0_15012,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_8789]),
    [final] ).

cnf(i_0_15013,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk218_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_8790]),
    [final] ).

cnf(i_0_15014,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_8791]),
    [final] ).

cnf(i_0_15015,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_7061]),
    [final] ).

cnf(i_0_15016,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_8792]),
    [final] ).

cnf(i_0_15017,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_8793,c_0_6181]),c_0_6181]),
    [final] ).

cnf(i_0_15018,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_8794]),
    [final] ).

cnf(i_0_15019,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_8794]),
    [final] ).

cnf(i_0_15020,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_8795]),
    [final] ).

cnf(i_0_15021,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk383_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_8796]),
    [final] ).

cnf(i_0_15022,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_8624]),
    [final] ).

cnf(i_0_15023,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_8797]),
    [final] ).

cnf(i_0_15024,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_8798]),
    [final] ).

cnf(i_0_15025,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_8799]),
    [final] ).

cnf(i_0_15026,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_8800]),
    [final] ).

cnf(i_0_15027,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_8801]),
    [final] ).

cnf(i_0_15028,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_8802]),
    [final] ).

cnf(i_0_15029,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_8803]),
    [final] ).

cnf(i_0_15030,plain,
    ( hBOOL(hAPP(X1,X3))
    | ~ hBOOL(hAPP(X1,esk191_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_8664]),
    [final] ).

cnf(i_0_15031,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_8804]),
    [final] ).

cnf(i_0_15032,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_8805]),
    [final] ).

cnf(i_0_15033,plain,
    ( hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2)))
    | ~ hBOOL(hAPP(X1,esk65_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(split_conjunct,[status(thm)],[i_0_8727]),
    [final] ).

cnf(i_0_15034,plain,
    ( hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2)))
    | ~ hBOOL(hAPP(X1,esk64_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(split_conjunct,[status(thm)],[i_0_8728]),
    [final] ).

cnf(i_0_15035,plain,
    ( hBOOL(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X2)))
    | ~ hBOOL(hAPP(X1,esk58_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(split_conjunct,[status(thm)],[i_0_8177]),
    [final] ).

cnf(i_0_15036,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk384_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_8806]),
    [final] ).

cnf(i_0_15037,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),esk470_3(X2,X3,X1)))
    | ~ c_List_Olinorder__class_Osorted(X1,X3)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8576]),
    [final] ).

cnf(i_0_15038,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),esk394_3(X3,X2,X1)))
    | ~ c_List_Olinorder__class_Osorted(X1,X3)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8577]),
    [final] ).

cnf(i_0_15039,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),esk391_3(X3,X2,X1)))
    | ~ c_List_Olinorder__class_Osorted(X1,X3)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8578]),
    [final] ).

cnf(i_0_15040,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_8807]),
    [final] ).

cnf(i_0_15041,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(X1,X4)),X2),X5))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X4),X3),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_7252]),
    [final] ).

cnf(i_0_15042,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(X1,X4)),X2),X5))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X4),X3),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_8808]),
    [final] ).

cnf(i_0_15043,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_8809]),
    [final] ).

cnf(i_0_15044,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_8810,c_0_6713]),
    [final] ).

cnf(i_0_15045,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_8811]),
    [final] ).

cnf(i_0_15046,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_8812]),
    [final] ).

cnf(i_0_15047,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_8813]),
    [final] ).

cnf(i_0_15048,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_8814]),
    [final] ).

cnf(i_0_15049,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_8813]),
    [final] ).

cnf(i_0_15050,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_8815]),
    [final] ).

cnf(i_0_15051,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_8816]),
    [final] ).

cnf(i_0_15052,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_8817]),
    [final] ).

cnf(i_0_15053,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_8197]),
    [final] ).

cnf(i_0_15054,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_8198]),
    [final] ).

cnf(i_0_15055,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_8818]),
    [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),X2)))
    | ~ c_Wellfounded_OwfP(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8199]),
    [final] ).

cnf(i_0_15057,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_7731]),
    [final] ).

cnf(i_0_15058,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_8819]),
    [final] ).

cnf(i_0_15059,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_8820]),
    [final] ).

cnf(i_0_15060,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_8821]),
    [final] ).

cnf(i_0_15061,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_8822]),
    [final] ).

cnf(i_0_15062,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_8823]),
    [final] ).

cnf(i_0_15063,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_8824]),
    [final] ).

cnf(i_0_15064,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk219_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_8825]),
    [final] ).

cnf(i_0_15065,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_8826]),
    [final] ).

cnf(i_0_15066,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_8827]),
    [final] ).

cnf(i_0_15067,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_8828]),
    [final] ).

cnf(i_0_15068,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_8377]),
    [final] ).

cnf(i_0_15069,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_8378]),
    [final] ).

cnf(i_0_15070,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_8379]),
    [final] ).

cnf(i_0_15071,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X1)),esk338_3(X2,X3,X1)),X2))
    | c_Hoare__Mirabelle_Ohoare__valids(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7271]),
    [final] ).

cnf(i_0_15072,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_8829,c_0_6097]),
    [final] ).

cnf(i_0_15073,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_8830,c_0_6097]),
    [final] ).

cnf(i_0_15074,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_8831]),
    [final] ).

cnf(i_0_15075,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_8832]),
    [final] ).

cnf(i_0_15076,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_8833]),
    [final] ).

cnf(i_0_15077,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_8834]),
    [final] ).

cnf(i_0_15078,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_8835]),
    [final] ).

cnf(i_0_15079,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_8836]),
    [final] ).

cnf(i_0_15080,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_8837]),
    [final] ).

cnf(i_0_15081,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_Oplus__class_Oplus(tc_Int_Oint),X2),X2)) = 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)],[i_0_8838,c_0_6063]),c_0_6063]),c_0_6063]),
    [final] ).

cnf(i_0_15082,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_8839,c_0_6063]),c_0_6063]),c_0_6063]),
    [final] ).

cnf(i_0_15083,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_8840]),
    [final] ).

cnf(i_0_15084,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_8841]),
    [final] ).

cnf(i_0_15085,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_8842]),
    [final] ).

cnf(i_0_15086,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_8843]),
    [final] ).

cnf(i_0_15087,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_8844]),
    [final] ).

cnf(i_0_15088,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_8845]),
    [final] ).

cnf(i_0_15089,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_8846]),
    [final] ).

cnf(i_0_15090,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_8847]),
    [final] ).

cnf(i_0_15091,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_8848]),
    [final] ).

cnf(i_0_15092,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_8740]),
    [final] ).

cnf(i_0_15093,plain,
    hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),esk420_1(X1)),c_Int_OInteg)),
    inference(split_conjunct,[status(thm)],[i_0_8849]),
    [final] ).

cnf(i_0_15094,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_8850,c_0_6181]),c_0_6181]),
    [final] ).

cnf(i_0_15095,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_8851,c_0_6181]),c_0_6181]),
    [final] ).

cnf(i_0_15096,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_8852]),
    [final] ).

cnf(i_0_15097,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_8853]),
    [final] ).

cnf(i_0_15098,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_8431]),
    [final] ).

cnf(i_0_15099,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_8854]),
    [final] ).

cnf(i_0_15100,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_8855]),
    [final] ).

cnf(i_0_15101,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_8856]),
    [final] ).

cnf(i_0_15102,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_8857]),
    [final] ).

cnf(i_0_15103,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_8858]),
    [final] ).

cnf(i_0_15104,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_8859]),
    [final] ).

cnf(i_0_15105,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_8860]),
    [final] ).

cnf(i_0_15106,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_8860]),
    [final] ).

cnf(i_0_15107,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_8861]),
    [final] ).

cnf(i_0_15108,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_8862]),
    [final] ).

cnf(i_0_15109,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,esk61_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8161]),
    [final] ).

cnf(i_0_15110,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_8821]),
    [final] ).

cnf(i_0_15111,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_8863]),
    [final] ).

cnf(i_0_15112,plain,
    ( hBOOL(hAPP(X1,esk190_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_8628]),
    [final] ).

cnf(i_0_15113,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_8864]),
    [final] ).

cnf(i_0_15114,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_8865]),
    [final] ).

cnf(i_0_15115,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_8866]),
    [final] ).

cnf(i_0_15116,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_8867]),
    [final] ).

cnf(i_0_15117,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_8868]),
    [final] ).

cnf(i_0_15118,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_8869]),
    [final] ).

cnf(i_0_15119,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_8870]),
    [final] ).

cnf(i_0_15120,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_8871]),
    [final] ).

cnf(i_0_15121,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_8872]),
    [final] ).

cnf(i_0_15122,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_8873]),
    [final] ).

cnf(i_0_15123,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_8874]),
    [final] ).

cnf(i_0_15124,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_8875]),
    [final] ).

cnf(i_0_15125,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_8876]),
    [final] ).

cnf(i_0_15126,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_8877]),
    [final] ).

cnf(i_0_15127,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_8878]),
    [final] ).

cnf(i_0_15128,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_8879]),
    [final] ).

cnf(i_0_15129,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_8880]),
    [final] ).

cnf(i_0_15130,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_8881]),
    [final] ).

cnf(i_0_15131,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_8882]),
    [final] ).

cnf(i_0_15132,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_8656]),
    [final] ).

cnf(i_0_15133,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_8883]),
    [final] ).

cnf(i_0_15134,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_8884]),
    [final] ).

cnf(i_0_15135,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_8885]),
    [final] ).

cnf(i_0_15136,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_8886]),
    [final] ).

cnf(i_0_15137,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_8887]),
    [final] ).

cnf(i_0_15138,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_8888]),
    [final] ).

cnf(i_0_15139,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_8889]),
    [final] ).

cnf(i_0_15140,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_8890]),
    [final] ).

cnf(i_0_15141,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_8891]),
    [final] ).

cnf(i_0_15142,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_8892]),
    [final] ).

cnf(i_0_15143,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_8893]),
    [final] ).

cnf(i_0_15144,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_8894]),
    [final] ).

cnf(i_0_15145,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_8895]),
    [final] ).

cnf(i_0_15146,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_8896,c_0_6063]),
    [final] ).

cnf(i_0_15147,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_8740]),
    [final] ).

cnf(i_0_15148,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_8897]),
    [final] ).

cnf(i_0_15149,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_8230]),
    [final] ).

cnf(i_0_15150,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_8898]),
    [final] ).

cnf(i_0_15151,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk330_3(X2,X3,X1)),X2))
    | hBOOL(hAPP(c_Predicate_OPowp(X1,X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8899]),
    [final] ).

cnf(i_0_15152,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_8900]),
    [final] ).

cnf(i_0_15153,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk189_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_8628]),
    [final] ).

cnf(i_0_15154,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_8901]),
    [final] ).

cnf(i_0_15155,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_8902]),
    [final] ).

cnf(i_0_15156,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_8903]),
    [final] ).

cnf(i_0_15157,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_8904,c_0_6063]),
    [final] ).

cnf(i_0_15158,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_8149]),
    [final] ).

cnf(i_0_15159,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_8277]),
    [final] ).

cnf(i_0_15160,plain,
    ( hBOOL(hAPP(X1,esk56_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_7625]),
    [final] ).

cnf(i_0_15161,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_8905]),
    [final] ).

cnf(i_0_15162,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_8906]),
    [final] ).

cnf(i_0_15163,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_7932]),
    [final] ).

cnf(i_0_15164,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_7931]),
    [final] ).

cnf(i_0_15165,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_8907,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_15166,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_8410]),
    [final] ).

cnf(i_0_15167,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_8410]),
    [final] ).

cnf(i_0_15168,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_8472]),
    [final] ).

cnf(i_0_15169,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_7613]),
    [final] ).

cnf(i_0_15170,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_7716]),
    [final] ).

cnf(i_0_15171,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_8908]),
    [final] ).

cnf(i_0_15172,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_8691]),
    [final] ).

cnf(i_0_15173,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_7731]),
    [final] ).

cnf(i_0_15174,plain,
    ( X4 = hAPP(hAPP(hAPP(c_Natural_Oupdate,X3),X1),hAPP(X2,X3))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(X1,X2)),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8909]),
    [final] ).

cnf(i_0_15175,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,esk561_2(X2,X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_8910]),
    [final] ).

cnf(i_0_15176,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_6611]),
    [final] ).

cnf(i_0_15177,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_8911,c_0_6181]),
    [final] ).

cnf(i_0_15178,plain,
    ( X2 = X3
    | hAPP(hAPP(c_List_Onth(X1),X2),esk320_3(X1,X3,X2)) != hAPP(hAPP(c_List_Onth(X1),X3),esk320_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_8602]),
    [final] ).

cnf(i_0_15179,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_8684]),
    [final] ).

cnf(i_0_15180,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_8677]),
    [final] ).

cnf(i_0_15181,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_8895]),
    [final] ).

cnf(i_0_15182,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_8912]),
    [final] ).

cnf(i_0_15183,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_7061]),
    [final] ).

cnf(i_0_15184,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_8913]),
    [final] ).

cnf(i_0_15185,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_8799]),
    [final] ).

cnf(i_0_15186,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_8913]),
    [final] ).

cnf(i_0_15187,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_8799]),
    [final] ).

cnf(i_0_15188,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_8800]),
    [final] ).

cnf(i_0_15189,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_8914]),
    [final] ).

cnf(i_0_15190,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_8800]),
    [final] ).

cnf(i_0_15191,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_8914]),
    [final] ).

cnf(i_0_15192,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_8803]),
    [final] ).

cnf(i_0_15193,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_8803]),
    [final] ).

cnf(i_0_15194,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
    | epred2_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk572_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7651]),
    [final] ).

cnf(i_0_15195,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_8915]),
    [final] ).

cnf(i_0_15196,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_8916]),
    [final] ).

cnf(i_0_15197,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_8917]),
    [final] ).

cnf(i_0_15198,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_8918]),
    [final] ).

cnf(i_0_15199,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_8919]),
    [final] ).

cnf(i_0_15200,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_8920]),
    [final] ).

cnf(i_0_15201,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_8921]),
    [final] ).

cnf(i_0_15202,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_8922]),
    [final] ).

cnf(i_0_15203,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_8729]),
    [final] ).

cnf(i_0_15204,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_8424]),
    [final] ).

cnf(i_0_15205,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_8923]),
    [final] ).

cnf(i_0_15206,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_8924]),
    [final] ).

cnf(i_0_15207,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_8327]),
    [final] ).

cnf(i_0_15208,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_8925]),
    [final] ).

cnf(i_0_15209,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_8926]),
    [final] ).

cnf(i_0_15210,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_8927]),
    [final] ).

cnf(i_0_15211,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_8928]),
    [final] ).

cnf(i_0_15212,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,esk58_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8177]),
    [final] ).

cnf(i_0_15213,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk192_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_8664]),
    [final] ).

cnf(i_0_15214,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | epred2_3(X2,X3,X1)
    | ~ hBOOL(hAPP(X2,esk570_3(X1,X3,X2)))
    | ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7651]),
    [final] ).

cnf(i_0_15215,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_8929,c_0_6063]),
    [final] ).

cnf(i_0_15216,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_8930,c_0_6063]),
    [final] ).

cnf(i_0_15217,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_8931,c_0_6063]),
    [final] ).

cnf(i_0_15218,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_8932,c_0_6063]),
    [final] ).

cnf(i_0_15219,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_8933,c_0_6063]),
    [final] ).

cnf(i_0_15220,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_8934]),
    [final] ).

cnf(i_0_15221,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_8935,c_0_8936]),c_0_8936]),
    [final] ).

cnf(i_0_15222,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_8937,c_0_6097]),
    [final] ).

cnf(i_0_15223,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_8938,c_0_6097]),
    [final] ).

cnf(i_0_15224,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_8364]),
    [final] ).

cnf(i_0_15225,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
    | epred1_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk569_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7661]),
    [final] ).

cnf(i_0_15226,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_8939]),
    [final] ).

cnf(i_0_15227,plain,
    ( hBOOL(hAPP(hAPP(X1,esk85_3(X2,X1,X3)),X2))
    | hBOOL(hAPP(c_Wellfounded_Oaccp(X3,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8940]),
    [final] ).

cnf(i_0_15228,plain,
    ( hBOOL(hAPP(hAPP(X1,esk84_3(X2,X1,X3)),X2))
    | hBOOL(hAPP(c_Wellfounded_Oaccp(X3,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8941]),
    [final] ).

cnf(i_0_15229,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_8942,c_0_6088]),
    [final] ).

cnf(i_0_15230,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_8523]),
    [final] ).

cnf(i_0_15231,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_8943]),
    [final] ).

cnf(i_0_15232,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_8944,c_0_6216]),
    [final] ).

cnf(i_0_15233,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_8945]),
    [final] ).

cnf(i_0_15234,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_8946]),
    [final] ).

cnf(i_0_15235,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_8947]),
    [final] ).

cnf(i_0_15236,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_8948]),
    [final] ).

cnf(i_0_15237,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_8949]),
    [final] ).

cnf(i_0_15238,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_8950]),
    [final] ).

cnf(i_0_15239,plain,
    ( c_Hoare__Mirabelle_Otriple__valid(X1,X2,X4)
    | ~ c_Hoare__Mirabelle_Otriple__valid(X1,hAPP(c_Nat_OSuc,X2),esk335_3(X2,X3,X1))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X1)),X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8380]),
    [final] ).

cnf(i_0_15240,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_8951]),
    [final] ).

cnf(i_0_15241,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk116_3(X2,X3,X1)),X3))
    | c_Relation_Ototal__on(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6799]),
    [final] ).

cnf(i_0_15242,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk115_3(X2,X3,X1)),X3))
    | c_Relation_Ototal__on(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6799]),
    [final] ).

cnf(i_0_15243,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)
    | esk385_2(X1,X2) != c_List_Olist_ONil(X2) ),
    inference(rw,[status(thm)],[i_0_8952,c_0_6138]),
    [final] ).

cnf(i_0_15244,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)
    | esk386_2(X1,X2) != c_List_Olist_ONil(X2) ),
    inference(rw,[status(thm)],[i_0_8953,c_0_6138]),
    [final] ).

cnf(i_0_15245,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_8954]),
    [final] ).

cnf(i_0_15246,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_8955]),
    [final] ).

cnf(i_0_15247,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | epred1_3(X2,X3,X1)
    | ~ hBOOL(hAPP(X2,esk567_3(X1,X3,X2)))
    | ~ hBOOL(hAPP(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7661]),
    [final] ).

cnf(i_0_15248,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_8956]),
    [final] ).

cnf(i_0_15249,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_8957]),
    [final] ).

cnf(i_0_15250,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_8958]),
    [final] ).

cnf(i_0_15251,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_8959]),
    [final] ).

cnf(i_0_15252,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_8960]),
    [final] ).

cnf(i_0_15253,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_8577]),
    [final] ).

cnf(i_0_15254,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_8578]),
    [final] ).

cnf(i_0_15255,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_8961]),
    [final] ).

cnf(i_0_15256,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_15257,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_8962,c_0_6097]),
    [final] ).

cnf(i_0_15258,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_8963]),
    [final] ).

cnf(i_0_15259,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_8964]),
    [final] ).

cnf(i_0_15260,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_8965,c_0_6097]),
    [final] ).

cnf(i_0_15261,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),esk367_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_8498]),
    [final] ).

cnf(i_0_15262,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_8966]),
    [final] ).

cnf(i_0_15263,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_8967]),
    [final] ).

cnf(i_0_15264,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_8968]),
    [final] ).

cnf(i_0_15265,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_8968]),
    [final] ).

cnf(i_0_15266,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_8213]),
    [final] ).

cnf(i_0_15267,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_8969]),
    [final] ).

cnf(i_0_15268,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_8970]),
    [final] ).

cnf(i_0_15269,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_8971]),
    [final] ).

cnf(i_0_15270,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_8972]),
    [final] ).

cnf(i_0_15271,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_8973]),
    [final] ).

cnf(i_0_15272,plain,
    ( hBOOL(hAPP(X1,esk56_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_7625]),
    [final] ).

cnf(i_0_15273,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_8974,c_0_6138]),
    [final] ).

cnf(i_0_15274,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_8975]),
    [final] ).

cnf(i_0_15275,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_8976]),
    [final] ).

cnf(i_0_15276,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_8977]),
    [final] ).

cnf(i_0_15277,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_8978]),
    [final] ).

cnf(i_0_15278,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_8979]),
    [final] ).

cnf(i_0_15279,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_8980]),
    [final] ).

cnf(i_0_15280,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_8730]),
    [final] ).

cnf(i_0_15281,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_8981]),
    [final] ).

cnf(i_0_15282,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_8982]),
    [final] ).

cnf(i_0_15283,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_8983]),
    [final] ).

cnf(i_0_15284,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_8433]),
    [final] ).

cnf(i_0_15285,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_8984]),
    [final] ).

cnf(i_0_15286,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_8985]),
    [final] ).

cnf(i_0_15287,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_8986]),
    [final] ).

cnf(i_0_15288,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_8987]),
    [final] ).

cnf(i_0_15289,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_8988]),
    [final] ).

cnf(i_0_15290,plain,
    ( hBOOL(hAPP(X1,X3))
    | ~ hBOOL(hAPP(X1,esk219_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_8825]),
    [final] ).

cnf(i_0_15291,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_8989]),
    [final] ).

cnf(i_0_15292,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_8990,c_0_6097]),
    [final] ).

cnf(i_0_15293,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_8991]),
    [final] ).

cnf(i_0_15294,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_8992]),
    [final] ).

cnf(i_0_15295,plain,
    c_Hoare__Mirabelle_Otriple_Otriple__case(X1,X2,X3,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X4),X5),X6)) = hAPP(hAPP(hAPP(X3,X4),X5),X6),
    inference(split_conjunct,[status(thm)],[i_0_8993]),
    [final] ).

cnf(i_0_15296,plain,
    c_Hoare__Mirabelle_Otriple_Otriple__rec(X1,X2,X3,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X4),X5),X6)) = hAPP(hAPP(hAPP(X3,X4),X5),X6),
    inference(split_conjunct,[status(thm)],[i_0_8994]),
    [final] ).

cnf(i_0_15297,plain,
    ( hBOOL(hAPP(hAPP(X3,esk304_2(X4,X3)),X4))
    | ~ hBOOL(hAPP(c_Predicate_ORangeP(X1,X2,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8995]),
    [final] ).

cnf(i_0_15298,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_8996]),
    [final] ).

cnf(i_0_15299,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_8997]),
    [final] ).

cnf(i_0_15300,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_8998]),
    [final] ).

cnf(i_0_15301,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_8999]),
    [final] ).

cnf(i_0_15302,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_9000]),
    [final] ).

cnf(i_0_15303,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_9001,c_0_6181]),
    [final] ).

cnf(i_0_15304,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_9002]),
    [final] ).

cnf(i_0_15305,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_9003]),
    [final] ).

cnf(i_0_15306,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_7639]),
    [final] ).

cnf(i_0_15307,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_9004]),
    [final] ).

cnf(i_0_15308,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_9005]),
    [final] ).

cnf(i_0_15309,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),esk515_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_7220]),
    [final] ).

cnf(i_0_15310,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_9006]),
    [final] ).

cnf(i_0_15311,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk217_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_8790]),
    [final] ).

cnf(i_0_15312,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_9007]),
    [final] ).

cnf(i_0_15313,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_9008]),
    [final] ).

cnf(i_0_15314,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_8381]),
    [final] ).

cnf(i_0_15315,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_9009]),
    [final] ).

cnf(i_0_15316,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_9010]),
    [final] ).

cnf(i_0_15317,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_9011]),
    [final] ).

cnf(i_0_15318,plain,
    hAPP(hAPP(hAPP(c_COMBC(X1,X2,X3),X4),X5),X6) = hAPP(hAPP(X4,X6),X5),
    inference(split_conjunct,[status(thm)],[i_0_9012]),
    [final] ).

cnf(i_0_15319,plain,
    hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
    inference(split_conjunct,[status(thm)],[i_0_9013]),
    [final] ).

cnf(i_0_15320,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_9014]),
    [final] ).

cnf(i_0_15321,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_8885]),
    [final] ).

cnf(i_0_15322,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_8885]),
    [final] ).

cnf(i_0_15323,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_9015]),
    [final] ).

cnf(i_0_15324,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_9016]),
    [final] ).

cnf(i_0_15325,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_7400]),
    [final] ).

cnf(i_0_15326,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_7401]),
    [final] ).

cnf(i_0_15327,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_7402]),
    [final] ).

cnf(i_0_15328,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_9017]),
    [final] ).

cnf(i_0_15329,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_9018]),
    [final] ).

cnf(i_0_15330,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_9019]),
    [final] ).

cnf(i_0_15331,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_9020]),
    [final] ).

cnf(i_0_15332,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_7302]),
    [final] ).

cnf(i_0_15333,plain,
    ( hBOOL(hAPP(X1,esk515_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_7220]),
    [final] ).

cnf(i_0_15334,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_9021]),
    [final] ).

cnf(i_0_15335,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_9022]),
    [final] ).

cnf(i_0_15336,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_9023]),
    [final] ).

cnf(i_0_15337,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_9024]),
    [final] ).

cnf(i_0_15338,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_9025]),
    [final] ).

cnf(i_0_15339,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_9026]),
    [final] ).

cnf(i_0_15340,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_9027]),
    [final] ).

cnf(i_0_15341,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_9028]),
    [final] ).

cnf(i_0_15342,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_9029]),
    [final] ).

cnf(i_0_15343,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_9030]),
    [final] ).

cnf(i_0_15344,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk572_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_7651]),
    [final] ).

cnf(i_0_15345,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk569_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_7661]),
    [final] ).

cnf(i_0_15346,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_8401]),
    [final] ).

cnf(i_0_15347,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_9031]),
    [final] ).

cnf(i_0_15348,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_9032]),
    [final] ).

cnf(i_0_15349,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_8768]),
    [final] ).

cnf(i_0_15350,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_9033]),
    [final] ).

cnf(i_0_15351,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_8769]),
    [final] ).

cnf(i_0_15352,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_9034]),
    [final] ).

cnf(i_0_15353,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_8860]),
    [final] ).

cnf(i_0_15354,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_8860]),
    [final] ).

cnf(i_0_15355,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_8861]),
    [final] ).

cnf(i_0_15356,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_8862]),
    [final] ).

cnf(i_0_15357,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_9035]),
    [final] ).

cnf(i_0_15358,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_9036]),
    [final] ).

cnf(i_0_15359,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_9037]),
    [final] ).

cnf(i_0_15360,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),esk85_3(X3,X2,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8940]),
    [final] ).

cnf(i_0_15361,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),esk84_3(X3,X2,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8941]),
    [final] ).

cnf(i_0_15362,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_8401]),
    [final] ).

cnf(i_0_15363,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_9038,c_0_6088]),c_0_6088]),
    [final] ).

cnf(i_0_15364,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_9039]),
    [final] ).

cnf(i_0_15365,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_9040]),
    [final] ).

cnf(i_0_15366,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),esk371_2(X2,X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8508]),
    [final] ).

cnf(i_0_15367,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_9041]),
    [final] ).

cnf(i_0_15368,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_9042]),
    [final] ).

cnf(i_0_15369,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk220_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_8825]),
    [final] ).

cnf(i_0_15370,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_9043]),
    [final] ).

cnf(i_0_15371,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_9044]),
    [final] ).

cnf(i_0_15372,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_9045]),
    [final] ).

cnf(i_0_15373,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_9046]),
    [final] ).

cnf(i_0_15374,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_8730]),
    [final] ).

cnf(i_0_15375,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_9047]),
    [final] ).

cnf(i_0_15376,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_9048]),
    [final] ).

cnf(i_0_15377,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_9049]),
    [final] ).

cnf(i_0_15378,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_9050]),
    [final] ).

cnf(i_0_15379,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_9051]),
    [final] ).

cnf(i_0_15380,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_9052]),
    [final] ).

cnf(i_0_15381,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_9053]),
    [final] ).

cnf(i_0_15382,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_9054]),
    [final] ).

cnf(i_0_15383,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_9055]),
    [final] ).

cnf(i_0_15384,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_8499]),
    [final] ).

cnf(i_0_15385,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_9056]),
    [final] ).

cnf(i_0_15386,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_9057]),
    [final] ).

cnf(i_0_15387,plain,
    ( X5 = hAPP(hAPP(hAPP(c_Natural_Oupdate,X3),X1),hAPP(X2,X3))
    | ~ c_Natural_Oevaln(c_Com_Ocom_OAss(X1,X2),X3,X4,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_9058]),
    [final] ).

cnf(i_0_15388,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_9059]),
    [final] ).

cnf(i_0_15389,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_9060]),
    [final] ).

cnf(i_0_15390,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X2,X3,X1)
    | ~ hBOOL(hAPP(X2,esk570_3(X1,X3,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_7651]),
    [final] ).

cnf(i_0_15391,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X2,X3,X1)
    | ~ hBOOL(hAPP(X2,esk567_3(X1,X3,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_7661]),
    [final] ).

cnf(i_0_15392,plain,
    ( hBOOL(hAPP(X1,esk218_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_8790]),
    [final] ).

cnf(i_0_15393,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_9061]),
    [final] ).

cnf(i_0_15394,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_9062]),
    [final] ).

cnf(i_0_15395,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_9063,c_0_6063]),c_0_6063]),
    [final] ).

cnf(i_0_15396,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_9064]),
    [final] ).

cnf(i_0_15397,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_9065]),
    [final] ).

cnf(i_0_15398,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_9066]),
    [final] ).

cnf(i_0_15399,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_9067]),
    [final] ).

cnf(i_0_15400,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_8452]),
    [final] ).

cnf(i_0_15401,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)
    | esk341_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_8151]),
    [final] ).

cnf(i_0_15402,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_9068]),
    [final] ).

cnf(i_0_15403,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_9069]),
    [final] ).

cnf(i_0_15404,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_9069]),
    [final] ).

cnf(i_0_15405,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_9070]),
    [final] ).

cnf(i_0_15406,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_7330]),
    [final] ).

cnf(i_0_15407,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_7331]),
    [final] ).

cnf(i_0_15408,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_7332]),
    [final] ).

cnf(i_0_15409,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_7333]),
    [final] ).

cnf(i_0_15410,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_9071]),
    [final] ).

cnf(i_0_15411,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_7878]),
    [final] ).

cnf(i_0_15412,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_7061]),
    [final] ).

cnf(i_0_15413,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_8996]),
    [final] ).

cnf(i_0_15414,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_9072]),
    [final] ).

cnf(i_0_15415,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_9073]),
    [final] ).

cnf(i_0_15416,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_9074]),
    [final] ).

cnf(i_0_15417,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_9075]),
    [final] ).

cnf(i_0_15418,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_8652]),
    [final] ).

cnf(i_0_15419,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_8653]),
    [final] ).

cnf(i_0_15420,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_9076]),
    [final] ).

cnf(i_0_15421,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_9077]),
    [final] ).

cnf(i_0_15422,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_9078]),
    [final] ).

cnf(i_0_15423,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_9079]),
    [final] ).

cnf(i_0_15424,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_9080]),
    [final] ).

cnf(i_0_15425,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_9081]),
    [final] ).

cnf(i_0_15426,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_9082]),
    [final] ).

cnf(i_0_15427,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_9083]),
    [final] ).

cnf(i_0_15428,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_9084]),
    [final] ).

cnf(i_0_15429,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_9085]),
    [final] ).

cnf(i_0_15430,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)),esk571_3(X1,X2,X3)))
    | epred2_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7651]),
    [final] ).

cnf(i_0_15431,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_9086]),
    [final] ).

cnf(i_0_15432,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_9041]),
    [final] ).

cnf(i_0_15433,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_9041]),
    [final] ).

cnf(i_0_15434,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_9087]),
    [final] ).

cnf(i_0_15435,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_9088]),
    [final] ).

cnf(i_0_15436,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_9089]),
    [final] ).

cnf(i_0_15437,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_8889]),
    [final] ).

cnf(i_0_15438,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_9090]),
    [final] ).

cnf(i_0_15439,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_9091]),
    [final] ).

cnf(i_0_15440,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_9092]),
    [final] ).

cnf(i_0_15441,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_9093]),
    [final] ).

cnf(i_0_15442,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_9094]),
    [final] ).

cnf(i_0_15443,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_9095]),
    [final] ).

cnf(i_0_15444,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_8700]),
    [final] ).

cnf(i_0_15445,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_9096]),
    [final] ).

cnf(i_0_15446,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_9097]),
    [final] ).

cnf(i_0_15447,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_9098]),
    [final] ).

cnf(i_0_15448,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_9099]),
    [final] ).

cnf(i_0_15449,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_9100]),
    [final] ).

cnf(i_0_15450,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk573_3(X1,X2,X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | epred2_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7651]),
    [final] ).

cnf(i_0_15451,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_9101]),
    [final] ).

cnf(i_0_15452,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_9102]),
    [final] ).

cnf(i_0_15453,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_9103]),
    [final] ).

cnf(i_0_15454,plain,
    ( hBOOL(hAPP(X1,X2))
    | X3 = X2
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X4)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7171]),
    [final] ).

cnf(i_0_15455,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_9104]),
    [final] ).

cnf(i_0_15456,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_9105]),
    [final] ).

cnf(i_0_15457,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_9105]),
    [final] ).

cnf(i_0_15458,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_9106]),
    [final] ).

cnf(i_0_15459,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_9107]),
    [final] ).

cnf(i_0_15460,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)),esk567_3(X1,X2,X3)))
    | epred1_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7661]),
    [final] ).

cnf(i_0_15461,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_8478]),
    [final] ).

cnf(i_0_15462,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_9108]),
    [final] ).

cnf(i_0_15463,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_9109]),
    [final] ).

cnf(i_0_15464,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_9110]),
    [final] ).

cnf(i_0_15465,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_9111]),
    [final] ).

cnf(i_0_15466,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_9112]),
    [final] ).

cnf(i_0_15467,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_9113]),
    [final] ).

cnf(i_0_15468,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_9114]),
    [final] ).

cnf(i_0_15469,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_9115]),
    [final] ).

cnf(i_0_15470,plain,
    ( c_Natural_Oevaln(X1,X2,esk18_3(X3,X2,X1),X3)
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9116]),
    [final] ).

cnf(i_0_15471,plain,
    ( c_Natural_Oevaln(X1,X2,esk15_3(X3,X2,X1),X3)
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9117]),
    [final] ).

cnf(i_0_15472,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_8474]),
    [final] ).

cnf(i_0_15473,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_9054]),
    [final] ).

cnf(i_0_15474,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_9118]),
    [final] ).

cnf(i_0_15475,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_9119]),
    [final] ).

cnf(i_0_15476,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_9120]),
    [final] ).

cnf(i_0_15477,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_8441]),
    [final] ).

cnf(i_0_15478,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_9121]),
    [final] ).

cnf(i_0_15479,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_8442]),
    [final] ).

cnf(i_0_15480,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_9122]),
    [final] ).

cnf(i_0_15481,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_9123]),
    [final] ).

cnf(i_0_15482,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_9124]),
    [final] ).

cnf(i_0_15483,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_9125]),
    [final] ).

cnf(i_0_15484,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_9126]),
    [final] ).

cnf(i_0_15485,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_9127]),
    [final] ).

cnf(i_0_15486,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_9128]),
    [final] ).

cnf(i_0_15487,plain,
    hAPP(c_Fun_Ocomp(X1,X1,X2,c_Fun_Oid(X1)),X3) = X3,
    inference(split_conjunct,[status(thm)],[i_0_9129]),
    [final] ).

cnf(i_0_15488,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_9130]),
    [final] ).

cnf(i_0_15489,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_9131,c_0_8319]),
    [final] ).

cnf(i_0_15490,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_9132]),
    [final] ).

cnf(i_0_15491,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_9133]),
    [final] ).

cnf(i_0_15492,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_9134]),
    [final] ).

cnf(i_0_15493,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk569_3(X1,X2,X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | epred1_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7661]),
    [final] ).

cnf(i_0_15494,plain,
    ( hBOOL(hAPP(hAPP(X3,X4),esk372_2(X4,X3)))
    | ~ hBOOL(hAPP(c_Predicate_ODomainP(X1,X2,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_9135]),
    [final] ).

cnf(i_0_15495,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_9136]),
    [final] ).

cnf(i_0_15496,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_9137]),
    [final] ).

cnf(i_0_15497,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_8920]),
    [final] ).

cnf(i_0_15498,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_9138]),
    [final] ).

cnf(i_0_15499,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_7673]),
    [final] ).

cnf(i_0_15500,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_7667]),
    [final] ).

cnf(i_0_15501,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_8727]),
    [final] ).

cnf(i_0_15502,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_8728]),
    [final] ).

cnf(i_0_15503,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_9139]),
    [final] ).

cnf(i_0_15504,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_9140]),
    [final] ).

cnf(i_0_15505,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_9141,c_0_6216]),
    [final] ).

cnf(i_0_15506,plain,
    ( hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk50_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_9142]),
    [final] ).

cnf(i_0_15507,plain,
    hAPP(c_List_Ofoldl(X1,X2,X3,X4),c_List_Olist_ONil(X2)) = X4,
    inference(split_conjunct,[status(thm)],[i_0_9143]),
    [final] ).

cnf(i_0_15508,plain,
    hAPP(c_List_Olist_Olist__case(X1,X2,X3,X4),c_List_Olist_ONil(X2)) = X3,
    inference(split_conjunct,[status(thm)],[i_0_9144]),
    [final] ).

cnf(i_0_15509,plain,
    hAPP(c_Fun_Ocomp(X1,X2,X1,X3),c_Fun_Oid(X1)) = X3,
    inference(split_conjunct,[status(thm)],[i_0_9145]),
    [final] ).

cnf(i_0_15510,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_9146]),
    [final] ).

cnf(i_0_15511,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_9146]),
    [final] ).

cnf(i_0_15512,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_9147,c_0_6181]),
    [final] ).

cnf(i_0_15513,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_9148]),
    [final] ).

cnf(i_0_15514,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_9149]),
    [final] ).

cnf(i_0_15515,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_9150]),
    [final] ).

cnf(i_0_15516,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_9151]),
    [final] ).

cnf(i_0_15517,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_8822]),
    [final] ).

cnf(i_0_15518,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_9152]),
    [final] ).

cnf(i_0_15519,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_8823]),
    [final] ).

cnf(i_0_15520,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_8824]),
    [final] ).

cnf(i_0_15521,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_9153,c_0_6063]),
    [final] ).

cnf(i_0_15522,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_9154,c_0_6063]),
    [final] ).

cnf(i_0_15523,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_9155,c_0_6063]),
    [final] ).

cnf(i_0_15524,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_9156,c_0_6063]),
    [final] ).

cnf(i_0_15525,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_9157]),
    [final] ).

cnf(i_0_15526,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_9158]),
    [final] ).

cnf(i_0_15527,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_9159]),
    [final] ).

cnf(i_0_15528,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_8498]),
    [final] ).

cnf(i_0_15529,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_9160]),
    [final] ).

cnf(i_0_15530,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_9161]),
    [final] ).

cnf(i_0_15531,plain,
    ( c_FunDef_OTHE__default(X2,X1,X3) = c_HOL_OThe(X2,X3)
    | esk527_4(X1,X2,X3,X4) != X4
    | ~ hBOOL(hAPP(X3,X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8045]),
    [final] ).

cnf(i_0_15532,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_9162]),
    [final] ).

cnf(i_0_15533,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),esk182_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_6745]),
    [final] ).

cnf(i_0_15534,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_9163]),
    [final] ).

cnf(i_0_15535,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_15536,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_9164]),
    [final] ).

cnf(i_0_15537,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_9165]),
    [final] ).

cnf(i_0_15538,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_9166]),
    [final] ).

cnf(i_0_15539,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_9167]),
    [final] ).

cnf(i_0_15540,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_9168]),
    [final] ).

cnf(i_0_15541,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_8679]),
    [final] ).

cnf(i_0_15542,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_8832]),
    [final] ).

cnf(i_0_15543,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_8833]),
    [final] ).

cnf(i_0_15544,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_9169]),
    [final] ).

cnf(i_0_15545,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_9170]),
    [final] ).

cnf(i_0_15546,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_9171]),
    [final] ).

cnf(i_0_15547,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_9172]),
    [final] ).

cnf(i_0_15548,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_9173]),
    [final] ).

cnf(i_0_15549,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_8751]),
    [final] ).

cnf(i_0_15550,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_9174]),
    [final] ).

cnf(i_0_15551,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_8219]),
    [final] ).

cnf(i_0_15552,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_8219]),
    [final] ).

cnf(i_0_15553,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_9175]),
    [final] ).

cnf(i_0_15554,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_8600]),
    [final] ).

cnf(i_0_15555,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_9176]),
    [final] ).

cnf(i_0_15556,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X4))
    | ~ c_Natural_Oevaln(X1,X2,X3,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_9177]),
    [final] ).

cnf(i_0_15557,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X4))
    | ~ c_Natural_Oevaln(X1,X2,X3,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_9117]),
    [final] ).

cnf(i_0_15558,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_15559,plain,
    c_Natural_Oevaln(c_Com_Ocom_OAss(X1,X2),X3,X4,hAPP(hAPP(hAPP(c_Natural_Oupdate,X3),X1),hAPP(X2,X3))),
    inference(split_conjunct,[status(thm)],[i_0_9178]),
    [final] ).

cnf(i_0_15560,plain,
    c_Natural_Oevaln(c_Com_Ocom_OAss(X1,X2),X3,X4,hAPP(hAPP(hAPP(c_Natural_Oupdate,X3),X1),hAPP(X2,X3))),
    inference(split_conjunct,[status(thm)],[i_0_9179]),
    [final] ).

cnf(i_0_15561,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_9180]),
    [final] ).

cnf(i_0_15562,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_9181]),
    [final] ).

cnf(i_0_15563,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_9182]),
    [final] ).

cnf(i_0_15564,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_9183]),
    [final] ).

cnf(i_0_15565,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_9184]),
    [final] ).

cnf(i_0_15566,plain,
    ( hBOOL(hAPP(X1,esk182_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_6745]),
    [final] ).

cnf(i_0_15567,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_9185]),
    [final] ).

cnf(i_0_15568,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_9146]),
    [final] ).

cnf(i_0_15569,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_9186,c_0_6713]),
    [final] ).

cnf(i_0_15570,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_9187]),
    [final] ).

cnf(i_0_15571,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_9188,c_0_6713]),
    [final] ).

cnf(i_0_15572,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_9189]),
    [final] ).

cnf(i_0_15573,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_8844]),
    [final] ).

cnf(i_0_15574,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_8845]),
    [final] ).

cnf(i_0_15575,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_9190]),
    [final] ).

cnf(i_0_15576,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_8846]),
    [final] ).

cnf(i_0_15577,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_8847]),
    [final] ).

cnf(i_0_15578,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_9191]),
    [final] ).

cnf(i_0_15579,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_9192]),
    [final] ).

cnf(i_0_15580,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_9193]),
    [final] ).

cnf(i_0_15581,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_9194]),
    [final] ).

cnf(i_0_15582,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_9195]),
    [final] ).

cnf(i_0_15583,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_9196]),
    [final] ).

cnf(i_0_15584,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_9197]),
    [final] ).

cnf(i_0_15585,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_9198]),
    [final] ).

cnf(i_0_15586,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_9199]),
    [final] ).

cnf(i_0_15587,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_9200]),
    [final] ).

cnf(i_0_15588,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_9201]),
    [final] ).

cnf(i_0_15589,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_9202]),
    [final] ).

cnf(i_0_15590,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_9203]),
    [final] ).

cnf(i_0_15591,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_8681]),
    [final] ).

cnf(i_0_15592,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_9204]),
    [final] ).

cnf(i_0_15593,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_8681]),
    [final] ).

cnf(i_0_15594,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_9205]),
    [final] ).

cnf(i_0_15595,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_9206]),
    [final] ).

cnf(i_0_15596,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_9207]),
    [final] ).

cnf(i_0_15597,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_8682]),
    [final] ).

cnf(i_0_15598,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_9208]),
    [final] ).

cnf(i_0_15599,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_8682]),
    [final] ).

cnf(i_0_15600,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_9209,c_0_6063]),
    [final] ).

cnf(i_0_15601,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_8999]),
    [final] ).

cnf(i_0_15602,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_9210]),
    [final] ).

cnf(i_0_15603,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_9004]),
    [final] ).

cnf(i_0_15604,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_9005]),
    [final] ).

cnf(i_0_15605,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_9211]),
    [final] ).

cnf(i_0_15606,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_9212]),
    [final] ).

cnf(i_0_15607,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_9213]),
    [final] ).

cnf(i_0_15608,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_9214]),
    [final] ).

cnf(i_0_15609,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_9215]),
    [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_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_8745]),
    [final] ).

cnf(i_0_15611,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_9216]),
    [final] ).

cnf(i_0_15612,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_9086]),
    [final] ).

cnf(i_0_15613,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_9217]),
    [final] ).

cnf(i_0_15614,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)),esk571_3(X1,X2,X3)))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7651]),
    [final] ).

cnf(i_0_15615,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)),esk567_3(X1,X2,X3)))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7661]),
    [final] ).

cnf(i_0_15616,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_9218]),
    [final] ).

cnf(i_0_15617,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_9219]),
    [final] ).

cnf(i_0_15618,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_9220]),
    [final] ).

cnf(i_0_15619,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_9221]),
    [final] ).

cnf(i_0_15620,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_8927]),
    [final] ).

cnf(i_0_15621,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_9222]),
    [final] ).

cnf(i_0_15622,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_9223]),
    [final] ).

cnf(i_0_15623,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_9223]),
    [final] ).

cnf(i_0_15624,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_9224]),
    [final] ).

cnf(i_0_15625,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_9224]),
    [final] ).

cnf(i_0_15626,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_9225]),
    [final] ).

cnf(i_0_15627,plain,
    ( X2 = esk521_3(X3,X4,X1)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
    | ~ hBOOL(hAPP(X4,X2))
    | ~ c_List_Olist__ex1(X1,X4,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7260]),
    [final] ).

cnf(i_0_15628,plain,
    ( X2 = esk510_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_7261]),
    [final] ).

cnf(i_0_15629,plain,
    ( hBOOL(hAPP(X1,esk68_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_7411]),
    [final] ).

cnf(i_0_15630,plain,
    ( c_Hoare__Mirabelle_Ohoare__valids(X1,X3,X2)
    | ~ c_Hoare__Mirabelle_Otriple__valid(X1,esk337_3(X2,X3,X1),esk338_3(X2,X3,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_7271]),
    [final] ).

cnf(i_0_15631,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_9226]),
    [final] ).

cnf(i_0_15632,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_9227]),
    [final] ).

cnf(i_0_15633,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_9228]),
    [final] ).

cnf(i_0_15634,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_9229,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_15635,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_9230,c_0_9231]),
    [final] ).

cnf(i_0_15636,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_9232]),
    [final] ).

cnf(i_0_15637,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_9233]),
    [final] ).

cnf(i_0_15638,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_8365]),
    [final] ).

cnf(i_0_15639,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_9234,c_0_6181]),
    [final] ).

cnf(i_0_15640,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_9235]),
    [final] ).

cnf(i_0_15641,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_9236]),
    [final] ).

cnf(i_0_15642,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk573_3(X1,X2,X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7651]),
    [final] ).

cnf(i_0_15643,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk569_3(X1,X2,X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7661]),
    [final] ).

cnf(i_0_15644,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_8627]),
    [final] ).

cnf(i_0_15645,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_9237]),
    [final] ).

cnf(i_0_15646,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_9039]),
    [final] ).

cnf(i_0_15647,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_9040]),
    [final] ).

cnf(i_0_15648,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_9238]),
    [final] ).

cnf(i_0_15649,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_9035]),
    [final] ).

cnf(i_0_15650,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_9239]),
    [final] ).

cnf(i_0_15651,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_9239]),
    [final] ).

cnf(i_0_15652,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_9240]),
    [final] ).

cnf(i_0_15653,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_9241]),
    [final] ).

cnf(i_0_15654,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_9242]),
    [final] ).

cnf(i_0_15655,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_9243,c_0_6216]),
    [final] ).

cnf(i_0_15656,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_9244]),
    [final] ).

cnf(i_0_15657,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_9245]),
    [final] ).

cnf(i_0_15658,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_9246]),
    [final] ).

cnf(i_0_15659,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_9247]),
    [final] ).

cnf(i_0_15660,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_9248]),
    [final] ).

cnf(i_0_15661,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_9249]),
    [final] ).

cnf(i_0_15662,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_9250]),
    [final] ).

cnf(i_0_15663,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_9251]),
    [final] ).

cnf(i_0_15664,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_9252]),
    [final] ).

cnf(i_0_15665,plain,
    ( esk231_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_7281]),
    [final] ).

cnf(i_0_15666,plain,
    ( hBOOL(hAPP(c_List_Olistsp(X3,X1),X2))
    | ~ hBOOL(hAPP(X1,esk363_3(X2,X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8708]),
    [final] ).

cnf(i_0_15667,plain,
    ( hBOOL(hAPP(c_Predicate_OPowp(X3,X1),X2))
    | ~ hBOOL(hAPP(X1,esk330_3(X2,X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8899]),
    [final] ).

cnf(i_0_15668,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_7061]),
    [final] ).

cnf(i_0_15669,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_9253]),
    [final] ).

cnf(i_0_15670,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_9254]),
    [final] ).

cnf(i_0_15671,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_9255,c_0_6181]),c_0_6181]),
    [final] ).

cnf(i_0_15672,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_9256]),
    [final] ).

cnf(i_0_15673,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_9257]),
    [final] ).

cnf(i_0_15674,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_9086]),
    [final] ).

cnf(i_0_15675,plain,
    ( hBOOL(hAPP(X1,X2))
    | X3 = X2
    | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X4),X2,X5,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7079]),
    [final] ).

cnf(i_0_15676,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_9258]),
    [final] ).

cnf(i_0_15677,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_9259]),
    [final] ).

cnf(i_0_15678,plain,
    ( c_Hoare__Mirabelle_Otriple__valid(X1,esk337_3(X4,X3,X1),X2)
    | c_Hoare__Mirabelle_Ohoare__valids(X1,X3,X4)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X1)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7271]),
    [final] ).

cnf(i_0_15679,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_9260]),
    [final] ).

cnf(i_0_15680,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_9261]),
    [final] ).

cnf(i_0_15681,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_9262]),
    [final] ).

cnf(i_0_15682,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_9263]),
    [final] ).

cnf(i_0_15683,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_9264]),
    [final] ).

cnf(i_0_15684,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_9265]),
    [final] ).

cnf(i_0_15685,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_9266]),
    [final] ).

cnf(i_0_15686,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_8758]),
    [final] ).

cnf(i_0_15687,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_9267]),
    [final] ).

cnf(i_0_15688,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_9268]),
    [final] ).

cnf(i_0_15689,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_9269]),
    [final] ).

cnf(i_0_15690,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),esk65_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_8727]),
    [final] ).

cnf(i_0_15691,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),esk64_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_8728]),
    [final] ).

cnf(i_0_15692,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_8612]),
    [final] ).

cnf(i_0_15693,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_9270]),
    [final] ).

cnf(i_0_15694,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_9271]),
    [final] ).

cnf(i_0_15695,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_9272]),
    [final] ).

cnf(i_0_15696,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_9273]),
    [final] ).

cnf(i_0_15697,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_9035]),
    [final] ).

cnf(i_0_15698,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_9274]),
    [final] ).

cnf(i_0_15699,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_9275]),
    [final] ).

cnf(i_0_15700,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_9276]),
    [final] ).

cnf(i_0_15701,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),esk69_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_7892]),
    [final] ).

cnf(i_0_15702,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),esk63_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_7000]),
    [final] ).

cnf(i_0_15703,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_9277]),
    [final] ).

cnf(i_0_15704,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_9278]),
    [final] ).

cnf(i_0_15705,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_9279]),
    [final] ).

cnf(i_0_15706,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_9280]),
    [final] ).

cnf(i_0_15707,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_9008]),
    [final] ).

cnf(i_0_15708,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_8773]),
    [final] ).

cnf(i_0_15709,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_8773]),
    [final] ).

cnf(i_0_15710,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_9281]),
    [final] ).

cnf(i_0_15711,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_9282]),
    [final] ).

cnf(i_0_15712,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_9283]),
    [final] ).

cnf(i_0_15713,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_9284]),
    [final] ).

cnf(i_0_15714,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_9285]),
    [final] ).

cnf(i_0_15715,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_9286]),
    [final] ).

cnf(i_0_15716,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_9287]),
    [final] ).

cnf(i_0_15717,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_9288]),
    [final] ).

cnf(i_0_15718,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_9289]),
    [final] ).

cnf(i_0_15719,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_9290]),
    [final] ).

cnf(i_0_15720,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_9291]),
    [final] ).

cnf(i_0_15721,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_9292]),
    [final] ).

cnf(i_0_15722,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_9189]),
    [final] ).

cnf(i_0_15723,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_8956]),
    [final] ).

cnf(i_0_15724,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_8957]),
    [final] ).

cnf(i_0_15725,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_8958]),
    [final] ).

cnf(i_0_15726,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_8959]),
    [final] ).

cnf(i_0_15727,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_9293]),
    [final] ).

cnf(i_0_15728,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_9294]),
    [final] ).

cnf(i_0_15729,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_9295]),
    [final] ).

cnf(i_0_15730,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_9296]),
    [final] ).

cnf(i_0_15731,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_9297]),
    [final] ).

cnf(i_0_15732,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_9298]),
    [final] ).

cnf(i_0_15733,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_9299]),
    [final] ).

cnf(i_0_15734,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_9300]),
    [final] ).

cnf(i_0_15735,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_9301]),
    [final] ).

cnf(i_0_15736,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_9302]),
    [final] ).

cnf(i_0_15737,plain,
    ( hAPP(hAPP(c_List_Onth(X1),X2),esk326_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_8277]),
    [final] ).

cnf(i_0_15738,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_8708]),
    [final] ).

cnf(i_0_15739,plain,
    ( esk233_3(X4,X3,X1) = X2
    | hAPP(X4,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,tc_Nat_Onat),X4),X3) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7289]),
    [final] ).

cnf(i_0_15740,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_9303]),
    [final] ).

cnf(i_0_15741,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_9304]),
    [final] ).

cnf(i_0_15742,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_9304]),
    [final] ).

cnf(i_0_15743,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_9305]),
    [final] ).

cnf(i_0_15744,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_9305]),
    [final] ).

cnf(i_0_15745,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_9306]),
    [final] ).

cnf(i_0_15746,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_9307]),
    [final] ).

cnf(i_0_15747,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_9308,c_0_6088]),
    [final] ).

cnf(i_0_15748,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_9193]),
    [final] ).

cnf(i_0_15749,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_9309,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_15750,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_9310]),
    [final] ).

cnf(i_0_15751,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_9311]),
    [final] ).

cnf(i_0_15752,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_9312,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_15753,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_9313,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_15754,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_9314]),
    [final] ).

cnf(i_0_15755,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_9315]),
    [final] ).

cnf(i_0_15756,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_9316]),
    [final] ).

cnf(i_0_15757,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_9317]),
    [final] ).

cnf(i_0_15758,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_9318]),
    [final] ).

cnf(i_0_15759,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_9319]),
    [final] ).

cnf(i_0_15760,plain,
    c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(X1,X2,X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X2)),c_Com_Ocom_Ocom__size(X3))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(split_conjunct,[status(thm)],[i_0_9320]),
    [final] ).

cnf(i_0_15761,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_9321]),
    [final] ).

cnf(i_0_15762,plain,
    ( c_List_OtakeWhile(X3,X1,X2) = X2
    | ~ hBOOL(hAPP(X1,esk397_3(X2,X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8767]),
    [final] ).

cnf(i_0_15763,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_9322]),
    [final] ).

cnf(i_0_15764,plain,
    ( c_List_Oall__interval__int(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk532_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8523]),
    [final] ).

cnf(i_0_15765,plain,
    ( c_List_Olist__all(X3,X1,X2)
    | ~ hBOOL(hAPP(X1,esk509_3(X2,X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8771]),
    [final] ).

cnf(i_0_15766,plain,
    ( c_List_Olist__all(X3,X1,X2)
    | ~ hBOOL(hAPP(X1,esk508_3(X1,X2,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8770]),
    [final] ).

cnf(i_0_15767,plain,
    ( c_List_Olist__all(X3,X1,X2)
    | ~ hBOOL(hAPP(X1,esk507_3(X2,X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8772]),
    [final] ).

cnf(i_0_15768,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_8817]),
    [final] ).

cnf(i_0_15769,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_9077]),
    [final] ).

cnf(i_0_15770,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_9078]),
    [final] ).

cnf(i_0_15771,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_9323]),
    [final] ).

cnf(i_0_15772,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_9324]),
    [final] ).

cnf(i_0_15773,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_8727]),
    [final] ).

cnf(i_0_15774,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_8728]),
    [final] ).

cnf(i_0_15775,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_9043]),
    [final] ).

cnf(i_0_15776,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_9044]),
    [final] ).

cnf(i_0_15777,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_9045]),
    [final] ).

cnf(i_0_15778,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_8831]),
    [final] ).

cnf(i_0_15779,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_9046]),
    [final] ).

cnf(i_0_15780,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_9047]),
    [final] ).

cnf(i_0_15781,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_9048]),
    [final] ).

cnf(i_0_15782,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_9049]),
    [final] ).

cnf(i_0_15783,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_9051]),
    [final] ).

cnf(i_0_15784,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_9050]),
    [final] ).

cnf(i_0_15785,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_9037]),
    [final] ).

cnf(i_0_15786,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_9325]),
    [final] ).

cnf(i_0_15787,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_9326]),
    [final] ).

cnf(i_0_15788,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_6599]),
    [final] ).

cnf(i_0_15789,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_6600]),
    [final] ).

cnf(i_0_15790,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_8926]),
    [final] ).

cnf(i_0_15791,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_9327]),
    [final] ).

cnf(i_0_15792,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_9328,c_0_6063]),
    [final] ).

cnf(i_0_15793,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_9329]),
    [final] ).

cnf(i_0_15794,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_9330]),
    [final] ).

cnf(i_0_15795,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ c_Wellfounded_Omax__extp(X1,X3,X2,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6599]),
    [final] ).

cnf(i_0_15796,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ c_Wellfounded_Omax__extp(X1,X3,X2,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6600]),
    [final] ).

cnf(i_0_15797,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ c_Wellfounded_Omax__extp(X1,X3,X4,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6599]),
    [final] ).

cnf(i_0_15798,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ c_Wellfounded_Omax__extp(X1,X3,X4,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6600]),
    [final] ).

cnf(i_0_15799,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_9331]),
    [final] ).

cnf(i_0_15800,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_8901]),
    [final] ).

cnf(i_0_15801,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_8751]),
    [final] ).

cnf(i_0_15802,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_8454]),
    [final] ).

cnf(i_0_15803,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_8454]),
    [final] ).

cnf(i_0_15804,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_9332]),
    [final] ).

cnf(i_0_15805,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_9333,c_0_6063]),c_0_6063]),
    [final] ).

cnf(i_0_15806,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_8831]),
    [final] ).

cnf(i_0_15807,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_9334]),
    [final] ).

cnf(i_0_15808,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_9335]),
    [final] ).

cnf(i_0_15809,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_9336,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_15810,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_9337,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_15811,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_9338,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_15812,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_9339,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_15813,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_9340]),
    [final] ).

cnf(i_0_15814,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_9341]),
    [final] ).

cnf(i_0_15815,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_9342]),
    [final] ).

cnf(i_0_15816,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_9088]),
    [final] ).

cnf(i_0_15817,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_9089]),
    [final] ).

cnf(i_0_15818,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_9343]),
    [final] ).

cnf(i_0_15819,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_9344]),
    [final] ).

cnf(i_0_15820,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_9345]),
    [final] ).

cnf(i_0_15821,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_9346]),
    [final] ).

cnf(i_0_15822,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_9347]),
    [final] ).

cnf(i_0_15823,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_9348]),
    [final] ).

cnf(i_0_15824,plain,
    ( epred1_3(X1,X2,X3)
    | ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_9349]),
    [final] ).

cnf(i_0_15825,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_9350]),
    [final] ).

cnf(i_0_15826,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_9351]),
    [final] ).

cnf(i_0_15827,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_9352]),
    [final] ).

cnf(i_0_15828,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_9353]),
    [final] ).

cnf(i_0_15829,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_9354]),
    [final] ).

cnf(i_0_15830,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_9355]),
    [final] ).

cnf(i_0_15831,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_9356]),
    [final] ).

cnf(i_0_15832,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_8391]),
    [final] ).

cnf(i_0_15833,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_9357]),
    [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_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_8794]),
    [final] ).

cnf(i_0_15835,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_5755]),
    [final] ).

cnf(i_0_15836,plain,
    ( c_Wellfounded_Owf(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),esk299_2(X2,X1)),c_Wellfounded_Oacc(X1,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9358]),
    [final] ).

cnf(i_0_15837,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_9359]),
    [final] ).

cnf(i_0_15838,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_9360]),
    [final] ).

cnf(i_0_15839,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_9361]),
    [final] ).

cnf(i_0_15840,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_8996]),
    [final] ).

cnf(i_0_15841,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_9362]),
    [final] ).

cnf(i_0_15842,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_9363]),
    [final] ).

cnf(i_0_15843,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_9364,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_15844,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_9365,c_0_6062]),c_0_6063]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_15845,plain,
    ( X1 = hAPP(hAPP(c_Set_Oinsert(X2),esk139_3(X3,X1,X2)),esk140_3(X3,X1,X2))
    | hAPP(c_Finite__Set_Ocard(X2),X1) != hAPP(c_Nat_OSuc,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7961]),
    [final] ).

cnf(i_0_15846,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_9366]),
    [final] ).

cnf(i_0_15847,plain,
    ( hAPP(c_List_Ofilter(X3,X1),X2) = X2
    | ~ hBOOL(hAPP(X1,esk384_3(X2,X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8806]),
    [final] ).

cnf(i_0_15848,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_9367]),
    [final] ).

cnf(i_0_15849,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_9368]),
    [final] ).

cnf(i_0_15850,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_9157]),
    [final] ).

cnf(i_0_15851,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_9369]),
    [final] ).

cnf(i_0_15852,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_9370]),
    [final] ).

cnf(i_0_15853,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_9371]),
    [final] ).

cnf(i_0_15854,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_9372]),
    [final] ).

cnf(i_0_15855,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_9373]),
    [final] ).

cnf(i_0_15856,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_9374]),
    [final] ).

cnf(i_0_15857,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_9375,c_0_7094]),
    [final] ).

cnf(i_0_15858,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_9376]),
    [final] ).

cnf(i_0_15859,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_9377]),
    [final] ).

cnf(i_0_15860,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_9378]),
    [final] ).

cnf(i_0_15861,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_9379]),
    [final] ).

cnf(i_0_15862,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_9380]),
    [final] ).

cnf(i_0_15863,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_9381]),
    [final] ).

cnf(i_0_15864,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_9382]),
    [final] ).

cnf(i_0_15865,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_9383]),
    [final] ).

cnf(i_0_15866,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_9384]),
    [final] ).

cnf(i_0_15867,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_9385]),
    [final] ).

cnf(i_0_15868,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_9386]),
    [final] ).

cnf(i_0_15869,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_9387]),
    [final] ).

cnf(i_0_15870,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),esk65_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_8727]),
    [final] ).

cnf(i_0_15871,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),esk64_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_8728]),
    [final] ).

cnf(i_0_15872,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_9388,c_0_8268]),
    [final] ).

cnf(i_0_15873,plain,
    ( hBOOL(hAPP(X3,esk537_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_9389]),
    [final] ).

cnf(i_0_15874,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_9254]),
    [final] ).

cnf(i_0_15875,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_9390]),
    [final] ).

cnf(i_0_15876,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_9391,c_0_6181]),
    [final] ).

cnf(i_0_15877,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_9392]),
    [final] ).

cnf(i_0_15878,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_9393]),
    [final] ).

cnf(i_0_15879,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_9394]),
    [final] ).

cnf(i_0_15880,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_9395]),
    [final] ).

cnf(i_0_15881,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_9396]),
    [final] ).

cnf(i_0_15882,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_9397]),
    [final] ).

cnf(i_0_15883,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_9398]),
    [final] ).

cnf(i_0_15884,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_9399]),
    [final] ).

cnf(i_0_15885,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_9400]),
    [final] ).

cnf(i_0_15886,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_9401]),
    [final] ).

cnf(i_0_15887,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_9402]),
    [final] ).

cnf(i_0_15888,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_9403]),
    [final] ).

cnf(i_0_15889,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_9404]),
    [final] ).

cnf(i_0_15890,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_9405]),
    [final] ).

cnf(i_0_15891,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_9406]),
    [final] ).

cnf(i_0_15892,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_9407]),
    [final] ).

cnf(i_0_15893,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_9408]),
    [final] ).

cnf(i_0_15894,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_9409]),
    [final] ).

cnf(i_0_15895,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_9410]),
    [final] ).

cnf(i_0_15896,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_9411]),
    [final] ).

cnf(i_0_15897,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_9412]),
    [final] ).

cnf(i_0_15898,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_9413]),
    [final] ).

cnf(i_0_15899,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_9414]),
    [final] ).

cnf(i_0_15900,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_9415]),
    [final] ).

cnf(i_0_15901,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_9416]),
    [final] ).

cnf(i_0_15902,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_9417]),
    [final] ).

cnf(i_0_15903,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_9418]),
    [final] ).

cnf(i_0_15904,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_9419]),
    [final] ).

cnf(i_0_15905,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_9226]),
    [final] ).

cnf(i_0_15906,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_5331]),
    [final] ).

cnf(i_0_15907,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_9420]),
    [final] ).

cnf(i_0_15908,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_9421]),
    [final] ).

cnf(i_0_15909,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_9422]),
    [final] ).

cnf(i_0_15910,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_9069]),
    [final] ).

cnf(i_0_15911,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_9423]),
    [final] ).

cnf(i_0_15912,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_9424]),
    [final] ).

cnf(i_0_15913,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_9425]),
    [final] ).

cnf(i_0_15914,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_9426]),
    [final] ).

cnf(i_0_15915,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_9427]),
    [final] ).

cnf(i_0_15916,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_9428]),
    [final] ).

cnf(i_0_15917,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_9429]),
    [final] ).

cnf(i_0_15918,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_9430]),
    [final] ).

cnf(i_0_15919,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_9431]),
    [final] ).

cnf(i_0_15920,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_9432]),
    [final] ).

cnf(i_0_15921,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_9433]),
    [final] ).

cnf(i_0_15922,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_9434]),
    [final] ).

cnf(i_0_15923,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_9435]),
    [final] ).

cnf(i_0_15924,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_8161]),
    [final] ).

cnf(i_0_15925,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_9436]),
    [final] ).

cnf(i_0_15926,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_9238]),
    [final] ).

cnf(i_0_15927,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_9437]),
    [final] ).

cnf(i_0_15928,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_9438]),
    [final] ).

cnf(i_0_15929,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_9439]),
    [final] ).

cnf(i_0_15930,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk389_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_9211]),
    [final] ).

cnf(i_0_15931,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_9440,c_0_6063]),
    [final] ).

cnf(i_0_15932,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_9441,c_0_6063]),
    [final] ).

cnf(i_0_15933,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_9442,c_0_6063]),
    [final] ).

cnf(i_0_15934,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_9443,c_0_6063]),
    [final] ).

cnf(i_0_15935,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_9444]),
    [final] ).

cnf(i_0_15936,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_9445]),
    [final] ).

cnf(i_0_15937,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_9446]),
    [final] ).

cnf(i_0_15938,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_9447]),
    [final] ).

cnf(i_0_15939,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_8767]),
    [final] ).

cnf(i_0_15940,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_8796]),
    [final] ).

cnf(i_0_15941,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_9448]),
    [final] ).

cnf(i_0_15942,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_9449]),
    [final] ).

cnf(i_0_15943,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_8771]),
    [final] ).

cnf(i_0_15944,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_8770]),
    [final] ).

cnf(i_0_15945,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_8772]),
    [final] ).

cnf(i_0_15946,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_9450,c_0_6088]),
    [final] ).

cnf(i_0_15947,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_9451,c_0_6088]),
    [final] ).

cnf(i_0_15948,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_9452]),
    [final] ).

cnf(i_0_15949,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_9453]),
    [final] ).

cnf(i_0_15950,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_9454]),
    [final] ).

cnf(i_0_15951,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_9455]),
    [final] ).

cnf(i_0_15952,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_9456]),
    [final] ).

cnf(i_0_15953,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_9457]),
    [final] ).

cnf(i_0_15954,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_9458]),
    [final] ).

cnf(i_0_15955,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_9459]),
    [final] ).

cnf(i_0_15956,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_9291]),
    [final] ).

cnf(i_0_15957,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_9292]),
    [final] ).

cnf(i_0_15958,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_9460]),
    [final] ).

cnf(i_0_15959,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_9461]),
    [final] ).

cnf(i_0_15960,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_9462]),
    [final] ).

cnf(i_0_15961,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_9463]),
    [final] ).

cnf(i_0_15962,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_9464]),
    [final] ).

cnf(i_0_15963,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_9465]),
    [final] ).

cnf(i_0_15964,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_9466]),
    [final] ).

cnf(i_0_15965,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_5330]),
    [final] ).

cnf(i_0_15966,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_9467]),
    [final] ).

cnf(i_0_15967,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_9468]),
    [final] ).

cnf(i_0_15968,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_9469]),
    [final] ).

cnf(i_0_15969,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_9470]),
    [final] ).

cnf(i_0_15970,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_9471,c_0_6097]),
    [final] ).

cnf(i_0_15971,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_9472]),
    [final] ).

cnf(i_0_15972,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_9363]),
    [final] ).

cnf(i_0_15973,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_9473]),
    [final] ).

cnf(i_0_15974,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_9474]),
    [final] ).

cnf(i_0_15975,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_9475]),
    [final] ).

cnf(i_0_15976,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_9329]),
    [final] ).

cnf(i_0_15977,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_9476,c_0_8319]),
    [final] ).

cnf(i_0_15978,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_9477,c_0_8319]),
    [final] ).

cnf(i_0_15979,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_9269]),
    [final] ).

cnf(i_0_15980,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_9478]),
    [final] ).

cnf(i_0_15981,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_8971]),
    [final] ).

cnf(i_0_15982,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_8970]),
    [final] ).

cnf(i_0_15983,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_9479]),
    [final] ).

cnf(i_0_15984,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_15985,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_9480]),
    [final] ).

cnf(i_0_15986,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_9481,c_0_6088]),
    [final] ).

cnf(i_0_15987,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_9482]),
    [final] ).

cnf(i_0_15988,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_9483]),
    [final] ).

cnf(i_0_15989,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_8726]),
    [final] ).

cnf(i_0_15990,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_8725]),
    [final] ).

cnf(i_0_15991,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_8703]),
    [final] ).

cnf(i_0_15992,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_8704]),
    [final] ).

cnf(i_0_15993,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_8705]),
    [final] ).

cnf(i_0_15994,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_9225]),
    [final] ).

cnf(i_0_15995,plain,
    ( X3 = X1
    | ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_9484]),
    [final] ).

cnf(i_0_15996,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_9485]),
    [final] ).

cnf(i_0_15997,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_9486]),
    [final] ).

cnf(i_0_15998,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_9487]),
    [final] ).

cnf(i_0_15999,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_6146]),
    [final] ).

cnf(i_0_16000,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_8968]),
    [final] ).

cnf(i_0_16001,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_9488]),
    [final] ).

cnf(i_0_16002,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_9489]),
    [final] ).

cnf(i_0_16003,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_9490]),
    [final] ).

cnf(i_0_16004,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_9491]),
    [final] ).

cnf(i_0_16005,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_9492]),
    [final] ).

cnf(i_0_16006,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_9493]),
    [final] ).

cnf(i_0_16007,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_9494]),
    [final] ).

cnf(i_0_16008,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_9495]),
    [final] ).

cnf(i_0_16009,plain,
    ( epred2_3(X1,X2,X3)
    | ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_9496]),
    [final] ).

cnf(i_0_16010,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_9497]),
    [final] ).

cnf(i_0_16011,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk43_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_9498]),
    [final] ).

cnf(i_0_16012,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_9499]),
    [final] ).

cnf(i_0_16013,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_9500]),
    [final] ).

cnf(i_0_16014,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_8943]),
    [final] ).

cnf(i_0_16015,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_8943]),
    [final] ).

cnf(i_0_16016,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_9269]),
    [final] ).

cnf(i_0_16017,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_9501]),
    [final] ).

cnf(i_0_16018,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_9502]),
    [final] ).

cnf(i_0_16019,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_8806]),
    [final] ).

cnf(i_0_16020,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_9503]),
    [final] ).

cnf(i_0_16021,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_9317]),
    [final] ).

cnf(i_0_16022,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_9318]),
    [final] ).

cnf(i_0_16023,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_9319]),
    [final] ).

cnf(i_0_16024,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_9504]),
    [final] ).

cnf(i_0_16025,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_9367]),
    [final] ).

cnf(i_0_16026,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_9368]),
    [final] ).

cnf(i_0_16027,plain,
    ( hBOOL(hAPP(hAPP(X1,esk552_1(X1)),esk552_1(X1)))
    | hBOOL(hAPP(hAPP(X1,esk551_1(X1)),esk552_1(X1)))
    | c_Equiv__Relations_Opart__equivp(X3,X1)
    | ~ hBOOL(hAPP(hAPP(X1,X2),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8558]),
    [final] ).

cnf(i_0_16028,plain,
    ( hBOOL(hAPP(hAPP(X1,esk551_1(X1)),esk551_1(X1)))
    | hBOOL(hAPP(hAPP(X1,esk551_1(X1)),esk552_1(X1)))
    | c_Equiv__Relations_Opart__equivp(X3,X1)
    | ~ hBOOL(hAPP(hAPP(X1,X2),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8558]),
    [final] ).

cnf(i_0_16029,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_9505]),
    [final] ).

cnf(i_0_16030,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_9271]),
    [final] ).

cnf(i_0_16031,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_9270]),
    [final] ).

cnf(i_0_16032,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_9272]),
    [final] ).

cnf(i_0_16033,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_9274]),
    [final] ).

cnf(i_0_16034,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_9273]),
    [final] ).

cnf(i_0_16035,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_9276]),
    [final] ).

cnf(i_0_16036,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_9506]),
    [final] ).

cnf(i_0_16037,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_9507]),
    [final] ).

cnf(i_0_16038,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_9508]),
    [final] ).

cnf(i_0_16039,plain,
    c_Hoare__Mirabelle_Otriple__valid(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X2),hAPP(c_Com_Ocom_OBODY,X3)),X4)),
    inference(split_conjunct,[status(thm)],[i_0_9509]),
    [final] ).

cnf(i_0_16040,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_9510]),
    [final] ).

cnf(i_0_16041,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_9511]),
    [final] ).

cnf(i_0_16042,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_9370]),
    [final] ).

cnf(i_0_16043,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_9512]),
    [final] ).

cnf(i_0_16044,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_9513]),
    [final] ).

cnf(i_0_16045,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_9514]),
    [final] ).

cnf(i_0_16046,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_9515]),
    [final] ).

cnf(i_0_16047,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_9516]),
    [final] ).

cnf(i_0_16048,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_9517]),
    [final] ).

cnf(i_0_16049,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_9412]),
    [final] ).

cnf(i_0_16050,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_9518]),
    [final] ).

cnf(i_0_16051,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_9519]),
    [final] ).

cnf(i_0_16052,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_9520]),
    [final] ).

cnf(i_0_16053,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_9521]),
    [final] ).

cnf(i_0_16054,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_9522]),
    [final] ).

cnf(i_0_16055,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_9523]),
    [final] ).

cnf(i_0_16056,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,esk31_2(X2,X1))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9524]),
    [final] ).

cnf(i_0_16057,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_9425]),
    [final] ).

cnf(i_0_16058,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_9426]),
    [final] ).

cnf(i_0_16059,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_9525,c_0_6181]),
    [final] ).

cnf(i_0_16060,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_9526]),
    [final] ).

cnf(i_0_16061,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_9527]),
    [final] ).

cnf(i_0_16062,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_9528]),
    [final] ).

cnf(i_0_16063,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_9529]),
    [final] ).

cnf(i_0_16064,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_7326]),
    [final] ).

cnf(i_0_16065,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_9530]),
    [final] ).

cnf(i_0_16066,plain,
    ( hBOOL(hAPP(c_Predicate_ODomainP(X4,X5,X1),X2))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9135]),
    [final] ).

cnf(i_0_16067,plain,
    ( hBOOL(hAPP(c_Predicate_ODomainP(X4,X5,X1),X2))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9531]),
    [final] ).

cnf(i_0_16068,plain,
    ( hBOOL(hAPP(c_Predicate_ORangeP(X4,X5,X1),X3))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8995]),
    [final] ).

cnf(i_0_16069,plain,
    ( hBOOL(hAPP(c_Predicate_ORangeP(X4,X5,X1),X3))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9532]),
    [final] ).

cnf(i_0_16070,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_8177]),
    [final] ).

cnf(i_0_16071,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_9533]),
    [final] ).

cnf(i_0_16072,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_9534]),
    [final] ).

cnf(i_0_16073,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_9535]),
    [final] ).

cnf(i_0_16074,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_9536]),
    [final] ).

cnf(i_0_16075,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,hAPP(c_Nat_OSuc,esk20_2(X2,X1))))
    | ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(split_conjunct,[status(thm)],[i_0_9537]),
    [final] ).

cnf(i_0_16076,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_9538,c_0_8268]),
    [final] ).

cnf(i_0_16077,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_9539]),
    [final] ).

cnf(i_0_16078,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_9099]),
    [final] ).

cnf(i_0_16079,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_9055]),
    [final] ).

cnf(i_0_16080,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_9540]),
    [final] ).

cnf(i_0_16081,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_9541]),
    [final] ).

cnf(i_0_16082,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_9542,c_0_6181]),
    [final] ).

cnf(i_0_16083,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_9543]),
    [final] ).

cnf(i_0_16084,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_9544]),
    [final] ).

cnf(i_0_16085,plain,
    ( X1 = X2
    | hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X1),X4),X5) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X2),X6),X7) ),
    inference(split_conjunct,[status(thm)],[i_0_9545]),
    [final] ).

cnf(i_0_16086,plain,
    ( X1 = X2
    | hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X4),X1),X5) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X6),X2),X7) ),
    inference(split_conjunct,[status(thm)],[i_0_9545]),
    [final] ).

cnf(i_0_16087,plain,
    ( X1 = X2
    | hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X4),X5),X1) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X3),X6),X7),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9545]),
    [final] ).

cnf(i_0_16088,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_7998]),
    [final] ).

cnf(i_0_16089,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_9546]),
    [final] ).

cnf(i_0_16090,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_9547]),
    [final] ).

cnf(i_0_16091,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk340_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_8312]),
    [final] ).

cnf(i_0_16092,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk339_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_8312]),
    [final] ).

cnf(i_0_16093,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_9548]),
    [final] ).

cnf(i_0_16094,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_9549]),
    [final] ).

cnf(i_0_16095,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_9550,c_0_6088]),
    [final] ).

cnf(i_0_16096,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_9551]),
    [final] ).

cnf(i_0_16097,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_9552]),
    [final] ).

cnf(i_0_16098,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_8553]),
    [final] ).

cnf(i_0_16099,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_9553]),
    [final] ).

cnf(i_0_16100,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_9554]),
    [final] ).

cnf(i_0_16101,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_9014]),
    [final] ).

cnf(i_0_16102,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_9555]),
    [final] ).

cnf(i_0_16103,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_9556]),
    [final] ).

cnf(i_0_16104,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_9557]),
    [final] ).

cnf(i_0_16105,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_9558]),
    [final] ).

cnf(i_0_16106,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_9559]),
    [final] ).

cnf(i_0_16107,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_9269]),
    [final] ).

cnf(i_0_16108,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_9560]),
    [final] ).

cnf(i_0_16109,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_9561]),
    [final] ).

cnf(i_0_16110,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_9562]),
    [final] ).

cnf(i_0_16111,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_9563]),
    [final] ).

cnf(i_0_16112,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_9564]),
    [final] ).

cnf(i_0_16113,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_9565]),
    [final] ).

cnf(i_0_16114,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_8186]),
    [final] ).

cnf(i_0_16115,plain,
    ( hAPP(X1,esk231_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_7281]),
    [final] ).

cnf(i_0_16116,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),esk50_2(X2,X3)))
    | ~ hBOOL(hAPP(X3,X1))
    | ~ hBOOL(hAPP(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9142]),
    [final] ).

cnf(i_0_16117,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_9566]),
    [final] ).

cnf(i_0_16118,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_9567]),
    [final] ).

cnf(i_0_16119,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_9568]),
    [final] ).

cnf(i_0_16120,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_9569]),
    [final] ).

cnf(i_0_16121,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_9570]),
    [final] ).

cnf(i_0_16122,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_9571]),
    [final] ).

cnf(i_0_16123,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_9572]),
    [final] ).

cnf(i_0_16124,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_9573]),
    [final] ).

cnf(i_0_16125,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_9574]),
    [final] ).

cnf(i_0_16126,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_9575]),
    [final] ).

cnf(i_0_16127,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_9576]),
    [final] ).

cnf(i_0_16128,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk538_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_9389]),
    [final] ).

cnf(i_0_16129,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_9577]),
    [final] ).

cnf(i_0_16130,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_9578]),
    [final] ).

cnf(i_0_16131,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_9579]),
    [final] ).

cnf(i_0_16132,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_9580]),
    [final] ).

cnf(i_0_16133,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_9581]),
    [final] ).

cnf(i_0_16134,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_9347]),
    [final] ).

cnf(i_0_16135,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_9348]),
    [final] ).

cnf(i_0_16136,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_9582]),
    [final] ).

cnf(i_0_16137,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_9583]),
    [final] ).

cnf(i_0_16138,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_9584]),
    [final] ).

cnf(i_0_16139,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_9585]),
    [final] ).

cnf(i_0_16140,plain,
    c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(X1,X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X1)),c_Com_Ocom_Ocom__size(X2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(split_conjunct,[status(thm)],[i_0_9586]),
    [final] ).

cnf(i_0_16141,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_9462]),
    [final] ).

cnf(i_0_16142,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_9460]),
    [final] ).

cnf(i_0_16143,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_9463]),
    [final] ).

cnf(i_0_16144,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_9461]),
    [final] ).

cnf(i_0_16145,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_9279]),
    [final] ).

cnf(i_0_16146,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_9587]),
    [final] ).

cnf(i_0_16147,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_9588]),
    [final] ).

cnf(i_0_16148,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_9551]),
    [final] ).

cnf(i_0_16149,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_9589]),
    [final] ).

cnf(i_0_16150,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_9590,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_16151,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_9591,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_16152,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_8915]),
    [final] ).

cnf(i_0_16153,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_9592]),
    [final] ).

cnf(i_0_16154,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_9593]),
    [final] ).

cnf(i_0_16155,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_9594]),
    [final] ).

cnf(i_0_16156,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_9595,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_16157,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_9596,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_16158,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_9597]),
    [final] ).

cnf(i_0_16159,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_9598]),
    [final] ).

cnf(i_0_16160,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_9599]),
    [final] ).

cnf(i_0_16161,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_9600]),
    [final] ).

cnf(i_0_16162,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_9601,c_0_6088]),
    [final] ).

cnf(i_0_16163,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_9602,c_0_6088]),
    [final] ).

cnf(i_0_16164,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_9603,c_0_6088]),
    [final] ).

cnf(i_0_16165,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_9604,c_0_8319]),
    [final] ).

cnf(i_0_16166,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_9605,c_0_8319]),
    [final] ).

cnf(i_0_16167,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_9606]),
    [final] ).

cnf(i_0_16168,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,esk230_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_8725]),
    [final] ).

cnf(i_0_16169,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,esk142_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_8726]),
    [final] ).

cnf(i_0_16170,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_9607]),
    [final] ).

cnf(i_0_16171,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_9608]),
    [final] ).

cnf(i_0_16172,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_9609]),
    [final] ).

cnf(i_0_16173,plain,
    ( hBOOL(hAPP(X3,X2))
    | hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X3,X4)),X2),X1))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_7171]),
    [final] ).

cnf(i_0_16174,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk118_2(X1,X2)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9610]),
    [final] ).

cnf(i_0_16175,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk120_2(X1,X2)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9611]),
    [final] ).

cnf(i_0_16176,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_9612]),
    [final] ).

cnf(i_0_16177,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_9613]),
    [final] ).

cnf(i_0_16178,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_9439]),
    [final] ).

cnf(i_0_16179,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_9614]),
    [final] ).

cnf(i_0_16180,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_9517]),
    [final] ).

cnf(i_0_16181,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_9615]),
    [final] ).

cnf(i_0_16182,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_9616]),
    [final] ).

cnf(i_0_16183,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_9617]),
    [final] ).

cnf(i_0_16184,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_9618]),
    [final] ).

cnf(i_0_16185,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_9619]),
    [final] ).

cnf(i_0_16186,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_9620]),
    [final] ).

cnf(i_0_16187,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_9621]),
    [final] ).

cnf(i_0_16188,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_9622]),
    [final] ).

cnf(i_0_16189,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_9623]),
    [final] ).

cnf(i_0_16190,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_9624]),
    [final] ).

cnf(i_0_16191,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_9625]),
    [final] ).

cnf(i_0_16192,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_9626]),
    [final] ).

cnf(i_0_16193,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_9627]),
    [final] ).

cnf(i_0_16194,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk401_2(X1,X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1)))
    | c_List_Olinorder__class_Osorted(X2,X1)
    | ~ class_Orderings_Olinorder(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7644]),
    [final] ).

cnf(i_0_16195,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)))
    | c_List_Olinorder__class_Osorted(X2,X1)
    | ~ class_Orderings_Olinorder(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7645]),
    [final] ).

cnf(i_0_16196,plain,
    ( hBOOL(hAPP(X1,X2))
    | hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X3)),X2),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7885]),
    [final] ).

cnf(i_0_16197,plain,
    ( hBOOL(hAPP(X1,X2))
    | hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X3)),X2),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9628]),
    [final] ).

cnf(i_0_16198,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_9629]),
    [final] ).

cnf(i_0_16199,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_9630]),
    [final] ).

cnf(i_0_16200,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_9631]),
    [final] ).

cnf(i_0_16201,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_9632]),
    [final] ).

cnf(i_0_16202,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_9633]),
    [final] ).

cnf(i_0_16203,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_9486]),
    [final] ).

cnf(i_0_16204,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_9634]),
    [final] ).

cnf(i_0_16205,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_9635]),
    [final] ).

cnf(i_0_16206,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_9636]),
    [final] ).

cnf(i_0_16207,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_9637]),
    [final] ).

cnf(i_0_16208,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_9638]),
    [final] ).

cnf(i_0_16209,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_9639]),
    [final] ).

cnf(i_0_16210,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_9640]),
    [final] ).

cnf(i_0_16211,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_9641]),
    [final] ).

cnf(i_0_16212,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_9642]),
    [final] ).

cnf(i_0_16213,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_9643]),
    [final] ).

cnf(i_0_16214,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_9644]),
    [final] ).

cnf(i_0_16215,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_9645]),
    [final] ).

cnf(i_0_16216,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_8940]),
    [final] ).

cnf(i_0_16217,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_8941]),
    [final] ).

cnf(i_0_16218,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_9646]),
    [final] ).

cnf(i_0_16219,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_9647]),
    [final] ).

cnf(i_0_16220,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_9648]),
    [final] ).

cnf(i_0_16221,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_9649]),
    [final] ).

cnf(i_0_16222,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_9650]),
    [final] ).

cnf(i_0_16223,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_9651]),
    [final] ).

cnf(i_0_16224,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_9652]),
    [final] ).

cnf(i_0_16225,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_9528]),
    [final] ).

cnf(i_0_16226,plain,
    ( hBOOL(hAPP(X1,esk402_3(X2,X1,X3)))
    | c_List_OtakeWhile(X3,X1,X2) = hAPP(c_List_Ofilter(X3,X1),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5443]),
    [final] ).

cnf(i_0_16227,plain,
    ( X4 = X3
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_9653]),
    [final] ).

cnf(i_0_16228,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_9654]),
    [final] ).

cnf(i_0_16229,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_9655]),
    [final] ).

cnf(i_0_16230,plain,
    ( hBOOL(hAPP(X2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk40_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_9656]),
    [final] ).

cnf(i_0_16231,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_9489]),
    [final] ).

cnf(i_0_16232,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_9490]),
    [final] ).

cnf(i_0_16233,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_9657]),
    [final] ).

cnf(i_0_16234,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_9658]),
    [final] ).

cnf(i_0_16235,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_9659]),
    [final] ).

cnf(i_0_16236,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_9660]),
    [final] ).

cnf(i_0_16237,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_9661]),
    [final] ).

cnf(i_0_16238,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_9662]),
    [final] ).

cnf(i_0_16239,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_9663,c_0_6181]),
    [final] ).

cnf(i_0_16240,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_6561]),
    [final] ).

cnf(i_0_16241,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_9664]),
    [final] ).

cnf(i_0_16242,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_9665]),
    [final] ).

cnf(i_0_16243,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_9666]),
    [final] ).

cnf(i_0_16244,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_9667]),
    [final] ).

cnf(i_0_16245,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_9668]),
    [final] ).

cnf(i_0_16246,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_9669]),
    [final] ).

cnf(i_0_16247,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_9670]),
    [final] ).

cnf(i_0_16248,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_9671]),
    [final] ).

cnf(i_0_16249,plain,
    ( hBOOL(hAPP(X2,esk45_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_9672]),
    [final] ).

cnf(i_0_16250,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_9666]),
    [final] ).

cnf(i_0_16251,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_9673]),
    [final] ).

cnf(i_0_16252,plain,
    ( hBOOL(hAPP(X1,esk536_3(X2,X1,X3)))
    | ~ c_List_Olist__ex(X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8703]),
    [final] ).

cnf(i_0_16253,plain,
    ( hBOOL(hAPP(X1,esk535_3(X1,X2,X3)))
    | ~ c_List_Olist__ex(X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8704]),
    [final] ).

cnf(i_0_16254,plain,
    ( hBOOL(hAPP(X1,esk521_3(X2,X1,X3)))
    | ~ c_List_Olist__ex1(X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7260]),
    [final] ).

cnf(i_0_16255,plain,
    ( hBOOL(hAPP(X1,esk510_3(X2,X1,X3)))
    | ~ c_List_Olist__ex1(X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7261]),
    [final] ).

cnf(i_0_16256,plain,
    ( hBOOL(hAPP(X1,esk478_3(X2,X1,X3)))
    | ~ c_List_Olist__ex(X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8705]),
    [final] ).

cnf(i_0_16257,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_9674,c_0_6063]),
    [final] ).

cnf(i_0_16258,plain,
    ( hAPP(X1,esk233_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_7289]),
    [final] ).

cnf(i_0_16259,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_9675]),
    [final] ).

cnf(i_0_16260,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_9676]),
    [final] ).

cnf(i_0_16261,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_9677]),
    [final] ).

cnf(i_0_16262,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_9678]),
    [final] ).

cnf(i_0_16263,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_9679]),
    [final] ).

cnf(i_0_16264,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_9680]),
    [final] ).

cnf(i_0_16265,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_9681]),
    [final] ).

cnf(i_0_16266,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_9682]),
    [final] ).

cnf(i_0_16267,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_9683]),
    [final] ).

cnf(i_0_16268,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_9684,c_0_6181]),
    [final] ).

cnf(i_0_16269,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_8899]),
    [final] ).

cnf(i_0_16270,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_9685]),
    [final] ).

cnf(i_0_16271,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_9686]),
    [final] ).

cnf(i_0_16272,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_9687]),
    [final] ).

cnf(i_0_16273,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_9688]),
    [final] ).

cnf(i_0_16274,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_9547]),
    [final] ).

cnf(i_0_16275,plain,
    ( hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)))
    | ~ epred1_3(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_9349]),
    [final] ).

cnf(i_0_16276,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_9689]),
    [final] ).

cnf(i_0_16277,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_9690]),
    [final] ).

cnf(i_0_16278,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_9691]),
    [final] ).

cnf(i_0_16279,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_9692]),
    [final] ).

cnf(i_0_16280,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_9693]),
    [final] ).

cnf(i_0_16281,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_9694]),
    [final] ).

cnf(i_0_16282,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_9695]),
    [final] ).

cnf(i_0_16283,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_9696]),
    [final] ).

cnf(i_0_16284,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_9697]),
    [final] ).

cnf(i_0_16285,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_9698]),
    [final] ).

cnf(i_0_16286,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_8961]),
    [final] ).

cnf(i_0_16287,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_9616]),
    [final] ).

cnf(i_0_16288,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk563_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_9699]),
    [final] ).

cnf(i_0_16289,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_9700]),
    [final] ).

cnf(i_0_16290,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | epred2_3(X2,X3,X1)
    | ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7651]),
    [final] ).

cnf(i_0_16291,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_9701]),
    [final] ).

cnf(i_0_16292,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_9702]),
    [final] ).

cnf(i_0_16293,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_9703]),
    [final] ).

cnf(i_0_16294,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_9704]),
    [final] ).

cnf(i_0_16295,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_9705]),
    [final] ).

cnf(i_0_16296,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_9706]),
    [final] ).

cnf(i_0_16297,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_9707]),
    [final] ).

cnf(i_0_16298,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_9708]),
    [final] ).

cnf(i_0_16299,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_9709]),
    [final] ).

cnf(i_0_16300,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_9710]),
    [final] ).

cnf(i_0_16301,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_9711,c_0_6713]),
    [final] ).

cnf(i_0_16302,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_9712]),
    [final] ).

cnf(i_0_16303,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_9713]),
    [final] ).

cnf(i_0_16304,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_9714]),
    [final] ).

cnf(i_0_16305,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_9715]),
    [final] ).

cnf(i_0_16306,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_9716]),
    [final] ).

cnf(i_0_16307,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_9717,c_0_7094]),
    [final] ).

cnf(i_0_16308,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_9718,c_0_8268]),
    [final] ).

cnf(i_0_16309,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_9719,c_0_6181]),
    [final] ).

cnf(i_0_16310,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_9720]),
    [final] ).

cnf(i_0_16311,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_9721]),
    [final] ).

cnf(i_0_16312,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_9722]),
    [final] ).

cnf(i_0_16313,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_9723]),
    [final] ).

cnf(i_0_16314,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_9724]),
    [final] ).

cnf(i_0_16315,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_9725]),
    [final] ).

cnf(i_0_16316,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_9726]),
    [final] ).

cnf(i_0_16317,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_9727]),
    [final] ).

cnf(i_0_16318,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_9728]),
    [final] ).

cnf(i_0_16319,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_9729]),
    [final] ).

cnf(i_0_16320,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_9730]),
    [final] ).

cnf(i_0_16321,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_9731]),
    [final] ).

cnf(i_0_16322,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_9732]),
    [final] ).

cnf(i_0_16323,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_9733]),
    [final] ).

cnf(i_0_16324,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_9734]),
    [final] ).

cnf(i_0_16325,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_9735]),
    [final] ).

cnf(i_0_16326,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_9736]),
    [final] ).

cnf(i_0_16327,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_8927]),
    [final] ).

cnf(i_0_16328,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_9222]),
    [final] ).

cnf(i_0_16329,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_9737]),
    [final] ).

cnf(i_0_16330,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_9738]),
    [final] ).

cnf(i_0_16331,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_9739]),
    [final] ).

cnf(i_0_16332,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_9332]),
    [final] ).

cnf(i_0_16333,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_9740]),
    [final] ).

cnf(i_0_16334,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_9741]),
    [final] ).

cnf(i_0_16335,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_9742]),
    [final] ).

cnf(i_0_16336,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_9743]),
    [final] ).

cnf(i_0_16337,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_9744]),
    [final] ).

cnf(i_0_16338,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_9745]),
    [final] ).

cnf(i_0_16339,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,hAPP(c_Code__Numeral_Oof__nat,esk563_2(X2,X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_9699]),
    [final] ).

cnf(i_0_16340,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,hAPP(c_Int_OAbs__Integ,esk419_2(X2,X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_8630]),
    [final] ).

cnf(i_0_16341,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_9746]),
    [final] ).

cnf(i_0_16342,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_9747]),
    [final] ).

cnf(i_0_16343,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),esk117_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_9610]),
    [final] ).

cnf(i_0_16344,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),esk119_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_9611]),
    [final] ).

cnf(i_0_16345,plain,
    ( X1 = hAPP(c_Code__Numeral_Onat__of,esk562_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_9748]),
    [final] ).

cnf(i_0_16346,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_5241]),
    [final] ).

cnf(i_0_16347,plain,
    ( hBOOL(hAPP(X1,hAPP(c_Int_Onat,X2)))
    | ~ hBOOL(hAPP(X1,esk46_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_9749]),
    [final] ).

cnf(i_0_16348,plain,
    hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))),
    inference(split_conjunct,[status(thm)],[i_0_9750]),
    [final] ).

cnf(i_0_16349,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_9387]),
    [final] ).

cnf(i_0_16350,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_16351,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | epred1_3(X2,X3,X1)
    | ~ hBOOL(hAPP(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7661]),
    [final] ).

cnf(i_0_16352,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_9587]),
    [final] ).

cnf(i_0_16353,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_9751]),
    [final] ).

cnf(i_0_16354,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_9752]),
    [final] ).

cnf(i_0_16355,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_8996]),
    [final] ).

cnf(i_0_16356,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_9753,c_0_6216]),
    [final] ).

cnf(i_0_16357,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_9754,c_0_6064]),
    [final] ).

cnf(i_0_16358,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_9755]),
    [final] ).

cnf(i_0_16359,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_8820]),
    [final] ).

cnf(i_0_16360,plain,
    ( hBOOL(hAPP(X1,X3))
    | ~ hBOOL(hAPP(X1,esk220_2(X1,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8825]),
    [final] ).

cnf(i_0_16361,plain,
    ( hBOOL(hAPP(X1,X3))
    | ~ hBOOL(hAPP(X1,esk192_2(X1,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8664]),
    [final] ).

cnf(i_0_16362,plain,
    ( hBOOL(hAPP(X3,X2))
    | c_Natural_Oevaln(c_Com_Ocom_OWhile(X3,X4),X2,X5,X1)
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_7079]),
    [final] ).

cnf(i_0_16363,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_9756]),
    [final] ).

cnf(i_0_16364,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_9757]),
    [final] ).

cnf(i_0_16365,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk27_2(X1,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9758]),
    [final] ).

cnf(i_0_16366,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_9759]),
    [final] ).

cnf(i_0_16367,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,esk37_2(X1,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9737]),
    [final] ).

cnf(i_0_16368,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_9330]),
    [final] ).

cnf(i_0_16369,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_9760]),
    [final] ).

cnf(i_0_16370,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_9761]),
    [final] ).

cnf(i_0_16371,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_9762,c_0_6216]),
    [final] ).

cnf(i_0_16372,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_9763]),
    [final] ).

cnf(i_0_16373,plain,
    ( hBOOL(hAPP(X1,X2))
    | c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X3),X2,X4,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7942]),
    [final] ).

cnf(i_0_16374,plain,
    ( hBOOL(hAPP(X1,X2))
    | c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X3),X2,X4,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9764]),
    [final] ).

cnf(i_0_16375,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_9765]),
    [final] ).

cnf(i_0_16376,plain,
    ( X2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk26_2(X2,X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9766]),
    [final] ).

cnf(i_0_16377,plain,
    ( X2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk23_2(X2,X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9767]),
    [final] ).

cnf(i_0_16378,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_9768]),
    [final] ).

cnf(i_0_16379,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_9769]),
    [final] ).

cnf(i_0_16380,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_9770,c_0_6097]),
    [final] ).

cnf(i_0_16381,plain,
    ( hAPP(X1,esk551_1(X1)) = hAPP(X1,esk552_1(X1))
    | hBOOL(hAPP(hAPP(X1,esk551_1(X1)),esk552_1(X1)))
    | c_Equiv__Relations_Opart__equivp(X3,X1)
    | ~ hBOOL(hAPP(hAPP(X1,X2),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8558]),
    [final] ).

cnf(i_0_16382,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_9771]),
    [final] ).

cnf(i_0_16383,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_9772]),
    [final] ).

cnf(i_0_16384,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_9773]),
    [final] ).

cnf(i_0_16385,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_9774]),
    [final] ).

cnf(i_0_16386,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_6446]),
    [final] ).

cnf(i_0_16387,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_9329]),
    [final] ).

cnf(i_0_16388,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_9269]),
    [final] ).

cnf(i_0_16389,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_9775]),
    [final] ).

cnf(i_0_16390,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_8629]),
    [final] ).

cnf(i_0_16391,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_9776]),
    [final] ).

cnf(i_0_16392,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_9675]),
    [final] ).

cnf(i_0_16393,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_9675]),
    [final] ).

cnf(i_0_16394,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_9777]),
    [final] ).

cnf(i_0_16395,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_6172]),
    [final] ).

cnf(i_0_16396,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_7961]),
    [final] ).

cnf(i_0_16397,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_8996]),
    [final] ).

cnf(i_0_16398,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk464_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_9778]),
    [final] ).

cnf(i_0_16399,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_9779]),
    [final] ).

cnf(i_0_16400,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_9780]),
    [final] ).

cnf(i_0_16401,plain,
    ( hBOOL(hAPP(X1,esk528_3(X2,X3,X1)))
    | c_FunDef_OTHE__default(X3,X2,X1) = X2 ),
    inference(split_conjunct,[status(thm)],[i_0_8045]),
    [final] ).

cnf(i_0_16402,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_9781]),
    [final] ).

cnf(i_0_16403,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_9782]),
    [final] ).

cnf(i_0_16404,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_9783]),
    [final] ).

cnf(i_0_16405,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_9784,c_0_6181]),
    [final] ).

cnf(i_0_16406,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_9785]),
    [final] ).

cnf(i_0_16407,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_9786]),
    [final] ).

cnf(i_0_16408,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_9787]),
    [final] ).

cnf(i_0_16409,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_9788]),
    [final] ).

cnf(i_0_16410,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_9789]),
    [final] ).

cnf(i_0_16411,plain,
    ( hBOOL(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X2),X3)))
    | ~ epred2_3(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_9496]),
    [final] ).

cnf(i_0_16412,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_9790]),
    [final] ).

cnf(i_0_16413,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_9790]),
    [final] ).

cnf(i_0_16414,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_9791]),
    [final] ).

cnf(i_0_16415,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_9792]),
    [final] ).

cnf(i_0_16416,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_9793]),
    [final] ).

cnf(i_0_16417,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_9794]),
    [final] ).

cnf(i_0_16418,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_9795]),
    [final] ).

cnf(i_0_16419,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_9796]),
    [final] ).

cnf(i_0_16420,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_9797]),
    [final] ).

cnf(i_0_16421,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_9798]),
    [final] ).

cnf(i_0_16422,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_9799]),
    [final] ).

cnf(i_0_16423,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_9679]),
    [final] ).

cnf(i_0_16424,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_9680]),
    [final] ).

cnf(i_0_16425,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_9800,c_0_7094]),
    [final] ).

cnf(i_0_16426,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_9801,c_0_7094]),
    [final] ).

cnf(i_0_16427,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_9802]),
    [final] ).

cnf(i_0_16428,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_16429,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_9803]),
    [final] ).

cnf(i_0_16430,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_9803]),
    [final] ).

cnf(i_0_16431,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_8329]),
    [final] ).

cnf(i_0_16432,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_8329]),
    [final] ).

cnf(i_0_16433,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_9804]),
    [final] ).

cnf(i_0_16434,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_8613]),
    [final] ).

cnf(i_0_16435,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_9805]),
    [final] ).

cnf(i_0_16436,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_9008]),
    [final] ).

cnf(i_0_16437,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_9536]),
    [final] ).

cnf(i_0_16438,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_9806]),
    [final] ).

cnf(i_0_16439,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_9807]),
    [final] ).

cnf(i_0_16440,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_9808]),
    [final] ).

cnf(i_0_16441,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_8161]),
    [final] ).

cnf(i_0_16442,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_9776]),
    [final] ).

cnf(i_0_16443,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_9524]),
    [final] ).

cnf(i_0_16444,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_9809]),
    [final] ).

cnf(i_0_16445,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_9810]),
    [final] ).

cnf(i_0_16446,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_9811]),
    [final] ).

cnf(i_0_16447,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_9810]),
    [final] ).

cnf(i_0_16448,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_9811]),
    [final] ).

cnf(i_0_16449,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_9812]),
    [final] ).

cnf(i_0_16450,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_9813]),
    [final] ).

cnf(i_0_16451,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_9814]),
    [final] ).

cnf(i_0_16452,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_9037]),
    [final] ).

cnf(i_0_16453,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_9631]),
    [final] ).

cnf(i_0_16454,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_9815]),
    [final] ).

cnf(i_0_16455,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_9816]),
    [final] ).

cnf(i_0_16456,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_9817]),
    [final] ).

cnf(i_0_16457,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_9818]),
    [final] ).

cnf(i_0_16458,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_9819]),
    [final] ).

cnf(i_0_16459,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_9820]),
    [final] ).

cnf(i_0_16460,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_9682]),
    [final] ).

cnf(i_0_16461,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_9735]),
    [final] ).

cnf(i_0_16462,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_9821]),
    [final] ).

cnf(i_0_16463,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_9822]),
    [final] ).

cnf(i_0_16464,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_9716]),
    [final] ).

cnf(i_0_16465,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_9647]),
    [final] ).

cnf(i_0_16466,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_9100]),
    [final] ).

cnf(i_0_16467,plain,
    ( hBOOL(hAPP(X1,esk383_3(X2,X1,X3)))
    | hAPP(c_List_Ofilter(X3,X1),X2) = c_List_Olist_ONil(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8796]),
    [final] ).

cnf(i_0_16468,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_9823]),
    [final] ).

cnf(i_0_16469,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_9824]),
    [final] ).

cnf(i_0_16470,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_9551]),
    [final] ).

cnf(i_0_16471,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_9825]),
    [final] ).

cnf(i_0_16472,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_9826]),
    [final] ).

cnf(i_0_16473,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_9827]),
    [final] ).

cnf(i_0_16474,plain,
    c_Hoare__Mirabelle_Otriple_Otriple__size(X1,X2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X3),X4),X5)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[i_0_9828]),
    [final] ).

cnf(i_0_16475,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_9321]),
    [final] ).

cnf(i_0_16476,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk36_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_9829]),
    [final] ).

cnf(i_0_16477,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_9830]),
    [final] ).

cnf(i_0_16478,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_9830]),
    [final] ).

cnf(i_0_16479,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_9831]),
    [final] ).

cnf(i_0_16480,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_9832]),
    [final] ).

cnf(i_0_16481,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_9833]),
    [final] ).

cnf(i_0_16482,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_9834]),
    [final] ).

cnf(i_0_16483,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_9835]),
    [final] ).

cnf(i_0_16484,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_9836]),
    [final] ).

cnf(i_0_16485,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_9837]),
    [final] ).

cnf(i_0_16486,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_9838]),
    [final] ).

cnf(i_0_16487,plain,
    c_Nat_Onat_Onat__case(X1,X2,X3,hAPP(c_Nat_OSuc,X4)) = hAPP(X3,X4),
    inference(split_conjunct,[status(thm)],[i_0_9839]),
    [final] ).

cnf(i_0_16488,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_9840]),
    [final] ).

cnf(i_0_16489,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_9841]),
    [final] ).

cnf(i_0_16490,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_9842]),
    [final] ).

cnf(i_0_16491,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_9843]),
    [final] ).

cnf(i_0_16492,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_9844]),
    [final] ).

cnf(i_0_16493,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_9845]),
    [final] ).

cnf(i_0_16494,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_9846]),
    [final] ).

cnf(i_0_16495,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_9617]),
    [final] ).

cnf(i_0_16496,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_9847]),
    [final] ).

cnf(i_0_16497,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_9848]),
    [final] ).

cnf(i_0_16498,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_9849]),
    [final] ).

cnf(i_0_16499,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_9850]),
    [final] ).

cnf(i_0_16500,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_9851]),
    [final] ).

cnf(i_0_16501,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_9852]),
    [final] ).

cnf(i_0_16502,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_9853]),
    [final] ).

cnf(i_0_16503,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_9854]),
    [final] ).

cnf(i_0_16504,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_9855]),
    [final] ).

cnf(i_0_16505,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_9856]),
    [final] ).

cnf(i_0_16506,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_9857]),
    [final] ).

cnf(i_0_16507,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_9858]),
    [final] ).

cnf(i_0_16508,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_16509,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_16510,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_16511,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_16512,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_9859]),
    [final] ).

cnf(i_0_16513,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_9860]),
    [final] ).

cnf(i_0_16514,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_9861]),
    [final] ).

cnf(i_0_16515,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_9862]),
    [final] ).

cnf(i_0_16516,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk50_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_9142]),
    [final] ).

cnf(i_0_16517,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3),X4),X1),X2))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9459]),
    [final] ).

cnf(i_0_16518,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_9863]),
    [final] ).

cnf(i_0_16519,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_9551]),
    [final] ).

cnf(i_0_16520,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_9845]),
    [final] ).

cnf(i_0_16521,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_9846]),
    [final] ).

cnf(i_0_16522,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_9864]),
    [final] ).

cnf(i_0_16523,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_9486]),
    [final] ).

cnf(i_0_16524,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_9865]),
    [final] ).

cnf(i_0_16525,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_9866]),
    [final] ).

cnf(i_0_16526,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_16527,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_9867]),
    [final] ).

cnf(i_0_16528,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_9315]),
    [final] ).

cnf(i_0_16529,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_9868]),
    [final] ).

cnf(i_0_16530,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_9869]),
    [final] ).

cnf(i_0_16531,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_9870,c_0_6064]),
    [final] ).

cnf(i_0_16532,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_9473]),
    [final] ).

cnf(i_0_16533,plain,
    ( esk121_3(X1,X2,X3) = esk122_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_8691]),
    [final] ).

cnf(i_0_16534,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_9871]),
    [final] ).

cnf(i_0_16535,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_9872]),
    [final] ).

cnf(i_0_16536,plain,
    ( X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk48_2(X2,X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9873]),
    [final] ).

cnf(i_0_16537,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_9874]),
    [final] ).

cnf(i_0_16538,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_9875]),
    [final] ).

cnf(i_0_16539,plain,
    ( hBOOL(hAPP(X1,esk217_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_8790]),
    [final] ).

cnf(i_0_16540,plain,
    ( hBOOL(hAPP(X1,esk189_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_8628]),
    [final] ).

cnf(i_0_16541,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_9876]),
    [final] ).

cnf(i_0_16542,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_9876]),
    [final] ).

cnf(i_0_16543,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,esk38_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_9877]),
    [final] ).

cnf(i_0_16544,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_9878]),
    [final] ).

cnf(i_0_16545,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_9879]),
    [final] ).

cnf(i_0_16546,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_9880]),
    [final] ).

cnf(i_0_16547,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_9881]),
    [final] ).

cnf(i_0_16548,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_9666]),
    [final] ).

cnf(i_0_16549,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_9882]),
    [final] ).

cnf(i_0_16550,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_9883]),
    [final] ).

cnf(i_0_16551,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_9530]),
    [final] ).

cnf(i_0_16552,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_9884]),
    [final] ).

cnf(i_0_16553,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_9776]),
    [final] ).

cnf(i_0_16554,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_9885]),
    [final] ).

cnf(i_0_16555,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk495_2(X2,X1)),esk494_2(X2,X1)))
    | c_Wellfounded_Owf(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7044]),
    [final] ).

cnf(i_0_16556,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_9886]),
    [final] ).

cnf(i_0_16557,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_9887]),
    [final] ).

cnf(i_0_16558,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_8905]),
    [final] ).

cnf(i_0_16559,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_9888]),
    [final] ).

cnf(i_0_16560,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_9551]),
    [final] ).

cnf(i_0_16561,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_9889]),
    [final] ).

cnf(i_0_16562,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_9890]),
    [final] ).

cnf(i_0_16563,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_9891]),
    [final] ).

cnf(i_0_16564,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_9891]),
    [final] ).

cnf(i_0_16565,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_9892]),
    [final] ).

cnf(i_0_16566,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_9893]),
    [final] ).

cnf(i_0_16567,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_9894]),
    [final] ).

cnf(i_0_16568,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_9895]),
    [final] ).

cnf(i_0_16569,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_9896]),
    [final] ).

cnf(i_0_16570,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_9897]),
    [final] ).

cnf(i_0_16571,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_9898]),
    [final] ).

cnf(i_0_16572,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_9899]),
    [final] ).

cnf(i_0_16573,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_9900]),
    [final] ).

cnf(i_0_16574,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_9900]),
    [final] ).

cnf(i_0_16575,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_9899]),
    [final] ).

cnf(i_0_16576,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_8177]),
    [final] ).

cnf(i_0_16577,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_7625]),
    [final] ).

cnf(i_0_16578,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_6561]),
    [final] ).

cnf(i_0_16579,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_9901]),
    [final] ).

cnf(i_0_16580,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_9902]),
    [final] ).

cnf(i_0_16581,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_9480]),
    [final] ).

cnf(i_0_16582,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_6850]),
    [final] ).

cnf(i_0_16583,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_9903]),
    [final] ).

cnf(i_0_16584,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_6851]),
    [final] ).

cnf(i_0_16585,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_6615]),
    [final] ).

cnf(i_0_16586,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_9904]),
    [final] ).

cnf(i_0_16587,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_6615]),
    [final] ).

cnf(i_0_16588,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_9905]),
    [final] ).

cnf(i_0_16589,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_9906]),
    [final] ).

cnf(i_0_16590,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_9907]),
    [final] ).

cnf(i_0_16591,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_9908]),
    [final] ).

cnf(i_0_16592,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_9876]),
    [final] ).

cnf(i_0_16593,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk400_2(X1,X2)),esk401_2(X1,X2)))
    | c_List_Olinorder__class_Osorted(X2,X1)
    | ~ class_Orderings_Olinorder(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7644]),
    [final] ).

cnf(i_0_16594,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk396_2(X1,X2)),esk395_2(X1,X2)))
    | c_List_Olinorder__class_Osorted(X2,X1)
    | ~ class_Orderings_Olinorder(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7645]),
    [final] ).

cnf(i_0_16595,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_9909]),
    [final] ).

cnf(i_0_16596,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_9910]),
    [final] ).

cnf(i_0_16597,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_9911]),
    [final] ).

cnf(i_0_16598,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_9912]),
    [final] ).

cnf(i_0_16599,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_9913]),
    [final] ).

cnf(i_0_16600,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_9914]),
    [final] ).

cnf(i_0_16601,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_9914]),
    [final] ).

cnf(i_0_16602,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_9915]),
    [final] ).

cnf(i_0_16603,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_9551]),
    [final] ).

cnf(i_0_16604,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_9916]),
    [final] ).

cnf(i_0_16605,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk41_1(X1)))
    | ~ hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9656]),
    [final] ).

cnf(i_0_16606,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_9917]),
    [final] ).

cnf(i_0_16607,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_9918]),
    [final] ).

cnf(i_0_16608,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_9919]),
    [final] ).

cnf(i_0_16609,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_9918]),
    [final] ).

cnf(i_0_16610,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X2,X3,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7651]),
    [final] ).

cnf(i_0_16611,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X2,X3,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7661]),
    [final] ).

cnf(i_0_16612,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_9920]),
    [final] ).

cnf(i_0_16613,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_9921]),
    [final] ).

cnf(i_0_16614,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(X1)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X2),X3),X4)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[i_0_9922]),
    [final] ).

cnf(i_0_16615,plain,
    ( c_Equiv__Relations_Oequivp(X2,X1)
    | ~ hBOOL(hAPP(hAPP(X1,esk253_1(X1)),esk254_1(X1)))
    | hAPP(X1,esk253_1(X1)) != hAPP(X1,esk254_1(X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9923]),
    [final] ).

cnf(i_0_16616,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_9924]),
    [final] ).

cnf(i_0_16617,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_9925]),
    [final] ).

cnf(i_0_16618,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_9926]),
    [final] ).

cnf(i_0_16619,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_9927]),
    [final] ).

cnf(i_0_16620,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_9928]),
    [final] ).

cnf(i_0_16621,plain,
    ( hBOOL(hAPP(X1,hAPP(c_Nat_OSuc,esk21_2(X2,X1))))
    | hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9929]),
    [final] ).

cnf(i_0_16622,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_9387]),
    [final] ).

cnf(i_0_16623,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_9438]),
    [final] ).

cnf(i_0_16624,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_9055]),
    [final] ).

cnf(i_0_16625,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_9930]),
    [final] ).

cnf(i_0_16626,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_9931]),
    [final] ).

cnf(i_0_16627,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_9680]),
    [final] ).

cnf(i_0_16628,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_9679]),
    [final] ).

cnf(i_0_16629,plain,
    ( hBOOL(hAPP(X1,hAPP(c_Int_Onat,X2)))
    | ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(X1,esk37_2(X2,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_9737]),
    [final] ).

cnf(i_0_16630,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_9751]),
    [final] ).

cnf(i_0_16631,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OLocal(X1,X2,X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X3)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(split_conjunct,[status(thm)],[i_0_9932]),
    [final] ).

cnf(i_0_16632,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_9933]),
    [final] ).

cnf(i_0_16633,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_9934]),
    [final] ).

cnf(i_0_16634,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_9935]),
    [final] ).

cnf(i_0_16635,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_8902]),
    [final] ).

cnf(i_0_16636,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_8902]),
    [final] ).

cnf(i_0_16637,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_9936]),
    [final] ).

cnf(i_0_16638,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_9937]),
    [final] ).

cnf(i_0_16639,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_9938]),
    [final] ).

cnf(i_0_16640,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_9939]),
    [final] ).

cnf(i_0_16641,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_7961]),
    [final] ).

cnf(i_0_16642,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_9940]),
    [final] ).

cnf(i_0_16643,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_9941]),
    [final] ).

cnf(i_0_16644,plain,
    ( hBOOL(hAPP(hAPP(X1,esk554_2(X1,X2)),esk554_2(X1,X2)))
    | ~ c_Equiv__Relations_Opart__equivp(X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9942]),
    [final] ).

cnf(i_0_16645,plain,
    ( hBOOL(hAPP(hAPP(X1,esk553_2(X1,X2)),esk553_2(X1,X2)))
    | ~ c_Equiv__Relations_Opart__equivp(X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9943]),
    [final] ).

cnf(i_0_16646,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_9944]),
    [final] ).

cnf(i_0_16647,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_9945]),
    [final] ).

cnf(i_0_16648,plain,
    c_List_Olistrelp(X1,X2,c_List_Olist_ONil(X1),c_List_Olist_ONil(X1)),
    inference(split_conjunct,[status(thm)],[i_0_9946]),
    [final] ).

cnf(i_0_16649,plain,
    c_List_Olistrelp(X1,X2,c_List_Olist_ONil(X1),c_List_Olist_ONil(X1)),
    inference(split_conjunct,[status(thm)],[i_0_9947]),
    [final] ).

cnf(i_0_16650,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_5943]),
    [final] ).

cnf(i_0_16651,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_16652,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_9790]),
    [final] ).

cnf(i_0_16653,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_9948]),
    [final] ).

cnf(i_0_16654,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_9824]),
    [final] ).

cnf(i_0_16655,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_9949]),
    [final] ).

cnf(i_0_16656,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_9950]),
    [final] ).

cnf(i_0_16657,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_9950]),
    [final] ).

cnf(i_0_16658,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_9951]),
    [final] ).

cnf(i_0_16659,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_9952]),
    [final] ).

cnf(i_0_16660,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_9899]),
    [final] ).

cnf(i_0_16661,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_9900]),
    [final] ).

cnf(i_0_16662,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_5332]),
    [final] ).

cnf(i_0_16663,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_9953]),
    [final] ).

cnf(i_0_16664,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_9954]),
    [final] ).

cnf(i_0_16665,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_9955]),
    [final] ).

cnf(i_0_16666,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_9956]),
    [final] ).

cnf(i_0_16667,plain,
    c_List_Omaps(X1,X2,X3,c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X2),
    inference(split_conjunct,[status(thm)],[i_0_9957]),
    [final] ).

cnf(i_0_16668,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_9767]),
    [final] ).

cnf(i_0_16669,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_9958,c_0_8268]),c_0_8268]),
    [final] ).

cnf(i_0_16670,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_9959]),
    [final] ).

cnf(i_0_16671,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_9960]),
    [final] ).

cnf(i_0_16672,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_9961]),
    [final] ).

cnf(i_0_16673,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_9962]),
    [final] ).

cnf(i_0_16674,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_9963]),
    [final] ).

cnf(i_0_16675,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_9964]),
    [final] ).

cnf(i_0_16676,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_9965]),
    [final] ).

cnf(i_0_16677,plain,
    c_Fun_Oinj__on(X1,X1,c_Fun_Oid(X1),X2),
    inference(split_conjunct,[status(thm)],[i_0_9966]),
    [final] ).

cnf(i_0_16678,plain,
    c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
    inference(split_conjunct,[status(thm)],[i_0_9967]),
    [final] ).

cnf(i_0_16679,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_7884]),
    [final] ).

cnf(i_0_16680,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_9968]),
    [final] ).

cnf(i_0_16681,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_9969]),
    [final] ).

cnf(i_0_16682,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_9970]),
    [final] ).

cnf(i_0_16683,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_9971,c_0_6097]),
    [final] ).

cnf(i_0_16684,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_9972]),
    [final] ).

cnf(i_0_16685,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_9973,c_0_8268]),
    [final] ).

cnf(i_0_16686,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_9974]),
    [final] ).

cnf(i_0_16687,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_9975]),
    [final] ).

cnf(i_0_16688,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_9976]),
    [final] ).

cnf(i_0_16689,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_6805]),
    [final] ).

cnf(i_0_16690,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_9977]),
    [final] ).

cnf(i_0_16691,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_9978]),
    [final] ).

cnf(i_0_16692,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_9979]),
    [final] ).

cnf(i_0_16693,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_9980]),
    [final] ).

cnf(i_0_16694,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_9981]),
    [final] ).

cnf(i_0_16695,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_9982]),
    [final] ).

cnf(i_0_16696,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_9983]),
    [final] ).

cnf(i_0_16697,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_9984,c_0_6063]),c_0_6063]),
    [final] ).

cnf(i_0_16698,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_9985]),
    [final] ).

cnf(i_0_16699,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_9986]),
    [final] ).

cnf(i_0_16700,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_9987]),
    [final] ).

cnf(i_0_16701,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_9988]),
    [final] ).

cnf(i_0_16702,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_9989]),
    [final] ).

cnf(i_0_16703,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_9990]),
    [final] ).

cnf(i_0_16704,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_5332]),
    [final] ).

cnf(i_0_16705,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_9991]),
    [final] ).

cnf(i_0_16706,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_9991]),
    [final] ).

cnf(i_0_16707,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_9992,c_0_6062]),c_0_6063]),c_0_6064]),c_0_6064]),
    [final] ).

cnf(i_0_16708,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_9993]),
    [final] ).

cnf(i_0_16709,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_9994]),
    [final] ).

cnf(i_0_16710,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_9995]),
    [final] ).

cnf(i_0_16711,plain,
    c_Natural_Oevaln(c_Com_Ocom_OSKIP,X1,X2,X1),
    inference(split_conjunct,[status(thm)],[i_0_9996]),
    [final] ).

cnf(i_0_16712,plain,
    c_Natural_Oevaln(c_Com_Ocom_OSKIP,X1,X2,X1),
    inference(split_conjunct,[status(thm)],[i_0_9997]),
    [final] ).

cnf(i_0_16713,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_9998]),
    [final] ).

cnf(i_0_16714,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_9999]),
    [final] ).

cnf(i_0_16715,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_10000]),
    [final] ).

cnf(i_0_16716,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_10001]),
    [final] ).

cnf(i_0_16717,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_10002]),
    [final] ).

cnf(i_0_16718,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_10003]),
    [final] ).

cnf(i_0_16719,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_10004,c_0_7958]),c_0_7959]),
    [final] ).

cnf(i_0_16720,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_10005]),
    [final] ).

cnf(i_0_16721,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_10006]),
    [final] ).

cnf(i_0_16722,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_10007]),
    [final] ).

cnf(i_0_16723,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_10008]),
    [final] ).

cnf(i_0_16724,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_10009]),
    [final] ).

cnf(i_0_16725,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_10010]),
    [final] ).

cnf(i_0_16726,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_10011]),
    [final] ).

cnf(i_0_16727,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_10012]),
    [final] ).

cnf(i_0_16728,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_10013]),
    [final] ).

cnf(i_0_16729,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_10014]),
    [final] ).

cnf(i_0_16730,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_10015]),
    [final] ).

cnf(i_0_16731,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_9664]),
    [final] ).

cnf(i_0_16732,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_9588]),
    [final] ).

cnf(i_0_16733,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_9588]),
    [final] ).

cnf(i_0_16734,plain,
    c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X1),
    inference(split_conjunct,[status(thm)],[i_0_10016]),
    [final] ).

cnf(i_0_16735,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_10000]),
    [final] ).

cnf(i_0_16736,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_10017]),
    [final] ).

cnf(i_0_16737,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_10001]),
    [final] ).

cnf(i_0_16738,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_10002]),
    [final] ).

cnf(i_0_16739,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_10018]),
    [final] ).

cnf(i_0_16740,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_10019]),
    [final] ).

cnf(i_0_16741,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_10020]),
    [final] ).

cnf(i_0_16742,plain,
    ( X2 = X3
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_10021]),
    [final] ).

cnf(i_0_16743,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_16744,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_10022]),
    [final] ).

cnf(i_0_16745,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_10023,c_0_6064]),
    [final] ).

cnf(i_0_16746,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_8996]),
    [final] ).

cnf(i_0_16747,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_10024]),
    [final] ).

cnf(i_0_16748,plain,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(X2),esk75_2(X1,X2)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_10025]),
    [final] ).

cnf(i_0_16749,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk74_2(X2,X1)),X2))
    | X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_10026]),
    [final] ).

cnf(i_0_16750,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_10027]),
    [final] ).

cnf(i_0_16751,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_10028,c_0_6181]),
    [final] ).

cnf(i_0_16752,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_9715]),
    [final] ).

cnf(i_0_16753,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3),X1),X4),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_9459]),
    [final] ).

cnf(i_0_16754,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_10029]),
    [final] ).

cnf(i_0_16755,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_10030]),
    [final] ).

cnf(i_0_16756,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_10031]),
    [final] ).

cnf(i_0_16757,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_10032]),
    [final] ).

cnf(i_0_16758,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_9534]),
    [final] ).

cnf(i_0_16759,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_10033]),
    [final] ).

cnf(i_0_16760,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_10034]),
    [final] ).

cnf(i_0_16761,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_10035]),
    [final] ).

cnf(i_0_16762,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_10036]),
    [final] ).

cnf(i_0_16763,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_10037]),
    [final] ).

cnf(i_0_16764,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_10038]),
    [final] ).

cnf(i_0_16765,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_10039]),
    [final] ).

cnf(i_0_16766,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_10040]),
    [final] ).

cnf(i_0_16767,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_10041]),
    [final] ).

cnf(i_0_16768,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_10042]),
    [final] ).

cnf(i_0_16769,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_10043,c_0_6181]),
    [final] ).

cnf(i_0_16770,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_10044,c_0_6181]),
    [final] ).

cnf(i_0_16771,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_10045,c_0_6181]),
    [final] ).

cnf(i_0_16772,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_10046]),
    [final] ).

cnf(i_0_16773,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_9541]),
    [final] ).

cnf(i_0_16774,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_10047]),
    [final] ).

cnf(i_0_16775,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_10048]),
    [final] ).

cnf(i_0_16776,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk120_2(X1,X2)),X1))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9611]),
    [final] ).

cnf(i_0_16777,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk118_2(X1,X2)),X1))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9610]),
    [final] ).

cnf(i_0_16778,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_9565]),
    [final] ).

cnf(i_0_16779,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_9564]),
    [final] ).

cnf(i_0_16780,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_10049]),
    [final] ).

cnf(i_0_16781,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_10050]),
    [final] ).

cnf(i_0_16782,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_10051]),
    [final] ).

cnf(i_0_16783,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_10052]),
    [final] ).

cnf(i_0_16784,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_10053]),
    [final] ).

cnf(i_0_16785,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_10054]),
    [final] ).

cnf(i_0_16786,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_10055]),
    [final] ).

cnf(i_0_16787,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_8558]),
    [final] ).

cnf(i_0_16788,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_8558]),
    [final] ).

cnf(i_0_16789,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_10056]),
    [final] ).

cnf(i_0_16790,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_10057]),
    [final] ).

cnf(i_0_16791,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_10058]),
    [final] ).

cnf(i_0_16792,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_9612]),
    [final] ).

cnf(i_0_16793,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_10059]),
    [final] ).

cnf(i_0_16794,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_10060]),
    [final] ).

cnf(i_0_16795,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_10061]),
    [final] ).

cnf(i_0_16796,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_10062]),
    [final] ).

cnf(i_0_16797,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_10063]),
    [final] ).

cnf(i_0_16798,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_10064]),
    [final] ).

cnf(i_0_16799,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_10065]),
    [final] ).

cnf(i_0_16800,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_10066]),
    [final] ).

cnf(i_0_16801,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_10067]),
    [final] ).

cnf(i_0_16802,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_10068]),
    [final] ).

cnf(i_0_16803,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_9709]),
    [final] ).

cnf(i_0_16804,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_10069]),
    [final] ).

cnf(i_0_16805,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_5962]),
    [final] ).

cnf(i_0_16806,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_10070]),
    [final] ).

cnf(i_0_16807,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_10071]),
    [final] ).

cnf(i_0_16808,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_10072]),
    [final] ).

cnf(i_0_16809,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_10073]),
    [final] ).

cnf(i_0_16810,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_9991]),
    [final] ).

cnf(i_0_16811,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_10074]),
    [final] ).

cnf(i_0_16812,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_10075]),
    [final] ).

cnf(i_0_16813,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_10076]),
    [final] ).

cnf(i_0_16814,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_10077]),
    [final] ).

cnf(i_0_16815,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_10078]),
    [final] ).

cnf(i_0_16816,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_10079]),
    [final] ).

cnf(i_0_16817,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_10080]),
    [final] ).

cnf(i_0_16818,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_10081]),
    [final] ).

cnf(i_0_16819,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_10082]),
    [final] ).

cnf(i_0_16820,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_10083]),
    [final] ).

cnf(i_0_16821,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_10084]),
    [final] ).

cnf(i_0_16822,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_10085]),
    [final] ).

cnf(i_0_16823,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_10086]),
    [final] ).

cnf(i_0_16824,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_10087]),
    [final] ).

cnf(i_0_16825,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_10088]),
    [final] ).

cnf(i_0_16826,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_10089]),
    [final] ).

cnf(i_0_16827,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_10090]),
    [final] ).

cnf(i_0_16828,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_10091]),
    [final] ).

cnf(i_0_16829,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_9807]),
    [final] ).

cnf(i_0_16830,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_10092]),
    [final] ).

cnf(i_0_16831,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X3)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10093]),
    [final] ).

cnf(i_0_16832,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_10094,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_16833,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_10095,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_16834,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_10096,c_0_6181]),
    [final] ).

cnf(i_0_16835,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_10097]),
    [final] ).

cnf(i_0_16836,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_10098]),
    [final] ).

cnf(i_0_16837,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_10099]),
    [final] ).

cnf(i_0_16838,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_10100]),
    [final] ).

cnf(i_0_16839,plain,
    ( c_Relation_Osingle__valued(X3,X2,X1)
    | esk446_3(X1,X2,X3) != esk447_3(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_6990]),
    [final] ).

cnf(i_0_16840,plain,
    ( c_Relation_Ototal__on(X3,X2,X1)
    | esk115_3(X1,X2,X3) != esk116_3(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_6799]),
    [final] ).

cnf(i_0_16841,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_10101]),
    [final] ).

cnf(i_0_16842,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_10102]),
    [final] ).

cnf(i_0_16843,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_10103]),
    [final] ).

cnf(i_0_16844,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_10104]),
    [final] ).

cnf(i_0_16845,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_9194]),
    [final] ).

cnf(i_0_16846,plain,
    ( c_Wellfounded_OwfP(X1,X2)
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),esk414_2(X2,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_10105]),
    [final] ).

cnf(i_0_16847,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_10106]),
    [final] ).

cnf(i_0_16848,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_10107,c_0_6181]),
    [final] ).

cnf(i_0_16849,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_9529]),
    [final] ).

cnf(i_0_16850,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_10108]),
    [final] ).

cnf(i_0_16851,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_10109]),
    [final] ).

cnf(i_0_16852,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_9847]),
    [final] ).

cnf(i_0_16853,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_10110]),
    [final] ).

cnf(i_0_16854,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_10111]),
    [final] ).

cnf(i_0_16855,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_10112]),
    [final] ).

cnf(i_0_16856,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_9641]),
    [final] ).

cnf(i_0_16857,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_10113]),
    [final] ).

cnf(i_0_16858,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_10114]),
    [final] ).

cnf(i_0_16859,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_10115]),
    [final] ).

cnf(i_0_16860,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_10116]),
    [final] ).

cnf(i_0_16861,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_10117]),
    [final] ).

cnf(i_0_16862,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_10118]),
    [final] ).

cnf(i_0_16863,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_10119]),
    [final] ).

cnf(i_0_16864,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_10120]),
    [final] ).

cnf(i_0_16865,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_10121]),
    [final] ).

cnf(i_0_16866,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_10122]),
    [final] ).

cnf(i_0_16867,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_10123]),
    [final] ).

cnf(i_0_16868,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_10124]),
    [final] ).

cnf(i_0_16869,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_10125,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_16870,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk27_2(X2,X1)) = X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9758]),
    [final] ).

cnf(i_0_16871,plain,
    ( X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk49_2(X2,X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10126]),
    [final] ).

cnf(i_0_16872,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_10127]),
    [final] ).

cnf(i_0_16873,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),esk37_2(X1,X2))
    | hBOOL(hAPP(X2,hAPP(c_Int_Onat,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_9737]),
    [final] ).

cnf(i_0_16874,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_10128]),
    [final] ).

cnf(i_0_16875,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_9876]),
    [final] ).

cnf(i_0_16876,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_10129]),
    [final] ).

cnf(i_0_16877,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_10130]),
    [final] ).

cnf(i_0_16878,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_10131]),
    [final] ).

cnf(i_0_16879,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_9640]),
    [final] ).

cnf(i_0_16880,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_10132]),
    [final] ).

cnf(i_0_16881,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_10133]),
    [final] ).

cnf(i_0_16882,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_9638]),
    [final] ).

cnf(i_0_16883,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_10134,c_0_6181]),
    [final] ).

cnf(i_0_16884,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_10135,c_0_6181]),
    [final] ).

cnf(i_0_16885,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_9645]),
    [final] ).

cnf(i_0_16886,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_10136]),
    [final] ).

cnf(i_0_16887,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_10137]),
    [final] ).

cnf(i_0_16888,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_10138]),
    [final] ).

cnf(i_0_16889,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_10139]),
    [final] ).

cnf(i_0_16890,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_10140,c_0_6216]),c_0_6064]),
    [final] ).

cnf(i_0_16891,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_9873]),
    [final] ).

cnf(i_0_16892,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_9930]),
    [final] ).

cnf(i_0_16893,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_9931]),
    [final] ).

cnf(i_0_16894,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_10141]),
    [final] ).

cnf(i_0_16895,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_10142]),
    [final] ).

cnf(i_0_16896,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_10143]),
    [final] ).

cnf(i_0_16897,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_10144]),
    [final] ).

cnf(i_0_16898,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_10145]),
    [final] ).

cnf(i_0_16899,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_10146]),
    [final] ).

cnf(i_0_16900,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_10147]),
    [final] ).

cnf(i_0_16901,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_10148]),
    [final] ).

cnf(i_0_16902,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_10149]),
    [final] ).

cnf(i_0_16903,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_10150]),
    [final] ).

cnf(i_0_16904,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_10151]),
    [final] ).

cnf(i_0_16905,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_10152]),
    [final] ).

cnf(i_0_16906,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_10153]),
    [final] ).

cnf(i_0_16907,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_10154]),
    [final] ).

cnf(i_0_16908,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_10155]),
    [final] ).

cnf(i_0_16909,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_10156]),
    [final] ).

cnf(i_0_16910,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_10157]),
    [final] ).

cnf(i_0_16911,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_10158,c_0_6064]),
    [final] ).

cnf(i_0_16912,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_8229]),
    [final] ).

cnf(i_0_16913,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_10159]),
    [final] ).

cnf(i_0_16914,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_10160]),
    [final] ).

cnf(i_0_16915,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_10161]),
    [final] ).

cnf(i_0_16916,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_10162]),
    [final] ).

cnf(i_0_16917,plain,
    ( hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(X1,esk21_2(X2,X1)))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9929]),
    [final] ).

cnf(i_0_16918,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_10163]),
    [final] ).

cnf(i_0_16919,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_10164]),
    [final] ).

cnf(i_0_16920,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_10165]),
    [final] ).

cnf(i_0_16921,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_10166]),
    [final] ).

cnf(i_0_16922,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_10167]),
    [final] ).

cnf(i_0_16923,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_10168]),
    [final] ).

cnf(i_0_16924,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_10169]),
    [final] ).

cnf(i_0_16925,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_10170]),
    [final] ).

cnf(i_0_16926,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_10171]),
    [final] ).

cnf(i_0_16927,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_10172]),
    [final] ).

cnf(i_0_16928,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_10173]),
    [final] ).

cnf(i_0_16929,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk42_1(X1)))
    | hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9498]),
    [final] ).

cnf(i_0_16930,plain,
    ( X2 = esk432_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_10174]),
    [final] ).

cnf(i_0_16931,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_9700]),
    [final] ).

cnf(i_0_16932,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_10175]),
    [final] ).

cnf(i_0_16933,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_10176]),
    [final] ).

cnf(i_0_16934,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_10177]),
    [final] ).

cnf(i_0_16935,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_10178]),
    [final] ).

cnf(i_0_16936,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_9457]),
    [final] ).

cnf(i_0_16937,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_10179]),
    [final] ).

cnf(i_0_16938,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_10026]),
    [final] ).

cnf(i_0_16939,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_10025]),
    [final] ).

cnf(i_0_16940,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_10180]),
    [final] ).

cnf(i_0_16941,plain,
    ( hBOOL(hAPP(X1,esk359_2(X2,X1)))
    | ~ hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X2,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_10181]),
    [final] ).

cnf(i_0_16942,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_10182]),
    [final] ).

cnf(i_0_16943,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_10183]),
    [final] ).

cnf(i_0_16944,plain,
    hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk564_1(X1)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(split_conjunct,[status(thm)],[i_0_10184]),
    [final] ).

cnf(i_0_16945,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_10185]),
    [final] ).

cnf(i_0_16946,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_10186]),
    [final] ).

cnf(i_0_16947,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_10187]),
    [final] ).

cnf(i_0_16948,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_10188]),
    [final] ).

cnf(i_0_16949,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_6805]),
    [final] ).

cnf(i_0_16950,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_6805]),
    [final] ).

cnf(i_0_16951,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_10189]),
    [final] ).

cnf(i_0_16952,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_10190]),
    [final] ).

cnf(i_0_16953,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_10191]),
    [final] ).

cnf(i_0_16954,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_10192]),
    [final] ).

cnf(i_0_16955,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_10193]),
    [final] ).

cnf(i_0_16956,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_10194]),
    [final] ).

cnf(i_0_16957,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_10195]),
    [final] ).

cnf(i_0_16958,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_10196]),
    [final] ).

cnf(i_0_16959,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_10197]),
    [final] ).

cnf(i_0_16960,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_10187]),
    [final] ).

cnf(i_0_16961,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_10188]),
    [final] ).

cnf(i_0_16962,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_10198]),
    [final] ).

cnf(i_0_16963,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_10199]),
    [final] ).

cnf(i_0_16964,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_10200]),
    [final] ).

cnf(i_0_16965,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_10201]),
    [final] ).

cnf(i_0_16966,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_10202]),
    [final] ).

cnf(i_0_16967,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_10203]),
    [final] ).

cnf(i_0_16968,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_10204]),
    [final] ).

cnf(i_0_16969,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_10205,c_0_6181]),
    [final] ).

cnf(i_0_16970,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_10206]),
    [final] ).

cnf(i_0_16971,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_10207,c_0_6062]),c_0_6063]),c_0_6064]),
    [final] ).

cnf(i_0_16972,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_10208]),
    [final] ).

cnf(i_0_16973,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_10209]),
    [final] ).

cnf(i_0_16974,plain,
    ~ hBOOL(hAPP(hAPP(c_List_Oset(X1),c_List_Olist_ONil(X1)),X2)),
    inference(rw,[status(thm)],[i_0_10210,c_0_8319]),
    [final] ).

cnf(i_0_16975,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_10211]),
    [final] ).

cnf(i_0_16976,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_10046]),
    [final] ).

cnf(i_0_16977,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_10212]),
    [final] ).

cnf(i_0_16978,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_8577]),
    [final] ).

cnf(i_0_16979,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_8578]),
    [final] ).

cnf(i_0_16980,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_7844]),
    [final] ).

cnf(i_0_16981,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_7844]),
    [final] ).

cnf(i_0_16982,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_9664]),
    [final] ).

cnf(i_0_16983,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_10213,c_0_7094]),
    [final] ).

cnf(i_0_16984,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_16985,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_10214]),
    [final] ).

cnf(i_0_16986,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_10215]),
    [final] ).

cnf(i_0_16987,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk348_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_9840]),
    [final] ).

cnf(i_0_16988,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_10216]),
    [final] ).

cnf(i_0_16989,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_10217]),
    [final] ).

cnf(i_0_16990,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_9813]),
    [final] ).

cnf(i_0_16991,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_10218]),
    [final] ).

cnf(i_0_16992,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_10219]),
    [final] ).

cnf(i_0_16993,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_9899]),
    [final] ).

cnf(i_0_16994,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_9900]),
    [final] ).

cnf(i_0_16995,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_10220]),
    [final] ).

cnf(i_0_16996,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_10221]),
    [final] ).

cnf(i_0_16997,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_10222]),
    [final] ).

cnf(i_0_16998,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_10223]),
    [final] ).

cnf(i_0_16999,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_10224]),
    [final] ).

cnf(i_0_17000,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_10225]),
    [final] ).

cnf(i_0_17001,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_10226]),
    [final] ).

cnf(i_0_17002,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_10227]),
    [final] ).

cnf(i_0_17003,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_10228]),
    [final] ).

cnf(i_0_17004,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_10229]),
    [final] ).

cnf(i_0_17005,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_10230]),
    [final] ).

cnf(i_0_17006,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_10231]),
    [final] ).

cnf(i_0_17007,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_10232]),
    [final] ).

cnf(i_0_17008,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_10233]),
    [final] ).

cnf(i_0_17009,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_10234]),
    [final] ).

cnf(i_0_17010,plain,
    ( hAPP(hAPP(c_List_Onth(X1),X2),esk339_2(X2,X1)) = hAPP(hAPP(c_List_Onth(X1),X2),esk340_2(X2,X1))
    | hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8312]),
    [final] ).

cnf(i_0_17011,plain,
    ( hBOOL(hAPP(X3,X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_10235]),
    [final] ).

cnf(i_0_17012,plain,
    c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(X1,X2,X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X3)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(split_conjunct,[status(thm)],[i_0_10236]),
    [final] ).

cnf(i_0_17013,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_10075]),
    [final] ).

cnf(i_0_17014,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_10078]),
    [final] ).

cnf(i_0_17015,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_10081]),
    [final] ).

cnf(i_0_17016,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_10083]),
    [final] ).

cnf(i_0_17017,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_10237,c_0_7094]),
    [final] ).

cnf(i_0_17018,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_10238]),
    [final] ).

cnf(i_0_17019,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_10239]),
    [final] ).

cnf(i_0_17020,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_10240]),
    [final] ).

cnf(i_0_17021,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_6850]),
    [final] ).

cnf(i_0_17022,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_6851]),
    [final] ).

cnf(i_0_17023,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_10241]),
    [final] ).

cnf(i_0_17024,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_10242]),
    [final] ).

cnf(i_0_17025,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_10243]),
    [final] ).

cnf(i_0_17026,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_10244]),
    [final] ).

cnf(i_0_17027,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_10245]),
    [final] ).

cnf(i_0_17028,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_10246]),
    [final] ).

cnf(i_0_17029,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_9771]),
    [final] ).

cnf(i_0_17030,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_9772]),
    [final] ).

cnf(i_0_17031,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_9773]),
    [final] ).

cnf(i_0_17032,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_9774]),
    [final] ).

cnf(i_0_17033,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_9346]),
    [final] ).

cnf(i_0_17034,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_10247]),
    [final] ).

cnf(i_0_17035,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_10248]),
    [final] ).

cnf(i_0_17036,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_10249]),
    [final] ).

cnf(i_0_17037,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_10250]),
    [final] ).

cnf(i_0_17038,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_10251]),
    [final] ).

cnf(i_0_17039,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_10252]),
    [final] ).

cnf(i_0_17040,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_10253]),
    [final] ).

cnf(i_0_17041,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_10254]),
    [final] ).

cnf(i_0_17042,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_10255]),
    [final] ).

cnf(i_0_17043,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_10256]),
    [final] ).

cnf(i_0_17044,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_9944]),
    [final] ).

cnf(i_0_17045,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_9945]),
    [final] ).

cnf(i_0_17046,plain,
    ( X1 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk36_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_9829]),
    [final] ).

cnf(i_0_17047,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)),esk113_1(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_9935]),
    [final] ).

cnf(i_0_17048,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_10257]),
    [final] ).

cnf(i_0_17049,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_10258]),
    [final] ).

cnf(i_0_17050,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_10259]),
    [final] ).

cnf(i_0_17051,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_9563]),
    [final] ).

cnf(i_0_17052,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_10260]),
    [final] ).

cnf(i_0_17053,plain,
    ( hBOOL(hAPP(X1,esk41_1(X1)))
    | ~ hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9656]),
    [final] ).

cnf(i_0_17054,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_5969]),
    [final] ).

cnf(i_0_17055,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_17056,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_10261,c_0_7094]),
    [final] ).

cnf(i_0_17057,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_10262]),
    [final] ).

cnf(i_0_17058,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_10263]),
    [final] ).

cnf(i_0_17059,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_10055]),
    [final] ).

cnf(i_0_17060,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_9943]),
    [final] ).

cnf(i_0_17061,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_10264]),
    [final] ).

cnf(i_0_17062,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_10265]),
    [final] ).

cnf(i_0_17063,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_10266]),
    [final] ).

cnf(i_0_17064,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,hAPP(c_Int_Onat,esk47_1(X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_9749]),
    [final] ).

cnf(i_0_17065,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_10267]),
    [final] ).

cnf(i_0_17066,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_10268]),
    [final] ).

cnf(i_0_17067,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_10269]),
    [final] ).

cnf(i_0_17068,plain,
    ( X1 = hAPP(c_Nat_OSuc,esk28_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_10270]),
    [final] ).

cnf(i_0_17069,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_10271]),
    [final] ).

cnf(i_0_17070,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_10272]),
    [final] ).

cnf(i_0_17071,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_10273]),
    [final] ).

cnf(i_0_17072,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_10274]),
    [final] ).

cnf(i_0_17073,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_10275]),
    [final] ).

cnf(i_0_17074,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_10276]),
    [final] ).

cnf(i_0_17075,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_10277]),
    [final] ).

cnf(i_0_17076,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_10070]),
    [final] ).

cnf(i_0_17077,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_10278]),
    [final] ).

cnf(i_0_17078,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_10071]),
    [final] ).

cnf(i_0_17079,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_10279]),
    [final] ).

cnf(i_0_17080,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_10280]),
    [final] ).

cnf(i_0_17081,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_10253]),
    [final] ).

cnf(i_0_17082,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_10254]),
    [final] ).

cnf(i_0_17083,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_10281]),
    [final] ).

cnf(i_0_17084,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_10282]),
    [final] ).

cnf(i_0_17085,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_10033]),
    [final] ).

cnf(i_0_17086,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_10283]),
    [final] ).

cnf(i_0_17087,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_10284]),
    [final] ).

cnf(i_0_17088,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OWhile(X1,X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(split_conjunct,[status(thm)],[i_0_10285]),
    [final] ).

cnf(i_0_17089,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_10286]),
    [final] ).

cnf(i_0_17090,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_10287]),
    [final] ).

cnf(i_0_17091,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_10288,c_0_6181]),
    [final] ).

cnf(i_0_17092,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_9988]),
    [final] ).

cnf(i_0_17093,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_17094,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_10289]),
    [final] ).

cnf(i_0_17095,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_10290]),
    [final] ).

cnf(i_0_17096,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_9358]),
    [final] ).

cnf(i_0_17097,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_9868]),
    [final] ).

cnf(i_0_17098,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_9869]),
    [final] ).

cnf(i_0_17099,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_8558]),
    [final] ).

cnf(i_0_17100,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_9923]),
    [final] ).

cnf(i_0_17101,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_10291]),
    [final] ).

cnf(i_0_17102,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_10292]),
    [final] ).

cnf(i_0_17103,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_10293]),
    [final] ).

cnf(i_0_17104,plain,
    ( hAPP(c_Finite__Set_Ocard(X1),esk140_3(X2,X3,X1)) = X2
    | hAPP(c_Finite__Set_Ocard(X1),X3) != hAPP(c_Nat_OSuc,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7961]),
    [final] ).

cnf(i_0_17105,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_10294]),
    [final] ).

cnf(i_0_17106,plain,
    ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X2),X1))
    | ~ hBOOL(hAPP(X1,esk466_2(X1,X2)))
    | ~ class_Enum_Oenum(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10295]),
    [final] ).

cnf(i_0_17107,plain,
    ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X2),X1))
    | ~ hBOOL(hAPP(X1,esk465_2(X1,X2)))
    | ~ class_Enum_Oenum(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10296]),
    [final] ).

cnf(i_0_17108,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_10225]),
    [final] ).

cnf(i_0_17109,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_10226]),
    [final] ).

cnf(i_0_17110,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_10297]),
    [final] ).

cnf(i_0_17111,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_10298,c_0_6181]),
    [final] ).

cnf(i_0_17112,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_9737]),
    [final] ).

cnf(i_0_17113,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_9846]),
    [final] ).

cnf(i_0_17114,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_9641]),
    [final] ).

cnf(i_0_17115,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_10299]),
    [final] ).

cnf(i_0_17116,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_10300]),
    [final] ).

cnf(i_0_17117,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_10301]),
    [final] ).

cnf(i_0_17118,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_10111]),
    [final] ).

cnf(i_0_17119,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_10111]),
    [final] ).

cnf(i_0_17120,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_9687]),
    [final] ).

cnf(i_0_17121,plain,
    ( X2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk37_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_9737]),
    [final] ).

cnf(i_0_17122,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_17123,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_10302,c_0_7295]),
    [final] ).

cnf(i_0_17124,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_10303]),
    [final] ).

cnf(i_0_17125,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_10304]),
    [final] ).

cnf(i_0_17126,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_10304]),
    [final] ).

cnf(i_0_17127,plain,
    ( c_Hoare__Mirabelle_Otriple__valid(X1,X2,X3)
    | ~ c_Hoare__Mirabelle_Otriple__valid(X1,hAPP(c_Nat_OSuc,X2),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10305]),
    [final] ).

cnf(i_0_17128,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_10306]),
    [final] ).

cnf(i_0_17129,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_6163]),
    [final] ).

cnf(i_0_17130,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_6164]),
    [final] ).

cnf(i_0_17131,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_9812]),
    [final] ).

cnf(i_0_17132,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_10307]),
    [final] ).

cnf(i_0_17133,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_9478]),
    [final] ).

cnf(i_0_17134,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_10308]),
    [final] ).

cnf(i_0_17135,plain,
    ( ~ class_Orderings_Opreorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10309]),
    [final] ).

cnf(i_0_17136,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_9252]),
    [final] ).

cnf(i_0_17137,plain,
    ( hBOOL(hAPP(hAPP(X1,esk253_1(X1)),esk254_1(X1)))
    | hAPP(X1,esk253_1(X1)) = hAPP(X1,esk254_1(X1))
    | c_Equiv__Relations_Oequivp(X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9923]),
    [final] ).

cnf(i_0_17138,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_10310]),
    [final] ).

cnf(i_0_17139,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_10311]),
    [final] ).

cnf(i_0_17140,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_10312]),
    [final] ).

cnf(i_0_17141,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_10313]),
    [final] ).

cnf(i_0_17142,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_10314]),
    [final] ).

cnf(i_0_17143,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_10315]),
    [final] ).

cnf(i_0_17144,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_10316]),
    [final] ).

cnf(i_0_17145,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_10317]),
    [final] ).

cnf(i_0_17146,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_10317]),
    [final] ).

cnf(i_0_17147,plain,
    ( X1 = X2
    | c_List_Oreplicate(X3,X1,X4) != c_List_Oreplicate(X3,X2,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_10303]),
    [final] ).

cnf(i_0_17148,plain,
    ( X1 = X2
    | c_Com_Ocom_OLocal(X1,X3,X4) != c_Com_Ocom_OLocal(X2,X5,X6) ),
    inference(split_conjunct,[status(thm)],[i_0_10318]),
    [final] ).

cnf(i_0_17149,plain,
    ( X1 = X2
    | c_Com_Ocom_OLocal(X3,X1,X4) != c_Com_Ocom_OLocal(X5,X2,X6) ),
    inference(split_conjunct,[status(thm)],[i_0_10318]),
    [final] ).

cnf(i_0_17150,plain,
    ( X1 = X2
    | c_Com_Ocom_OLocal(X3,X4,X1) != c_Com_Ocom_OLocal(X5,X6,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10318]),
    [final] ).

cnf(i_0_17151,plain,
    ( X1 = X2
    | c_Com_Ocom_OCond(X1,X3,X4) != c_Com_Ocom_OCond(X2,X5,X6) ),
    inference(split_conjunct,[status(thm)],[i_0_10319]),
    [final] ).

cnf(i_0_17152,plain,
    ( X1 = X2
    | c_Com_Ocom_OCond(X3,X1,X4) != c_Com_Ocom_OCond(X5,X2,X6) ),
    inference(split_conjunct,[status(thm)],[i_0_10319]),
    [final] ).

cnf(i_0_17153,plain,
    ( X1 = X2
    | c_Com_Ocom_OCond(X3,X4,X1) != c_Com_Ocom_OCond(X5,X6,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10319]),
    [final] ).

cnf(i_0_17154,plain,
    ( X1 = X2
    | c_Com_Ocom_OCall(X1,X3,X4) != c_Com_Ocom_OCall(X2,X5,X6) ),
    inference(split_conjunct,[status(thm)],[i_0_10320]),
    [final] ).

cnf(i_0_17155,plain,
    ( X1 = X2
    | c_Com_Ocom_OCall(X3,X1,X4) != c_Com_Ocom_OCall(X5,X2,X6) ),
    inference(split_conjunct,[status(thm)],[i_0_10320]),
    [final] ).

cnf(i_0_17156,plain,
    ( X1 = X2
    | c_Com_Ocom_OCall(X3,X4,X1) != c_Com_Ocom_OCall(X5,X6,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10320]),
    [final] ).

cnf(i_0_17157,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_10321]),
    [final] ).

cnf(i_0_17158,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_10322]),
    [final] ).

cnf(i_0_17159,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_9950]),
    [final] ).

cnf(i_0_17160,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_10323]),
    [final] ).

cnf(i_0_17161,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_9917]),
    [final] ).

cnf(i_0_17162,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_7061]),
    [final] ).

cnf(i_0_17163,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_10283]),
    [final] ).

cnf(i_0_17164,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_10284]),
    [final] ).

cnf(i_0_17165,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_10324]),
    [final] ).

cnf(i_0_17166,plain,
    c_Com_Ocom_OLocal(X1,X2,X3) != c_Com_Ocom_OCond(X4,X5,X6),
    inference(split_conjunct,[status(thm)],[i_0_10325]),
    [final] ).

cnf(i_0_17167,plain,
    c_Com_Ocom_OLocal(X1,X2,X3) != c_Com_Ocom_OCall(X4,X5,X6),
    inference(split_conjunct,[status(thm)],[i_0_10326]),
    [final] ).

cnf(i_0_17168,plain,
    c_Com_Ocom_OCond(X1,X2,X3) != c_Com_Ocom_OLocal(X4,X5,X6),
    inference(split_conjunct,[status(thm)],[i_0_10327]),
    [final] ).

cnf(i_0_17169,plain,
    c_Com_Ocom_OCall(X1,X2,X3) != c_Com_Ocom_OLocal(X4,X5,X6),
    inference(split_conjunct,[status(thm)],[i_0_10328]),
    [final] ).

cnf(i_0_17170,plain,
    c_Com_Ocom_OCond(X1,X2,X3) != c_Com_Ocom_OCall(X4,X5,X6),
    inference(split_conjunct,[status(thm)],[i_0_10329]),
    [final] ).

cnf(i_0_17171,plain,
    c_Com_Ocom_OCall(X1,X2,X3) != c_Com_Ocom_OCond(X4,X5,X6),
    inference(split_conjunct,[status(thm)],[i_0_10330]),
    [final] ).

cnf(i_0_17172,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_10238]),
    [final] ).

cnf(i_0_17173,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_10200]),
    [final] ).

cnf(i_0_17174,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_9414]),
    [final] ).

cnf(i_0_17175,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_10331]),
    [final] ).

cnf(i_0_17176,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_10332]),
    [final] ).

cnf(i_0_17177,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_10333]),
    [final] ).

cnf(i_0_17178,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_10334]),
    [final] ).

cnf(i_0_17179,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_6453]),
    [final] ).

cnf(i_0_17180,plain,
    ( hBOOL(hAPP(X1,esk20_2(X2,X1)))
    | hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(split_conjunct,[status(thm)],[i_0_9537]),
    [final] ).

cnf(i_0_17181,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_10335]),
    [final] ).

cnf(i_0_17182,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_10336]),
    [final] ).

cnf(i_0_17183,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_10337]),
    [final] ).

cnf(i_0_17184,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_10108]),
    [final] ).

cnf(i_0_17185,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_10109]),
    [final] ).

cnf(i_0_17186,plain,
    ( hBOOL(hAPP(c_List_Odistinct(X1),esk432_2(X2,X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10174]),
    [final] ).

cnf(i_0_17187,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_10338]),
    [final] ).

cnf(i_0_17188,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_10126]),
    [final] ).

cnf(i_0_17189,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_10339]),
    [final] ).

cnf(i_0_17190,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_10340]),
    [final] ).

cnf(i_0_17191,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_10064]),
    [final] ).

cnf(i_0_17192,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_10341]),
    [final] ).

cnf(i_0_17193,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_10342]),
    [final] ).

cnf(i_0_17194,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk44_1(X1)))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9672]),
    [final] ).

cnf(i_0_17195,plain,
    ( X1 = hAPP(hAPP(c_List_Olist_OCons(X2),esk406_2(X1,X2)),esk405_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_7339]),
    [final] ).

cnf(i_0_17196,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_10343]),
    [final] ).

cnf(i_0_17197,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_10343]),
    [final] ).

cnf(i_0_17198,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_10344]),
    [final] ).

cnf(i_0_17199,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_10345]),
    [final] ).

cnf(i_0_17200,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_10346]),
    [final] ).

cnf(i_0_17201,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_10294]),
    [final] ).

cnf(i_0_17202,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_9430]),
    [final] ).

cnf(i_0_17203,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_10347]),
    [final] ).

cnf(i_0_17204,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_9252]),
    [final] ).

cnf(i_0_17205,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_10348]),
    [final] ).

cnf(i_0_17206,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_17207,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_8701]),
    [final] ).

cnf(i_0_17208,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_10349]),
    [final] ).

cnf(i_0_17209,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_10350]),
    [final] ).

cnf(i_0_17210,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_10351]),
    [final] ).

cnf(i_0_17211,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_10352]),
    [final] ).

cnf(i_0_17212,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_10353]),
    [final] ).

cnf(i_0_17213,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_10354,c_0_6713]),
    [final] ).

cnf(i_0_17214,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_10355]),
    [final] ).

cnf(i_0_17215,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_10356]),
    [final] ).

cnf(i_0_17216,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_10357]),
    [final] ).

cnf(i_0_17217,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_10358]),
    [final] ).

cnf(i_0_17218,plain,
    c_Predicate_Oconversep(X1,X2,c_Predicate_Oconversep(X2,X1,X3)) = X3,
    inference(split_conjunct,[status(thm)],[i_0_10359]),
    [final] ).

cnf(i_0_17219,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_10360]),
    [final] ).

cnf(i_0_17220,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_9682]),
    [final] ).

cnf(i_0_17221,plain,
    ( hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))
    | ~ hBOOL(hAPP(X1,esk42_1(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_9498]),
    [final] ).

cnf(i_0_17222,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_10361]),
    [final] ).

cnf(i_0_17223,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_9712]),
    [final] ).

cnf(i_0_17224,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_9679]),
    [final] ).

cnf(i_0_17225,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_9680]),
    [final] ).

cnf(i_0_17226,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_10362]),
    [final] ).

cnf(i_0_17227,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_10363]),
    [final] ).

cnf(i_0_17228,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_10364]),
    [final] ).

cnf(i_0_17229,plain,
    ( X1 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk51_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_10365]),
    [final] ).

cnf(i_0_17230,plain,
    ( X1 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),esk57_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_10366]),
    [final] ).

cnf(i_0_17231,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_10367]),
    [final] ).

cnf(i_0_17232,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_10048]),
    [final] ).

cnf(i_0_17233,plain,
    ( c_Relation_Osym(X1,X2)
    | ~ c_Relation_Osym(X1,hAPP(c_Relation_Oconverse(X1,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10368]),
    [final] ).

cnf(i_0_17234,plain,
    ( c_Relation_Oantisym(X1,X2)
    | ~ c_Relation_Oantisym(X1,hAPP(c_Relation_Oconverse(X1,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10369]),
    [final] ).

cnf(i_0_17235,plain,
    ( c_Relation_Otrans(X1,X2)
    | ~ c_Relation_Otrans(X1,hAPP(c_Relation_Oconverse(X1,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10370]),
    [final] ).

cnf(i_0_17236,plain,
    ( c_Wellfounded_Oacyclic(X1,X2)
    | ~ c_Wellfounded_Oacyclic(X1,hAPP(c_Relation_Oconverse(X1,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10371]),
    [final] ).

cnf(i_0_17237,plain,
    ( X2 = esk528_3(X3,X4,X1)
    | c_FunDef_OTHE__default(X4,X3,X1) = X3
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8045]),
    [final] ).

cnf(i_0_17238,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_10015]),
    [final] ).

cnf(i_0_17239,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_10372]),
    [final] ).

cnf(i_0_17240,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_10373]),
    [final] ).

cnf(i_0_17241,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_10374]),
    [final] ).

cnf(i_0_17242,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_10375]),
    [final] ).

cnf(i_0_17243,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_10376]),
    [final] ).

cnf(i_0_17244,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_10246]),
    [final] ).

cnf(i_0_17245,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_10377]),
    [final] ).

cnf(i_0_17246,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_10378]),
    [final] ).

cnf(i_0_17247,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_10379]),
    [final] ).

cnf(i_0_17248,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_10380]),
    [final] ).

cnf(i_0_17249,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_10381]),
    [final] ).

cnf(i_0_17250,plain,
    ( hBOOL(hAPP(X2,esk416_2(X2,X1)))
    | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),X2))
    | ~ class_Enum_Oenum(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10382]),
    [final] ).

cnf(i_0_17251,plain,
    ( hBOOL(hAPP(X2,esk415_2(X2,X1)))
    | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),X2))
    | ~ class_Enum_Oenum(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10383]),
    [final] ).

cnf(i_0_17252,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_10384]),
    [final] ).

cnf(i_0_17253,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_10385]),
    [final] ).

cnf(i_0_17254,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_10386]),
    [final] ).

cnf(i_0_17255,plain,
    ( hBOOL(hAPP(hAPP(c_member(X3),X1),hAPP(c_fequal,X2)))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_10021]),
    [final] ).

cnf(i_0_17256,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_10387]),
    [final] ).

cnf(i_0_17257,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_10388]),
    [final] ).

cnf(i_0_17258,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_10389]),
    [final] ).

cnf(i_0_17259,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_10390]),
    [final] ).

cnf(i_0_17260,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_10391]),
    [final] ).

cnf(i_0_17261,plain,
    ( hBOOL(hAPP(hAPP(c_member(X3),X2),X1))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10235]),
    [final] ).

cnf(i_0_17262,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_10392]),
    [final] ).

cnf(i_0_17263,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_10393]),
    [final] ).

cnf(i_0_17264,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_10394]),
    [final] ).

cnf(i_0_17265,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_10395]),
    [final] ).

cnf(i_0_17266,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_10396]),
    [final] ).

cnf(i_0_17267,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_9899]),
    [final] ).

cnf(i_0_17268,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_9900]),
    [final] ).

cnf(i_0_17269,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_10397]),
    [final] ).

cnf(i_0_17270,plain,
    ( X1 != X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10000]),
    [final] ).

cnf(i_0_17271,plain,
    ( X1 != X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10001]),
    [final] ).

cnf(i_0_17272,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_10258]),
    [final] ).

cnf(i_0_17273,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | X2 != X1 ),
    inference(split_conjunct,[status(thm)],[i_0_10258]),
    [final] ).

cnf(i_0_17274,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | X2 != X1 ),
    inference(split_conjunct,[status(thm)],[i_0_10398]),
    [final] ).

cnf(i_0_17275,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_10399]),
    [final] ).

cnf(i_0_17276,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_10400,c_0_7094]),
    [final] ).

cnf(i_0_17277,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_10401]),
    [final] ).

cnf(i_0_17278,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_10402,c_0_7094]),
    [final] ).

cnf(i_0_17279,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_10403]),
    [final] ).

cnf(i_0_17280,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_10404]),
    [final] ).

cnf(i_0_17281,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_10405]),
    [final] ).

cnf(i_0_17282,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_10406]),
    [final] ).

cnf(i_0_17283,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_10407]),
    [final] ).

cnf(i_0_17284,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_10408]),
    [final] ).

cnf(i_0_17285,plain,
    ( X2 = X1
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10409]),
    [final] ).

cnf(i_0_17286,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_10410]),
    [final] ).

cnf(i_0_17287,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_10411]),
    [final] ).

cnf(i_0_17288,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_10412]),
    [final] ).

cnf(i_0_17289,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_10413]),
    [final] ).

cnf(i_0_17290,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_10414]),
    [final] ).

cnf(i_0_17291,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_10415]),
    [final] ).

cnf(i_0_17292,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_10416]),
    [final] ).

cnf(i_0_17293,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_10394]),
    [final] ).

cnf(i_0_17294,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_10395]),
    [final] ).

cnf(i_0_17295,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_10417]),
    [final] ).

cnf(i_0_17296,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_10418]),
    [final] ).

cnf(i_0_17297,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_10419]),
    [final] ).

cnf(i_0_17298,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_10395]),
    [final] ).

cnf(i_0_17299,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_10394]),
    [final] ).

cnf(i_0_17300,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_10420]),
    [final] ).

cnf(i_0_17301,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_10419]),
    [final] ).

cnf(i_0_17302,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_10418]),
    [final] ).

cnf(i_0_17303,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_10421]),
    [final] ).

cnf(i_0_17304,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_10422]),
    [final] ).

cnf(i_0_17305,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_10423]),
    [final] ).

cnf(i_0_17306,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_10424]),
    [final] ).

cnf(i_0_17307,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_10425]),
    [final] ).

cnf(i_0_17308,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_10426]),
    [final] ).

cnf(i_0_17309,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_9923]),
    [final] ).

cnf(i_0_17310,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_10192]),
    [final] ).

cnf(i_0_17311,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk47_1(X1)))
    | hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9749]),
    [final] ).

cnf(i_0_17312,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_10427]),
    [final] ).

cnf(i_0_17313,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
    inference(split_conjunct,[status(thm)],[i_0_10428]),
    [final] ).

cnf(i_0_17314,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
    inference(split_conjunct,[status(thm)],[i_0_10429]),
    [final] ).

cnf(i_0_17315,plain,
    ( hBOOL(hAPP(X1,hAPP(c_Int_Onat,esk44_1(X1))))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9672]),
    [final] ).

cnf(i_0_17316,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_10408]),
    [final] ).

cnf(i_0_17317,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_10430]),
    [final] ).

cnf(i_0_17318,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_10051]),
    [final] ).

cnf(i_0_17319,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_10431,c_0_6063]),c_0_6063]),
    [final] ).

cnf(i_0_17320,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_10432]),
    [final] ).

cnf(i_0_17321,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_10433]),
    [final] ).

cnf(i_0_17322,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_10434]),
    [final] ).

cnf(i_0_17323,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_10435]),
    [final] ).

cnf(i_0_17324,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_10436]),
    [final] ).

cnf(i_0_17325,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_10437]),
    [final] ).

cnf(i_0_17326,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_10438]),
    [final] ).

cnf(i_0_17327,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_9387]),
    [final] ).

cnf(i_0_17328,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_10439]),
    [final] ).

cnf(i_0_17329,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_8617]),
    [final] ).

cnf(i_0_17330,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_10440]),
    [final] ).

cnf(i_0_17331,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_10441]),
    [final] ).

cnf(i_0_17332,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_8619]),
    [final] ).

cnf(i_0_17333,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_10442]),
    [final] ).

cnf(i_0_17334,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_10443]),
    [final] ).

cnf(i_0_17335,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_10248]),
    [final] ).

cnf(i_0_17336,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_10444]),
    [final] ).

cnf(i_0_17337,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_10445]),
    [final] ).

cnf(i_0_17338,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_10446]),
    [final] ).

cnf(i_0_17339,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_10447]),
    [final] ).

cnf(i_0_17340,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_10448]),
    [final] ).

cnf(i_0_17341,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_10449]),
    [final] ).

cnf(i_0_17342,plain,
    ( c_Wellfounded_OwfP(X1,c_FunDef_Oin__rel(X1,X1,X2))
    | ~ c_Wellfounded_Owf(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10450]),
    [final] ).

cnf(i_0_17343,plain,
    ( c_Wellfounded_Owf(X1,c_Wellfounded_Omlex__prod(X1,X3,X2))
    | ~ c_Wellfounded_Owf(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10451]),
    [final] ).

cnf(i_0_17344,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_9716]),
    [final] ).

cnf(i_0_17345,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_10452]),
    [final] ).

cnf(i_0_17346,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_10280]),
    [final] ).

cnf(i_0_17347,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_10275]),
    [final] ).

cnf(i_0_17348,plain,
    ( hBOOL(hAPP(hAPP(X1,esk550_1(X1)),esk550_1(X1)))
    | ~ c_Equiv__Relations_Opart__equivp(X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8558]),
    [final] ).

cnf(i_0_17349,plain,
    ( c_Relation_Orefl__on(X1,X2,X3)
    | ~ c_Equiv__Relations_Oequiv(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10453]),
    [final] ).

cnf(i_0_17350,plain,
    ( c_Relation_Orefl__on(X1,X2,X3)
    | ~ c_Equiv__Relations_Oequiv(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10277]),
    [final] ).

cnf(i_0_17351,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_10454]),
    [final] ).

cnf(i_0_17352,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_10455]),
    [final] ).

cnf(i_0_17353,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_10456]),
    [final] ).

cnf(i_0_17354,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_10457]),
    [final] ).

cnf(i_0_17355,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_10458]),
    [final] ).

cnf(i_0_17356,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_10459]),
    [final] ).

cnf(i_0_17357,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_10460]),
    [final] ).

cnf(i_0_17358,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_10461]),
    [final] ).

cnf(i_0_17359,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_10462]),
    [final] ).

cnf(i_0_17360,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_10463]),
    [final] ).

cnf(i_0_17361,plain,
    ( esk140_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_7961]),
    [final] ).

cnf(i_0_17362,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_10228]),
    [final] ).

cnf(i_0_17363,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_10464]),
    [final] ).

cnf(i_0_17364,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_10465]),
    [final] ).

cnf(i_0_17365,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_10466]),
    [final] ).

cnf(i_0_17366,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_10467]),
    [final] ).

cnf(i_0_17367,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_10468]),
    [final] ).

cnf(i_0_17368,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_10469]),
    [final] ).

cnf(i_0_17369,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_10470]),
    [final] ).

cnf(i_0_17370,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_10471]),
    [final] ).

cnf(i_0_17371,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_10472]),
    [final] ).

cnf(i_0_17372,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_10473]),
    [final] ).

cnf(i_0_17373,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_10474]),
    [final] ).

cnf(i_0_17374,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_10465]),
    [final] ).

cnf(i_0_17375,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_10475]),
    [final] ).

cnf(i_0_17376,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_10476]),
    [final] ).

cnf(i_0_17377,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_10197]),
    [final] ).

cnf(i_0_17378,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_10477]),
    [final] ).

cnf(i_0_17379,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_10478]),
    [final] ).

cnf(i_0_17380,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_10479]),
    [final] ).

cnf(i_0_17381,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_10480]),
    [final] ).

cnf(i_0_17382,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_10481]),
    [final] ).

cnf(i_0_17383,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_10482]),
    [final] ).

cnf(i_0_17384,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_10183]),
    [final] ).

cnf(i_0_17385,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_10483]),
    [final] ).

cnf(i_0_17386,plain,
    hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2)),
    inference(split_conjunct,[status(thm)],[i_0_10484]),
    [final] ).

cnf(i_0_17387,plain,
    hAPP(c_Set_Ovimage(X1,X1,c_Fun_Oid(X1)),X2) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10485]),
    [final] ).

cnf(i_0_17388,plain,
    hAPP(c_Set_Ovimage(X1,X1,c_COMBI(X1)),X2) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10486]),
    [final] ).

cnf(i_0_17389,plain,
    hAPP(c_Set_Oimage(X1,X1,c_Fun_Oid(X1)),X2) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10487]),
    [final] ).

cnf(i_0_17390,plain,
    hAPP(c_Set_Oimage(X1,X1,c_COMBI(X1)),X2) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10488]),
    [final] ).

cnf(i_0_17391,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_9679]),
    [final] ).

cnf(i_0_17392,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_9680]),
    [final] ).

cnf(i_0_17393,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_10489]),
    [final] ).

cnf(i_0_17394,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_10187]),
    [final] ).

cnf(i_0_17395,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_10188]),
    [final] ).

cnf(i_0_17396,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_10490]),
    [final] ).

cnf(i_0_17397,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_10491,c_0_8268]),
    [final] ).

cnf(i_0_17398,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_10492,c_0_8268]),
    [final] ).

cnf(i_0_17399,plain,
    ( hBOOL(X2)
    | ~ hBOOL(hAPP(hAPP(c_fimplies,X1),X2))
    | ~ hBOOL(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10493]),
    [final] ).

cnf(i_0_17400,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_10494]),
    [final] ).

cnf(i_0_17401,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_10495]),
    [final] ).

cnf(i_0_17402,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_10496]),
    [final] ).

cnf(i_0_17403,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_10497]),
    [final] ).

cnf(i_0_17404,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_10498]),
    [final] ).

cnf(i_0_17405,plain,
    c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))),
    inference(split_conjunct,[status(thm)],[i_0_10499]),
    [final] ).

cnf(i_0_17406,plain,
    c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))),
    inference(split_conjunct,[status(thm)],[i_0_10500]),
    [final] ).

cnf(i_0_17407,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_10501]),
    [final] ).

cnf(i_0_17408,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_10502]),
    [final] ).

cnf(i_0_17409,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_10503]),
    [final] ).

cnf(i_0_17410,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_10504]),
    [final] ).

cnf(i_0_17411,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_10505]),
    [final] ).

cnf(i_0_17412,plain,
    ( hBOOL(hAPP(X1,esk538_2(X1,X2)))
    | ~ hBOOL(hAPP(X1,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9389]),
    [final] ).

cnf(i_0_17413,plain,
    ( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X3,X1)))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10181]),
    [final] ).

cnf(i_0_17414,plain,
    ( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X3,X1)))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10506]),
    [final] ).

cnf(i_0_17415,plain,
    ( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X3,X1)))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10507]),
    [final] ).

cnf(i_0_17416,plain,
    ( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X3,X1)))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10508]),
    [final] ).

cnf(i_0_17417,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_10365]),
    [final] ).

cnf(i_0_17418,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_10366]),
    [final] ).

cnf(i_0_17419,plain,
    ( hBOOL(X1)
    | hBOOL(X2)
    | ~ hBOOL(hAPP(hAPP(c_fdisj,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10509]),
    [final] ).

cnf(i_0_17420,plain,
    ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ epred2_3(X2,X3,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7651]),
    [final] ).

cnf(i_0_17421,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_10227]),
    [final] ).

cnf(i_0_17422,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_10510]),
    [final] ).

cnf(i_0_17423,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_10511]),
    [final] ).

cnf(i_0_17424,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_10271]),
    [final] ).

cnf(i_0_17425,plain,
    ( X1 = X2
    | hAPP(X1,esk1_2(X2,X1)) != hAPP(X2,esk1_2(X2,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_10512]),
    [final] ).

cnf(i_0_17426,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_10513]),
    [final] ).

cnf(i_0_17427,plain,
    ( hAPP(hAPP(X2,X4),X4) = X4
    | ~ c_Finite__Set_Ofolding__one__idem(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10514]),
    [final] ).

cnf(i_0_17428,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_10515]),
    [final] ).

cnf(i_0_17429,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCall(X1,X2,X3)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[i_0_10516]),
    [final] ).

cnf(i_0_17430,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_10187]),
    [final] ).

cnf(i_0_17431,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_10188]),
    [final] ).

cnf(i_0_17432,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_10517]),
    [final] ).

cnf(i_0_17433,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_10518]),
    [final] ).

cnf(i_0_17434,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_10473]),
    [final] ).

cnf(i_0_17435,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_10519]),
    [final] ).

cnf(i_0_17436,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_10520]),
    [final] ).

cnf(i_0_17437,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_10521]),
    [final] ).

cnf(i_0_17438,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_10522]),
    [final] ).

cnf(i_0_17439,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_10321]),
    [final] ).

cnf(i_0_17440,plain,
    ( hBOOL(X1)
    | ~ hBOOL(hAPP(hAPP(c_fconj,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10523]),
    [final] ).

cnf(i_0_17441,plain,
    ( hBOOL(X2)
    | ~ hBOOL(hAPP(hAPP(c_fconj,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10524]),
    [final] ).

cnf(i_0_17442,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_10525]),
    [final] ).

cnf(i_0_17443,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_10526]),
    [final] ).

cnf(i_0_17444,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_10527]),
    [final] ).

cnf(i_0_17445,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_10252]),
    [final] ).

cnf(i_0_17446,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk113_1(X1)),X1))
    | c_Nat__Transfer_Onat__set(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9935]),
    [final] ).

cnf(i_0_17447,plain,
    hAPP(c_List_Otl(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)) = X3,
    inference(split_conjunct,[status(thm)],[i_0_10528]),
    [final] ).

cnf(i_0_17448,plain,
    hAPP(c_List_Ohd(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10529]),
    [final] ).

cnf(i_0_17449,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_10530]),
    [final] ).

cnf(i_0_17450,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_10530]),
    [final] ).

cnf(i_0_17451,plain,
    ( hBOOL(hAPP(X2,X3))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ epred1_3(X2,X3,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7661]),
    [final] ).

cnf(i_0_17452,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_10531]),
    [final] ).

cnf(i_0_17453,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_10351]),
    [final] ).

cnf(i_0_17454,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_10353]),
    [final] ).

cnf(i_0_17455,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_10532]),
    [final] ).

cnf(i_0_17456,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_10533]),
    [final] ).

cnf(i_0_17457,plain,
    ( X1 = X2
    | ~ hBOOL(hAPP(hAPP(c_fequal,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10534]),
    [final] ).

cnf(i_0_17458,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_10535]),
    [final] ).

cnf(i_0_17459,plain,
    ( hAPP(c_List_Oset(X1),esk432_2(X2,X1)) = X2
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10174]),
    [final] ).

cnf(i_0_17460,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_10338]),
    [final] ).

cnf(i_0_17461,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_10536]),
    [final] ).

cnf(i_0_17462,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_10537]),
    [final] ).

cnf(i_0_17463,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_10538]),
    [final] ).

cnf(i_0_17464,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_10539]),
    [final] ).

cnf(i_0_17465,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_10255]),
    [final] ).

cnf(i_0_17466,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_10540]),
    [final] ).

cnf(i_0_17467,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_List_Oset(X1),X2))),
    inference(split_conjunct,[status(thm)],[i_0_10541]),
    [final] ).

cnf(i_0_17468,plain,
    hAPP(c_Relation_Oconverse(X1,X2),hAPP(c_Relation_Oconverse(X2,X1),X3)) = X3,
    inference(split_conjunct,[status(thm)],[i_0_10542]),
    [final] ).

cnf(i_0_17469,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_10303]),
    [final] ).

cnf(i_0_17470,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_17471,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_10543]),
    [final] ).

cnf(i_0_17472,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_10544]),
    [final] ).

cnf(i_0_17473,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_10545]),
    [final] ).

cnf(i_0_17474,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_10546]),
    [final] ).

cnf(i_0_17475,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_10547]),
    [final] ).

cnf(i_0_17476,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_10504]),
    [final] ).

cnf(i_0_17477,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_10504]),
    [final] ).

cnf(i_0_17478,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_10548]),
    [final] ).

cnf(i_0_17479,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_10505]),
    [final] ).

cnf(i_0_17480,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_10505]),
    [final] ).

cnf(i_0_17481,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_9627]),
    [final] ).

cnf(i_0_17482,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_9627]),
    [final] ).

cnf(i_0_17483,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_10549]),
    [final] ).

cnf(i_0_17484,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_9845]),
    [final] ).

cnf(i_0_17485,plain,
    c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(X1,X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(split_conjunct,[status(thm)],[i_0_10550]),
    [final] ).

cnf(i_0_17486,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_10551]),
    [final] ).

cnf(i_0_17487,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_10552]),
    [final] ).

cnf(i_0_17488,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_10553]),
    [final] ).

cnf(i_0_17489,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_10554]),
    [final] ).

cnf(i_0_17490,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_10555]),
    [final] ).

cnf(i_0_17491,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_10556]),
    [final] ).

cnf(i_0_17492,plain,
    ( c_Relation_Osym(X1,hAPP(c_Relation_Oconverse(X1,X1),X2))
    | ~ c_Relation_Osym(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10368]),
    [final] ).

cnf(i_0_17493,plain,
    ( c_Relation_Oantisym(X1,hAPP(c_Relation_Oconverse(X1,X1),X2))
    | ~ c_Relation_Oantisym(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10369]),
    [final] ).

cnf(i_0_17494,plain,
    ( c_Relation_Otrans(X1,hAPP(c_Relation_Oconverse(X1,X1),X2))
    | ~ c_Relation_Otrans(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10370]),
    [final] ).

cnf(i_0_17495,plain,
    ( c_Wellfounded_Oacyclic(X1,hAPP(c_Relation_Oconverse(X1,X1),X2))
    | ~ c_Wellfounded_Oacyclic(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10371]),
    [final] ).

cnf(i_0_17496,plain,
    ( c_List_Olinorder__class_Osorted(X1,esk432_2(X2,X1))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10174]),
    [final] ).

cnf(i_0_17497,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_10338]),
    [final] ).

cnf(i_0_17498,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_10557]),
    [final] ).

cnf(i_0_17499,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_10558]),
    [final] ).

cnf(i_0_17500,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_10559]),
    [final] ).

cnf(i_0_17501,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_10323]),
    [final] ).

cnf(i_0_17502,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X2))
    | ~ class_Orderings_Opreorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10560]),
    [final] ).

cnf(i_0_17503,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_10558]),
    [final] ).

cnf(i_0_17504,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_10558]),
    [final] ).

cnf(i_0_17505,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_10561]),
    [final] ).

cnf(i_0_17506,plain,
    c_Com_Ocom_Ocom__size(c_Com_Ocom_OCall(X1,X2,X3)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[i_0_10562]),
    [final] ).

cnf(i_0_17507,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_17508,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_17509,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_17510,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_10563]),
    [final] ).

cnf(i_0_17511,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_10564]),
    [final] ).

cnf(i_0_17512,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_10565]),
    [final] ).

cnf(i_0_17513,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_10566]),
    [final] ).

cnf(i_0_17514,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_10567]),
    [final] ).

cnf(i_0_17515,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_10568]),
    [final] ).

cnf(i_0_17516,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_10569]),
    [final] ).

cnf(i_0_17517,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_10570]),
    [final] ).

cnf(i_0_17518,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_10571]),
    [final] ).

cnf(i_0_17519,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_10572]),
    [final] ).

cnf(i_0_17520,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_10573]),
    [final] ).

cnf(i_0_17521,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_10574]),
    [final] ).

cnf(i_0_17522,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_10575]),
    [final] ).

cnf(i_0_17523,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_10576]),
    [final] ).

cnf(i_0_17524,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_10577]),
    [final] ).

cnf(i_0_17525,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_10350]),
    [final] ).

cnf(i_0_17526,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_9357]),
    [final] ).

cnf(i_0_17527,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_10194]),
    [final] ).

cnf(i_0_17528,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_10578]),
    [final] ).

cnf(i_0_17529,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_10579]),
    [final] ).

cnf(i_0_17530,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_10310]),
    [final] ).

cnf(i_0_17531,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_5232]),
    [final] ).

cnf(i_0_17532,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_5230]),
    [final] ).

cnf(i_0_17533,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_10580]),
    [final] ).

cnf(i_0_17534,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_10581]),
    [final] ).

cnf(i_0_17535,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_10582]),
    [final] ).

cnf(i_0_17536,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_5232]),
    [final] ).

cnf(i_0_17537,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_5230]),
    [final] ).

cnf(i_0_17538,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_10583]),
    [final] ).

cnf(i_0_17539,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_10583]),
    [final] ).

cnf(i_0_17540,plain,
    c_Com_Ocom_OLocal(X1,X2,X3) != c_Com_Ocom_OWhile(X4,X5),
    inference(split_conjunct,[status(thm)],[i_0_10584]),
    [final] ).

cnf(i_0_17541,plain,
    c_Com_Ocom_OLocal(X1,X2,X3) != c_Com_Ocom_OAss(X4,X5),
    inference(split_conjunct,[status(thm)],[i_0_10585]),
    [final] ).

cnf(i_0_17542,plain,
    c_Com_Ocom_OLocal(X1,X2,X3) != c_Com_Ocom_OSemi(X4,X5),
    inference(split_conjunct,[status(thm)],[i_0_10586]),
    [final] ).

cnf(i_0_17543,plain,
    c_Com_Ocom_OCond(X1,X2,X3) != c_Com_Ocom_OWhile(X4,X5),
    inference(split_conjunct,[status(thm)],[i_0_10587]),
    [final] ).

cnf(i_0_17544,plain,
    c_Com_Ocom_OCond(X1,X2,X3) != c_Com_Ocom_OAss(X4,X5),
    inference(split_conjunct,[status(thm)],[i_0_10588]),
    [final] ).

cnf(i_0_17545,plain,
    c_Com_Ocom_OCond(X1,X2,X3) != c_Com_Ocom_OSemi(X4,X5),
    inference(split_conjunct,[status(thm)],[i_0_10589]),
    [final] ).

cnf(i_0_17546,plain,
    c_Com_Ocom_OCall(X1,X2,X3) != c_Com_Ocom_OWhile(X4,X5),
    inference(split_conjunct,[status(thm)],[i_0_10590]),
    [final] ).

cnf(i_0_17547,plain,
    c_Com_Ocom_OCall(X1,X2,X3) != c_Com_Ocom_OAss(X4,X5),
    inference(split_conjunct,[status(thm)],[i_0_10591]),
    [final] ).

cnf(i_0_17548,plain,
    c_Com_Ocom_OCall(X1,X2,X3) != c_Com_Ocom_OSemi(X4,X5),
    inference(split_conjunct,[status(thm)],[i_0_10592]),
    [final] ).

cnf(i_0_17549,plain,
    c_Com_Ocom_OWhile(X1,X2) != c_Com_Ocom_OLocal(X3,X4,X5),
    inference(split_conjunct,[status(thm)],[i_0_10593]),
    [final] ).

cnf(i_0_17550,plain,
    c_Com_Ocom_OWhile(X1,X2) != c_Com_Ocom_OCond(X3,X4,X5),
    inference(split_conjunct,[status(thm)],[i_0_10594]),
    [final] ).

cnf(i_0_17551,plain,
    c_Com_Ocom_OWhile(X1,X2) != c_Com_Ocom_OCall(X3,X4,X5),
    inference(split_conjunct,[status(thm)],[i_0_10595]),
    [final] ).

cnf(i_0_17552,plain,
    c_Com_Ocom_OAss(X1,X2) != c_Com_Ocom_OLocal(X3,X4,X5),
    inference(split_conjunct,[status(thm)],[i_0_10596]),
    [final] ).

cnf(i_0_17553,plain,
    c_Com_Ocom_OAss(X1,X2) != c_Com_Ocom_OCond(X3,X4,X5),
    inference(split_conjunct,[status(thm)],[i_0_10597]),
    [final] ).

cnf(i_0_17554,plain,
    c_Com_Ocom_OAss(X1,X2) != c_Com_Ocom_OCall(X3,X4,X5),
    inference(split_conjunct,[status(thm)],[i_0_10598]),
    [final] ).

cnf(i_0_17555,plain,
    c_Com_Ocom_OSemi(X1,X2) != c_Com_Ocom_OLocal(X3,X4,X5),
    inference(split_conjunct,[status(thm)],[i_0_10599]),
    [final] ).

cnf(i_0_17556,plain,
    c_Com_Ocom_OSemi(X1,X2) != c_Com_Ocom_OCond(X3,X4,X5),
    inference(split_conjunct,[status(thm)],[i_0_10600]),
    [final] ).

cnf(i_0_17557,plain,
    c_Com_Ocom_OSemi(X1,X2) != c_Com_Ocom_OCall(X3,X4,X5),
    inference(split_conjunct,[status(thm)],[i_0_10601]),
    [final] ).

cnf(i_0_17558,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_10602,c_0_8936]),
    [final] ).

cnf(i_0_17559,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_10511]),
    [final] ).

cnf(i_0_17560,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_10603]),
    [final] ).

cnf(i_0_17561,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_10604]),
    [final] ).

cnf(i_0_17562,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_10605]),
    [final] ).

cnf(i_0_17563,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_10360]),
    [final] ).

cnf(i_0_17564,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_10606]),
    [final] ).

cnf(i_0_17565,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_10607]),
    [final] ).

cnf(i_0_17566,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_10608]),
    [final] ).

cnf(i_0_17567,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_10609]),
    [final] ).

cnf(i_0_17568,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_10610]),
    [final] ).

cnf(i_0_17569,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_10611]),
    [final] ).

cnf(i_0_17570,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_10612]),
    [final] ).

cnf(i_0_17571,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_10613]),
    [final] ).

cnf(i_0_17572,plain,
    c_Com_Ocom_OLocal(X1,X2,X3) != hAPP(c_Com_Ocom_OBODY,X4),
    inference(split_conjunct,[status(thm)],[i_0_10614]),
    [final] ).

cnf(i_0_17573,plain,
    c_Com_Ocom_OCond(X1,X2,X3) != hAPP(c_Com_Ocom_OBODY,X4),
    inference(split_conjunct,[status(thm)],[i_0_10615]),
    [final] ).

cnf(i_0_17574,plain,
    c_Com_Ocom_OCall(X1,X2,X3) != hAPP(c_Com_Ocom_OBODY,X4),
    inference(split_conjunct,[status(thm)],[i_0_10616]),
    [final] ).

cnf(i_0_17575,plain,
    hAPP(c_Com_Ocom_OBODY,X1) != c_Com_Ocom_OLocal(X2,X3,X4),
    inference(split_conjunct,[status(thm)],[i_0_10617]),
    [final] ).

cnf(i_0_17576,plain,
    hAPP(c_Com_Ocom_OBODY,X1) != c_Com_Ocom_OCond(X2,X3,X4),
    inference(split_conjunct,[status(thm)],[i_0_10618]),
    [final] ).

cnf(i_0_17577,plain,
    hAPP(c_Com_Ocom_OBODY,X1) != c_Com_Ocom_OCall(X2,X3,X4),
    inference(split_conjunct,[status(thm)],[i_0_10619]),
    [final] ).

cnf(i_0_17578,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_10620]),
    [final] ).

cnf(i_0_17579,plain,
    hAPP(hAPP(c_List_Omap(X1,X1),c_COMBI(X1)),X2) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10621]),
    [final] ).

cnf(i_0_17580,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))
    | ~ c_Wellfounded_OwfP(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10105]),
    [final] ).

cnf(i_0_17581,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))
    | ~ c_Wellfounded_OwfP(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10622]),
    [final] ).

cnf(i_0_17582,plain,
    ( hBOOL(hAPP(hAPP(X2,X3),X3))
    | ~ c_Predicate_Oreflp(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10623]),
    [final] ).

cnf(i_0_17583,plain,
    ( hBOOL(hAPP(hAPP(X2,X3),X3))
    | ~ c_Equiv__Relations_Oequivp(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10624]),
    [final] ).

cnf(i_0_17584,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_10394]),
    [final] ).

cnf(i_0_17585,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_10395]),
    [final] ).

cnf(i_0_17586,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_10295]),
    [final] ).

cnf(i_0_17587,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_10296]),
    [final] ).

cnf(i_0_17588,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_10504]),
    [final] ).

cnf(i_0_17589,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_10505]),
    [final] ).

cnf(i_0_17590,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_10385]),
    [final] ).

cnf(i_0_17591,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_10384]),
    [final] ).

cnf(i_0_17592,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_10386]),
    [final] ).

cnf(i_0_17593,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_10625]),
    [final] ).

cnf(i_0_17594,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_10626]),
    [final] ).

cnf(i_0_17595,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_10627]),
    [final] ).

cnf(i_0_17596,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_10628]),
    [final] ).

cnf(i_0_17597,plain,
    ( hBOOL(hAPP(X1,X3))
    | ~ hBOOL(hAPP(X1,X2))
    | X3 != c_Hilbert__Choice_OEps(X4,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10629]),
    [final] ).

cnf(i_0_17598,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_10630]),
    [final] ).

cnf(i_0_17599,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_10631]),
    [final] ).

cnf(i_0_17600,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_10632]),
    [final] ).

cnf(i_0_17601,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_10633]),
    [final] ).

cnf(i_0_17602,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_10634]),
    [final] ).

cnf(i_0_17603,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_10635]),
    [final] ).

cnf(i_0_17604,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_10636]),
    [final] ).

cnf(i_0_17605,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_10637]),
    [final] ).

cnf(i_0_17606,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_10637]),
    [final] ).

cnf(i_0_17607,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_10638]),
    [final] ).

cnf(i_0_17608,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_10638]),
    [final] ).

cnf(i_0_17609,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_10639]),
    [final] ).

cnf(i_0_17610,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_10640]),
    [final] ).

cnf(i_0_17611,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_10641]),
    [final] ).

cnf(i_0_17612,plain,
    ( c_Relation_Osym(X1,X2)
    | ~ c_Equiv__Relations_Oequiv(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10453]),
    [final] ).

cnf(i_0_17613,plain,
    ( c_Relation_Osym(X1,X2)
    | ~ c_Equiv__Relations_Oequiv(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10277]),
    [final] ).

cnf(i_0_17614,plain,
    ( c_Relation_Otrans(X1,X2)
    | ~ c_Equiv__Relations_Oequiv(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10453]),
    [final] ).

cnf(i_0_17615,plain,
    ( c_Relation_Otrans(X1,X2)
    | ~ c_Equiv__Relations_Oequiv(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10277]),
    [final] ).

cnf(i_0_17616,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_10642]),
    [final] ).

cnf(i_0_17617,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_10643]),
    [final] ).

cnf(i_0_17618,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_9529]),
    [final] ).

cnf(i_0_17619,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_10644,c_0_8936]),
    [final] ).

cnf(i_0_17620,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_9778]),
    [final] ).

cnf(i_0_17621,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_10645]),
    [final] ).

cnf(i_0_17622,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_10406]),
    [final] ).

cnf(i_0_17623,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_10407]),
    [final] ).

cnf(i_0_17624,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_10405]),
    [final] ).

cnf(i_0_17625,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_10646]),
    [final] ).

cnf(i_0_17626,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_10647]),
    [final] ).

cnf(i_0_17627,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_10002]),
    [final] ).

cnf(i_0_17628,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_10019]),
    [final] ).

cnf(i_0_17629,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_10648]),
    [final] ).

cnf(i_0_17630,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_10382]),
    [final] ).

cnf(i_0_17631,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_10383]),
    [final] ).

cnf(i_0_17632,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_10649]),
    [final] ).

cnf(i_0_17633,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_10530]),
    [final] ).

cnf(i_0_17634,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_10650]),
    [final] ).

cnf(i_0_17635,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_10636]),
    [final] ).

cnf(i_0_17636,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_10636]),
    [final] ).

cnf(i_0_17637,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_10636]),
    [final] ).

cnf(i_0_17638,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_10636]),
    [final] ).

cnf(i_0_17639,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_10552]),
    [final] ).

cnf(i_0_17640,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_10651]),
    [final] ).

cnf(i_0_17641,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_10652]),
    [final] ).

cnf(i_0_17642,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_10653]),
    [final] ).

cnf(i_0_17643,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_10470]),
    [final] ).

cnf(i_0_17644,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_10654]),
    [final] ).

cnf(i_0_17645,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_10655]),
    [final] ).

cnf(i_0_17646,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_10656]),
    [final] ).

cnf(i_0_17647,plain,
    ~ c_List_Olist__ex1(X1,X2,c_List_Olist_ONil(X1)),
    inference(split_conjunct,[status(thm)],[i_0_10657]),
    [final] ).

cnf(i_0_17648,plain,
    ~ c_List_Olist__ex(X1,X2,c_List_Olist_ONil(X1)),
    inference(split_conjunct,[status(thm)],[i_0_10658]),
    [final] ).

cnf(i_0_17649,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_10659]),
    [final] ).

cnf(i_0_17650,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_17651,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X1)),
    inference(split_conjunct,[status(thm)],[i_0_10660]),
    [final] ).

cnf(i_0_17652,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X1)),
    inference(split_conjunct,[status(thm)],[i_0_10661]),
    [final] ).

cnf(i_0_17653,plain,
    hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X1),X1)),
    inference(split_conjunct,[status(thm)],[i_0_10662]),
    [final] ).

cnf(i_0_17654,plain,
    hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X1),X1)),
    inference(split_conjunct,[status(thm)],[i_0_10663]),
    [final] ).

cnf(i_0_17655,plain,
    hBOOL(hAPP(c_List_Olistsp(X1,X2),c_List_Olist_ONil(X1))),
    inference(split_conjunct,[status(thm)],[i_0_10664]),
    [final] ).

cnf(i_0_17656,plain,
    hBOOL(hAPP(c_List_Olistsp(X1,X2),c_List_Olist_ONil(X1))),
    inference(split_conjunct,[status(thm)],[i_0_10665]),
    [final] ).

cnf(i_0_17657,plain,
    hBOOL(hAPP(c_List_Odistinct(X1),c_List_Oremdups(X1,X2))),
    inference(split_conjunct,[status(thm)],[i_0_10666]),
    [final] ).

cnf(i_0_17658,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_10504]),
    [final] ).

cnf(i_0_17659,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_10504]),
    [final] ).

cnf(i_0_17660,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_10505]),
    [final] ).

cnf(i_0_17661,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_10505]),
    [final] ).

cnf(i_0_17662,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_10667]),
    [final] ).

cnf(i_0_17663,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_10667]),
    [final] ).

cnf(i_0_17664,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_10668]),
    [final] ).

cnf(i_0_17665,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_10668]),
    [final] ).

cnf(i_0_17666,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_10669,c_0_6064]),
    [final] ).

cnf(i_0_17667,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_10670,c_0_6216]),
    [final] ).

cnf(i_0_17668,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_10671,c_0_6181]),
    [final] ).

cnf(i_0_17669,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_10672]),
    [final] ).

cnf(i_0_17670,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_10673]),
    [final] ).

cnf(i_0_17671,plain,
    hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
    inference(split_conjunct,[status(thm)],[i_0_10674]),
    [final] ).

cnf(i_0_17672,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_10675,c_0_6181]),
    [final] ).

cnf(i_0_17673,plain,
    c_Lazy__Sequence_Olazy__sequence_OInsert(X1,X2,X3) != c_Lazy__Sequence_Olazy__sequence_OEmpty(X1),
    inference(split_conjunct,[status(thm)],[i_0_10676]),
    [final] ).

cnf(i_0_17674,plain,
    c_Lazy__Sequence_Olazy__sequence_OEmpty(X1) != c_Lazy__Sequence_Olazy__sequence_OInsert(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[i_0_10677]),
    [final] ).

cnf(i_0_17675,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_10678]),
    [final] ).

cnf(i_0_17676,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_10679]),
    [final] ).

cnf(i_0_17677,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_10680]),
    [final] ).

cnf(i_0_17678,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_10681]),
    [final] ).

cnf(i_0_17679,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_10682]),
    [final] ).

cnf(i_0_17680,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_10683]),
    [final] ).

cnf(i_0_17681,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_10684]),
    [final] ).

cnf(i_0_17682,plain,
    ( hBOOL(hAPP(hAPP(c_fconj,X1),X2))
    | ~ hBOOL(X1)
    | ~ hBOOL(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10685]),
    [final] ).

cnf(i_0_17683,plain,
    ( hBOOL(hAPP(X1,esk290_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_10532]),
    [final] ).

cnf(i_0_17684,plain,
    ( hBOOL(hAPP(X1,esk289_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_10533]),
    [final] ).

cnf(i_0_17685,plain,
    ( X2 = c_List_Olist_ONil(X1)
    | hAPP(hAPP(c_List_Oappend(X1),X2),X3) != X3 ),
    inference(split_conjunct,[status(thm)],[i_0_10686]),
    [final] ).

cnf(i_0_17686,plain,
    ( X3 = c_List_Olist_ONil(X1)
    | hAPP(hAPP(c_List_Oappend(X1),X2),X3) != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_10687]),
    [final] ).

cnf(i_0_17687,plain,
    ( X3 = c_List_Olist_ONil(X2)
    | X1 != hAPP(hAPP(c_List_Oappend(X2),X1),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10688]),
    [final] ).

cnf(i_0_17688,plain,
    ( X3 = c_List_Olist_ONil(X2)
    | X1 != hAPP(hAPP(c_List_Oappend(X2),X3),X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10689]),
    [final] ).

cnf(i_0_17689,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_10690]),
    [final] ).

cnf(i_0_17690,plain,
    hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3) != c_List_Olist_ONil(X1),
    inference(split_conjunct,[status(thm)],[i_0_10691]),
    [final] ).

cnf(i_0_17691,plain,
    c_List_Olist_ONil(X1) != hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3),
    inference(split_conjunct,[status(thm)],[i_0_10692]),
    [final] ).

cnf(i_0_17692,plain,
    hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(X1,X2))),
    inference(split_conjunct,[status(thm)],[i_0_10693]),
    [final] ).

cnf(i_0_17693,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_10548]),
    [final] ).

cnf(i_0_17694,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_10694,c_0_6216]),
    [final] ).

cnf(i_0_17695,plain,
    ( hBOOL(hAPP(c_List_Odistinct(X2),X1))
    | esk339_2(X1,X2) != esk340_2(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8312]),
    [final] ).

cnf(i_0_17696,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_10690]),
    [final] ).

cnf(i_0_17697,plain,
    c_Com_Ocom_OLocal(X1,X2,X3) != c_Com_Ocom_OSKIP,
    inference(split_conjunct,[status(thm)],[i_0_10695]),
    [final] ).

cnf(i_0_17698,plain,
    c_Com_Ocom_OCond(X1,X2,X3) != c_Com_Ocom_OSKIP,
    inference(split_conjunct,[status(thm)],[i_0_10696]),
    [final] ).

cnf(i_0_17699,plain,
    c_Com_Ocom_OCall(X1,X2,X3) != c_Com_Ocom_OSKIP,
    inference(split_conjunct,[status(thm)],[i_0_10697]),
    [final] ).

cnf(i_0_17700,plain,
    c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[i_0_10698]),
    [final] ).

cnf(i_0_17701,plain,
    c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[i_0_10699]),
    [final] ).

cnf(i_0_17702,plain,
    c_Com_Ocom_OSKIP != c_Com_Ocom_OCall(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[i_0_10700]),
    [final] ).

cnf(i_0_17703,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_10701]),
    [final] ).

cnf(i_0_17704,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_10702]),
    [final] ).

cnf(i_0_17705,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_10703]),
    [final] ).

cnf(i_0_17706,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_10704]),
    [final] ).

cnf(i_0_17707,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_10705]),
    [final] ).

cnf(i_0_17708,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_10706]),
    [final] ).

cnf(i_0_17709,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_10707]),
    [final] ).

cnf(i_0_17710,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_17711,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_17712,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_17713,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_17714,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_17715,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_10708]),
    [final] ).

cnf(i_0_17716,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_10709]),
    [final] ).

cnf(i_0_17717,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_10710]),
    [final] ).

cnf(i_0_17718,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_10711]),
    [final] ).

cnf(i_0_17719,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_10712]),
    [final] ).

cnf(i_0_17720,plain,
    hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3) != X3,
    inference(split_conjunct,[status(thm)],[i_0_10713]),
    [final] ).

cnf(i_0_17721,plain,
    X1 != hAPP(hAPP(c_List_Olist_OCons(X2),X3),X1),
    inference(split_conjunct,[status(thm)],[i_0_10714]),
    [final] ).

cnf(i_0_17722,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_10715]),
    [final] ).

cnf(i_0_17723,plain,
    ( hBOOL(hAPP(hAPP(c_fdisj,X1),X2))
    | ~ hBOOL(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10716]),
    [final] ).

cnf(i_0_17724,plain,
    ( hBOOL(hAPP(hAPP(c_fdisj,X2),X1))
    | ~ hBOOL(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10717]),
    [final] ).

cnf(i_0_17725,plain,
    ( hBOOL(hAPP(hAPP(c_fimplies,X2),X1))
    | ~ hBOOL(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10718]),
    [final] ).

cnf(i_0_17726,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_10719]),
    [final] ).

cnf(i_0_17727,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_10720]),
    [final] ).

cnf(i_0_17728,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_10721]),
    [final] ).

cnf(i_0_17729,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_10722]),
    [final] ).

cnf(i_0_17730,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_10723]),
    [final] ).

cnf(i_0_17731,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_10724]),
    [final] ).

cnf(i_0_17732,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_10725]),
    [final] ).

cnf(i_0_17733,plain,
    ( c_List_Oremdups(X1,X2) = X2
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10726]),
    [final] ).

cnf(i_0_17734,plain,
    ( c_List_Oremdups(X1,X2) = X2
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10727]),
    [final] ).

cnf(i_0_17735,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_10728,c_0_7958]),
    [final] ).

cnf(i_0_17736,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_10729]),
    [final] ).

cnf(i_0_17737,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_10730]),
    [final] ).

cnf(i_0_17738,plain,
    ( hBOOL(X1)
    | hBOOL(hAPP(hAPP(c_fimplies,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10731]),
    [final] ).

cnf(i_0_17739,plain,
    c_Relation_Osingle__valued(X1,X1,c_Relation_OId__on(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_10732]),
    [final] ).

cnf(i_0_17740,plain,
    c_Relation_Orefl__on(X1,X2,c_Relation_OId__on(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_10733]),
    [final] ).

cnf(i_0_17741,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_10734]),
    [final] ).

cnf(i_0_17742,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_10734]),
    [final] ).

cnf(i_0_17743,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_10735]),
    [final] ).

cnf(i_0_17744,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_10735]),
    [final] ).

cnf(i_0_17745,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_10736]),
    [final] ).

cnf(i_0_17746,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_10736]),
    [final] ).

cnf(i_0_17747,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_10637]),
    [final] ).

cnf(i_0_17748,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_10638]),
    [final] ).

cnf(i_0_17749,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_10737]),
    [final] ).

cnf(i_0_17750,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_10738]),
    [final] ).

cnf(i_0_17751,plain,
    ( hBOOL(hAPP(hAPP(c_fequal,X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_10739]),
    [final] ).

cnf(i_0_17752,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_10740]),
    [final] ).

cnf(i_0_17753,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_10741]),
    [final] ).

cnf(i_0_17754,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_10742]),
    [final] ).

cnf(i_0_17755,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_10743]),
    [final] ).

cnf(i_0_17756,plain,
    ( c_Wellfounded_Owf(X2,X1)
    | esk436_2(X1,X2) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_8204]),
    [final] ).

cnf(i_0_17757,plain,
    ( c_Relation_Osym(X1,X2)
    | hAPP(c_Relation_Oconverse(X1,X1),X2) != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_10744]),
    [final] ).

cnf(i_0_17758,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_10745]),
    [final] ).

cnf(i_0_17759,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_10746]),
    [final] ).

cnf(i_0_17760,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_10583]),
    [final] ).

cnf(i_0_17761,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_10747]),
    [final] ).

cnf(i_0_17762,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_10748]),
    [final] ).

cnf(i_0_17763,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_10749]),
    [final] ).

cnf(i_0_17764,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_10750]),
    [final] ).

cnf(i_0_17765,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_10394]),
    [final] ).

cnf(i_0_17766,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_10395]),
    [final] ).

cnf(i_0_17767,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_10751]),
    [final] ).

cnf(i_0_17768,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_10752]),
    [final] ).

cnf(i_0_17769,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_10753]),
    [final] ).

cnf(i_0_17770,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_10754]),
    [final] ).

cnf(i_0_17771,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_10755]),
    [final] ).

cnf(i_0_17772,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_10756]),
    [final] ).

cnf(i_0_17773,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_10757]),
    [final] ).

cnf(i_0_17774,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_10758]),
    [final] ).

cnf(i_0_17775,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_10759]),
    [final] ).

cnf(i_0_17776,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_10760]),
    [final] ).

cnf(i_0_17777,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_10761]),
    [final] ).

cnf(i_0_17778,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_10762]),
    [final] ).

cnf(i_0_17779,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_10763]),
    [final] ).

cnf(i_0_17780,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_10764]),
    [final] ).

cnf(i_0_17781,plain,
    ( c_List_Olinorder__class_Osorted(X1,esk405_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_7339]),
    [final] ).

cnf(i_0_17782,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_10765]),
    [final] ).

cnf(i_0_17783,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_10766]),
    [final] ).

cnf(i_0_17784,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_10311]),
    [final] ).

cnf(i_0_17785,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_10767]),
    [final] ).

cnf(i_0_17786,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_10768,c_0_6063]),
    [final] ).

cnf(i_0_17787,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_10769,c_0_6063]),
    [final] ).

cnf(i_0_17788,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_10770]),
    [final] ).

cnf(i_0_17789,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_10667]),
    [final] ).

cnf(i_0_17790,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_10668]),
    [final] ).

cnf(i_0_17791,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_10771]),
    [final] ).

cnf(i_0_17792,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1) != c_Int_OMin,
    inference(rw,[status(thm)],[i_0_10772,c_0_6063]),
    [final] ).

cnf(i_0_17793,plain,
    c_Int_OMin != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1),
    inference(rw,[status(thm)],[i_0_10773,c_0_6063]),
    [final] ).

cnf(i_0_17794,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_10774]),
    [final] ).

cnf(i_0_17795,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_10775]),
    [final] ).

cnf(i_0_17796,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_10776]),
    [final] ).

cnf(i_0_17797,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_10777]),
    [final] ).

cnf(i_0_17798,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_10778]),
    [final] ).

cnf(i_0_17799,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_10779]),
    [final] ).

cnf(i_0_17800,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_10780]),
    [final] ).

cnf(i_0_17801,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_10781]),
    [final] ).

cnf(i_0_17802,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_10782]),
    [final] ).

cnf(i_0_17803,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_10783]),
    [final] ).

cnf(i_0_17804,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_10784]),
    [final] ).

cnf(i_0_17805,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_10785]),
    [final] ).

cnf(i_0_17806,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_10786]),
    [final] ).

cnf(i_0_17807,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_10787]),
    [final] ).

cnf(i_0_17808,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_10788]),
    [final] ).

cnf(i_0_17809,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_10789]),
    [final] ).

cnf(i_0_17810,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_10626]),
    [final] ).

cnf(i_0_17811,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_10790]),
    [final] ).

cnf(i_0_17812,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_10511]),
    [final] ).

cnf(i_0_17813,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_10608]),
    [final] ).

cnf(i_0_17814,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_10608]),
    [final] ).

cnf(i_0_17815,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_10640]),
    [final] ).

cnf(i_0_17816,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_10641]),
    [final] ).

cnf(i_0_17817,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_10791]),
    [final] ).

cnf(i_0_17818,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_10792]),
    [final] ).

cnf(i_0_17819,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_10793]),
    [final] ).

cnf(i_0_17820,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_10794]),
    [final] ).

cnf(i_0_17821,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_10795]),
    [final] ).

cnf(i_0_17822,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_10796]),
    [final] ).

cnf(i_0_17823,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_10797]),
    [final] ).

cnf(i_0_17824,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_10798]),
    [final] ).

cnf(i_0_17825,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_10799]),
    [final] ).

cnf(i_0_17826,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_10800]),
    [final] ).

cnf(i_0_17827,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_10801]),
    [final] ).

cnf(i_0_17828,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_10802]),
    [final] ).

cnf(i_0_17829,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_10803]),
    [final] ).

cnf(i_0_17830,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_10804]),
    [final] ).

cnf(i_0_17831,plain,
    ( X1 = hAPP(hAPP(c_List_Oappend(X3),c_List_Olist_ONil(X3)),X2)
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_10805]),
    [final] ).

cnf(i_0_17832,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_10651]),
    [final] ).

cnf(i_0_17833,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_10790]),
    [final] ).

cnf(i_0_17834,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_10806]),
    [final] ).

cnf(i_0_17835,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_10807]),
    [final] ).

cnf(i_0_17836,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_10808]),
    [final] ).

cnf(i_0_17837,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_10809]),
    [final] ).

cnf(i_0_17838,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_10810]),
    [final] ).

cnf(i_0_17839,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_10811]),
    [final] ).

cnf(i_0_17840,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_10812]),
    [final] ).

cnf(i_0_17841,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_10813]),
    [final] ).

cnf(i_0_17842,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_10814]),
    [final] ).

cnf(i_0_17843,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_10815]),
    [final] ).

cnf(i_0_17844,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_10548]),
    [final] ).

cnf(i_0_17845,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_10646]),
    [final] ).

cnf(i_0_17846,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_10647]),
    [final] ).

cnf(i_0_17847,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_10498]),
    [final] ).

cnf(i_0_17848,plain,
    hAPP(c_Relation_ODomain(X1,X1),c_Relation_OId__on(X1,X2)) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10816]),
    [final] ).

cnf(i_0_17849,plain,
    hAPP(c_Relation_ORange(X1,X1),c_Relation_OId__on(X1,X2)) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10817]),
    [final] ).

cnf(i_0_17850,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_10818]),
    [final] ).

cnf(i_0_17851,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_10819]),
    [final] ).

cnf(i_0_17852,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_10820]),
    [final] ).

cnf(i_0_17853,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_10821]),
    [final] ).

cnf(i_0_17854,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_10822]),
    [final] ).

cnf(i_0_17855,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_10823]),
    [final] ).

cnf(i_0_17856,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_10824]),
    [final] ).

cnf(i_0_17857,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_10825]),
    [final] ).

cnf(i_0_17858,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_10826]),
    [final] ).

cnf(i_0_17859,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_10827]),
    [final] ).

cnf(i_0_17860,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_10828]),
    [final] ).

cnf(i_0_17861,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_10829]),
    [final] ).

cnf(i_0_17862,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_10830]),
    [final] ).

cnf(i_0_17863,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_10831]),
    [final] ).

cnf(i_0_17864,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_10832]),
    [final] ).

cnf(i_0_17865,plain,
    ( hBOOL(hAPP(c_List_Odistinct(X1),X2))
    | c_List_Oremdups(X1,X2) != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_10727]),
    [final] ).

cnf(i_0_17866,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_10833]),
    [final] ).

cnf(i_0_17867,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_10834]),
    [final] ).

cnf(i_0_17868,plain,
    hAPP(c_List_Oset(X1),c_List_Oremdups(X1,X2)) = hAPP(c_List_Oset(X1),X2),
    inference(split_conjunct,[status(thm)],[i_0_10835]),
    [final] ).

cnf(i_0_17869,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_10836]),
    [final] ).

cnf(i_0_17870,plain,
    ( X2 = X3
    | hAPP(c_List_Orev(X1),X2) != hAPP(c_List_Orev(X1),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10837]),
    [final] ).

cnf(i_0_17871,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_8272]),
    [final] ).

cnf(i_0_17872,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_10498]),
    [final] ).

cnf(i_0_17873,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_10838]),
    [final] ).

cnf(i_0_17874,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_10839]),
    [final] ).

cnf(i_0_17875,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_17876,plain,
    hAPP(hAPP(c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10840]),
    [final] ).

cnf(i_0_17877,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_10649]),
    [final] ).

cnf(i_0_17878,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_10841]),
    [final] ).

cnf(i_0_17879,plain,
    c_List_Osublist(X1,c_List_Olist_ONil(X1),X2) = c_List_Olist_ONil(X1),
    inference(split_conjunct,[status(thm)],[i_0_10842]),
    [final] ).

cnf(i_0_17880,plain,
    c_List_OtakeWhile(X1,X2,c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
    inference(split_conjunct,[status(thm)],[i_0_10843]),
    [final] ).

cnf(i_0_17881,plain,
    c_List_Oremove1(X1,X2,c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
    inference(split_conjunct,[status(thm)],[i_0_10844]),
    [final] ).

cnf(i_0_17882,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_10652]),
    [final] ).

cnf(i_0_17883,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_10653]),
    [final] ).

cnf(i_0_17884,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_10845]),
    [final] ).

cnf(i_0_17885,plain,
    ( hAPP(c_Relation_Oconverse(X1,X1),X2) = X2
    | ~ c_Relation_Osym(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10744]),
    [final] ).

cnf(i_0_17886,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_10846]),
    [final] ).

cnf(i_0_17887,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_10847]),
    [final] ).

cnf(i_0_17888,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_10848]),
    [final] ).

cnf(i_0_17889,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_10849]),
    [final] ).

cnf(i_0_17890,plain,
    ( c_Relation_Osym(X1,c_Transitive__Closure_Ortrancl(X1,X2))
    | ~ c_Relation_Osym(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10850]),
    [final] ).

cnf(i_0_17891,plain,
    ( c_Relation_Oantisym(X1,c_Transitive__Closure_Ortrancl(X1,X2))
    | ~ c_Wellfounded_Oacyclic(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10851]),
    [final] ).

cnf(i_0_17892,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_10852]),
    [final] ).

cnf(i_0_17893,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_10853]),
    [final] ).

cnf(i_0_17894,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_10854]),
    [final] ).

cnf(i_0_17895,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_10649]),
    [final] ).

cnf(i_0_17896,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_10855]),
    [final] ).

cnf(i_0_17897,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_10855]),
    [final] ).

cnf(i_0_17898,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_10856]),
    [final] ).

cnf(i_0_17899,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_10856]),
    [final] ).

cnf(i_0_17900,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_10857]),
    [final] ).

cnf(i_0_17901,plain,
    ( hAPP(hAPP(c_List_Oappend(X2),X1),X3) = X3
    | X1 != c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10686]),
    [final] ).

cnf(i_0_17902,plain,
    ( hAPP(hAPP(c_List_Oappend(X2),X3),X1) = X3
    | X1 != c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10687]),
    [final] ).

cnf(i_0_17903,plain,
    ( X3 = hAPP(hAPP(c_List_Oappend(X2),X1),X3)
    | X1 != c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10689]),
    [final] ).

cnf(i_0_17904,plain,
    ( X3 = hAPP(hAPP(c_List_Oappend(X2),X3),X1)
    | X1 != c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10688]),
    [final] ).

cnf(i_0_17905,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_10858]),
    [final] ).

cnf(i_0_17906,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_10859]),
    [final] ).

cnf(i_0_17907,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_10860]),
    [final] ).

cnf(i_0_17908,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_10861]),
    [final] ).

cnf(i_0_17909,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_10862]),
    [final] ).

cnf(i_0_17910,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_10863]),
    [final] ).

cnf(i_0_17911,plain,
    c_Lazy__Sequence_Oappend(X1,c_Lazy__Sequence_Olazy__sequence_OEmpty(X1),X2) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10864]),
    [final] ).

cnf(i_0_17912,plain,
    c_List_Osplice(X1,c_List_Olist_ONil(X1),X2) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10865]),
    [final] ).

cnf(i_0_17913,plain,
    c_List_Osplice(X1,X2,c_List_Olist_ONil(X1)) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10866]),
    [final] ).

cnf(i_0_17914,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_10867]),
    [final] ).

cnf(i_0_17915,plain,
    c_List_Olist__all(X1,X2,c_List_Olist_ONil(X1)),
    inference(split_conjunct,[status(thm)],[i_0_10868]),
    [final] ).

cnf(i_0_17916,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_10636]),
    [final] ).

cnf(i_0_17917,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_10734]),
    [final] ).

cnf(i_0_17918,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_10735]),
    [final] ).

cnf(i_0_17919,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_10736]),
    [final] ).

cnf(i_0_17920,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_10869]),
    [final] ).

cnf(i_0_17921,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_10870]),
    [final] ).

cnf(i_0_17922,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X2) = X2
    | ~ class_Lattices_Olattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10871]),
    [final] ).

cnf(i_0_17923,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X2) = X2
    | ~ class_Lattices_Olattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10872]),
    [final] ).

cnf(i_0_17924,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_10873]),
    [final] ).

cnf(i_0_17925,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_10874]),
    [final] ).

cnf(i_0_17926,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X2) = X2
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10875]),
    [final] ).

cnf(i_0_17927,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X2) = X2
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10876]),
    [final] ).

cnf(i_0_17928,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X2) = X2
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10877]),
    [final] ).

cnf(i_0_17929,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X2) = X2
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10878]),
    [final] ).

cnf(i_0_17930,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_10879]),
    [final] ).

cnf(i_0_17931,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_10880]),
    [final] ).

cnf(i_0_17932,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_10881]),
    [final] ).

cnf(i_0_17933,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_10882]),
    [final] ).

cnf(i_0_17934,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_10883]),
    [final] ).

cnf(i_0_17935,plain,
    hAPP(c_New__DSequence_Opos__single(X1,X2),X3) = hAPP(c_Lazy__Sequence_Osingle(X1),X2),
    inference(split_conjunct,[status(thm)],[i_0_10884]),
    [final] ).

cnf(i_0_17936,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_6224]),
    [final] ).

cnf(i_0_17937,plain,
    hAPP(hAPP(c_List_Odrop(X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10885]),
    [final] ).

cnf(i_0_17938,plain,
    hAPP(hAPP(c_List_Oappend(X1),X2),c_List_Olist_ONil(X1)) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10886]),
    [final] ).

cnf(i_0_17939,plain,
    hAPP(c_List_Orev(X1),hAPP(c_List_Orev(X1),X2)) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10887]),
    [final] ).

cnf(i_0_17940,plain,
    ( c_Relation_Oantisym(X2,X1)
    | esk546_2(X1,X2) != esk547_2(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7056]),
    [final] ).

cnf(i_0_17941,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_10888]),
    [final] ).

cnf(i_0_17942,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_10889]),
    [final] ).

cnf(i_0_17943,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_10890]),
    [final] ).

cnf(i_0_17944,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_17945,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_10891]),
    [final] ).

cnf(i_0_17946,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_10892]),
    [final] ).

cnf(i_0_17947,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_10893]),
    [final] ).

cnf(i_0_17948,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_10894]),
    [final] ).

cnf(i_0_17949,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_10895]),
    [final] ).

cnf(i_0_17950,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_10896]),
    [final] ).

cnf(i_0_17951,plain,
    hAPP(c_List_Omap(X1,X1),c_COMBI(X1)) = c_Fun_Oid(tc_List_Olist(X1)),
    inference(split_conjunct,[status(thm)],[i_0_10897]),
    [final] ).

cnf(i_0_17952,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_10898]),
    [final] ).

cnf(i_0_17953,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_10899]),
    [final] ).

cnf(i_0_17954,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_10742]),
    [final] ).

cnf(i_0_17955,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_10743]),
    [final] ).

cnf(i_0_17956,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_10900]),
    [final] ).

cnf(i_0_17957,plain,
    ( hAPP(c_List_Orev(X2),X1) = X3
    | X1 != hAPP(c_List_Orev(X2),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10901]),
    [final] ).

cnf(i_0_17958,plain,
    ( X2 = hAPP(c_List_Orev(X1),X3)
    | hAPP(c_List_Orev(X1),X2) != X3 ),
    inference(split_conjunct,[status(thm)],[i_0_10901]),
    [final] ).

cnf(i_0_17959,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_10902]),
    [final] ).

cnf(i_0_17960,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_10903]),
    [final] ).

cnf(i_0_17961,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_10904]),
    [final] ).

cnf(i_0_17962,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_10905]),
    [final] ).

cnf(i_0_17963,plain,
    hBOOL(hAPP(c_List_Odistinct(X1),c_List_Olist_ONil(X1))),
    inference(split_conjunct,[status(thm)],[i_0_10906]),
    [final] ).

cnf(i_0_17964,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_9514]),
    [final] ).

cnf(i_0_17965,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_9551]),
    [final] ).

cnf(i_0_17966,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_8991]),
    [final] ).

cnf(i_0_17967,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_10712]),
    [final] ).

cnf(i_0_17968,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_10712]),
    [final] ).

cnf(i_0_17969,plain,
    hAPP(c_New__DSequence_Oneg__single(X1,X2),X3) = c_Lazy__Sequence_Ohb__single(X1,X2),
    inference(split_conjunct,[status(thm)],[i_0_10907]),
    [final] ).

cnf(i_0_17970,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_10908]),
    [final] ).

cnf(i_0_17971,plain,
    c_List_Oremdups(X1,c_List_Oremdups(X1,X2)) = c_List_Oremdups(X1,X2),
    inference(split_conjunct,[status(thm)],[i_0_10909]),
    [final] ).

cnf(i_0_17972,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_10910]),
    [final] ).

cnf(i_0_17973,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_10911]),
    [final] ).

cnf(i_0_17974,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_10912]),
    [final] ).

cnf(i_0_17975,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_10913]),
    [final] ).

cnf(i_0_17976,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_10914]),
    [final] ).

cnf(i_0_17977,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_10915]),
    [final] ).

cnf(i_0_17978,plain,
    c_Predicate_Oconversep(X1,X1,c_fequal) = c_fequal,
    inference(split_conjunct,[status(thm)],[i_0_10916]),
    [final] ).

cnf(i_0_17979,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_9075]),
    [final] ).

cnf(i_0_17980,plain,
    ( c_List_Otranspose(X2,X1) = c_List_Olist_ONil(tc_List_Olist(X2))
    | esk389_2(X1,X2) != c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9211]),
    [final] ).

cnf(i_0_17981,plain,
    ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(split_conjunct,[status(thm)],[i_0_10917]),
    [final] ).

cnf(i_0_17982,plain,
    ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(split_conjunct,[status(thm)],[i_0_10918]),
    [final] ).

cnf(i_0_17983,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_10919]),
    [final] ).

cnf(i_0_17984,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_10920]),
    [final] ).

cnf(i_0_17985,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_10921]),
    [final] ).

cnf(i_0_17986,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_10922]),
    [final] ).

cnf(i_0_17987,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_10894]),
    [final] ).

cnf(i_0_17988,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_10923]),
    [final] ).

cnf(i_0_17989,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_10924]),
    [final] ).

cnf(i_0_17990,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_10925]),
    [final] ).

cnf(i_0_17991,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_10926]),
    [final] ).

cnf(i_0_17992,plain,
    ( ~ hBOOL(hAPP(c_fNot,X1))
    | ~ hBOOL(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10927]),
    [final] ).

cnf(i_0_17993,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_10928]),
    [final] ).

cnf(i_0_17994,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_10929]),
    [final] ).

cnf(i_0_17995,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_10930]),
    [final] ).

cnf(i_0_17996,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_10931]),
    [final] ).

cnf(i_0_17997,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_10932]),
    [final] ).

cnf(i_0_17998,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_10933]),
    [final] ).

cnf(i_0_17999,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_10934]),
    [final] ).

cnf(i_0_18000,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_10935]),
    [final] ).

cnf(i_0_18001,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_18002,plain,
    hAPP(c_List_Ofilter(X1,X2),c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
    inference(split_conjunct,[status(thm)],[i_0_10936]),
    [final] ).

cnf(i_0_18003,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ class_Finite__Set_Ofinite(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10937]),
    [final] ).

cnf(i_0_18004,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ class_Finite__Set_Ofinite(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10938]),
    [final] ).

cnf(i_0_18005,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_10939]),
    [final] ).

cnf(i_0_18006,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_10940]),
    [final] ).

cnf(i_0_18007,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_18008,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_10941,c_0_6063]),
    [final] ).

cnf(i_0_18009,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_10942,c_0_6063]),
    [final] ).

cnf(i_0_18010,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_18011,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_10943]),
    [final] ).

cnf(i_0_18012,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_10944]),
    [final] ).

cnf(i_0_18013,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_10187]),
    [final] ).

cnf(i_0_18014,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_10188]),
    [final] ).

cnf(i_0_18015,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_10945]),
    [final] ).

cnf(i_0_18016,plain,
    ( X1 = X2
    | c_Com_Ocom_OWhile(X1,X3) != c_Com_Ocom_OWhile(X2,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_10946]),
    [final] ).

cnf(i_0_18017,plain,
    ( X1 = X2
    | c_Com_Ocom_OWhile(X3,X1) != c_Com_Ocom_OWhile(X4,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10946]),
    [final] ).

cnf(i_0_18018,plain,
    ( X1 = X2
    | c_Com_Ocom_OAss(X1,X3) != c_Com_Ocom_OAss(X2,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_10947]),
    [final] ).

cnf(i_0_18019,plain,
    ( X1 = X2
    | c_Com_Ocom_OAss(X3,X1) != c_Com_Ocom_OAss(X4,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10947]),
    [final] ).

cnf(i_0_18020,plain,
    ( X1 = X2
    | c_Com_Ocom_OSemi(X1,X3) != c_Com_Ocom_OSemi(X2,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_10948]),
    [final] ).

cnf(i_0_18021,plain,
    ( X1 = X2
    | c_Com_Ocom_OSemi(X3,X1) != c_Com_Ocom_OSemi(X4,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10948]),
    [final] ).

cnf(i_0_18022,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_10949]),
    [final] ).

cnf(i_0_18023,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_10950]),
    [final] ).

cnf(i_0_18024,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OAss(X1,X2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[i_0_10951]),
    [final] ).

cnf(i_0_18025,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OPls) = X1,
    inference(split_conjunct,[status(thm)],[i_0_10952]),
    [final] ).

cnf(i_0_18026,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OPls) = X1,
    inference(split_conjunct,[status(thm)],[i_0_10953]),
    [final] ).

cnf(i_0_18027,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_10954]),
    [final] ).

cnf(i_0_18028,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_10955]),
    [final] ).

cnf(i_0_18029,plain,
    ( class_Enum_Oenum(tc_sum(X1,X2))
    | ~ class_Enum_Oenum(X1)
    | ~ class_Enum_Oenum(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10956]),
    [final] ).

cnf(i_0_18030,plain,
    ( class_Enum_Oenum(tc_prod(X1,X2))
    | ~ class_Enum_Oenum(X1)
    | ~ class_Enum_Oenum(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10957]),
    [final] ).

cnf(i_0_18031,plain,
    ( class_Enum_Oenum(tc_fun(X1,X2))
    | ~ class_Enum_Oenum(X1)
    | ~ class_Enum_Oenum(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10958]),
    [final] ).

cnf(i_0_18032,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_10959]),
    [final] ).

cnf(i_0_18033,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_10960]),
    [final] ).

cnf(i_0_18034,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_10961]),
    [final] ).

cnf(i_0_18035,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_10962]),
    [final] ).

cnf(i_0_18036,plain,
    c_Com_Ocom_OWhile(X1,X2) != c_Com_Ocom_OAss(X3,X4),
    inference(split_conjunct,[status(thm)],[i_0_10963]),
    [final] ).

cnf(i_0_18037,plain,
    c_Com_Ocom_OWhile(X1,X2) != c_Com_Ocom_OSemi(X3,X4),
    inference(split_conjunct,[status(thm)],[i_0_10964]),
    [final] ).

cnf(i_0_18038,plain,
    c_Com_Ocom_OAss(X1,X2) != c_Com_Ocom_OWhile(X3,X4),
    inference(split_conjunct,[status(thm)],[i_0_10965]),
    [final] ).

cnf(i_0_18039,plain,
    c_Com_Ocom_OSemi(X1,X2) != c_Com_Ocom_OWhile(X3,X4),
    inference(split_conjunct,[status(thm)],[i_0_10966]),
    [final] ).

cnf(i_0_18040,plain,
    c_Com_Ocom_OAss(X1,X2) != c_Com_Ocom_OSemi(X3,X4),
    inference(split_conjunct,[status(thm)],[i_0_10967]),
    [final] ).

cnf(i_0_18041,plain,
    c_Com_Ocom_OSemi(X1,X2) != c_Com_Ocom_OAss(X3,X4),
    inference(split_conjunct,[status(thm)],[i_0_10968]),
    [final] ).

cnf(i_0_18042,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_18043,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_18044,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X1) = X1,
    inference(split_conjunct,[status(thm)],[i_0_10969]),
    [final] ).

cnf(i_0_18045,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_10857]),
    [final] ).

cnf(i_0_18046,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_10970]),
    [final] ).

cnf(i_0_18047,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_10971]),
    [final] ).

cnf(i_0_18048,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_10972]),
    [final] ).

cnf(i_0_18049,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_10881]),
    [final] ).

cnf(i_0_18050,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_10973]),
    [final] ).

cnf(i_0_18051,plain,
    c_Relation_Otrans(tc_fun(X1,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(X1)),
    inference(split_conjunct,[status(thm)],[i_0_10974]),
    [final] ).

cnf(i_0_18052,plain,
    c_Wellfounded_Owf(tc_fun(X1,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(X1)),
    inference(split_conjunct,[status(thm)],[i_0_10975]),
    [final] ).

cnf(i_0_18053,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),hAPP(c_Com_Ocom_OBODY,X1)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[i_0_10976]),
    [final] ).

cnf(i_0_18054,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_10977]),
    [final] ).

cnf(i_0_18055,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_10197]),
    [final] ).

cnf(i_0_18056,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_9917]),
    [final] ).

cnf(i_0_18057,plain,
    hAPP(c_Com_Ocom_OBODY,X1) != c_Com_Ocom_OWhile(X2,X3),
    inference(split_conjunct,[status(thm)],[i_0_10978]),
    [final] ).

cnf(i_0_18058,plain,
    hAPP(c_Com_Ocom_OBODY,X1) != c_Com_Ocom_OAss(X2,X3),
    inference(split_conjunct,[status(thm)],[i_0_10979]),
    [final] ).

cnf(i_0_18059,plain,
    hAPP(c_Com_Ocom_OBODY,X1) != c_Com_Ocom_OSemi(X2,X3),
    inference(split_conjunct,[status(thm)],[i_0_10980]),
    [final] ).

cnf(i_0_18060,plain,
    c_Com_Ocom_OWhile(X1,X2) != hAPP(c_Com_Ocom_OBODY,X3),
    inference(split_conjunct,[status(thm)],[i_0_10981]),
    [final] ).

cnf(i_0_18061,plain,
    c_Com_Ocom_OAss(X1,X2) != hAPP(c_Com_Ocom_OBODY,X3),
    inference(split_conjunct,[status(thm)],[i_0_10982]),
    [final] ).

cnf(i_0_18062,plain,
    c_Com_Ocom_OSemi(X1,X2) != hAPP(c_Com_Ocom_OBODY,X3),
    inference(split_conjunct,[status(thm)],[i_0_10983]),
    [final] ).

cnf(i_0_18063,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_10984,c_0_6064]),
    [final] ).

cnf(i_0_18064,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_10985,c_0_6063]),
    [final] ).

cnf(i_0_18065,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_10986,c_0_6216]),
    [final] ).

cnf(i_0_18066,plain,
    ( X1 = X2
    | hAPP(c_Code__Numeral_Onat__of,X1) != hAPP(c_Code__Numeral_Onat__of,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10987]),
    [final] ).

cnf(i_0_18067,plain,
    ( X1 = X2
    | hAPP(c_Code__Numeral_Onat__of,X1) != hAPP(c_Code__Numeral_Onat__of,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10988]),
    [final] ).

cnf(i_0_18068,plain,
    ( X1 = X2
    | hAPP(c_Code__Numeral_Oof__nat,X1) != hAPP(c_Code__Numeral_Oof__nat,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10989]),
    [final] ).

cnf(i_0_18069,plain,
    ( X1 = X2
    | hAPP(c_Int_ORep__Integ,X1) != hAPP(c_Int_ORep__Integ,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10990]),
    [final] ).

cnf(i_0_18070,plain,
    ( X1 = X2
    | hAPP(c_Nat_OSuc,X1) != hAPP(c_Nat_OSuc,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10991]),
    [final] ).

cnf(i_0_18071,plain,
    ( X1 = X2
    | hAPP(c_Nat_OSuc,X1) != hAPP(c_Nat_OSuc,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10992]),
    [final] ).

cnf(i_0_18072,plain,
    ( X1 = X2
    | hAPP(c_Com_Ocom_OBODY,X1) != hAPP(c_Com_Ocom_OBODY,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10993]),
    [final] ).

cnf(i_0_18073,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_10994]),
    [final] ).

cnf(i_0_18074,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_10995]),
    [final] ).

cnf(i_0_18075,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_10996]),
    [final] ).

cnf(i_0_18076,plain,
    c_Relation_Osym(X1,c_Relation_OId__on(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_10997]),
    [final] ).

cnf(i_0_18077,plain,
    c_Relation_Oantisym(X1,c_Relation_OId__on(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_10998]),
    [final] ).

cnf(i_0_18078,plain,
    c_Relation_Otrans(X1,c_Transitive__Closure_Ortrancl(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_10999]),
    [final] ).

cnf(i_0_18079,plain,
    c_Relation_Otrans(X1,c_Relation_OId__on(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_11000]),
    [final] ).

cnf(i_0_18080,plain,
    c_Wellfounded_Owf(X1,c_List_Omeasures(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_11001]),
    [final] ).

cnf(i_0_18081,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_10925]),
    [final] ).

cnf(i_0_18082,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_10926]),
    [final] ).

cnf(i_0_18083,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_10924]),
    [final] ).

cnf(i_0_18084,plain,
    ( ~ class_Rings_Osemiring__1(X1)
    | ~ c_Int_Oiszero(X1,c_Groups_Oone__class_Oone(X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_11002]),
    [final] ).

cnf(i_0_18085,plain,
    c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_11003]),
    [final] ).

cnf(i_0_18086,plain,
    c_Hilbert__Choice_OEps(X1,hAPP(c_fequal,X2)) = X2,
    inference(split_conjunct,[status(thm)],[i_0_11004]),
    [final] ).

cnf(i_0_18087,plain,
    c_HOL_OThe(X1,hAPP(c_fequal,X2)) = X2,
    inference(split_conjunct,[status(thm)],[i_0_11005]),
    [final] ).

cnf(i_0_18088,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_11006]),
    [final] ).

cnf(i_0_18089,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_11007]),
    [final] ).

cnf(i_0_18090,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_11008]),
    [final] ).

cnf(i_0_18091,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_11009]),
    [final] ).

cnf(i_0_18092,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_11010]),
    [final] ).

cnf(i_0_18093,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_11011]),
    [final] ).

cnf(i_0_18094,plain,
    ( class_Lattices_Obounded__lattice(tc_fun(X2,X1))
    | ~ class_Lattices_Obounded__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11012]),
    [final] ).

cnf(i_0_18095,plain,
    ( class_Lattices_Obounded__lattice__top(tc_fun(X2,X1))
    | ~ class_Lattices_Obounded__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11013]),
    [final] ).

cnf(i_0_18096,plain,
    ( class_Orderings_Otop(tc_fun(X2,X1))
    | ~ class_Orderings_Otop(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11014]),
    [final] ).

cnf(i_0_18097,plain,
    ( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X2,X1))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11015]),
    [final] ).

cnf(i_0_18098,plain,
    ( class_Lattices_Odistrib__lattice(tc_fun(X2,X1))
    | ~ class_Lattices_Odistrib__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11016]),
    [final] ).

cnf(i_0_18099,plain,
    ( class_Lattices_Osemilattice__inf(tc_fun(X2,X1))
    | ~ class_Lattices_Olattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11017]),
    [final] ).

cnf(i_0_18100,plain,
    ( class_Lattices_Olattice(tc_fun(X2,X1))
    | ~ class_Lattices_Olattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11018]),
    [final] ).

cnf(i_0_18101,plain,
    ( class_Lattices_Osemilattice__sup(tc_fun(X2,X1))
    | ~ class_Lattices_Olattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11019]),
    [final] ).

cnf(i_0_18102,plain,
    ( class_Lattices_Obounded__lattice__bot(tc_fun(X2,X1))
    | ~ class_Lattices_Obounded__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11020]),
    [final] ).

cnf(i_0_18103,plain,
    ( class_Groups_Ominus(tc_fun(X2,X1))
    | ~ class_Groups_Ominus(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11021]),
    [final] ).

cnf(i_0_18104,plain,
    ( class_Groups_Ouminus(tc_fun(X2,X1))
    | ~ class_Groups_Ouminus(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11022]),
    [final] ).

cnf(i_0_18105,plain,
    ( class_Lattices_Oboolean__algebra(tc_fun(X2,X1))
    | ~ class_Lattices_Oboolean__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11023]),
    [final] ).

cnf(i_0_18106,plain,
    ( class_Orderings_Oord(tc_fun(X2,X1))
    | ~ class_Orderings_Oord(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11024]),
    [final] ).

cnf(i_0_18107,plain,
    ( class_Orderings_Oorder(tc_fun(X2,X1))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11025]),
    [final] ).

cnf(i_0_18108,plain,
    ( class_Orderings_Opreorder(tc_fun(X2,X1))
    | ~ class_Orderings_Opreorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11026]),
    [final] ).

cnf(i_0_18109,plain,
    ( class_Orderings_Obot(tc_fun(X2,X1))
    | ~ class_Orderings_Obot(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11027]),
    [final] ).

cnf(i_0_18110,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_5241]),
    [final] ).

cnf(i_0_18111,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_10939]),
    [final] ).

cnf(i_0_18112,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_10940]),
    [final] ).

cnf(i_0_18113,plain,
    ( c_Equiv__Relations_Opart__equivp(X1,X2)
    | ~ c_Equiv__Relations_Oequivp(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_11028]),
    [final] ).

cnf(i_0_18114,plain,
    ( c_Predicate_Osymp(X1,X2)
    | ~ c_Equiv__Relations_Opart__equivp(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9942]),
    [final] ).

cnf(i_0_18115,plain,
    ( c_Predicate_Osymp(X1,X2)
    | ~ c_Equiv__Relations_Opart__equivp(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9943]),
    [final] ).

cnf(i_0_18116,plain,
    ( c_Predicate_Osymp(X1,X2)
    | ~ c_Equiv__Relations_Oequivp(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10723]),
    [final] ).

cnf(i_0_18117,plain,
    ( c_Predicate_Osymp(X1,X2)
    | ~ c_Equiv__Relations_Oequivp(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_11029]),
    [final] ).

cnf(i_0_18118,plain,
    ( c_Predicate_Otransp(X1,X2)
    | ~ c_Equiv__Relations_Opart__equivp(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9942]),
    [final] ).

cnf(i_0_18119,plain,
    ( c_Predicate_Otransp(X1,X2)
    | ~ c_Equiv__Relations_Opart__equivp(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9943]),
    [final] ).

cnf(i_0_18120,plain,
    ( c_Predicate_Otransp(X1,X2)
    | ~ c_Equiv__Relations_Oequivp(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10723]),
    [final] ).

cnf(i_0_18121,plain,
    ( c_Predicate_Otransp(X1,X2)
    | ~ c_Equiv__Relations_Oequivp(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_11029]),
    [final] ).

cnf(i_0_18122,plain,
    ( c_Wellfounded_Oacyclic(X1,X2)
    | ~ c_Nitpick_Owf_H(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9917]),
    [final] ).

cnf(i_0_18123,plain,
    ( c_Wellfounded_Oacyclic(X1,X2)
    | ~ c_Wellfounded_Owf(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_11030]),
    [final] ).

cnf(i_0_18124,plain,
    ( c_Predicate_Oreflp(X1,X2)
    | ~ c_Equiv__Relations_Oequivp(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10723]),
    [final] ).

cnf(i_0_18125,plain,
    ( c_Predicate_Oreflp(X1,X2)
    | ~ c_Equiv__Relations_Oequivp(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_11029]),
    [final] ).

cnf(i_0_18126,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_10949]),
    [final] ).

cnf(i_0_18127,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_10950]),
    [final] ).

cnf(i_0_18128,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_11031]),
    [final] ).

cnf(i_0_18129,plain,
    hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,X1)) = X1,
    inference(split_conjunct,[status(thm)],[i_0_11032]),
    [final] ).

cnf(i_0_18130,plain,
    hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X1)) = X1,
    inference(split_conjunct,[status(thm)],[i_0_11033]),
    [final] ).

cnf(i_0_18131,plain,
    hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X1)) = X1,
    inference(split_conjunct,[status(thm)],[i_0_11034]),
    [final] ).

cnf(i_0_18132,plain,
    hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,X1)) = X1,
    inference(split_conjunct,[status(thm)],[i_0_11035]),
    [final] ).

cnf(i_0_18133,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_11036]),
    [final] ).

cnf(i_0_18134,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_11037]),
    [final] ).

cnf(i_0_18135,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_11038]),
    [final] ).

cnf(i_0_18136,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_11039]),
    [final] ).

cnf(i_0_18137,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_11040]),
    [final] ).

cnf(i_0_18138,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_11041]),
    [final] ).

cnf(i_0_18139,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_11042]),
    [final] ).

cnf(i_0_18140,plain,
    ( X2 = c_List_Olist_ONil(X1)
    | c_List_Oremdups(X1,X2) != c_List_Olist_ONil(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11043]),
    [final] ).

cnf(i_0_18141,plain,
    ( X2 = c_List_Olist_ONil(X1)
    | c_List_Olist_ONil(X1) != c_List_Oremdups(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_11044]),
    [final] ).

cnf(i_0_18142,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_10033]),
    [final] ).

cnf(i_0_18143,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_10994]),
    [final] ).

cnf(i_0_18144,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_10970]),
    [final] ).

cnf(i_0_18145,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_10971]),
    [final] ).

cnf(i_0_18146,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_10972]),
    [final] ).

cnf(i_0_18147,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_18148,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_18149,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_18150,plain,
    c_Com_Ocom_Ocom__size(c_Com_Ocom_OAss(X1,X2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[i_0_11045]),
    [final] ).

cnf(i_0_18151,plain,
    ( hBOOL(X1)
    | hBOOL(hAPP(c_fNot,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_11046]),
    [final] ).

cnf(i_0_18152,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_11047]),
    [final] ).

cnf(i_0_18153,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_11048]),
    [final] ).

cnf(i_0_18154,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_11049]),
    [final] ).

cnf(i_0_18155,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_18156,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | esk348_1(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_9840]),
    [final] ).

cnf(i_0_18157,plain,
    hAPP(c_List_Orev(X1),c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
    inference(split_conjunct,[status(thm)],[i_0_11050]),
    [final] ).

cnf(i_0_18158,plain,
    hAPP(c_List_Otl(X1),c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
    inference(split_conjunct,[status(thm)],[i_0_11051]),
    [final] ).

cnf(i_0_18159,plain,
    hAPP(c_List_Orotate1(X1),c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
    inference(split_conjunct,[status(thm)],[i_0_9819]),
    [final] ).

cnf(i_0_18160,plain,
    class_Nat_Osize(tc_sum(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_11052]),
    [final] ).

cnf(i_0_18161,plain,
    class_Nat_Osize(tc_prod(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_11053]),
    [final] ).

cnf(i_0_18162,plain,
    class_Nat_Osize(tc_Nitpick_Opair__box(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_11054]),
    [final] ).

cnf(i_0_18163,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_7339]),
    [final] ).

cnf(i_0_18164,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_11036]),
    [final] ).

cnf(i_0_18165,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_11055]),
    [final] ).

cnf(i_0_18166,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_11056]),
    [final] ).

cnf(i_0_18167,plain,
    c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY,X1)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[i_0_11057]),
    [final] ).

cnf(i_0_18168,plain,
    ( c_List_Olinorder__class_Osorted(X1,c_List_Olist_ONil(X1))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11058]),
    [final] ).

cnf(i_0_18169,plain,
    ( c_List_Olinorder__class_Osorted(X1,c_List_Olist_ONil(X1))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11059]),
    [final] ).

cnf(i_0_18170,plain,
    ( c_Int_Oiszero(X1,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Osemiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11060]),
    [final] ).

cnf(i_0_18171,plain,
    ( c_List_Oremdups(X2,X1) = c_List_Olist_ONil(X2)
    | X1 != c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_11043]),
    [final] ).

cnf(i_0_18172,plain,
    ( c_List_Olist_ONil(X2) = c_List_Oremdups(X2,X1)
    | X1 != c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_11044]),
    [final] ).

cnf(i_0_18173,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_11037]),
    [final] ).

cnf(i_0_18174,plain,
    hAPP(c_New__DSequence_Opos__empty(X1),X2) = c_Lazy__Sequence_Oempty(X1),
    inference(split_conjunct,[status(thm)],[i_0_11061]),
    [final] ).

cnf(i_0_18175,plain,
    c_List_Oremdups(X1,c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
    inference(split_conjunct,[status(thm)],[i_0_11062]),
    [final] ).

cnf(i_0_18176,plain,
    c_List_Obutlast(X1,c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
    inference(split_conjunct,[status(thm)],[i_0_11063]),
    [final] ).

cnf(i_0_18177,plain,
    hAPP(c_Nat_OSuc,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[i_0_11064]),
    [final] ).

cnf(i_0_18178,plain,
    hAPP(c_Nat_OSuc,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[i_0_11065]),
    [final] ).

cnf(i_0_18179,plain,
    hAPP(c_Nat_OSuc,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[i_0_11066]),
    [final] ).

cnf(i_0_18180,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
    inference(split_conjunct,[status(thm)],[i_0_11067]),
    [final] ).

cnf(i_0_18181,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
    inference(split_conjunct,[status(thm)],[i_0_11068]),
    [final] ).

cnf(i_0_18182,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
    inference(split_conjunct,[status(thm)],[i_0_11069]),
    [final] ).

cnf(i_0_18183,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 = hAPP(c_Nat_OSuc,esk22_1(X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_11070]),
    [final] ).

cnf(i_0_18184,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 = hAPP(c_Nat_OSuc,esk19_1(X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_11071]),
    [final] ).

cnf(i_0_18185,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_18186,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_18187,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_18188,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_18189,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_18190,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_18191,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_18192,plain,
    c_Com_Ocom_OWhile(X1,X2) != c_Com_Ocom_OSKIP,
    inference(split_conjunct,[status(thm)],[i_0_11072]),
    [final] ).

cnf(i_0_18193,plain,
    c_Com_Ocom_OAss(X1,X2) != c_Com_Ocom_OSKIP,
    inference(split_conjunct,[status(thm)],[i_0_11073]),
    [final] ).

cnf(i_0_18194,plain,
    c_Com_Ocom_OSemi(X1,X2) != c_Com_Ocom_OSKIP,
    inference(split_conjunct,[status(thm)],[i_0_11074]),
    [final] ).

cnf(i_0_18195,plain,
    c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(X1,X2),
    inference(split_conjunct,[status(thm)],[i_0_11075]),
    [final] ).

cnf(i_0_18196,plain,
    c_Com_Ocom_OSKIP != c_Com_Ocom_OAss(X1,X2),
    inference(split_conjunct,[status(thm)],[i_0_11076]),
    [final] ).

cnf(i_0_18197,plain,
    c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(X1,X2),
    inference(split_conjunct,[status(thm)],[i_0_11077]),
    [final] ).

cnf(i_0_18198,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_11078]),
    [final] ).

cnf(i_0_18199,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_11079]),
    [final] ).

cnf(i_0_18200,plain,
    hAPP(c_Nat_OSuc,X1) != X1,
    inference(split_conjunct,[status(thm)],[i_0_11080]),
    [final] ).

cnf(i_0_18201,plain,
    X1 != hAPP(c_Nat_OSuc,X1),
    inference(split_conjunct,[status(thm)],[i_0_11081]),
    [final] ).

cnf(i_0_18202,plain,
    hAPP(c_Fun_Oid(X1),X2) = X2,
    inference(split_conjunct,[status(thm)],[i_0_11082]),
    [final] ).

cnf(i_0_18203,plain,
    hAPP(c_Fun_Oid(X1),X2) = X2,
    inference(split_conjunct,[status(thm)],[i_0_11083]),
    [final] ).

cnf(i_0_18204,plain,
    hAPP(c_Set_OCollect(X1),X2) = X2,
    inference(split_conjunct,[status(thm)],[i_0_11084]),
    [final] ).

cnf(i_0_18205,plain,
    hAPP(c_COMBI(X1),X2) = X2,
    inference(split_conjunct,[status(thm)],[i_0_11085]),
    [final] ).

cnf(i_0_18206,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_10275]),
    [final] ).

cnf(i_0_18207,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_5267]),
    [final] ).

cnf(i_0_18208,plain,
    ( c_Nitpick_Onat__gcd(X2,X1) = X2
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_10475]),
    [final] ).

cnf(i_0_18209,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_18210,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_11086]),
    [final] ).

cnf(i_0_18211,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_11087]),
    [final] ).

cnf(i_0_18212,plain,
    hAPP(c_Com_Ocom_OBODY,X1) != c_Com_Ocom_OSKIP,
    inference(split_conjunct,[status(thm)],[i_0_11088]),
    [final] ).

cnf(i_0_18213,plain,
    c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,X1),
    inference(split_conjunct,[status(thm)],[i_0_11089]),
    [final] ).

cnf(i_0_18214,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_10839]),
    [final] ).

cnf(i_0_18215,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_11090]),
    [final] ).

cnf(i_0_18216,plain,
    X1 = hAPP(c_Code__Numeral_Oof__nat,esk564_1(X1)),
    inference(split_conjunct,[status(thm)],[i_0_10184]),
    [final] ).

cnf(i_0_18217,plain,
    X1 = hAPP(c_Int_OAbs__Integ,esk420_1(X1)),
    inference(split_conjunct,[status(thm)],[i_0_8849]),
    [final] ).

cnf(i_0_18218,plain,
    c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(X1)),
    inference(split_conjunct,[status(thm)],[i_0_11091]),
    [final] ).

cnf(i_0_18219,plain,
    c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(X1)),
    inference(split_conjunct,[status(thm)],[i_0_11092]),
    [final] ).

cnf(i_0_18220,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_18221,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[fact_com_Osize_I9_J]),
    [final] ).

cnf(i_0_18222,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_18223,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_18224,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_18225,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_18226,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_18227,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_18228,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_18229,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_18230,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_18231,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_18232,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_18233,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1) = X1,
    inference(split_conjunct,[status(thm)],[i_0_11093]),
    [final] ).

cnf(i_0_18234,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X1) = X1,
    inference(split_conjunct,[status(thm)],[i_0_11094]),
    [final] ).

cnf(i_0_18235,plain,
    ( class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(X1))
    | ~ class_Lazy__Sequence_Osmall__lazy(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11095]),
    [final] ).

cnf(i_0_18236,plain,
    ( class_Enum_Oenum(tc_Option_Ooption(X1))
    | ~ class_Enum_Oenum(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11096]),
    [final] ).

cnf(i_0_18237,plain,
    ( class_Finite__Set_Ofinite(tc_Option_Ooption(X1))
    | ~ class_Finite__Set_Ofinite(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11097]),
    [final] ).

cnf(i_0_18238,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_18239,plain,
    c_Equiv__Relations_Oequivp(X1,c_fequal),
    inference(split_conjunct,[status(thm)],[i_0_11098]),
    [final] ).

cnf(i_0_18240,plain,
    c_Relation_Otrans(tc_Nat_Onat,c_Wellfounded_Oless__than),
    inference(split_conjunct,[status(thm)],[fact_trans__less__than]),
    [final] ).

cnf(i_0_18241,plain,
    c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat),
    inference(split_conjunct,[status(thm)],[fact_wf__pred__nat]),
    [final] ).

cnf(i_0_18242,plain,
    c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than),
    inference(split_conjunct,[status(thm)],[fact_wf__less__than]),
    [final] ).

cnf(i_0_18243,plain,
    class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(X1)),
    inference(split_conjunct,[status(thm)],[i_0_11099]),
    [final] ).

cnf(i_0_18244,plain,
    class_Nat_Osize(tc_List_Olist(X1)),
    inference(split_conjunct,[status(thm)],[i_0_11100]),
    [final] ).

cnf(i_0_18245,plain,
    class_Nat_Osize(tc_Option_Ooption(X1)),
    inference(split_conjunct,[status(thm)],[i_0_11101]),
    [final] ).

cnf(i_0_18246,plain,
    class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(X1)),
    inference(split_conjunct,[status(thm)],[i_0_11102]),
    [final] ).

cnf(i_0_18247,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_18248,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_18249,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_18250,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_18251,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_18252,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_18253,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_18254,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_18255,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_18256,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_18257,plain,
    c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[fact_com_Osize_I1_J]),
    [final] ).

cnf(i_0_18258,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_18259,plain,
    ~ hBOOL(c_fFalse),
    inference(split_conjunct,[status(thm)],[i_0_11103]),
    [final] ).

cnf(i_0_18260,plain,
    class_Lattices_Obounded__lattice(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Obounded__lattice]),
    [final] ).

cnf(i_0_18261,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_18262,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_18263,plain,
    class_Enum_Oenum(tc_Product__Type_Ounit),
    inference(split_conjunct,[status(thm)],[arity_Product____Type__Ounit__Enum_Oenum]),
    [final] ).

cnf(i_0_18264,plain,
    class_Enum_Oenum(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Enum_Oenum]),
    [final] ).

cnf(i_0_18265,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_18266,plain,
    class_Groups_Osemigroup__add(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Osemigroup__add]),
    [final] ).

cnf(i_0_18267,plain,
    class_Groups_Osemigroup__add(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Osemigroup__add]),
    [final] ).

cnf(i_0_18268,plain,
    class_Orderings_Owellorder(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Owellorder]),
    [final] ).

cnf(i_0_18269,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_18270,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_18271,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_18272,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_18273,plain,
    class_Orderings_Otop(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Otop]),
    [final] ).

cnf(i_0_18274,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_18275,plain,
    class_Lattices_Odistrib__lattice(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Lattices_Odistrib__lattice]),
    [final] ).

cnf(i_0_18276,plain,
    class_Lattices_Odistrib__lattice(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Lattices_Odistrib__lattice]),
    [final] ).

cnf(i_0_18277,plain,
    class_Lattices_Odistrib__lattice(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Odistrib__lattice]),
    [final] ).

cnf(i_0_18278,plain,
    class_Lattices_Osemilattice__inf(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Lattices_Osemilattice__inf]),
    [final] ).

cnf(i_0_18279,plain,
    class_Lattices_Osemilattice__inf(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Lattices_Osemilattice__inf]),
    [final] ).

cnf(i_0_18280,plain,
    class_Lattices_Osemilattice__inf(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Osemilattice__inf]),
    [final] ).

cnf(i_0_18281,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_18282,plain,
    class_Finite__Set_Ofinite(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Finite__Set_Ofinite]),
    [final] ).

cnf(i_0_18283,plain,
    class_Lattices_Olattice(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Lattices_Olattice]),
    [final] ).

cnf(i_0_18284,plain,
    class_Lattices_Olattice(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Lattices_Olattice]),
    [final] ).

cnf(i_0_18285,plain,
    class_Lattices_Olattice(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Olattice]),
    [final] ).

cnf(i_0_18286,plain,
    class_Lattices_Osemilattice__sup(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Lattices_Osemilattice__sup]),
    [final] ).

cnf(i_0_18287,plain,
    class_Lattices_Osemilattice__sup(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Lattices_Osemilattice__sup]),
    [final] ).

cnf(i_0_18288,plain,
    class_Lattices_Osemilattice__sup(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Osemilattice__sup]),
    [final] ).

cnf(i_0_18289,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_18290,plain,
    class_Nat_Osize(tc_Code__Evaluation_Oterm),
    inference(split_conjunct,[status(thm)],[arity_Code____Evaluation__Oterm__Nat_Osize]),
    [final] ).

cnf(i_0_18291,plain,
    class_Nat_Osize(tc_Product__Type_Ounit),
    inference(split_conjunct,[status(thm)],[arity_Product____Type__Ounit__Nat_Osize]),
    [final] ).

cnf(i_0_18292,plain,
    class_Nat_Osize(tc_Com_Ovname),
    inference(split_conjunct,[status(thm)],[arity_Com__Ovname__Nat_Osize]),
    [final] ).

cnf(i_0_18293,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_18294,plain,
    class_Nat_Osize(tc_Com_Ostate),
    inference(split_conjunct,[status(thm)],[arity_Com__Ostate__Nat_Osize]),
    [final] ).

cnf(i_0_18295,plain,
    class_Nat_Osize(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Nat_Osize]),
    [final] ).

cnf(i_0_18296,plain,
    class_Nat_Osize(tc_Com_Ocom),
    inference(split_conjunct,[status(thm)],[arity_Com__Ocom__Nat_Osize]),
    [final] ).

cnf(i_0_18297,plain,
    class_Nat_Osize(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Nat_Osize]),
    [final] ).

cnf(i_0_18298,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_18299,plain,
    class_Rings_Osemiring__0(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Osemiring__0]),
    [final] ).

cnf(i_0_18300,plain,
    class_Rings_Osemiring__0(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Osemiring__0]),
    [final] ).

cnf(i_0_18301,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_18302,plain,
    class_Power_Opower(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Power_Opower]),
    [final] ).

cnf(i_0_18303,plain,
    class_Power_Opower(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Power_Opower]),
    [final] ).

cnf(i_0_18304,plain,
    class_Groups_Oabs__if(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oabs__if]),
    [final] ).

cnf(i_0_18305,plain,
    class_Rings_Oordered__ring__abs(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__ring__abs]),
    [final] ).

cnf(i_0_18306,plain,
    class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oordered__ab__group__add__abs]),
    [final] ).

cnf(i_0_18307,plain,
    class_Int_Onumber(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Int_Onumber]),
    [final] ).

cnf(i_0_18308,plain,
    class_Int_Onumber(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Int_Onumber]),
    [final] ).

cnf(i_0_18309,plain,
    class_Int_Onumber(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Int_Onumber]),
    [final] ).

cnf(i_0_18310,plain,
    class_Int_Onumber__ring(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Int_Onumber__ring]),
    [final] ).

cnf(i_0_18311,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_18312,plain,
    class_Groups_Ominus(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ominus]),
    [final] ).

cnf(i_0_18313,plain,
    class_Groups_Ominus(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ominus]),
    [final] ).

cnf(i_0_18314,plain,
    class_Groups_Ominus(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Groups_Ominus]),
    [final] ).

cnf(i_0_18315,plain,
    class_Groups_Ouminus(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ouminus]),
    [final] ).

cnf(i_0_18316,plain,
    class_Groups_Ouminus(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Groups_Ouminus]),
    [final] ).

cnf(i_0_18317,plain,
    class_Divides_Oring__div(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Divides_Oring__div]),
    [final] ).

cnf(i_0_18318,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_18319,plain,
    class_Divides_Osemiring__div(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Divides_Osemiring__div]),
    [final] ).

cnf(i_0_18320,plain,
    class_Divides_Osemiring__div(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Divides_Osemiring__div]),
    [final] ).

cnf(i_0_18321,plain,
    class_Groups_Osgn__if(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Osgn__if]),
    [final] ).

cnf(i_0_18322,plain,
    class_Lattices_Oboolean__algebra(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Oboolean__algebra]),
    [final] ).

cnf(i_0_18323,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_18324,plain,
    class_Rings_Olinordered__semiring(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring]),
    [final] ).

cnf(i_0_18325,plain,
    class_Rings_Olinordered__semiring(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semiring]),
    [final] ).

cnf(i_0_18326,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_18327,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_18328,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_18329,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_18330,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_18331,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_18332,plain,
    class_Rings_Oordered__semiring(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__semiring]),
    [final] ).

cnf(i_0_18333,plain,
    class_Rings_Oordered__semiring(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Oordered__semiring]),
    [final] ).

cnf(i_0_18334,plain,
    class_Rings_Oordered__ring(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__ring]),
    [final] ).

cnf(i_0_18335,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_18336,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_18337,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_18338,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_18339,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_18340,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_18341,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_18342,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_18343,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_18344,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_18345,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_18346,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_18347,plain,
    class_Groups_Omonoid__mult(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Omonoid__mult]),
    [final] ).

cnf(i_0_18348,plain,
    class_Groups_Omonoid__mult(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__mult]),
    [final] ).

cnf(i_0_18349,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_18350,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_18351,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_18352,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_18353,plain,
    class_Groups_Oone(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oone]),
    [final] ).

cnf(i_0_18354,plain,
    class_Groups_Oone(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oone]),
    [final] ).

cnf(i_0_18355,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_18356,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_18357,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_18358,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_18359,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_18360,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_18361,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_18362,plain,
    class_Rings_Olinordered__ring(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__ring]),
    [final] ).

cnf(i_0_18363,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_18364,plain,
    class_Rings_Osemiring(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Osemiring]),
    [final] ).

cnf(i_0_18365,plain,
    class_Rings_Osemiring(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Osemiring]),
    [final] ).

cnf(i_0_18366,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_18367,plain,
    class_Rings_Ocomm__semiring(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring]),
    [final] ).

cnf(i_0_18368,plain,
    class_Rings_Ocomm__semiring(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring]),
    [final] ).

cnf(i_0_18369,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_18370,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_18371,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_18372,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_18373,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_18374,plain,
    class_Rings_Omult__zero(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Omult__zero]),
    [final] ).

cnf(i_0_18375,plain,
    class_Rings_Omult__zero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Omult__zero]),
    [final] ).

cnf(i_0_18376,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_18377,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_18378,plain,
    class_Groups_Ogroup__add(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ogroup__add]),
    [final] ).

cnf(i_0_18379,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_18380,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_18381,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_18382,plain,
    class_Rings_Oring__1(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oring__1]),
    [final] ).

cnf(i_0_18383,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_18384,plain,
    class_Rings_Oring(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oring]),
    [final] ).

cnf(i_0_18385,plain,
    class_Rings_Oidom(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oidom]),
    [final] ).

cnf(i_0_18386,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_18387,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_18388,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_18389,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_18390,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_18391,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_18392,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_18393,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_18394,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_18395,plain,
    class_Rings_Olinordered__semidom(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semidom]),
    [final] ).

cnf(i_0_18396,plain,
    class_Rings_Olinordered__semidom(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semidom]),
    [final] ).

cnf(i_0_18397,plain,
    class_Rings_Olinordered__idom(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__idom]),
    [final] ).

cnf(i_0_18398,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_18399,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_18400,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_18401,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_18402,plain,
    class_Groups_Omonoid__add(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Omonoid__add]),
    [final] ).

cnf(i_0_18403,plain,
    class_Groups_Omonoid__add(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__add]),
    [final] ).

cnf(i_0_18404,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_18405,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_18406,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_18407,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_18408,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_18409,plain,
    class_Orderings_Oord(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Oord]),
    [final] ).

cnf(i_0_18410,plain,
    class_Orderings_Oord(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oord]),
    [final] ).

cnf(i_0_18411,plain,
    class_Orderings_Oord(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oord]),
    [final] ).

cnf(i_0_18412,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_18413,plain,
    class_Orderings_Oorder(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Oorder]),
    [final] ).

cnf(i_0_18414,plain,
    class_Orderings_Oorder(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oorder]),
    [final] ).

cnf(i_0_18415,plain,
    class_Orderings_Oorder(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oorder]),
    [final] ).

cnf(i_0_18416,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_18417,plain,
    class_Orderings_Opreorder(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Opreorder]),
    [final] ).

cnf(i_0_18418,plain,
    class_Orderings_Opreorder(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Opreorder]),
    [final] ).

cnf(i_0_18419,plain,
    class_Orderings_Opreorder(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Opreorder]),
    [final] ).

cnf(i_0_18420,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_18421,plain,
    class_Orderings_Olinorder(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Olinorder]),
    [final] ).

cnf(i_0_18422,plain,
    class_Orderings_Olinorder(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Olinorder]),
    [final] ).

cnf(i_0_18423,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_18424,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_18425,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_18426,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_18427,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_18428,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_18429,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_18430,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_18431,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_18432,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_18433,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_18434,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_18435,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_18436,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_18437,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_18438,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_18439,plain,
    class_Rings_Osemiring__1(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Osemiring__1]),
    [final] ).

cnf(i_0_18440,plain,
    class_Rings_Osemiring__1(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Osemiring__1]),
    [final] ).

cnf(i_0_18441,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_18442,plain,
    class_Groups_Ozero(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ozero]),
    [final] ).

cnf(i_0_18443,plain,
    class_Groups_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ozero]),
    [final] ).

cnf(i_0_18444,plain,
    hBOOL(c_fTrue),
    inference(split_conjunct,[status(thm)],[help_c__fTrue__1]),
    [final] ).

cnf(i_0_18445,plain,
    class_Orderings_Obot(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Obot]),
    [final] ).

cnf(i_0_18446,plain,
    class_Orderings_Obot(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Obot]),
    [final] ).

cnf(i_0_18447,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_18448,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_18449,plain,
    c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[fact_Pls__def]),
    [final] ).

cnf(i_0_18450,plain,
    c_Int_OMin != c_Int_OPls,
    inference(split_conjunct,[status(thm)],[fact_rel__simps_I40_J]),
    [final] ).

cnf(i_0_18451,plain,
    c_Int_OPls != c_Int_OMin,
    inference(split_conjunct,[status(thm)],[fact_rel__simps_I37_J]),
    [final] ).

cnf(i_0_18452,axiom,
    X1 = X1 ).

cnf(i_0_18453,axiom,
    ( X1 = X2
    | X2 != X1 ) ).

cnf(i_0_18454,axiom,
    ( X1 = X2
    | X1 != X3
    | X3 != X2 ) ).

cnf(i_0_18455,axiom,
    ( X1 != X2
    | hAPP(X1,X3) = hAPP(X2,X3) ) ).

cnf(i_0_18456,axiom,
    ( X1 != X2
    | hAPP(X3,X1) = hAPP(X3,X2) ) ).

cnf(i_0_18457,axiom,
    ( X1 != X2
    | c_Big__Operators_Olinorder__class_OMin(X1,X3) = c_Big__Operators_Olinorder__class_OMin(X2,X3) ) ).

cnf(i_0_18458,axiom,
    ( X1 != X2
    | c_Big__Operators_Olinorder__class_OMin(X3,X1) = c_Big__Operators_Olinorder__class_OMin(X3,X2) ) ).

cnf(i_0_18459,axiom,
    ( X1 != X2
    | c_Big__Operators_Olinorder__class_OMax(X1,X3) = c_Big__Operators_Olinorder__class_OMax(X2,X3) ) ).

cnf(i_0_18460,axiom,
    ( X1 != X2
    | c_Big__Operators_Olinorder__class_OMax(X3,X1) = c_Big__Operators_Olinorder__class_OMax(X3,X2) ) ).

cnf(i_0_18461,axiom,
    ( X1 != X2
    | c_List_Olistrel(X1,X3) = c_List_Olistrel(X2,X3) ) ).

cnf(i_0_18462,axiom,
    ( X1 != X2
    | c_List_Olistrel(X3,X1) = c_List_Olistrel(X3,X2) ) ).

cnf(i_0_18463,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_18464,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_18465,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_18466,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_18467,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_18468,axiom,
    ( X1 != X2
    | c_List_Opartition(X1,X3,X4) = c_List_Opartition(X2,X3,X4) ) ).

cnf(i_0_18469,axiom,
    ( X1 != X2
    | c_List_Opartition(X3,X1,X4) = c_List_Opartition(X3,X2,X4) ) ).

cnf(i_0_18470,axiom,
    ( X1 != X2
    | c_List_Opartition(X3,X4,X1) = c_List_Opartition(X3,X4,X2) ) ).

cnf(i_0_18471,axiom,
    ( X1 != X2
    | c_Com_Ocom_OAss(X1,X3) = c_Com_Ocom_OAss(X2,X3) ) ).

cnf(i_0_18472,axiom,
    ( X1 != X2
    | c_Com_Ocom_OAss(X3,X1) = c_Com_Ocom_OAss(X3,X2) ) ).

cnf(i_0_18473,axiom,
    ( X1 != X2
    | c_Wellfounded_Olex__prod(X1,X3,X4,X5) = c_Wellfounded_Olex__prod(X2,X3,X4,X5) ) ).

cnf(i_0_18474,axiom,
    ( X1 != X2
    | c_Wellfounded_Olex__prod(X3,X1,X4,X5) = c_Wellfounded_Olex__prod(X3,X2,X4,X5) ) ).

cnf(i_0_18475,axiom,
    ( X1 != X2
    | c_Wellfounded_Olex__prod(X3,X4,X1,X5) = c_Wellfounded_Olex__prod(X3,X4,X2,X5) ) ).

cnf(i_0_18476,axiom,
    ( X1 != X2
    | c_Wellfounded_Olex__prod(X3,X4,X5,X1) = c_Wellfounded_Olex__prod(X3,X4,X5,X2) ) ).

cnf(i_0_18477,axiom,
    ( X1 != X2
    | c_Power_Opower__class_Opower(X1) = c_Power_Opower__class_Opower(X2) ) ).

cnf(i_0_18478,axiom,
    ( X1 != X2
    | c_List_Osublist(X1,X3,X4) = c_List_Osublist(X2,X3,X4) ) ).

cnf(i_0_18479,axiom,
    ( X1 != X2
    | c_List_Osublist(X3,X1,X4) = c_List_Osublist(X3,X2,X4) ) ).

cnf(i_0_18480,axiom,
    ( X1 != X2
    | c_List_Osublist(X3,X4,X1) = c_List_Osublist(X3,X4,X2) ) ).

cnf(i_0_18481,axiom,
    ( X1 != X2
    | c_List_Otranspose(X1,X3) = c_List_Otranspose(X2,X3) ) ).

cnf(i_0_18482,axiom,
    ( X1 != X2
    | c_List_Otranspose(X3,X1) = c_List_Otranspose(X3,X2) ) ).

cnf(i_0_18483,axiom,
    ( X1 != X2
    | c_List_Olist_ONil(X1) = c_List_Olist_ONil(X2) ) ).

cnf(i_0_18484,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_18485,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_18486,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_18487,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_18488,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_18489,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_18490,axiom,
    ( X1 != X2
    | c_Complete__Lattice_OInf__class_OInf(X1,X3) = c_Complete__Lattice_OInf__class_OInf(X2,X3) ) ).

cnf(i_0_18491,axiom,
    ( X1 != X2
    | c_Complete__Lattice_OInf__class_OInf(X3,X1) = c_Complete__Lattice_OInf__class_OInf(X3,X2) ) ).

cnf(i_0_18492,axiom,
    ( X1 != X2
    | c_Complete__Lattice_OSup__class_OSup(X1,X3) = c_Complete__Lattice_OSup__class_OSup(X2,X3) ) ).

cnf(i_0_18493,axiom,
    ( X1 != X2
    | c_Complete__Lattice_OSup__class_OSup(X3,X1) = c_Complete__Lattice_OSup__class_OSup(X3,X2) ) ).

cnf(i_0_18494,axiom,
    ( X1 != X2
    | c_Divides_Odivmod__int__rel(X1,X3) = c_Divides_Odivmod__int__rel(X2,X3) ) ).

cnf(i_0_18495,axiom,
    ( X1 != X2
    | c_Divides_Odivmod__int__rel(X3,X1) = c_Divides_Odivmod__int__rel(X3,X2) ) ).

cnf(i_0_18496,axiom,
    ( X1 != X2
    | c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ozero__class_Ozero(X2) ) ).

cnf(i_0_18497,axiom,
    ( X1 != X2
    | c_Set_Othe__elem(X1,X3) = c_Set_Othe__elem(X2,X3) ) ).

cnf(i_0_18498,axiom,
    ( X1 != X2
    | c_Set_Othe__elem(X3,X1) = c_Set_Othe__elem(X3,X2) ) ).

cnf(i_0_18499,axiom,
    ( X1 != X2
    | c_Nitpick_Osetsum_H(X1,X3,X4,X5) = c_Nitpick_Osetsum_H(X2,X3,X4,X5) ) ).

cnf(i_0_18500,axiom,
    ( X1 != X2
    | c_Nitpick_Osetsum_H(X3,X1,X4,X5) = c_Nitpick_Osetsum_H(X3,X2,X4,X5) ) ).

cnf(i_0_18501,axiom,
    ( X1 != X2
    | c_Nitpick_Osetsum_H(X3,X4,X1,X5) = c_Nitpick_Osetsum_H(X3,X4,X2,X5) ) ).

cnf(i_0_18502,axiom,
    ( X1 != X2
    | c_Nitpick_Osetsum_H(X3,X4,X5,X1) = c_Nitpick_Osetsum_H(X3,X4,X5,X2) ) ).

cnf(i_0_18503,axiom,
    ( X1 != X2
    | c_List_Omonoid__add__class_Olistsum(X1) = c_List_Omonoid__add__class_Olistsum(X2) ) ).

cnf(i_0_18504,axiom,
    ( X1 != X2
    | c_Hilbert__Choice_OEps(X1,X3) = c_Hilbert__Choice_OEps(X2,X3) ) ).

cnf(i_0_18505,axiom,
    ( X1 != X2
    | c_Hilbert__Choice_OEps(X3,X1) = c_Hilbert__Choice_OEps(X3,X2) ) ).

cnf(i_0_18506,axiom,
    ( X1 != X2
    | esk559_6(X1,X3,X4,X5,X6,X7) = esk559_6(X2,X3,X4,X5,X6,X7) ) ).

cnf(i_0_18507,axiom,
    ( X1 != X2
    | esk559_6(X3,X1,X4,X5,X6,X7) = esk559_6(X3,X2,X4,X5,X6,X7) ) ).

cnf(i_0_18508,axiom,
    ( X1 != X2
    | esk559_6(X3,X4,X1,X5,X6,X7) = esk559_6(X3,X4,X2,X5,X6,X7) ) ).

cnf(i_0_18509,axiom,
    ( X1 != X2
    | esk559_6(X3,X4,X5,X1,X6,X7) = esk559_6(X3,X4,X5,X2,X6,X7) ) ).

cnf(i_0_18510,axiom,
    ( X1 != X2
    | esk559_6(X3,X4,X5,X6,X1,X7) = esk559_6(X3,X4,X5,X6,X2,X7) ) ).

cnf(i_0_18511,axiom,
    ( X1 != X2
    | esk559_6(X3,X4,X5,X6,X7,X1) = esk559_6(X3,X4,X5,X6,X7,X2) ) ).

cnf(i_0_18512,axiom,
    ( X1 != X2
    | esk560_6(X1,X3,X4,X5,X6,X7) = esk560_6(X2,X3,X4,X5,X6,X7) ) ).

cnf(i_0_18513,axiom,
    ( X1 != X2
    | esk560_6(X3,X1,X4,X5,X6,X7) = esk560_6(X3,X2,X4,X5,X6,X7) ) ).

cnf(i_0_18514,axiom,
    ( X1 != X2
    | esk560_6(X3,X4,X1,X5,X6,X7) = esk560_6(X3,X4,X2,X5,X6,X7) ) ).

cnf(i_0_18515,axiom,
    ( X1 != X2
    | esk560_6(X3,X4,X5,X1,X6,X7) = esk560_6(X3,X4,X5,X2,X6,X7) ) ).

cnf(i_0_18516,axiom,
    ( X1 != X2
    | esk560_6(X3,X4,X5,X6,X1,X7) = esk560_6(X3,X4,X5,X6,X2,X7) ) ).

cnf(i_0_18517,axiom,
    ( X1 != X2
    | esk560_6(X3,X4,X5,X6,X7,X1) = esk560_6(X3,X4,X5,X6,X7,X2) ) ).

cnf(i_0_18518,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_18519,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_18520,axiom,
    ( X1 != X2
    | c_Groups_Ominus__class_Ominus(X1) = c_Groups_Ominus__class_Ominus(X2) ) ).

cnf(i_0_18521,axiom,
    ( X1 != X2
    | c_Random__Sequence_ORandom(X1,X3,X4,X5) = c_Random__Sequence_ORandom(X2,X3,X4,X5) ) ).

cnf(i_0_18522,axiom,
    ( X1 != X2
    | c_Random__Sequence_ORandom(X3,X1,X4,X5) = c_Random__Sequence_ORandom(X3,X2,X4,X5) ) ).

cnf(i_0_18523,axiom,
    ( X1 != X2
    | c_Random__Sequence_ORandom(X3,X4,X1,X5) = c_Random__Sequence_ORandom(X3,X4,X2,X5) ) ).

cnf(i_0_18524,axiom,
    ( X1 != X2
    | c_Random__Sequence_ORandom(X3,X4,X5,X1) = c_Random__Sequence_ORandom(X3,X4,X5,X2) ) ).

cnf(i_0_18525,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohb__not__seq(X1) = c_Lazy__Sequence_Ohb__not__seq(X2) ) ).

cnf(i_0_18526,axiom,
    ( X1 != X2
    | c_Wellfounded_Omax__ext(X1,X3) = c_Wellfounded_Omax__ext(X2,X3) ) ).

cnf(i_0_18527,axiom,
    ( X1 != X2
    | c_Wellfounded_Omax__ext(X3,X1) = c_Wellfounded_Omax__ext(X3,X2) ) ).

cnf(i_0_18528,axiom,
    ( X1 != X2
    | c_Divides_Odiv__class_Omod(X1,X3,X4) = c_Divides_Odiv__class_Omod(X2,X3,X4) ) ).

cnf(i_0_18529,axiom,
    ( X1 != X2
    | c_Divides_Odiv__class_Omod(X3,X1,X4) = c_Divides_Odiv__class_Omod(X3,X2,X4) ) ).

cnf(i_0_18530,axiom,
    ( X1 != X2
    | c_Divides_Odiv__class_Omod(X3,X4,X1) = c_Divides_Odiv__class_Omod(X3,X4,X2) ) ).

cnf(i_0_18531,axiom,
    ( X1 != X2
    | c_Wellfounded_Omin__ext(X1,X3) = c_Wellfounded_Omin__ext(X2,X3) ) ).

cnf(i_0_18532,axiom,
    ( X1 != X2
    | c_Wellfounded_Omin__ext(X3,X1) = c_Wellfounded_Omin__ext(X3,X2) ) ).

cnf(i_0_18533,axiom,
    ( X1 != X2
    | c_Com_Ocom_OCond(X1,X3,X4) = c_Com_Ocom_OCond(X2,X3,X4) ) ).

cnf(i_0_18534,axiom,
    ( X1 != X2
    | c_Com_Ocom_OCond(X3,X1,X4) = c_Com_Ocom_OCond(X3,X2,X4) ) ).

cnf(i_0_18535,axiom,
    ( X1 != X2
    | c_Com_Ocom_OCond(X3,X4,X1) = c_Com_Ocom_OCond(X3,X4,X2) ) ).

cnf(i_0_18536,axiom,
    ( X1 != X2
    | c_Wellfounded_Ofinite__psubset(X1) = c_Wellfounded_Ofinite__psubset(X2) ) ).

cnf(i_0_18537,axiom,
    ( X1 != X2
    | c_Nitpick_Ocard_H(X1,X3) = c_Nitpick_Ocard_H(X2,X3) ) ).

cnf(i_0_18538,axiom,
    ( X1 != X2
    | c_Nitpick_Ocard_H(X3,X1) = c_Nitpick_Ocard_H(X3,X2) ) ).

cnf(i_0_18539,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_18540,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_18541,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_18542,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_18543,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_18544,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_18545,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_18546,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_18547,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_18548,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_18549,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_18550,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_18551,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_18552,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_18553,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_18554,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_18555,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_18556,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_18557,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_18558,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_18559,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_18560,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_18561,axiom,
    ( X1 != X2
    | c_Int_Onumber__class_Onumber__of(X1) = c_Int_Onumber__class_Onumber__of(X2) ) ).

cnf(i_0_18562,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_18563,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_18564,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oappend(X1,X3,X4) = c_Lazy__Sequence_Oappend(X2,X3,X4) ) ).

cnf(i_0_18565,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oappend(X3,X1,X4) = c_Lazy__Sequence_Oappend(X3,X2,X4) ) ).

cnf(i_0_18566,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oappend(X3,X4,X1) = c_Lazy__Sequence_Oappend(X3,X4,X2) ) ).

cnf(i_0_18567,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oproduct(X1,X3,X4,X5) = c_Lazy__Sequence_Oproduct(X2,X3,X4,X5) ) ).

cnf(i_0_18568,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oproduct(X3,X1,X4,X5) = c_Lazy__Sequence_Oproduct(X3,X2,X4,X5) ) ).

cnf(i_0_18569,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oproduct(X3,X4,X1,X5) = c_Lazy__Sequence_Oproduct(X3,X4,X2,X5) ) ).

cnf(i_0_18570,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oproduct(X3,X4,X5,X1) = c_Lazy__Sequence_Oproduct(X3,X4,X5,X2) ) ).

cnf(i_0_18571,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oempty(X1) = c_Lazy__Sequence_Oempty(X2) ) ).

cnf(i_0_18572,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_18573,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_18574,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_18575,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_18576,axiom,
    ( X1 != X2
    | c_New__DSequence_Oneg__bind(X1,X3,X4,X5) = c_New__DSequence_Oneg__bind(X2,X3,X4,X5) ) ).

cnf(i_0_18577,axiom,
    ( X1 != X2
    | c_New__DSequence_Oneg__bind(X3,X1,X4,X5) = c_New__DSequence_Oneg__bind(X3,X2,X4,X5) ) ).

cnf(i_0_18578,axiom,
    ( X1 != X2
    | c_New__DSequence_Oneg__bind(X3,X4,X1,X5) = c_New__DSequence_Oneg__bind(X3,X4,X2,X5) ) ).

cnf(i_0_18579,axiom,
    ( X1 != X2
    | c_New__DSequence_Oneg__bind(X3,X4,X5,X1) = c_New__DSequence_Oneg__bind(X3,X4,X5,X2) ) ).

cnf(i_0_18580,axiom,
    ( X1 != X2
    | c_Groups_Oone__class_Oone(X1) = c_Groups_Oone__class_Oone(X2) ) ).

cnf(i_0_18581,axiom,
    ( X1 != X2
    | esk450_5(X1,X3,X4,X5,X6) = esk450_5(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18582,axiom,
    ( X1 != X2
    | esk450_5(X3,X1,X4,X5,X6) = esk450_5(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18583,axiom,
    ( X1 != X2
    | esk450_5(X3,X4,X1,X5,X6) = esk450_5(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18584,axiom,
    ( X1 != X2
    | esk450_5(X3,X4,X5,X1,X6) = esk450_5(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18585,axiom,
    ( X1 != X2
    | esk450_5(X3,X4,X5,X6,X1) = esk450_5(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18586,axiom,
    ( X1 != X2
    | esk451_5(X1,X3,X4,X5,X6) = esk451_5(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18587,axiom,
    ( X1 != X2
    | esk451_5(X3,X1,X4,X5,X6) = esk451_5(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18588,axiom,
    ( X1 != X2
    | esk451_5(X3,X4,X1,X5,X6) = esk451_5(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18589,axiom,
    ( X1 != X2
    | esk451_5(X3,X4,X5,X1,X6) = esk451_5(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18590,axiom,
    ( X1 != X2
    | esk451_5(X3,X4,X5,X6,X1) = esk451_5(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18591,axiom,
    ( X1 != X2
    | esk449_5(X1,X3,X4,X5,X6) = esk449_5(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18592,axiom,
    ( X1 != X2
    | esk449_5(X3,X1,X4,X5,X6) = esk449_5(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18593,axiom,
    ( X1 != X2
    | esk449_5(X3,X4,X1,X5,X6) = esk449_5(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18594,axiom,
    ( X1 != X2
    | esk449_5(X3,X4,X5,X1,X6) = esk449_5(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18595,axiom,
    ( X1 != X2
    | esk449_5(X3,X4,X5,X6,X1) = esk449_5(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18596,axiom,
    ( X1 != X2
    | esk448_5(X1,X3,X4,X5,X6) = esk448_5(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18597,axiom,
    ( X1 != X2
    | esk448_5(X3,X1,X4,X5,X6) = esk448_5(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18598,axiom,
    ( X1 != X2
    | esk448_5(X3,X4,X1,X5,X6) = esk448_5(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18599,axiom,
    ( X1 != X2
    | esk448_5(X3,X4,X5,X1,X6) = esk448_5(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18600,axiom,
    ( X1 != X2
    | esk448_5(X3,X4,X5,X6,X1) = esk448_5(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18601,axiom,
    ( X1 != X2
    | c_HOL_OThe(X1,X3) = c_HOL_OThe(X2,X3) ) ).

cnf(i_0_18602,axiom,
    ( X1 != X2
    | c_HOL_OThe(X3,X1) = c_HOL_OThe(X3,X2) ) ).

cnf(i_0_18603,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Opos__bind(X1,X3,X4,X5) = c_New__Random__Sequence_Opos__bind(X2,X3,X4,X5) ) ).

cnf(i_0_18604,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Opos__bind(X3,X1,X4,X5) = c_New__Random__Sequence_Opos__bind(X3,X2,X4,X5) ) ).

cnf(i_0_18605,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Opos__bind(X3,X4,X1,X5) = c_New__Random__Sequence_Opos__bind(X3,X4,X2,X5) ) ).

cnf(i_0_18606,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Opos__bind(X3,X4,X5,X1) = c_New__Random__Sequence_Opos__bind(X3,X4,X5,X2) ) ).

cnf(i_0_18607,axiom,
    ( X1 != X2
    | c_New__DSequence_Opos__bind(X1,X3,X4,X5) = c_New__DSequence_Opos__bind(X2,X3,X4,X5) ) ).

cnf(i_0_18608,axiom,
    ( X1 != X2
    | c_New__DSequence_Opos__bind(X3,X1,X4,X5) = c_New__DSequence_Opos__bind(X3,X2,X4,X5) ) ).

cnf(i_0_18609,axiom,
    ( X1 != X2
    | c_New__DSequence_Opos__bind(X3,X4,X1,X5) = c_New__DSequence_Opos__bind(X3,X4,X2,X5) ) ).

cnf(i_0_18610,axiom,
    ( X1 != X2
    | c_New__DSequence_Opos__bind(X3,X4,X5,X1) = c_New__DSequence_Opos__bind(X3,X4,X5,X2) ) ).

cnf(i_0_18611,axiom,
    ( X1 != X2
    | c_Nitpick_Oprod(X1,X3,X4,X5) = c_Nitpick_Oprod(X2,X3,X4,X5) ) ).

cnf(i_0_18612,axiom,
    ( X1 != X2
    | c_Nitpick_Oprod(X3,X1,X4,X5) = c_Nitpick_Oprod(X3,X2,X4,X5) ) ).

cnf(i_0_18613,axiom,
    ( X1 != X2
    | c_Nitpick_Oprod(X3,X4,X1,X5) = c_Nitpick_Oprod(X3,X4,X2,X5) ) ).

cnf(i_0_18614,axiom,
    ( X1 != X2
    | c_Nitpick_Oprod(X3,X4,X5,X1) = c_Nitpick_Oprod(X3,X4,X5,X2) ) ).

cnf(i_0_18615,axiom,
    ( X1 != X2
    | c_List_OtakeWhile(X1,X3,X4) = c_List_OtakeWhile(X2,X3,X4) ) ).

cnf(i_0_18616,axiom,
    ( X1 != X2
    | c_List_OtakeWhile(X3,X1,X4) = c_List_OtakeWhile(X3,X2,X4) ) ).

cnf(i_0_18617,axiom,
    ( X1 != X2
    | c_List_OtakeWhile(X3,X4,X1) = c_List_OtakeWhile(X3,X4,X2) ) ).

cnf(i_0_18618,axiom,
    ( X1 != X2
    | c_Fun_Oid(X1) = c_Fun_Oid(X2) ) ).

cnf(i_0_18619,axiom,
    ( X1 != X2
    | esk239_6(X1,X3,X4,X5,X6,X7) = esk239_6(X2,X3,X4,X5,X6,X7) ) ).

cnf(i_0_18620,axiom,
    ( X1 != X2
    | esk239_6(X3,X1,X4,X5,X6,X7) = esk239_6(X3,X2,X4,X5,X6,X7) ) ).

cnf(i_0_18621,axiom,
    ( X1 != X2
    | esk239_6(X3,X4,X1,X5,X6,X7) = esk239_6(X3,X4,X2,X5,X6,X7) ) ).

cnf(i_0_18622,axiom,
    ( X1 != X2
    | esk239_6(X3,X4,X5,X1,X6,X7) = esk239_6(X3,X4,X5,X2,X6,X7) ) ).

cnf(i_0_18623,axiom,
    ( X1 != X2
    | esk239_6(X3,X4,X5,X6,X1,X7) = esk239_6(X3,X4,X5,X6,X2,X7) ) ).

cnf(i_0_18624,axiom,
    ( X1 != X2
    | esk239_6(X3,X4,X5,X6,X7,X1) = esk239_6(X3,X4,X5,X6,X7,X2) ) ).

cnf(i_0_18625,axiom,
    ( X1 != X2
    | esk238_6(X1,X3,X4,X5,X6,X7) = esk238_6(X2,X3,X4,X5,X6,X7) ) ).

cnf(i_0_18626,axiom,
    ( X1 != X2
    | esk238_6(X3,X1,X4,X5,X6,X7) = esk238_6(X3,X2,X4,X5,X6,X7) ) ).

cnf(i_0_18627,axiom,
    ( X1 != X2
    | esk238_6(X3,X4,X1,X5,X6,X7) = esk238_6(X3,X4,X2,X5,X6,X7) ) ).

cnf(i_0_18628,axiom,
    ( X1 != X2
    | esk238_6(X3,X4,X5,X1,X6,X7) = esk238_6(X3,X4,X5,X2,X6,X7) ) ).

cnf(i_0_18629,axiom,
    ( X1 != X2
    | esk238_6(X3,X4,X5,X6,X1,X7) = esk238_6(X3,X4,X5,X6,X2,X7) ) ).

cnf(i_0_18630,axiom,
    ( X1 != X2
    | esk238_6(X3,X4,X5,X6,X7,X1) = esk238_6(X3,X4,X5,X6,X7,X2) ) ).

cnf(i_0_18631,axiom,
    ( X1 != X2
    | c_Enum_On__lists(X1,X3,X4) = c_Enum_On__lists(X2,X3,X4) ) ).

cnf(i_0_18632,axiom,
    ( X1 != X2
    | c_Enum_On__lists(X3,X1,X4) = c_Enum_On__lists(X3,X2,X4) ) ).

cnf(i_0_18633,axiom,
    ( X1 != X2
    | c_Enum_On__lists(X3,X4,X1) = c_Enum_On__lists(X3,X4,X2) ) ).

cnf(i_0_18634,axiom,
    ( X1 != X2
    | c_Nitpick_Otimes__frac(X1,X3,X4) = c_Nitpick_Otimes__frac(X2,X3,X4) ) ).

cnf(i_0_18635,axiom,
    ( X1 != X2
    | c_Nitpick_Otimes__frac(X3,X1,X4) = c_Nitpick_Otimes__frac(X3,X2,X4) ) ).

cnf(i_0_18636,axiom,
    ( X1 != X2
    | c_Nitpick_Otimes__frac(X3,X4,X1) = c_Nitpick_Otimes__frac(X3,X4,X2) ) ).

cnf(i_0_18637,axiom,
    ( X1 != X2
    | c_Divides_OnegDivAlg(X1,X3) = c_Divides_OnegDivAlg(X2,X3) ) ).

cnf(i_0_18638,axiom,
    ( X1 != X2
    | c_Divides_OnegDivAlg(X3,X1) = c_Divides_OnegDivAlg(X3,X2) ) ).

cnf(i_0_18639,axiom,
    ( X1 != X2
    | c_Divides_OposDivAlg(X1,X3) = c_Divides_OposDivAlg(X2,X3) ) ).

cnf(i_0_18640,axiom,
    ( X1 != X2
    | c_Divides_OposDivAlg(X3,X1) = c_Divides_OposDivAlg(X3,X2) ) ).

cnf(i_0_18641,axiom,
    ( X1 != X2
    | c_Nat_Osemiring__1__class_Oof__nat(X1) = c_Nat_Osemiring__1__class_Oof__nat(X2) ) ).

cnf(i_0_18642,axiom,
    ( X1 != X2
    | c_Nat_Onat_Onat__case(X1,X3,X4,X5) = c_Nat_Onat_Onat__case(X2,X3,X4,X5) ) ).

cnf(i_0_18643,axiom,
    ( X1 != X2
    | c_Nat_Onat_Onat__case(X3,X1,X4,X5) = c_Nat_Onat_Onat__case(X3,X2,X4,X5) ) ).

cnf(i_0_18644,axiom,
    ( X1 != X2
    | c_Nat_Onat_Onat__case(X3,X4,X1,X5) = c_Nat_Onat_Onat__case(X3,X4,X2,X5) ) ).

cnf(i_0_18645,axiom,
    ( X1 != X2
    | c_Nat_Onat_Onat__case(X3,X4,X5,X1) = c_Nat_Onat_Onat__case(X3,X4,X5,X2) ) ).

cnf(i_0_18646,axiom,
    ( X1 != X2
    | c_Relation_OId__on(X1,X3) = c_Relation_OId__on(X2,X3) ) ).

cnf(i_0_18647,axiom,
    ( X1 != X2
    | c_Relation_OId__on(X3,X1) = c_Relation_OId__on(X3,X2) ) ).

cnf(i_0_18648,axiom,
    ( X1 != X2
    | c_Int_Oint__ge__less__than(X1) = c_Int_Oint__ge__less__than(X2) ) ).

cnf(i_0_18649,axiom,
    ( X1 != X2
    | c_List_Olistrel1(X1,X3) = c_List_Olistrel1(X2,X3) ) ).

cnf(i_0_18650,axiom,
    ( X1 != X2
    | c_List_Olistrel1(X3,X1) = c_List_Olistrel1(X3,X2) ) ).

cnf(i_0_18651,axiom,
    ( X1 != X2
    | c_Finite__Set_Ofold(X1,X3,X4) = c_Finite__Set_Ofold(X2,X3,X4) ) ).

cnf(i_0_18652,axiom,
    ( X1 != X2
    | c_Finite__Set_Ofold(X3,X1,X4) = c_Finite__Set_Ofold(X3,X2,X4) ) ).

cnf(i_0_18653,axiom,
    ( X1 != X2
    | c_Finite__Set_Ofold(X3,X4,X1) = c_Finite__Set_Ofold(X3,X4,X2) ) ).

cnf(i_0_18654,axiom,
    ( X1 != X2
    | c_Nitpick_Ouminus__frac(X1,X3) = c_Nitpick_Ouminus__frac(X2,X3) ) ).

cnf(i_0_18655,axiom,
    ( X1 != X2
    | c_Nitpick_Ouminus__frac(X3,X1) = c_Nitpick_Ouminus__frac(X3,X2) ) ).

cnf(i_0_18656,axiom,
    ( X1 != X2
    | c_Nitpick_OAbs__Frac(X1,X3) = c_Nitpick_OAbs__Frac(X2,X3) ) ).

cnf(i_0_18657,axiom,
    ( X1 != X2
    | c_Nitpick_OAbs__Frac(X3,X1) = c_Nitpick_OAbs__Frac(X3,X2) ) ).

cnf(i_0_18658,axiom,
    ( X1 != X2
    | esk345_4(X1,X3,X4,X5) = esk345_4(X2,X3,X4,X5) ) ).

cnf(i_0_18659,axiom,
    ( X1 != X2
    | esk345_4(X3,X1,X4,X5) = esk345_4(X3,X2,X4,X5) ) ).

cnf(i_0_18660,axiom,
    ( X1 != X2
    | esk345_4(X3,X4,X1,X5) = esk345_4(X3,X4,X2,X5) ) ).

cnf(i_0_18661,axiom,
    ( X1 != X2
    | esk345_4(X3,X4,X5,X1) = esk345_4(X3,X4,X5,X2) ) ).

cnf(i_0_18662,axiom,
    ( X1 != X2
    | esk344_4(X1,X3,X4,X5) = esk344_4(X2,X3,X4,X5) ) ).

cnf(i_0_18663,axiom,
    ( X1 != X2
    | esk344_4(X3,X1,X4,X5) = esk344_4(X3,X2,X4,X5) ) ).

cnf(i_0_18664,axiom,
    ( X1 != X2
    | esk344_4(X3,X4,X1,X5) = esk344_4(X3,X4,X2,X5) ) ).

cnf(i_0_18665,axiom,
    ( X1 != X2
    | esk344_4(X3,X4,X5,X1) = esk344_4(X3,X4,X5,X2) ) ).

cnf(i_0_18666,axiom,
    ( X1 != X2
    | c_Orderings_Obot__class_Obot(X1) = c_Orderings_Obot__class_Obot(X2) ) ).

cnf(i_0_18667,axiom,
    ( X1 != X2
    | c_Hilbert__Choice_Oinv__into(X1,X3,X4,X5) = c_Hilbert__Choice_Oinv__into(X2,X3,X4,X5) ) ).

cnf(i_0_18668,axiom,
    ( X1 != X2
    | c_Hilbert__Choice_Oinv__into(X3,X1,X4,X5) = c_Hilbert__Choice_Oinv__into(X3,X2,X4,X5) ) ).

cnf(i_0_18669,axiom,
    ( X1 != X2
    | c_Hilbert__Choice_Oinv__into(X3,X4,X1,X5) = c_Hilbert__Choice_Oinv__into(X3,X4,X2,X5) ) ).

cnf(i_0_18670,axiom,
    ( X1 != X2
    | c_Hilbert__Choice_Oinv__into(X3,X4,X5,X1) = c_Hilbert__Choice_Oinv__into(X3,X4,X5,X2) ) ).

cnf(i_0_18671,axiom,
    ( X1 != X2
    | c_List_Olistsp(X1,X3) = c_List_Olistsp(X2,X3) ) ).

cnf(i_0_18672,axiom,
    ( X1 != X2
    | c_List_Olistsp(X3,X1) = c_List_Olistsp(X3,X2) ) ).

cnf(i_0_18673,axiom,
    ( X1 != X2
    | c_List_Olists(X1,X3) = c_List_Olists(X2,X3) ) ).

cnf(i_0_18674,axiom,
    ( X1 != X2
    | c_List_Olists(X3,X1) = c_List_Olists(X3,X2) ) ).

cnf(i_0_18675,axiom,
    ( X1 != X2
    | c_Orderings_Oord__class_Omax(X1) = c_Orderings_Oord__class_Omax(X2) ) ).

cnf(i_0_18676,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice_OInf__fin(X1,X3,X4) = c_Big__Operators_Olattice_OInf__fin(X2,X3,X4) ) ).

cnf(i_0_18677,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice_OInf__fin(X3,X1,X4) = c_Big__Operators_Olattice_OInf__fin(X3,X2,X4) ) ).

cnf(i_0_18678,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice_OInf__fin(X3,X4,X1) = c_Big__Operators_Olattice_OInf__fin(X3,X4,X2) ) ).

cnf(i_0_18679,axiom,
    ( X1 != X2
    | c_Orderings_Oord__class_Omin(X1) = c_Orderings_Oord__class_Omin(X2) ) ).

cnf(i_0_18680,axiom,
    ( X1 != X2
    | c_Int_Oint__ge__less__than2(X1) = c_Int_Oint__ge__less__than2(X2) ) ).

cnf(i_0_18681,axiom,
    ( X1 != X2
    | c_Nitpick_Oof__frac(X1,X3,X4) = c_Nitpick_Oof__frac(X2,X3,X4) ) ).

cnf(i_0_18682,axiom,
    ( X1 != X2
    | c_Nitpick_Oof__frac(X3,X1,X4) = c_Nitpick_Oof__frac(X3,X2,X4) ) ).

cnf(i_0_18683,axiom,
    ( X1 != X2
    | c_Nitpick_Oof__frac(X3,X4,X1) = c_Nitpick_Oof__frac(X3,X4,X2) ) ).

cnf(i_0_18684,axiom,
    ( X1 != X2
    | c_List_Omeasures(X1,X3) = c_List_Omeasures(X2,X3) ) ).

cnf(i_0_18685,axiom,
    ( X1 != X2
    | c_List_Omeasures(X3,X1) = c_List_Omeasures(X3,X2) ) ).

cnf(i_0_18686,axiom,
    ( X1 != X2
    | c_Random__Sequence_Omap(X1,X3,X4,X5) = c_Random__Sequence_Omap(X2,X3,X4,X5) ) ).

cnf(i_0_18687,axiom,
    ( X1 != X2
    | c_Random__Sequence_Omap(X3,X1,X4,X5) = c_Random__Sequence_Omap(X3,X2,X4,X5) ) ).

cnf(i_0_18688,axiom,
    ( X1 != X2
    | c_Random__Sequence_Omap(X3,X4,X1,X5) = c_Random__Sequence_Omap(X3,X4,X2,X5) ) ).

cnf(i_0_18689,axiom,
    ( X1 != X2
    | c_Random__Sequence_Omap(X3,X4,X5,X1) = c_Random__Sequence_Omap(X3,X4,X5,X2) ) ).

cnf(i_0_18690,axiom,
    ( X1 != X2
    | c_Random__Sequence_Obind(X1,X3,X4,X5) = c_Random__Sequence_Obind(X2,X3,X4,X5) ) ).

cnf(i_0_18691,axiom,
    ( X1 != X2
    | c_Random__Sequence_Obind(X3,X1,X4,X5) = c_Random__Sequence_Obind(X3,X2,X4,X5) ) ).

cnf(i_0_18692,axiom,
    ( X1 != X2
    | c_Random__Sequence_Obind(X3,X4,X1,X5) = c_Random__Sequence_Obind(X3,X4,X2,X5) ) ).

cnf(i_0_18693,axiom,
    ( X1 != X2
    | c_Random__Sequence_Obind(X3,X4,X5,X1) = c_Random__Sequence_Obind(X3,X4,X5,X2) ) ).

cnf(i_0_18694,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X4) ) ).

cnf(i_0_18695,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastAtMost(X3,X1,X4) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X2,X4) ) ).

cnf(i_0_18696,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X2) ) ).

cnf(i_0_18697,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice_OSup__fin(X1,X3,X4) = c_Big__Operators_Olattice_OSup__fin(X2,X3,X4) ) ).

cnf(i_0_18698,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice_OSup__fin(X3,X1,X4) = c_Big__Operators_Olattice_OSup__fin(X3,X2,X4) ) ).

cnf(i_0_18699,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice_OSup__fin(X3,X4,X1) = c_Big__Operators_Olattice_OSup__fin(X3,X4,X2) ) ).

cnf(i_0_18700,axiom,
    ( X1 != X2
    | c_Lattices_Osemilattice__inf__class_Oinf(X1) = c_Lattices_Osemilattice__inf__class_Oinf(X2) ) ).

cnf(i_0_18701,axiom,
    ( X1 != X2
    | c_List_Olist_Olist__size(X1,X3,X4) = c_List_Olist_Olist__size(X2,X3,X4) ) ).

cnf(i_0_18702,axiom,
    ( X1 != X2
    | c_List_Olist_Olist__size(X3,X1,X4) = c_List_Olist_Olist__size(X3,X2,X4) ) ).

cnf(i_0_18703,axiom,
    ( X1 != X2
    | c_List_Olist_Olist__size(X3,X4,X1) = c_List_Olist_Olist__size(X3,X4,X2) ) ).

cnf(i_0_18704,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice__class_OSup__fin(X1,X3) = c_Big__Operators_Olattice__class_OSup__fin(X2,X3) ) ).

cnf(i_0_18705,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice__class_OSup__fin(X3,X1) = c_Big__Operators_Olattice__class_OSup__fin(X3,X2) ) ).

cnf(i_0_18706,axiom,
    ( X1 != X2
    | c_Lattices_Osemilattice__sup__class_Osup(X1) = c_Lattices_Osemilattice__sup__class_Osup(X2) ) ).

cnf(i_0_18707,axiom,
    ( X1 != X2
    | c_Enum_Osublists(X1,X3) = c_Enum_Osublists(X2,X3) ) ).

cnf(i_0_18708,axiom,
    ( X1 != X2
    | c_Enum_Osublists(X3,X1) = c_Enum_Osublists(X3,X2) ) ).

cnf(i_0_18709,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice__class_OInf__fin(X1,X3) = c_Big__Operators_Olattice__class_OInf__fin(X2,X3) ) ).

cnf(i_0_18710,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice__class_OInf__fin(X3,X1) = c_Big__Operators_Olattice__class_OInf__fin(X3,X2) ) ).

cnf(i_0_18711,axiom,
    ( X1 != X2
    | c_Random_Oselect__weight(X1,X3) = c_Random_Oselect__weight(X2,X3) ) ).

cnf(i_0_18712,axiom,
    ( X1 != X2
    | c_Random_Oselect__weight(X3,X1) = c_Random_Oselect__weight(X3,X2) ) ).

cnf(i_0_18713,axiom,
    ( X1 != X2
    | c_Random_Opick(X1,X3) = c_Random_Opick(X2,X3) ) ).

cnf(i_0_18714,axiom,
    ( X1 != X2
    | c_Random_Opick(X3,X1) = c_Random_Opick(X3,X2) ) ).

cnf(i_0_18715,axiom,
    ( X1 != X2
    | c_Fun_Ofun__upd(X1,X3,X4,X5,X6) = c_Fun_Ofun__upd(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18716,axiom,
    ( X1 != X2
    | c_Fun_Ofun__upd(X3,X1,X4,X5,X6) = c_Fun_Ofun__upd(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18717,axiom,
    ( X1 != X2
    | c_Fun_Ofun__upd(X3,X4,X1,X5,X6) = c_Fun_Ofun__upd(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18718,axiom,
    ( X1 != X2
    | c_Fun_Ofun__upd(X3,X4,X5,X1,X6) = c_Fun_Ofun__upd(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18719,axiom,
    ( X1 != X2
    | c_Fun_Ofun__upd(X3,X4,X5,X6,X1) = c_Fun_Ofun__upd(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18720,axiom,
    ( X1 != X2
    | c_List_Oset__Cons(X1,X3,X4) = c_List_Oset__Cons(X2,X3,X4) ) ).

cnf(i_0_18721,axiom,
    ( X1 != X2
    | c_List_Oset__Cons(X3,X1,X4) = c_List_Oset__Cons(X3,X2,X4) ) ).

cnf(i_0_18722,axiom,
    ( X1 != X2
    | c_List_Oset__Cons(X3,X4,X1) = c_List_Oset__Cons(X3,X4,X2) ) ).

cnf(i_0_18723,axiom,
    ( X1 != X2
    | c_Wellfounded_Omlex__prod(X1,X3,X4) = c_Wellfounded_Omlex__prod(X2,X3,X4) ) ).

cnf(i_0_18724,axiom,
    ( X1 != X2
    | c_Wellfounded_Omlex__prod(X3,X1,X4) = c_Wellfounded_Omlex__prod(X3,X2,X4) ) ).

cnf(i_0_18725,axiom,
    ( X1 != X2
    | c_Wellfounded_Omlex__prod(X3,X4,X1) = c_Wellfounded_Omlex__prod(X3,X4,X2) ) ).

cnf(i_0_18726,axiom,
    ( X1 != X2
    | c_Nitpick_Onorm__frac(X1,X3) = c_Nitpick_Onorm__frac(X2,X3) ) ).

cnf(i_0_18727,axiom,
    ( X1 != X2
    | c_Nitpick_Onorm__frac(X3,X1) = c_Nitpick_Onorm__frac(X3,X2) ) ).

cnf(i_0_18728,axiom,
    ( X1 != X2
    | c_List_Oremove1(X1,X3,X4) = c_List_Oremove1(X2,X3,X4) ) ).

cnf(i_0_18729,axiom,
    ( X1 != X2
    | c_List_Oremove1(X3,X1,X4) = c_List_Oremove1(X3,X2,X4) ) ).

cnf(i_0_18730,axiom,
    ( X1 != X2
    | c_List_Oremove1(X3,X4,X1) = c_List_Oremove1(X3,X4,X2) ) ).

cnf(i_0_18731,axiom,
    ( X1 != X2
    | esk525_4(X1,X3,X4,X5) = esk525_4(X2,X3,X4,X5) ) ).

cnf(i_0_18732,axiom,
    ( X1 != X2
    | esk525_4(X3,X1,X4,X5) = esk525_4(X3,X2,X4,X5) ) ).

cnf(i_0_18733,axiom,
    ( X1 != X2
    | esk525_4(X3,X4,X1,X5) = esk525_4(X3,X4,X2,X5) ) ).

cnf(i_0_18734,axiom,
    ( X1 != X2
    | esk525_4(X3,X4,X5,X1) = esk525_4(X3,X4,X5,X2) ) ).

cnf(i_0_18735,axiom,
    ( X1 != X2
    | esk524_4(X1,X3,X4,X5) = esk524_4(X2,X3,X4,X5) ) ).

cnf(i_0_18736,axiom,
    ( X1 != X2
    | esk524_4(X3,X1,X4,X5) = esk524_4(X3,X2,X4,X5) ) ).

cnf(i_0_18737,axiom,
    ( X1 != X2
    | esk524_4(X3,X4,X1,X5) = esk524_4(X3,X4,X2,X5) ) ).

cnf(i_0_18738,axiom,
    ( X1 != X2
    | esk524_4(X3,X4,X5,X1) = esk524_4(X3,X4,X5,X2) ) ).

cnf(i_0_18739,axiom,
    ( X1 != X2
    | c_Com_Ocom_OSemi(X1,X3) = c_Com_Ocom_OSemi(X2,X3) ) ).

cnf(i_0_18740,axiom,
    ( X1 != X2
    | c_Com_Ocom_OSemi(X3,X1) = c_Com_Ocom_OSemi(X3,X2) ) ).

cnf(i_0_18741,axiom,
    ( X1 != X2
    | esk116_3(X1,X3,X4) = esk116_3(X2,X3,X4) ) ).

cnf(i_0_18742,axiom,
    ( X1 != X2
    | esk116_3(X3,X1,X4) = esk116_3(X3,X2,X4) ) ).

cnf(i_0_18743,axiom,
    ( X1 != X2
    | esk116_3(X3,X4,X1) = esk116_3(X3,X4,X2) ) ).

cnf(i_0_18744,axiom,
    ( X1 != X2
    | esk115_3(X1,X3,X4) = esk115_3(X2,X3,X4) ) ).

cnf(i_0_18745,axiom,
    ( X1 != X2
    | esk115_3(X3,X1,X4) = esk115_3(X3,X2,X4) ) ).

cnf(i_0_18746,axiom,
    ( X1 != X2
    | esk115_3(X3,X4,X1) = esk115_3(X3,X4,X2) ) ).

cnf(i_0_18747,axiom,
    ( X1 != X2
    | c_Random_Oselect(X1,X3) = c_Random_Oselect(X2,X3) ) ).

cnf(i_0_18748,axiom,
    ( X1 != X2
    | c_Random_Oselect(X3,X1) = c_Random_Oselect(X3,X2) ) ).

cnf(i_0_18749,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_18750,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_18751,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_18752,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_18753,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_18754,axiom,
    ( X1 != X2
    | c_Finite__Set_Ofold1(X1,X3) = c_Finite__Set_Ofold1(X2,X3) ) ).

cnf(i_0_18755,axiom,
    ( X1 != X2
    | c_Finite__Set_Ofold1(X3,X1) = c_Finite__Set_Ofold1(X3,X2) ) ).

cnf(i_0_18756,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_18757,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_18758,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_18759,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_18760,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_18761,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_18762,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_18763,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_18764,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_18765,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_18766,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_18767,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_18768,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_18769,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_18770,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_18771,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_18772,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_18773,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_18774,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_18775,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Olazy__sequence_OInsert(X1,X3,X4) = c_Lazy__Sequence_Olazy__sequence_OInsert(X2,X3,X4) ) ).

cnf(i_0_18776,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Olazy__sequence_OInsert(X3,X1,X4) = c_Lazy__Sequence_Olazy__sequence_OInsert(X3,X2,X4) ) ).

cnf(i_0_18777,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Olazy__sequence_OInsert(X3,X4,X1) = c_Lazy__Sequence_Olazy__sequence_OInsert(X3,X4,X2) ) ).

cnf(i_0_18778,axiom,
    ( X1 != X2
    | c_Divides_Odivmod__int(X1,X3) = c_Divides_Odivmod__int(X2,X3) ) ).

cnf(i_0_18779,axiom,
    ( X1 != X2
    | c_Divides_Odivmod__int(X3,X1) = c_Divides_Odivmod__int(X3,X2) ) ).

cnf(i_0_18780,axiom,
    ( X1 != X2
    | esk249_5(X1,X3,X4,X5,X6) = esk249_5(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18781,axiom,
    ( X1 != X2
    | esk249_5(X3,X1,X4,X5,X6) = esk249_5(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18782,axiom,
    ( X1 != X2
    | esk249_5(X3,X4,X1,X5,X6) = esk249_5(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18783,axiom,
    ( X1 != X2
    | esk249_5(X3,X4,X5,X1,X6) = esk249_5(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18784,axiom,
    ( X1 != X2
    | esk249_5(X3,X4,X5,X6,X1) = esk249_5(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18785,axiom,
    ( X1 != X2
    | esk447_3(X1,X3,X4) = esk447_3(X2,X3,X4) ) ).

cnf(i_0_18786,axiom,
    ( X1 != X2
    | esk447_3(X3,X1,X4) = esk447_3(X3,X2,X4) ) ).

cnf(i_0_18787,axiom,
    ( X1 != X2
    | esk447_3(X3,X4,X1) = esk447_3(X3,X4,X2) ) ).

cnf(i_0_18788,axiom,
    ( X1 != X2
    | esk446_3(X1,X3,X4) = esk446_3(X2,X3,X4) ) ).

cnf(i_0_18789,axiom,
    ( X1 != X2
    | esk446_3(X3,X1,X4) = esk446_3(X3,X2,X4) ) ).

cnf(i_0_18790,axiom,
    ( X1 != X2
    | esk446_3(X3,X4,X1) = esk446_3(X3,X4,X2) ) ).

cnf(i_0_18791,axiom,
    ( X1 != X2
    | c_Groups_Osgn__class_Osgn(X1,X3) = c_Groups_Osgn__class_Osgn(X2,X3) ) ).

cnf(i_0_18792,axiom,
    ( X1 != X2
    | c_Groups_Osgn__class_Osgn(X3,X1) = c_Groups_Osgn__class_Osgn(X3,X2) ) ).

cnf(i_0_18793,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_18794,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_18795,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_18796,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_18797,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_18798,axiom,
    ( X1 != X2
    | esk409_2(X1,X3) = esk409_2(X2,X3) ) ).

cnf(i_0_18799,axiom,
    ( X1 != X2
    | esk409_2(X3,X1) = esk409_2(X3,X2) ) ).

cnf(i_0_18800,axiom,
    ( X1 != X2
    | esk410_2(X1,X3) = esk410_2(X2,X3) ) ).

cnf(i_0_18801,axiom,
    ( X1 != X2
    | esk410_2(X3,X1) = esk410_2(X3,X2) ) ).

cnf(i_0_18802,axiom,
    ( X1 != X2
    | c_Nitpick_Onat__gcd(X1,X3) = c_Nitpick_Onat__gcd(X2,X3) ) ).

cnf(i_0_18803,axiom,
    ( X1 != X2
    | c_Nitpick_Onat__gcd(X3,X1) = c_Nitpick_Onat__gcd(X3,X2) ) ).

cnf(i_0_18804,axiom,
    ( X1 != X2
    | c_Divides_Opdivmod(X1,X3) = c_Divides_Opdivmod(X2,X3) ) ).

cnf(i_0_18805,axiom,
    ( X1 != X2
    | c_Divides_Opdivmod(X3,X1) = c_Divides_Opdivmod(X3,X2) ) ).

cnf(i_0_18806,axiom,
    ( X1 != X2
    | c_List_Oremdups(X1,X3) = c_List_Oremdups(X2,X3) ) ).

cnf(i_0_18807,axiom,
    ( X1 != X2
    | c_List_Oremdups(X3,X1) = c_List_Oremdups(X3,X2) ) ).

cnf(i_0_18808,axiom,
    ( X1 != X2
    | c_Partial__Function_Oflat__lub(X1,X3,X4) = c_Partial__Function_Oflat__lub(X2,X3,X4) ) ).

cnf(i_0_18809,axiom,
    ( X1 != X2
    | c_Partial__Function_Oflat__lub(X3,X1,X4) = c_Partial__Function_Oflat__lub(X3,X2,X4) ) ).

cnf(i_0_18810,axiom,
    ( X1 != X2
    | c_Partial__Function_Oflat__lub(X3,X4,X1) = c_Partial__Function_Oflat__lub(X3,X4,X2) ) ).

cnf(i_0_18811,axiom,
    ( X1 != X2
    | c_List_Olenlex(X1,X3) = c_List_Olenlex(X2,X3) ) ).

cnf(i_0_18812,axiom,
    ( X1 != X2
    | c_List_Olenlex(X3,X1) = c_List_Olenlex(X3,X2) ) ).

cnf(i_0_18813,axiom,
    ( X1 != X2
    | c_Product__Type_Ocurry(X1,X3,X4,X5) = c_Product__Type_Ocurry(X2,X3,X4,X5) ) ).

cnf(i_0_18814,axiom,
    ( X1 != X2
    | c_Product__Type_Ocurry(X3,X1,X4,X5) = c_Product__Type_Ocurry(X3,X2,X4,X5) ) ).

cnf(i_0_18815,axiom,
    ( X1 != X2
    | c_Product__Type_Ocurry(X3,X4,X1,X5) = c_Product__Type_Ocurry(X3,X4,X2,X5) ) ).

cnf(i_0_18816,axiom,
    ( X1 != X2
    | c_Product__Type_Ocurry(X3,X4,X5,X1) = c_Product__Type_Ocurry(X3,X4,X5,X2) ) ).

cnf(i_0_18817,axiom,
    ( X1 != X2
    | c_List_Oreplicate(X1,X3,X4) = c_List_Oreplicate(X2,X3,X4) ) ).

cnf(i_0_18818,axiom,
    ( X1 != X2
    | c_List_Oreplicate(X3,X1,X4) = c_List_Oreplicate(X3,X2,X4) ) ).

cnf(i_0_18819,axiom,
    ( X1 != X2
    | c_List_Oreplicate(X3,X4,X1) = c_List_Oreplicate(X3,X4,X2) ) ).

cnf(i_0_18820,axiom,
    ( X1 != X2
    | c_List_Olex(X1,X3) = c_List_Olex(X2,X3) ) ).

cnf(i_0_18821,axiom,
    ( X1 != X2
    | c_List_Olex(X3,X1) = c_List_Olex(X3,X2) ) ).

cnf(i_0_18822,axiom,
    ( X1 != X2
    | esk93_3(X1,X3,X4) = esk93_3(X2,X3,X4) ) ).

cnf(i_0_18823,axiom,
    ( X1 != X2
    | esk93_3(X3,X1,X4) = esk93_3(X3,X2,X4) ) ).

cnf(i_0_18824,axiom,
    ( X1 != X2
    | esk93_3(X3,X4,X1) = esk93_3(X3,X4,X2) ) ).

cnf(i_0_18825,axiom,
    ( X1 != X2
    | esk556_3(X1,X3,X4) = esk556_3(X2,X3,X4) ) ).

cnf(i_0_18826,axiom,
    ( X1 != X2
    | esk556_3(X3,X1,X4) = esk556_3(X3,X2,X4) ) ).

cnf(i_0_18827,axiom,
    ( X1 != X2
    | esk556_3(X3,X4,X1) = esk556_3(X3,X4,X2) ) ).

cnf(i_0_18828,axiom,
    ( X1 != X2
    | esk522_4(X1,X3,X4,X5) = esk522_4(X2,X3,X4,X5) ) ).

cnf(i_0_18829,axiom,
    ( X1 != X2
    | esk522_4(X3,X1,X4,X5) = esk522_4(X3,X2,X4,X5) ) ).

cnf(i_0_18830,axiom,
    ( X1 != X2
    | esk522_4(X3,X4,X1,X5) = esk522_4(X3,X4,X2,X5) ) ).

cnf(i_0_18831,axiom,
    ( X1 != X2
    | esk522_4(X3,X4,X5,X1) = esk522_4(X3,X4,X5,X2) ) ).

cnf(i_0_18832,axiom,
    ( X1 != X2
    | esk511_4(X1,X3,X4,X5) = esk511_4(X2,X3,X4,X5) ) ).

cnf(i_0_18833,axiom,
    ( X1 != X2
    | esk511_4(X3,X1,X4,X5) = esk511_4(X3,X2,X4,X5) ) ).

cnf(i_0_18834,axiom,
    ( X1 != X2
    | esk511_4(X3,X4,X1,X5) = esk511_4(X3,X4,X2,X5) ) ).

cnf(i_0_18835,axiom,
    ( X1 != X2
    | esk511_4(X3,X4,X5,X1) = esk511_4(X3,X4,X5,X2) ) ).

cnf(i_0_18836,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X1,X3,X4,X5) = c_List_Ofoldl(X2,X3,X4,X5) ) ).

cnf(i_0_18837,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X3,X1,X4,X5) = c_List_Ofoldl(X3,X2,X4,X5) ) ).

cnf(i_0_18838,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X3,X4,X1,X5) = c_List_Ofoldl(X3,X4,X2,X5) ) ).

cnf(i_0_18839,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X3,X4,X5,X1) = c_List_Ofoldl(X3,X4,X5,X2) ) ).

cnf(i_0_18840,axiom,
    ( X1 != X2
    | esk232_4(X1,X3,X4,X5) = esk232_4(X2,X3,X4,X5) ) ).

cnf(i_0_18841,axiom,
    ( X1 != X2
    | esk232_4(X3,X1,X4,X5) = esk232_4(X3,X2,X4,X5) ) ).

cnf(i_0_18842,axiom,
    ( X1 != X2
    | esk232_4(X3,X4,X1,X5) = esk232_4(X3,X4,X2,X5) ) ).

cnf(i_0_18843,axiom,
    ( X1 != X2
    | esk232_4(X3,X4,X5,X1) = esk232_4(X3,X4,X5,X2) ) ).

cnf(i_0_18844,axiom,
    ( X1 != X2
    | esk234_4(X1,X3,X4,X5) = esk234_4(X2,X3,X4,X5) ) ).

cnf(i_0_18845,axiom,
    ( X1 != X2
    | esk234_4(X3,X1,X4,X5) = esk234_4(X3,X2,X4,X5) ) ).

cnf(i_0_18846,axiom,
    ( X1 != X2
    | esk234_4(X3,X4,X1,X5) = esk234_4(X3,X4,X2,X5) ) ).

cnf(i_0_18847,axiom,
    ( X1 != X2
    | esk234_4(X3,X4,X5,X1) = esk234_4(X3,X4,X5,X2) ) ).

cnf(i_0_18848,axiom,
    ( X1 != X2
    | c_Enum_Oproduct(X1,X3,X4,X5) = c_Enum_Oproduct(X2,X3,X4,X5) ) ).

cnf(i_0_18849,axiom,
    ( X1 != X2
    | c_Enum_Oproduct(X3,X1,X4,X5) = c_Enum_Oproduct(X3,X2,X4,X5) ) ).

cnf(i_0_18850,axiom,
    ( X1 != X2
    | c_Enum_Oproduct(X3,X4,X1,X5) = c_Enum_Oproduct(X3,X4,X2,X5) ) ).

cnf(i_0_18851,axiom,
    ( X1 != X2
    | c_Enum_Oproduct(X3,X4,X5,X1) = c_Enum_Oproduct(X3,X4,X5,X2) ) ).

cnf(i_0_18852,axiom,
    ( X1 != X2
    | esk216_4(X1,X3,X4,X5) = esk216_4(X2,X3,X4,X5) ) ).

cnf(i_0_18853,axiom,
    ( X1 != X2
    | esk216_4(X3,X1,X4,X5) = esk216_4(X3,X2,X4,X5) ) ).

cnf(i_0_18854,axiom,
    ( X1 != X2
    | esk216_4(X3,X4,X1,X5) = esk216_4(X3,X4,X2,X5) ) ).

cnf(i_0_18855,axiom,
    ( X1 != X2
    | esk216_4(X3,X4,X5,X1) = esk216_4(X3,X4,X5,X2) ) ).

cnf(i_0_18856,axiom,
    ( X1 != X2
    | esk215_4(X1,X3,X4,X5) = esk215_4(X2,X3,X4,X5) ) ).

cnf(i_0_18857,axiom,
    ( X1 != X2
    | esk215_4(X3,X1,X4,X5) = esk215_4(X3,X2,X4,X5) ) ).

cnf(i_0_18858,axiom,
    ( X1 != X2
    | esk215_4(X3,X4,X1,X5) = esk215_4(X3,X4,X2,X5) ) ).

cnf(i_0_18859,axiom,
    ( X1 != X2
    | esk215_4(X3,X4,X5,X1) = esk215_4(X3,X4,X5,X2) ) ).

cnf(i_0_18860,axiom,
    ( X1 != X2
    | c_Fun_Ocomp(X1,X3,X4,X5) = c_Fun_Ocomp(X2,X3,X4,X5) ) ).

cnf(i_0_18861,axiom,
    ( X1 != X2
    | c_Fun_Ocomp(X3,X1,X4,X5) = c_Fun_Ocomp(X3,X2,X4,X5) ) ).

cnf(i_0_18862,axiom,
    ( X1 != X2
    | c_Fun_Ocomp(X3,X4,X1,X5) = c_Fun_Ocomp(X3,X4,X2,X5) ) ).

cnf(i_0_18863,axiom,
    ( X1 != X2
    | c_Fun_Ocomp(X3,X4,X5,X1) = c_Fun_Ocomp(X3,X4,X5,X2) ) ).

cnf(i_0_18864,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_18865,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_18866,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_18867,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_18868,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_18869,axiom,
    ( X1 != X2
    | c_Nitpick_Opair__box_OPairBox(X1,X3,X4,X5) = c_Nitpick_Opair__box_OPairBox(X2,X3,X4,X5) ) ).

cnf(i_0_18870,axiom,
    ( X1 != X2
    | c_Nitpick_Opair__box_OPairBox(X3,X1,X4,X5) = c_Nitpick_Opair__box_OPairBox(X3,X2,X4,X5) ) ).

cnf(i_0_18871,axiom,
    ( X1 != X2
    | c_Nitpick_Opair__box_OPairBox(X3,X4,X1,X5) = c_Nitpick_Opair__box_OPairBox(X3,X4,X2,X5) ) ).

cnf(i_0_18872,axiom,
    ( X1 != X2
    | c_Nitpick_Opair__box_OPairBox(X3,X4,X5,X1) = c_Nitpick_Opair__box_OPairBox(X3,X4,X5,X2) ) ).

cnf(i_0_18873,axiom,
    ( X1 != X2
    | esk379_3(X1,X3,X4) = esk379_3(X2,X3,X4) ) ).

cnf(i_0_18874,axiom,
    ( X1 != X2
    | esk379_3(X3,X1,X4) = esk379_3(X3,X2,X4) ) ).

cnf(i_0_18875,axiom,
    ( X1 != X2
    | esk379_3(X3,X4,X1) = esk379_3(X3,X4,X2) ) ).

cnf(i_0_18876,axiom,
    ( X1 != X2
    | esk380_3(X1,X3,X4) = esk380_3(X2,X3,X4) ) ).

cnf(i_0_18877,axiom,
    ( X1 != X2
    | esk380_3(X3,X1,X4) = esk380_3(X3,X2,X4) ) ).

cnf(i_0_18878,axiom,
    ( X1 != X2
    | esk380_3(X3,X4,X1) = esk380_3(X3,X4,X2) ) ).

cnf(i_0_18879,axiom,
    ( X1 != X2
    | esk248_4(X1,X3,X4,X5) = esk248_4(X2,X3,X4,X5) ) ).

cnf(i_0_18880,axiom,
    ( X1 != X2
    | esk248_4(X3,X1,X4,X5) = esk248_4(X3,X2,X4,X5) ) ).

cnf(i_0_18881,axiom,
    ( X1 != X2
    | esk248_4(X3,X4,X1,X5) = esk248_4(X3,X4,X2,X5) ) ).

cnf(i_0_18882,axiom,
    ( X1 != X2
    | esk248_4(X3,X4,X5,X1) = esk248_4(X3,X4,X5,X2) ) ).

cnf(i_0_18883,axiom,
    ( X1 != X2
    | c_Nitpick_Oplus__frac(X1,X3,X4) = c_Nitpick_Oplus__frac(X2,X3,X4) ) ).

cnf(i_0_18884,axiom,
    ( X1 != X2
    | c_Nitpick_Oplus__frac(X3,X1,X4) = c_Nitpick_Oplus__frac(X3,X2,X4) ) ).

cnf(i_0_18885,axiom,
    ( X1 != X2
    | c_Nitpick_Oplus__frac(X3,X4,X1) = c_Nitpick_Oplus__frac(X3,X4,X2) ) ).

cnf(i_0_18886,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_18887,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_18888,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_18889,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_18890,axiom,
    ( X1 != X2
    | c_Sum__Type_OPlus(X1,X3,X4,X5) = c_Sum__Type_OPlus(X2,X3,X4,X5) ) ).

cnf(i_0_18891,axiom,
    ( X1 != X2
    | c_Sum__Type_OPlus(X3,X1,X4,X5) = c_Sum__Type_OPlus(X3,X2,X4,X5) ) ).

cnf(i_0_18892,axiom,
    ( X1 != X2
    | c_Sum__Type_OPlus(X3,X4,X1,X5) = c_Sum__Type_OPlus(X3,X4,X2,X5) ) ).

cnf(i_0_18893,axiom,
    ( X1 != X2
    | c_Sum__Type_OPlus(X3,X4,X5,X1) = c_Sum__Type_OPlus(X3,X4,X5,X2) ) ).

cnf(i_0_18894,axiom,
    ( X1 != X2
    | esk374_3(X1,X3,X4) = esk374_3(X2,X3,X4) ) ).

cnf(i_0_18895,axiom,
    ( X1 != X2
    | esk374_3(X3,X1,X4) = esk374_3(X3,X2,X4) ) ).

cnf(i_0_18896,axiom,
    ( X1 != X2
    | esk374_3(X3,X4,X1) = esk374_3(X3,X4,X2) ) ).

cnf(i_0_18897,axiom,
    ( X1 != X2
    | esk373_3(X1,X3,X4) = esk373_3(X2,X3,X4) ) ).

cnf(i_0_18898,axiom,
    ( X1 != X2
    | esk373_3(X3,X1,X4) = esk373_3(X3,X2,X4) ) ).

cnf(i_0_18899,axiom,
    ( X1 != X2
    | esk373_3(X3,X4,X1) = esk373_3(X3,X4,X2) ) ).

cnf(i_0_18900,axiom,
    ( X1 != X2
    | c_List_Oupto(X1,X3) = c_List_Oupto(X2,X3) ) ).

cnf(i_0_18901,axiom,
    ( X1 != X2
    | c_List_Oupto(X3,X1) = c_List_Oupto(X3,X2) ) ).

cnf(i_0_18902,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_18903,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_18904,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_18905,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_18906,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_18907,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_18908,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_18909,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_18910,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_18911,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_18912,axiom,
    ( X1 != X2
    | c_List_Olast(X1,X3) = c_List_Olast(X2,X3) ) ).

cnf(i_0_18913,axiom,
    ( X1 != X2
    | c_List_Olast(X3,X1) = c_List_Olast(X3,X2) ) ).

cnf(i_0_18914,axiom,
    ( X1 != X2
    | c_List_Obutlast(X1,X3) = c_List_Obutlast(X2,X3) ) ).

cnf(i_0_18915,axiom,
    ( X1 != X2
    | c_List_Obutlast(X3,X1) = c_List_Obutlast(X3,X2) ) ).

cnf(i_0_18916,axiom,
    ( X1 != X2
    | esk547_2(X1,X3) = esk547_2(X2,X3) ) ).

cnf(i_0_18917,axiom,
    ( X1 != X2
    | esk547_2(X3,X1) = esk547_2(X3,X2) ) ).

cnf(i_0_18918,axiom,
    ( X1 != X2
    | c_Nitpick_Oint__lcm(X1,X3) = c_Nitpick_Oint__lcm(X2,X3) ) ).

cnf(i_0_18919,axiom,
    ( X1 != X2
    | c_Nitpick_Oint__lcm(X3,X1) = c_Nitpick_Oint__lcm(X3,X2) ) ).

cnf(i_0_18920,axiom,
    ( X1 != X2
    | esk546_2(X1,X3) = esk546_2(X2,X3) ) ).

cnf(i_0_18921,axiom,
    ( X1 != X2
    | esk546_2(X3,X1) = esk546_2(X3,X2) ) ).

cnf(i_0_18922,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohb__bind(X1,X3,X4,X5) = c_Lazy__Sequence_Ohb__bind(X2,X3,X4,X5) ) ).

cnf(i_0_18923,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohb__bind(X3,X1,X4,X5) = c_Lazy__Sequence_Ohb__bind(X3,X2,X4,X5) ) ).

cnf(i_0_18924,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohb__bind(X3,X4,X1,X5) = c_Lazy__Sequence_Ohb__bind(X3,X4,X2,X5) ) ).

cnf(i_0_18925,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohb__bind(X3,X4,X5,X1) = c_Lazy__Sequence_Ohb__bind(X3,X4,X5,X2) ) ).

cnf(i_0_18926,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Olazy__sequence_OEmpty(X1) = c_Lazy__Sequence_Olazy__sequence_OEmpty(X2) ) ).

cnf(i_0_18927,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_18928,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_18929,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_18930,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_18931,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_18932,axiom,
    ( X1 != X2
    | esk140_3(X1,X3,X4) = esk140_3(X2,X3,X4) ) ).

cnf(i_0_18933,axiom,
    ( X1 != X2
    | esk140_3(X3,X1,X4) = esk140_3(X3,X2,X4) ) ).

cnf(i_0_18934,axiom,
    ( X1 != X2
    | esk140_3(X3,X4,X1) = esk140_3(X3,X4,X2) ) ).

cnf(i_0_18935,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Osmall__lazy_H(X1,X3) = c_Lazy__Sequence_Osmall__lazy_H(X2,X3) ) ).

cnf(i_0_18936,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Osmall__lazy_H(X3,X1) = c_Lazy__Sequence_Osmall__lazy_H(X3,X2) ) ).

cnf(i_0_18937,axiom,
    ( X1 != X2
    | esk527_4(X1,X3,X4,X5) = esk527_4(X2,X3,X4,X5) ) ).

cnf(i_0_18938,axiom,
    ( X1 != X2
    | esk527_4(X3,X1,X4,X5) = esk527_4(X3,X2,X4,X5) ) ).

cnf(i_0_18939,axiom,
    ( X1 != X2
    | esk527_4(X3,X4,X1,X5) = esk527_4(X3,X4,X2,X5) ) ).

cnf(i_0_18940,axiom,
    ( X1 != X2
    | esk527_4(X3,X4,X5,X1) = esk527_4(X3,X4,X5,X2) ) ).

cnf(i_0_18941,axiom,
    ( X1 != X2
    | c_FunDef_OTHE__default(X1,X3,X4) = c_FunDef_OTHE__default(X2,X3,X4) ) ).

cnf(i_0_18942,axiom,
    ( X1 != X2
    | c_FunDef_OTHE__default(X3,X1,X4) = c_FunDef_OTHE__default(X3,X2,X4) ) ).

cnf(i_0_18943,axiom,
    ( X1 != X2
    | c_FunDef_OTHE__default(X3,X4,X1) = c_FunDef_OTHE__default(X3,X4,X2) ) ).

cnf(i_0_18944,axiom,
    ( X1 != X2
    | c_List_Omaps(X1,X3,X4,X5) = c_List_Omaps(X2,X3,X4,X5) ) ).

cnf(i_0_18945,axiom,
    ( X1 != X2
    | c_List_Omaps(X3,X1,X4,X5) = c_List_Omaps(X3,X2,X4,X5) ) ).

cnf(i_0_18946,axiom,
    ( X1 != X2
    | c_List_Omaps(X3,X4,X1,X5) = c_List_Omaps(X3,X4,X2,X5) ) ).

cnf(i_0_18947,axiom,
    ( X1 != X2
    | c_List_Omaps(X3,X4,X5,X1) = c_List_Omaps(X3,X4,X5,X2) ) ).

cnf(i_0_18948,axiom,
    ( X1 != X2
    | esk436_2(X1,X3) = esk436_2(X2,X3) ) ).

cnf(i_0_18949,axiom,
    ( X1 != X2
    | esk436_2(X3,X1) = esk436_2(X3,X2) ) ).

cnf(i_0_18950,axiom,
    ( X1 != X2
    | esk385_2(X1,X3) = esk385_2(X2,X3) ) ).

cnf(i_0_18951,axiom,
    ( X1 != X2
    | esk385_2(X3,X1) = esk385_2(X3,X2) ) ).

cnf(i_0_18952,axiom,
    ( X1 != X2
    | esk386_2(X1,X3) = esk386_2(X2,X3) ) ).

cnf(i_0_18953,axiom,
    ( X1 != X2
    | esk386_2(X3,X1) = esk386_2(X3,X2) ) ).

cnf(i_0_18954,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_18955,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_18956,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_18957,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_18958,axiom,
    ( X1 != X2
    | c_Orderings_Otop__class_Otop(X1) = c_Orderings_Otop__class_Otop(X2) ) ).

cnf(i_0_18959,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X3,X4) = c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X4) ) ).

cnf(i_0_18960,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X1,X4) = c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X2,X4) ) ).

cnf(i_0_18961,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X1) = c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X2) ) ).

cnf(i_0_18962,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X3,X4) = c_SetInterval_Oord__class_OgreaterThanLessThan(X2,X3,X4) ) ).

cnf(i_0_18963,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OgreaterThanLessThan(X3,X1,X4) = c_SetInterval_Oord__class_OgreaterThanLessThan(X3,X2,X4) ) ).

cnf(i_0_18964,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OgreaterThanLessThan(X3,X4,X1) = c_SetInterval_Oord__class_OgreaterThanLessThan(X3,X4,X2) ) ).

cnf(i_0_18965,axiom,
    ( X1 != X2
    | c_Predicate_Opred__comp(X1,X3,X4,X5,X6) = c_Predicate_Opred__comp(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18966,axiom,
    ( X1 != X2
    | c_Predicate_Opred__comp(X3,X1,X4,X5,X6) = c_Predicate_Opred__comp(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18967,axiom,
    ( X1 != X2
    | c_Predicate_Opred__comp(X3,X4,X1,X5,X6) = c_Predicate_Opred__comp(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18968,axiom,
    ( X1 != X2
    | c_Predicate_Opred__comp(X3,X4,X5,X1,X6) = c_Predicate_Opred__comp(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18969,axiom,
    ( X1 != X2
    | c_Predicate_Opred__comp(X3,X4,X5,X6,X1) = c_Predicate_Opred__comp(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18970,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_18971,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_18972,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_18973,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_18974,axiom,
    ( X1 != X2
    | c_Power_Opower_Opower(X1,X3,X4) = c_Power_Opower_Opower(X2,X3,X4) ) ).

cnf(i_0_18975,axiom,
    ( X1 != X2
    | c_Power_Opower_Opower(X3,X1,X4) = c_Power_Opower_Opower(X3,X2,X4) ) ).

cnf(i_0_18976,axiom,
    ( X1 != X2
    | c_Power_Opower_Opower(X3,X4,X1) = c_Power_Opower_Opower(X3,X4,X2) ) ).

cnf(i_0_18977,axiom,
    ( X1 != X2
    | esk341_2(X1,X3) = esk341_2(X2,X3) ) ).

cnf(i_0_18978,axiom,
    ( X1 != X2
    | esk341_2(X3,X1) = esk341_2(X3,X2) ) ).

cnf(i_0_18979,axiom,
    ( X1 != X2
    | c_Transitive__Closure_Ortrancl(X1,X3) = c_Transitive__Closure_Ortrancl(X2,X3) ) ).

cnf(i_0_18980,axiom,
    ( X1 != X2
    | c_Transitive__Closure_Ortrancl(X3,X1) = c_Transitive__Closure_Ortrancl(X3,X2) ) ).

cnf(i_0_18981,axiom,
    ( X1 != X2
    | esk231_3(X1,X3,X4) = esk231_3(X2,X3,X4) ) ).

cnf(i_0_18982,axiom,
    ( X1 != X2
    | esk231_3(X3,X1,X4) = esk231_3(X3,X2,X4) ) ).

cnf(i_0_18983,axiom,
    ( X1 != X2
    | esk231_3(X3,X4,X1) = esk231_3(X3,X4,X2) ) ).

cnf(i_0_18984,axiom,
    ( X1 != X2
    | esk233_3(X1,X3,X4) = esk233_3(X2,X3,X4) ) ).

cnf(i_0_18985,axiom,
    ( X1 != X2
    | esk233_3(X3,X1,X4) = esk233_3(X3,X2,X4) ) ).

cnf(i_0_18986,axiom,
    ( X1 != X2
    | esk233_3(X3,X4,X1) = esk233_3(X3,X4,X2) ) ).

cnf(i_0_18987,axiom,
    ( X1 != X2
    | esk122_3(X1,X3,X4) = esk122_3(X2,X3,X4) ) ).

cnf(i_0_18988,axiom,
    ( X1 != X2
    | esk122_3(X3,X1,X4) = esk122_3(X3,X2,X4) ) ).

cnf(i_0_18989,axiom,
    ( X1 != X2
    | esk122_3(X3,X4,X1) = esk122_3(X3,X4,X2) ) ).

cnf(i_0_18990,axiom,
    ( X1 != X2
    | esk121_3(X1,X3,X4) = esk121_3(X2,X3,X4) ) ).

cnf(i_0_18991,axiom,
    ( X1 != X2
    | esk121_3(X3,X1,X4) = esk121_3(X3,X2,X4) ) ).

cnf(i_0_18992,axiom,
    ( X1 != X2
    | esk121_3(X3,X4,X1) = esk121_3(X3,X4,X2) ) ).

cnf(i_0_18993,axiom,
    ( X1 != X2
    | esk521_3(X1,X3,X4) = esk521_3(X2,X3,X4) ) ).

cnf(i_0_18994,axiom,
    ( X1 != X2
    | esk521_3(X3,X1,X4) = esk521_3(X3,X2,X4) ) ).

cnf(i_0_18995,axiom,
    ( X1 != X2
    | esk521_3(X3,X4,X1) = esk521_3(X3,X4,X2) ) ).

cnf(i_0_18996,axiom,
    ( X1 != X2
    | esk510_3(X1,X3,X4) = esk510_3(X2,X3,X4) ) ).

cnf(i_0_18997,axiom,
    ( X1 != X2
    | esk510_3(X3,X1,X4) = esk510_3(X3,X2,X4) ) ).

cnf(i_0_18998,axiom,
    ( X1 != X2
    | esk510_3(X3,X4,X1) = esk510_3(X3,X4,X2) ) ).

cnf(i_0_18999,axiom,
    ( X1 != X2
    | c_List_Osplice(X1,X3,X4) = c_List_Osplice(X2,X3,X4) ) ).

cnf(i_0_19000,axiom,
    ( X1 != X2
    | c_List_Osplice(X3,X1,X4) = c_List_Osplice(X3,X2,X4) ) ).

cnf(i_0_19001,axiom,
    ( X1 != X2
    | c_List_Osplice(X3,X4,X1) = c_List_Osplice(X3,X4,X2) ) ).

cnf(i_0_19002,axiom,
    ( X1 != X2
    | c_Hoare__Mirabelle_Otriple_Otriple__case(X1,X3,X4,X5) = c_Hoare__Mirabelle_Otriple_Otriple__case(X2,X3,X4,X5) ) ).

cnf(i_0_19003,axiom,
    ( X1 != X2
    | c_Hoare__Mirabelle_Otriple_Otriple__case(X3,X1,X4,X5) = c_Hoare__Mirabelle_Otriple_Otriple__case(X3,X2,X4,X5) ) ).

cnf(i_0_19004,axiom,
    ( X1 != X2
    | c_Hoare__Mirabelle_Otriple_Otriple__case(X3,X4,X1,X5) = c_Hoare__Mirabelle_Otriple_Otriple__case(X3,X4,X2,X5) ) ).

cnf(i_0_19005,axiom,
    ( X1 != X2
    | c_Hoare__Mirabelle_Otriple_Otriple__case(X3,X4,X5,X1) = c_Hoare__Mirabelle_Otriple_Otriple__case(X3,X4,X5,X2) ) ).

cnf(i_0_19006,axiom,
    ( X1 != X2
    | c_Hoare__Mirabelle_Otriple_Otriple__rec(X1,X3,X4,X5) = c_Hoare__Mirabelle_Otriple_Otriple__rec(X2,X3,X4,X5) ) ).

cnf(i_0_19007,axiom,
    ( X1 != X2
    | c_Hoare__Mirabelle_Otriple_Otriple__rec(X3,X1,X4,X5) = c_Hoare__Mirabelle_Otriple_Otriple__rec(X3,X2,X4,X5) ) ).

cnf(i_0_19008,axiom,
    ( X1 != X2
    | c_Hoare__Mirabelle_Otriple_Otriple__rec(X3,X4,X1,X5) = c_Hoare__Mirabelle_Otriple_Otriple__rec(X3,X4,X2,X5) ) ).

cnf(i_0_19009,axiom,
    ( X1 != X2
    | c_Hoare__Mirabelle_Otriple_Otriple__rec(X3,X4,X5,X1) = c_Hoare__Mirabelle_Otriple_Otriple__rec(X3,X4,X5,X2) ) ).

cnf(i_0_19010,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohit__bound(X1) = c_Lazy__Sequence_Ohit__bound(X2) ) ).

cnf(i_0_19011,axiom,
    ( X1 != X2
    | c_Nat__Transfer_Otsub(X1,X3) = c_Nat__Transfer_Otsub(X2,X3) ) ).

cnf(i_0_19012,axiom,
    ( X1 != X2
    | c_Nat__Transfer_Otsub(X3,X1) = c_Nat__Transfer_Otsub(X3,X2) ) ).

cnf(i_0_19013,axiom,
    ( X1 != X2
    | c_Random_Olog(X1,X3) = c_Random_Olog(X2,X3) ) ).

cnf(i_0_19014,axiom,
    ( X1 != X2
    | c_Random_Olog(X3,X1) = c_Random_Olog(X3,X2) ) ).

cnf(i_0_19015,axiom,
    ( X1 != X2
    | c_Com_Ocom_Ocom__size(X1) = c_Com_Ocom_Ocom__size(X2) ) ).

cnf(i_0_19016,axiom,
    ( X1 != X2
    | c_Random_Ominus__shift(X1,X3,X4) = c_Random_Ominus__shift(X2,X3,X4) ) ).

cnf(i_0_19017,axiom,
    ( X1 != X2
    | c_Random_Ominus__shift(X3,X1,X4) = c_Random_Ominus__shift(X3,X2,X4) ) ).

cnf(i_0_19018,axiom,
    ( X1 != X2
    | c_Random_Ominus__shift(X3,X4,X1) = c_Random_Ominus__shift(X3,X4,X2) ) ).

cnf(i_0_19019,axiom,
    ( X1 != X2
    | c_Random__Sequence_Oempty(X1,X3,X4) = c_Random__Sequence_Oempty(X2,X3,X4) ) ).

cnf(i_0_19020,axiom,
    ( X1 != X2
    | c_Random__Sequence_Oempty(X3,X1,X4) = c_Random__Sequence_Oempty(X3,X2,X4) ) ).

cnf(i_0_19021,axiom,
    ( X1 != X2
    | c_Random__Sequence_Oempty(X3,X4,X1) = c_Random__Sequence_Oempty(X3,X4,X2) ) ).

cnf(i_0_19022,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_19023,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_19024,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_19025,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_19026,axiom,
    ( X1 != X2
    | esk389_2(X1,X3) = esk389_2(X2,X3) ) ).

cnf(i_0_19027,axiom,
    ( X1 != X2
    | esk389_2(X3,X1) = esk389_2(X3,X2) ) ).

cnf(i_0_19028,axiom,
    ( X1 != X2
    | c_List_Olistset(X1,X3) = c_List_Olistset(X2,X3) ) ).

cnf(i_0_19029,axiom,
    ( X1 != X2
    | c_List_Olistset(X3,X1) = c_List_Olistset(X3,X2) ) ).

cnf(i_0_19030,axiom,
    ( X1 != X2
    | c_Code__Numeral_Odiv__mod__code__numeral(X1,X3) = c_Code__Numeral_Odiv__mod__code__numeral(X2,X3) ) ).

cnf(i_0_19031,axiom,
    ( X1 != X2
    | c_Code__Numeral_Odiv__mod__code__numeral(X3,X1) = c_Code__Numeral_Odiv__mod__code__numeral(X3,X2) ) ).

cnf(i_0_19032,axiom,
    ( X1 != X2
    | esk340_2(X1,X3) = esk340_2(X2,X3) ) ).

cnf(i_0_19033,axiom,
    ( X1 != X2
    | esk340_2(X3,X1) = esk340_2(X3,X2) ) ).

cnf(i_0_19034,axiom,
    ( X1 != X2
    | esk339_2(X1,X3) = esk339_2(X2,X3) ) ).

cnf(i_0_19035,axiom,
    ( X1 != X2
    | esk339_2(X3,X1) = esk339_2(X3,X2) ) ).

cnf(i_0_19036,axiom,
    ( X1 != X2
    | c_List_Oinsert(X1,X3,X4) = c_List_Oinsert(X2,X3,X4) ) ).

cnf(i_0_19037,axiom,
    ( X1 != X2
    | c_List_Oinsert(X3,X1,X4) = c_List_Oinsert(X3,X2,X4) ) ).

cnf(i_0_19038,axiom,
    ( X1 != X2
    | c_List_Oinsert(X3,X4,X1) = c_List_Oinsert(X3,X4,X2) ) ).

cnf(i_0_19039,axiom,
    ( X1 != X2
    | c_Int_Oring__1__class_Oof__int(X1) = c_Int_Oring__1__class_Oof__int(X2) ) ).

cnf(i_0_19040,axiom,
    ( X1 != X2
    | esk528_3(X1,X3,X4) = esk528_3(X2,X3,X4) ) ).

cnf(i_0_19041,axiom,
    ( X1 != X2
    | esk528_3(X3,X1,X4) = esk528_3(X3,X2,X4) ) ).

cnf(i_0_19042,axiom,
    ( X1 != X2
    | esk528_3(X3,X4,X1) = esk528_3(X3,X4,X2) ) ).

cnf(i_0_19043,axiom,
    ( X1 != X2
    | c_SMT_Oz3div(X1,X3) = c_SMT_Oz3div(X2,X3) ) ).

cnf(i_0_19044,axiom,
    ( X1 != X2
    | c_SMT_Oz3div(X3,X1) = c_SMT_Oz3div(X3,X2) ) ).

cnf(i_0_19045,axiom,
    ( X1 != X2
    | c_Hoare__Mirabelle_Otriple_Otriple__size(X1,X3,X4) = c_Hoare__Mirabelle_Otriple_Otriple__size(X2,X3,X4) ) ).

cnf(i_0_19046,axiom,
    ( X1 != X2
    | c_Hoare__Mirabelle_Otriple_Otriple__size(X3,X1,X4) = c_Hoare__Mirabelle_Otriple_Otriple__size(X3,X2,X4) ) ).

cnf(i_0_19047,axiom,
    ( X1 != X2
    | c_Hoare__Mirabelle_Otriple_Otriple__size(X3,X4,X1) = c_Hoare__Mirabelle_Otriple_Otriple__size(X3,X4,X2) ) ).

cnf(i_0_19048,axiom,
    ( X1 != X2
    | c_Orderings_Oord_Omax(X1,X3) = c_Orderings_Oord_Omax(X2,X3) ) ).

cnf(i_0_19049,axiom,
    ( X1 != X2
    | c_Orderings_Oord_Omax(X3,X1) = c_Orderings_Oord_Omax(X3,X2) ) ).

cnf(i_0_19050,axiom,
    ( X1 != X2
    | c_Orderings_Oord_Omin(X1,X3) = c_Orderings_Oord_Omin(X2,X3) ) ).

cnf(i_0_19051,axiom,
    ( X1 != X2
    | c_Orderings_Oord_Omin(X3,X1) = c_Orderings_Oord_Omin(X3,X2) ) ).

cnf(i_0_19052,axiom,
    ( X1 != X2
    | c_Com_Ocom_OLocal(X1,X3,X4) = c_Com_Ocom_OLocal(X2,X3,X4) ) ).

cnf(i_0_19053,axiom,
    ( X1 != X2
    | c_Com_Ocom_OLocal(X3,X1,X4) = c_Com_Ocom_OLocal(X3,X2,X4) ) ).

cnf(i_0_19054,axiom,
    ( X1 != X2
    | c_Com_Ocom_OLocal(X3,X4,X1) = c_Com_Ocom_OLocal(X3,X4,X2) ) ).

cnf(i_0_19055,axiom,
    ( X1 != X2
    | c_Predicate_Oconversep(X1,X3,X4) = c_Predicate_Oconversep(X2,X3,X4) ) ).

cnf(i_0_19056,axiom,
    ( X1 != X2
    | c_Predicate_Oconversep(X3,X1,X4) = c_Predicate_Oconversep(X3,X2,X4) ) ).

cnf(i_0_19057,axiom,
    ( X1 != X2
    | c_Predicate_Oconversep(X3,X4,X1) = c_Predicate_Oconversep(X3,X4,X2) ) ).

cnf(i_0_19058,axiom,
    ( X1 != X2
    | c_New__DSequence_Opos__single(X1,X3) = c_New__DSequence_Opos__single(X2,X3) ) ).

cnf(i_0_19059,axiom,
    ( X1 != X2
    | c_New__DSequence_Opos__single(X3,X1) = c_New__DSequence_Opos__single(X3,X2) ) ).

cnf(i_0_19060,axiom,
    ( X1 != X2
    | c_New__DSequence_Oneg__single(X1,X3) = c_New__DSequence_Oneg__single(X2,X3) ) ).

cnf(i_0_19061,axiom,
    ( X1 != X2
    | c_New__DSequence_Oneg__single(X3,X1) = c_New__DSequence_Oneg__single(X3,X2) ) ).

cnf(i_0_19062,axiom,
    ( X1 != X2
    | c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(X1) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(X2) ) ).

cnf(i_0_19063,axiom,
    ( X1 != X2
    | c_SMT_Oz3mod(X1,X3) = c_SMT_Oz3mod(X2,X3) ) ).

cnf(i_0_19064,axiom,
    ( X1 != X2
    | c_SMT_Oz3mod(X3,X1) = c_SMT_Oz3mod(X3,X2) ) ).

cnf(i_0_19065,axiom,
    ( X1 != X2
    | esk432_2(X1,X3) = esk432_2(X2,X3) ) ).

cnf(i_0_19066,axiom,
    ( X1 != X2
    | esk432_2(X3,X1) = esk432_2(X3,X2) ) ).

cnf(i_0_19067,axiom,
    ( X1 != X2
    | esk348_1(X1) = esk348_1(X2) ) ).

cnf(i_0_19068,axiom,
    ( X1 != X2
    | c_Com_Ocom_OCall(X1,X3,X4) = c_Com_Ocom_OCall(X2,X3,X4) ) ).

cnf(i_0_19069,axiom,
    ( X1 != X2
    | c_Com_Ocom_OCall(X3,X1,X4) = c_Com_Ocom_OCall(X3,X2,X4) ) ).

cnf(i_0_19070,axiom,
    ( X1 != X2
    | c_Com_Ocom_OCall(X3,X4,X1) = c_Com_Ocom_OCall(X3,X4,X2) ) ).

cnf(i_0_19071,axiom,
    ( X1 != X2
    | c_Quickcheck_Obeyond(X1,X3) = c_Quickcheck_Obeyond(X2,X3) ) ).

cnf(i_0_19072,axiom,
    ( X1 != X2
    | c_Quickcheck_Obeyond(X3,X1) = c_Quickcheck_Obeyond(X3,X2) ) ).

cnf(i_0_19073,axiom,
    ( X1 != X2
    | c_Nat_Onat_Onat__size(X1) = c_Nat_Onat_Onat__size(X2) ) ).

cnf(i_0_19074,axiom,
    ( X1 != X2
    | c_Random_Oinc__shift(X1,X3) = c_Random_Oinc__shift(X2,X3) ) ).

cnf(i_0_19075,axiom,
    ( X1 != X2
    | c_Random_Oinc__shift(X3,X1) = c_Random_Oinc__shift(X3,X2) ) ).

cnf(i_0_19076,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohb__single(X1,X3) = c_Lazy__Sequence_Ohb__single(X2,X3) ) ).

cnf(i_0_19077,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohb__single(X3,X1) = c_Lazy__Sequence_Ohb__single(X3,X2) ) ).

cnf(i_0_19078,axiom,
    ( X1 != X2
    | c_HOL_Obool_Obool__size(X1) = c_HOL_Obool_Obool__size(X2) ) ).

cnf(i_0_19079,axiom,
    ( X1 != X2
    | c_Divides_Oadjust(X1) = c_Divides_Oadjust(X2) ) ).

cnf(i_0_19080,axiom,
    ( X1 != X2
    | c_FunDef_Orp__inv__image(X1,X3) = c_FunDef_Orp__inv__image(X2,X3) ) ).

cnf(i_0_19081,axiom,
    ( X1 != X2
    | c_FunDef_Orp__inv__image(X3,X1) = c_FunDef_Orp__inv__image(X3,X2) ) ).

cnf(i_0_19082,axiom,
    ( X1 != X2
    | c_Com_Ocom_OWhile(X1,X3) = c_Com_Ocom_OWhile(X2,X3) ) ).

cnf(i_0_19083,axiom,
    ( X1 != X2
    | c_Com_Ocom_OWhile(X3,X1) = c_Com_Ocom_OWhile(X3,X2) ) ).

cnf(i_0_19084,axiom,
    ( X1 != X2
    | ~ hBOOL(X1)
    | hBOOL(X2) ) ).

cnf(i_0_19085,axiom,
    ( X1 != X2
    | ~ class_Groups_Ocomm__monoid__add(X1)
    | class_Groups_Ocomm__monoid__add(X2) ) ).

cnf(i_0_19086,axiom,
    ( X1 != X2
    | ~ class_Int_Oring__char__0(X1)
    | class_Int_Oring__char__0(X2) ) ).

cnf(i_0_19087,axiom,
    ( X1 != X2
    | ~ class_Rings_Oordered__semiring(X1)
    | class_Rings_Oordered__semiring(X2) ) ).

cnf(i_0_19088,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__semiring__strict(X1)
    | class_Rings_Olinordered__semiring__strict(X2) ) ).

cnf(i_0_19089,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__semiring(X1)
    | class_Rings_Olinordered__semiring(X2) ) ).

cnf(i_0_19090,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | class_Groups_Oordered__ab__semigroup__add__imp__le(X2) ) ).

cnf(i_0_19091,axiom,
    ( X1 != X2
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ) ).

cnf(i_0_19092,axiom,
    ( X1 != X2
    | ~ c_Predicate_Oreflp(X1,X3)
    | c_Predicate_Oreflp(X2,X3) ) ).

cnf(i_0_19093,axiom,
    ( X1 != X2
    | ~ c_Predicate_Oreflp(X3,X1)
    | c_Predicate_Oreflp(X3,X2) ) ).

cnf(i_0_19094,axiom,
    ( X1 != X2
    | ~ class_Rings_Oordered__comm__semiring(X1)
    | class_Rings_Oordered__comm__semiring(X2) ) ).

cnf(i_0_19095,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__comm__semiring__strict(X1)
    | class_Rings_Olinordered__comm__semiring__strict(X2) ) ).

cnf(i_0_19096,axiom,
    ( X1 != X2
    | ~ c_Predicate_Osymp(X1,X3)
    | c_Predicate_Osymp(X2,X3) ) ).

cnf(i_0_19097,axiom,
    ( X1 != X2
    | ~ c_Predicate_Osymp(X3,X1)
    | c_Predicate_Osymp(X3,X2) ) ).

cnf(i_0_19098,axiom,
    ( X1 != X2
    | ~ class_Rings_Oring__1(X1)
    | class_Rings_Oring__1(X2) ) ).

cnf(i_0_19099,axiom,
    ( X1 != X2
    | ~ c_Predicate_Otransp(X1,X3)
    | c_Predicate_Otransp(X2,X3) ) ).

cnf(i_0_19100,axiom,
    ( X1 != X2
    | ~ c_Predicate_Otransp(X3,X1)
    | c_Predicate_Otransp(X3,X2) ) ).

cnf(i_0_19101,axiom,
    ( X1 != X2
    | ~ class_Divides_Oring__div(X1)
    | class_Divides_Oring__div(X2) ) ).

cnf(i_0_19102,axiom,
    ( X1 != X2
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | class_Groups_Olinordered__ab__group__add(X2) ) ).

cnf(i_0_19103,axiom,
    ( X1 != X2
    | ~ class_Rings_Oordered__cancel__semiring(X1)
    | class_Rings_Oordered__cancel__semiring(X2) ) ).

cnf(i_0_19104,axiom,
    ( X1 != X2
    | ~ class_Rings_Oordered__ring__abs(X1)
    | class_Rings_Oordered__ring__abs(X2) ) ).

cnf(i_0_19105,axiom,
    ( X1 != X2
    | ~ class_Orderings_Owellorder(X1)
    | class_Orderings_Owellorder(X2) ) ).

cnf(i_0_19106,axiom,
    ( X1 != X2
    | ~ class_Lattices_Oboolean__algebra(X1)
    | class_Lattices_Oboolean__algebra(X2) ) ).

cnf(i_0_19107,axiom,
    ( X1 != X2
    | ~ class_Rings_Odivision__ring(X1)
    | class_Rings_Odivision__ring(X2) ) ).

cnf(i_0_19108,axiom,
    ( X1 != X2
    | ~ class_Rings_Ocomm__semiring(X1)
    | class_Rings_Ocomm__semiring(X2) ) ).

cnf(i_0_19109,axiom,
    ( X1 != X2
    | ~ class_Groups_Ominus(X1)
    | class_Groups_Ominus(X2) ) ).

cnf(i_0_19110,axiom,
    ( X1 != X2
    | ~ class_Groups_Ocomm__monoid__mult(X1)
    | class_Groups_Ocomm__monoid__mult(X2) ) ).

cnf(i_0_19111,axiom,
    ( X1 != X2
    | ~ class_Orderings_Opreorder(X1)
    | class_Orderings_Opreorder(X2) ) ).

cnf(i_0_19112,axiom,
    ( X1 != X2
    | ~ class_Groups_Ogroup__add(X1)
    | class_Groups_Ogroup__add(X2) ) ).

cnf(i_0_19113,axiom,
    ( X1 != X2
    | ~ c_Nat__Transfer_Otransfer__morphism(X1,X3,X4,X5)
    | c_Nat__Transfer_Otransfer__morphism(X2,X3,X4,X5) ) ).

cnf(i_0_19114,axiom,
    ( X1 != X2
    | ~ c_Nat__Transfer_Otransfer__morphism(X3,X1,X4,X5)
    | c_Nat__Transfer_Otransfer__morphism(X3,X2,X4,X5) ) ).

cnf(i_0_19115,axiom,
    ( X1 != X2
    | ~ c_Nat__Transfer_Otransfer__morphism(X3,X4,X1,X5)
    | c_Nat__Transfer_Otransfer__morphism(X3,X4,X2,X5) ) ).

cnf(i_0_19116,axiom,
    ( X1 != X2
    | ~ c_Nat__Transfer_Otransfer__morphism(X3,X4,X5,X1)
    | c_Nat__Transfer_Otransfer__morphism(X3,X4,X5,X2) ) ).

cnf(i_0_19117,axiom,
    ( X1 != X2
    | ~ class_Nat_Osemiring__char__0(X1)
    | class_Nat_Osemiring__char__0(X2) ) ).

cnf(i_0_19118,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Owf_H(X1,X3)
    | c_Nitpick_Owf_H(X2,X3) ) ).

cnf(i_0_19119,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Owf_H(X3,X1)
    | c_Nitpick_Owf_H(X3,X2) ) ).

cnf(i_0_19120,axiom,
    ( X1 != X2
    | ~ c_List_Onat__list(X1)
    | c_List_Onat__list(X2) ) ).

cnf(i_0_19121,axiom,
    ( X1 != X2
    | ~ class_Groups_Osgn__if(X1)
    | class_Groups_Osgn__if(X2) ) ).

cnf(i_0_19122,axiom,
    ( X1 != X2
    | ~ class_Power_Opower(X1)
    | class_Power_Opower(X2) ) ).

cnf(i_0_19123,axiom,
    ( X1 != X2
    | ~ class_Groups_Oabs__if(X1)
    | class_Groups_Oabs__if(X2) ) ).

cnf(i_0_19124,axiom,
    ( X1 != X2
    | ~ class_Groups_Ouminus(X1)
    | class_Groups_Ouminus(X2) ) ).

cnf(i_0_19125,axiom,
    ( X1 != X2
    | ~ class_Orderings_Oord(X1)
    | class_Orderings_Oord(X2) ) ).

cnf(i_0_19126,axiom,
    ( X1 != X2
    | ~ c_Big__Operators_Osemilattice__big(X1,X3,X4)
    | c_Big__Operators_Osemilattice__big(X2,X3,X4) ) ).

cnf(i_0_19127,axiom,
    ( X1 != X2
    | ~ c_Big__Operators_Osemilattice__big(X3,X1,X4)
    | c_Big__Operators_Osemilattice__big(X3,X2,X4) ) ).

cnf(i_0_19128,axiom,
    ( X1 != X2
    | ~ c_Big__Operators_Osemilattice__big(X3,X4,X1)
    | c_Big__Operators_Osemilattice__big(X3,X4,X2) ) ).

cnf(i_0_19129,axiom,
    ( X1 != X2
    | ~ class_Rings_Oidom(X1)
    | class_Rings_Oidom(X2) ) ).

cnf(i_0_19130,axiom,
    ( X1 != X2
    | ~ class_Rings_Ocomm__ring__1(X1)
    | class_Rings_Ocomm__ring__1(X2) ) ).

cnf(i_0_19131,axiom,
    ( X1 != X2
    | ~ class_Groups_Ocancel__semigroup__add(X1)
    | class_Groups_Ocancel__semigroup__add(X2) ) ).

cnf(i_0_19132,axiom,
    ( X1 != X2
    | ~ class_Groups_Ocancel__ab__semigroup__add(X1)
    | class_Groups_Ocancel__ab__semigroup__add(X2) ) ).

cnf(i_0_19133,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Ounknown(X1)
    | c_Nitpick_Ounknown(X2) ) ).

cnf(i_0_19134,axiom,
    ( X1 != X2
    | ~ class_Finite__Set_Ofinite(X1)
    | class_Finite__Set_Ofinite(X2) ) ).

cnf(i_0_19135,axiom,
    ( X1 != X2
    | ~ class_Orderings_Obot(X1)
    | class_Orderings_Obot(X2) ) ).

cnf(i_0_19136,axiom,
    ( X1 != X2
    | ~ class_Orderings_Otop(X1)
    | class_Orderings_Otop(X2) ) ).

cnf(i_0_19137,axiom,
    ( X1 != X2
    | ~ class_Rings_Omult__zero(X1)
    | class_Rings_Omult__zero(X2) ) ).

cnf(i_0_19138,axiom,
    ( X1 != X2
    | ~ class_Groups_Olinordered__ab__semigroup__add(X1)
    | class_Groups_Olinordered__ab__semigroup__add(X2) ) ).

cnf(i_0_19139,axiom,
    ( X1 != X2
    | ~ class_Rings_Ozero__neq__one(X1)
    | class_Rings_Ozero__neq__one(X2) ) ).

cnf(i_0_19140,axiom,
    ( X1 != X2
    | ~ class_Rings_Oring__no__zero__divisors(X1)
    | class_Rings_Oring__no__zero__divisors(X2) ) ).

cnf(i_0_19141,axiom,
    ( X1 != X2
    | ~ class_Lattices_Obounded__lattice__top(X1)
    | class_Lattices_Obounded__lattice__top(X2) ) ).

cnf(i_0_19142,axiom,
    ( X1 != X2
    | ~ class_Lattices_Obounded__lattice__bot(X1)
    | class_Lattices_Obounded__lattice__bot(X2) ) ).

cnf(i_0_19143,axiom,
    ( X1 != X2
    | ~ class_Rings_Odivision__ring__inverse__zero(X1)
    | class_Rings_Odivision__ring__inverse__zero(X2) ) ).

cnf(i_0_19144,axiom,
    ( X1 != X2
    | ~ class_Lattices_Obounded__lattice(X1)
    | class_Lattices_Obounded__lattice(X2) ) ).

cnf(i_0_19145,axiom,
    ( X1 != X2
    | ~ class_Nat_Osize(X1)
    | class_Nat_Osize(X2) ) ).

cnf(i_0_19146,axiom,
    ( X1 != X2
    | ~ class_Groups_Oone(X1)
    | class_Groups_Oone(X2) ) ).

cnf(i_0_19147,axiom,
    ( X1 != X2
    | ~ class_Groups_Ozero(X1)
    | class_Groups_Ozero(X2) ) ).

cnf(i_0_19148,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_19149,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_19150,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_19151,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_19152,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_19153,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_19154,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__idom(X1)
    | class_Rings_Olinordered__idom(X2) ) ).

cnf(i_0_19155,axiom,
    ( X1 != X2
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | class_Complete__Lattice_Ocomplete__lattice(X2) ) ).

cnf(i_0_19156,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_19157,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_19158,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_19159,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_19160,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_19161,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_19162,axiom,
    ( X1 != X2
    | ~ class_Int_Onumber__ring(X1)
    | class_Int_Onumber__ring(X2) ) ).

cnf(i_0_19163,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_19164,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_19165,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_19166,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_19167,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_19168,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_19169,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Opart__equivp(X1,X3)
    | c_Equiv__Relations_Opart__equivp(X2,X3) ) ).

cnf(i_0_19170,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Opart__equivp(X3,X1)
    | c_Equiv__Relations_Opart__equivp(X3,X2) ) ).

cnf(i_0_19171,axiom,
    ( X1 != X2
    | ~ c_Relation_Orefl__on(X1,X3,X4)
    | c_Relation_Orefl__on(X2,X3,X4) ) ).

cnf(i_0_19172,axiom,
    ( X1 != X2
    | ~ c_Relation_Orefl__on(X3,X1,X4)
    | c_Relation_Orefl__on(X3,X2,X4) ) ).

cnf(i_0_19173,axiom,
    ( X1 != X2
    | ~ c_Relation_Orefl__on(X3,X4,X1)
    | c_Relation_Orefl__on(X3,X4,X2) ) ).

cnf(i_0_19174,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Omax__extp(X1,X3,X4,X5)
    | c_Wellfounded_Omax__extp(X2,X3,X4,X5) ) ).

cnf(i_0_19175,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Omax__extp(X3,X1,X4,X5)
    | c_Wellfounded_Omax__extp(X3,X2,X4,X5) ) ).

cnf(i_0_19176,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Omax__extp(X3,X4,X1,X5)
    | c_Wellfounded_Omax__extp(X3,X4,X2,X5) ) ).

cnf(i_0_19177,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Omax__extp(X3,X4,X5,X1)
    | c_Wellfounded_Omax__extp(X3,X4,X5,X2) ) ).

cnf(i_0_19178,axiom,
    ( X1 != X2
    | ~ c_List_Olistrelp(X1,X3,X4,X5)
    | c_List_Olistrelp(X2,X3,X4,X5) ) ).

cnf(i_0_19179,axiom,
    ( X1 != X2
    | ~ c_List_Olistrelp(X3,X1,X4,X5)
    | c_List_Olistrelp(X3,X2,X4,X5) ) ).

cnf(i_0_19180,axiom,
    ( X1 != X2
    | ~ c_List_Olistrelp(X3,X4,X1,X5)
    | c_List_Olistrelp(X3,X4,X2,X5) ) ).

cnf(i_0_19181,axiom,
    ( X1 != X2
    | ~ c_List_Olistrelp(X3,X4,X5,X1)
    | c_List_Olistrelp(X3,X4,X5,X2) ) ).

cnf(i_0_19182,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Oequivp(X1,X3)
    | c_Equiv__Relations_Oequivp(X2,X3) ) ).

cnf(i_0_19183,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Oequivp(X3,X1)
    | c_Equiv__Relations_Oequivp(X3,X2) ) ).

cnf(i_0_19184,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Owf(X1,X3)
    | c_Wellfounded_Owf(X2,X3) ) ).

cnf(i_0_19185,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Owf(X3,X1)
    | c_Wellfounded_Owf(X3,X2) ) ).

cnf(i_0_19186,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_OwfP(X1,X3)
    | c_Wellfounded_OwfP(X2,X3) ) ).

cnf(i_0_19187,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_OwfP(X3,X1)
    | c_Wellfounded_OwfP(X3,X2) ) ).

cnf(i_0_19188,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofun__left__comm(X1,X3,X4)
    | c_Finite__Set_Ofun__left__comm(X2,X3,X4) ) ).

cnf(i_0_19189,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofun__left__comm(X3,X1,X4)
    | c_Finite__Set_Ofun__left__comm(X3,X2,X4) ) ).

cnf(i_0_19190,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofun__left__comm(X3,X4,X1)
    | c_Finite__Set_Ofun__left__comm(X3,X4,X2) ) ).

cnf(i_0_19191,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__semidom(X1)
    | class_Rings_Olinordered__semidom(X2) ) ).

cnf(i_0_19192,axiom,
    ( X1 != X2
    | ~ class_Lazy__Sequence_Osmall__lazy(X1)
    | class_Lazy__Sequence_Osmall__lazy(X2) ) ).

cnf(i_0_19193,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Oequiv(X1,X3,X4)
    | c_Equiv__Relations_Oequiv(X2,X3,X4) ) ).

cnf(i_0_19194,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Oequiv(X3,X1,X4)
    | c_Equiv__Relations_Oequiv(X3,X2,X4) ) ).

cnf(i_0_19195,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Oequiv(X3,X4,X1)
    | c_Equiv__Relations_Oequiv(X3,X4,X2) ) ).

cnf(i_0_19196,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__ab__group__add(X1)
    | class_Groups_Oordered__ab__group__add(X2) ) ).

cnf(i_0_19197,axiom,
    ( X1 != X2
    | ~ class_Groups_Omonoid__mult(X1)
    | class_Groups_Omonoid__mult(X2) ) ).

cnf(i_0_19198,axiom,
    ( X1 != X2
    | ~ class_Groups_Oab__semigroup__mult(X1)
    | class_Groups_Oab__semigroup__mult(X2) ) ).

cnf(i_0_19199,axiom,
    ( X1 != X2
    | ~ class_Groups_Omonoid__add(X1)
    | class_Groups_Omonoid__add(X2) ) ).

cnf(i_0_19200,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__ab__semigroup__add(X1)
    | class_Groups_Oordered__ab__semigroup__add(X2) ) ).

cnf(i_0_19201,axiom,
    ( X1 != X2
    | ~ c_List_Olist__all2(X1,X3,X4,X5,X6)
    | c_List_Olist__all2(X2,X3,X4,X5,X6) ) ).

cnf(i_0_19202,axiom,
    ( X1 != X2
    | ~ c_List_Olist__all2(X3,X1,X4,X5,X6)
    | c_List_Olist__all2(X3,X2,X4,X5,X6) ) ).

cnf(i_0_19203,axiom,
    ( X1 != X2
    | ~ c_List_Olist__all2(X3,X4,X1,X5,X6)
    | c_List_Olist__all2(X3,X4,X2,X5,X6) ) ).

cnf(i_0_19204,axiom,
    ( X1 != X2
    | ~ c_List_Olist__all2(X3,X4,X5,X1,X6)
    | c_List_Olist__all2(X3,X4,X5,X2,X6) ) ).

cnf(i_0_19205,axiom,
    ( X1 != X2
    | ~ c_List_Olist__all2(X3,X4,X5,X6,X1)
    | c_List_Olist__all2(X3,X4,X5,X6,X2) ) ).

cnf(i_0_19206,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
    | class_Groups_Oordered__cancel__ab__semigroup__add(X2) ) ).

cnf(i_0_19207,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__one__idem(X1,X3,X4)
    | c_Finite__Set_Ofolding__one__idem(X2,X3,X4) ) ).

cnf(i_0_19208,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__one__idem(X3,X1,X4)
    | c_Finite__Set_Ofolding__one__idem(X3,X2,X4) ) ).

cnf(i_0_19209,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__one__idem(X3,X4,X1)
    | c_Finite__Set_Ofolding__one__idem(X3,X4,X2) ) ).

cnf(i_0_19210,axiom,
    ( X1 != X2
    | ~ class_Rings_Ocomm__semiring__1(X1)
    | class_Rings_Ocomm__semiring__1(X2) ) ).

cnf(i_0_19211,axiom,
    ( X1 != X2
    | ~ class_Rings_Osemiring__1(X1)
    | class_Rings_Osemiring__1(X2) ) ).

cnf(i_0_19212,axiom,
    ( X1 != X2
    | ~ class_Rings_Osemiring__0(X1)
    | class_Rings_Osemiring__0(X2) ) ).

cnf(i_0_19213,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__one(X1,X3,X4)
    | c_Finite__Set_Ofolding__one(X2,X3,X4) ) ).

cnf(i_0_19214,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__one(X3,X1,X4)
    | c_Finite__Set_Ofolding__one(X3,X2,X4) ) ).

cnf(i_0_19215,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__one(X3,X4,X1)
    | c_Finite__Set_Ofolding__one(X3,X4,X2) ) ).

cnf(i_0_19216,axiom,
    ( X1 != X2
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | class_Fields_Olinordered__field__inverse__zero(X2) ) ).

cnf(i_0_19217,axiom,
    ( X1 != X2
    | ~ c_FunDef_Oreduction__pair(X1,X3)
    | c_FunDef_Oreduction__pair(X2,X3) ) ).

cnf(i_0_19218,axiom,
    ( X1 != X2
    | ~ c_FunDef_Oreduction__pair(X3,X1)
    | c_FunDef_Oreduction__pair(X3,X2) ) ).

cnf(i_0_19219,axiom,
    ( X1 != X2
    | ~ c_List_Olinorder__class_Osorted(X1,X3)
    | c_List_Olinorder__class_Osorted(X2,X3) ) ).

cnf(i_0_19220,axiom,
    ( X1 != X2
    | ~ c_List_Olinorder__class_Osorted(X3,X1)
    | c_List_Olinorder__class_Osorted(X3,X2) ) ).

cnf(i_0_19221,axiom,
    ( X1 != X2
    | ~ class_Orderings_Oorder(X1)
    | class_Orderings_Oorder(X2) ) ).

cnf(i_0_19222,axiom,
    ( X1 != X2
    | ~ class_Enum_Oenum(X1)
    | class_Enum_Oenum(X2) ) ).

cnf(i_0_19223,axiom,
    ( X1 != X2
    | ~ c_Nat__Transfer_Ois__nat(X1)
    | c_Nat__Transfer_Ois__nat(X2) ) ).

cnf(i_0_19224,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Oless__eq__frac(X1,X3,X4)
    | c_Nitpick_Oless__eq__frac(X2,X3,X4) ) ).

cnf(i_0_19225,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Oless__eq__frac(X3,X1,X4)
    | c_Nitpick_Oless__eq__frac(X3,X2,X4) ) ).

cnf(i_0_19226,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Oless__eq__frac(X3,X4,X1)
    | c_Nitpick_Oless__eq__frac(X3,X4,X2) ) ).

cnf(i_0_19227,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Oless__frac(X1,X3,X4)
    | c_Nitpick_Oless__frac(X2,X3,X4) ) ).

cnf(i_0_19228,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Oless__frac(X3,X1,X4)
    | c_Nitpick_Oless__frac(X3,X2,X4) ) ).

cnf(i_0_19229,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Oless__frac(X3,X4,X1)
    | c_Nitpick_Oless__frac(X3,X4,X2) ) ).

cnf(i_0_19230,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__comm__monoid__add(X1)
    | class_Groups_Oordered__comm__monoid__add(X2) ) ).

cnf(i_0_19231,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X1,X3,X4,X5)
    | c_Fun_Oinj__on(X2,X3,X4,X5) ) ).

cnf(i_0_19232,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X1,X4,X5)
    | c_Fun_Oinj__on(X3,X2,X4,X5) ) ).

cnf(i_0_19233,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X4,X1,X5)
    | c_Fun_Oinj__on(X3,X4,X2,X5) ) ).

cnf(i_0_19234,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X4,X5,X1)
    | c_Fun_Oinj__on(X3,X4,X5,X2) ) ).

cnf(i_0_19235,axiom,
    ( X1 != X2
    | ~ class_Rings_Oordered__ring(X1)
    | class_Rings_Oordered__ring(X2) ) ).

cnf(i_0_19236,axiom,
    ( X1 != X2
    | ~ class_Groups_Oab__group__add(X1)
    | class_Groups_Oab__group__add(X2) ) ).

cnf(i_0_19237,axiom,
    ( X1 != X2
    | ~ class_Rings_Oinverse(X1)
    | class_Rings_Oinverse(X2) ) ).

cnf(i_0_19238,axiom,
    ( X1 != X2
    | ~ class_Fields_Ofield(X1)
    | class_Fields_Ofield(X2) ) ).

cnf(i_0_19239,axiom,
    ( X1 != X2
    | ~ c_List_Olist__ex1(X1,X3,X4)
    | c_List_Olist__ex1(X2,X3,X4) ) ).

cnf(i_0_19240,axiom,
    ( X1 != X2
    | ~ c_List_Olist__ex1(X3,X1,X4)
    | c_List_Olist__ex1(X3,X2,X4) ) ).

cnf(i_0_19241,axiom,
    ( X1 != X2
    | ~ c_List_Olist__ex1(X3,X4,X1)
    | c_List_Olist__ex1(X3,X4,X2) ) ).

cnf(i_0_19242,axiom,
    ( X1 != X2
    | ~ c_List_Olist__all(X1,X3,X4)
    | c_List_Olist__all(X2,X3,X4) ) ).

cnf(i_0_19243,axiom,
    ( X1 != X2
    | ~ c_List_Olist__all(X3,X1,X4)
    | c_List_Olist__all(X3,X2,X4) ) ).

cnf(i_0_19244,axiom,
    ( X1 != X2
    | ~ c_List_Olist__all(X3,X4,X1)
    | c_List_Olist__all(X3,X4,X2) ) ).

cnf(i_0_19245,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_19246,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_19247,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_19248,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_19249,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_19250,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_19251,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__ab__group__add__abs(X1)
    | class_Groups_Oordered__ab__group__add__abs(X2) ) ).

cnf(i_0_19252,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_19253,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_19254,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_19255,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_19256,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_19257,axiom,
    ( X1 != X2
    | ~ class_Rings_Oring__1__no__zero__divisors(X1)
    | class_Rings_Oring__1__no__zero__divisors(X2) ) ).

cnf(i_0_19258,axiom,
    ( X1 != X2
    | ~ class_Orderings_Olinorder(X1)
    | class_Orderings_Olinorder(X2) ) ).

cnf(i_0_19259,axiom,
    ( X1 != X2
    | ~ c_Nat__Transfer_Onat__set(X1)
    | c_Nat__Transfer_Onat__set(X2) ) ).

cnf(i_0_19260,axiom,
    ( X1 != X2
    | ~ c_Fun_Obij__betw(X1,X3,X4,X5,X6)
    | c_Fun_Obij__betw(X2,X3,X4,X5,X6) ) ).

cnf(i_0_19261,axiom,
    ( X1 != X2
    | ~ c_Fun_Obij__betw(X3,X1,X4,X5,X6)
    | c_Fun_Obij__betw(X3,X2,X4,X5,X6) ) ).

cnf(i_0_19262,axiom,
    ( X1 != X2
    | ~ c_Fun_Obij__betw(X3,X4,X1,X5,X6)
    | c_Fun_Obij__betw(X3,X4,X2,X5,X6) ) ).

cnf(i_0_19263,axiom,
    ( X1 != X2
    | ~ c_Fun_Obij__betw(X3,X4,X5,X1,X6)
    | c_Fun_Obij__betw(X3,X4,X5,X2,X6) ) ).

cnf(i_0_19264,axiom,
    ( X1 != X2
    | ~ c_Fun_Obij__betw(X3,X4,X5,X6,X1)
    | c_Fun_Obij__betw(X3,X4,X5,X6,X2) ) ).

cnf(i_0_19265,axiom,
    ( X1 != X2
    | ~ class_Fields_Ofield__inverse__zero(X1)
    | class_Fields_Ofield__inverse__zero(X2) ) ).

cnf(i_0_19266,axiom,
    ( X1 != X2
    | ~ c_Relation_Otrans(X1,X3)
    | c_Relation_Otrans(X2,X3) ) ).

cnf(i_0_19267,axiom,
    ( X1 != X2
    | ~ c_Relation_Otrans(X3,X1)
    | c_Relation_Otrans(X3,X2) ) ).

cnf(i_0_19268,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_19269,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_19270,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_19271,axiom,
    ( X1 != X2
    | ~ class_Lattices_Osemilattice__sup(X1)
    | class_Lattices_Osemilattice__sup(X2) ) ).

cnf(i_0_19272,axiom,
    ( X1 != X2
    | ~ c_Int_Oiszero(X1,X3)
    | c_Int_Oiszero(X2,X3) ) ).

cnf(i_0_19273,axiom,
    ( X1 != X2
    | ~ c_Int_Oiszero(X3,X1)
    | c_Int_Oiszero(X3,X2) ) ).

cnf(i_0_19274,axiom,
    ( X1 != X2
    | ~ c_Relation_Ototal__on(X1,X3,X4)
    | c_Relation_Ototal__on(X2,X3,X4) ) ).

cnf(i_0_19275,axiom,
    ( X1 != X2
    | ~ c_Relation_Ototal__on(X3,X1,X4)
    | c_Relation_Ototal__on(X3,X2,X4) ) ).

cnf(i_0_19276,axiom,
    ( X1 != X2
    | ~ c_Relation_Ototal__on(X3,X4,X1)
    | c_Relation_Ototal__on(X3,X4,X2) ) ).

cnf(i_0_19277,axiom,
    ( X1 != X2
    | ~ c_Relation_Osingle__valued(X1,X3,X4)
    | c_Relation_Osingle__valued(X2,X3,X4) ) ).

cnf(i_0_19278,axiom,
    ( X1 != X2
    | ~ c_Relation_Osingle__valued(X3,X1,X4)
    | c_Relation_Osingle__valued(X3,X2,X4) ) ).

cnf(i_0_19279,axiom,
    ( X1 != X2
    | ~ c_Relation_Osingle__valued(X3,X4,X1)
    | c_Relation_Osingle__valued(X3,X4,X2) ) ).

cnf(i_0_19280,axiom,
    ( X1 != X2
    | ~ class_Int_Onumber(X1)
    | class_Int_Onumber(X2) ) ).

cnf(i_0_19281,axiom,
    ( X1 != X2
    | ~ class_Lattices_Odistrib__lattice(X1)
    | class_Lattices_Odistrib__lattice(X2) ) ).

cnf(i_0_19282,axiom,
    ( X1 != X2
    | ~ c_Hoare__Mirabelle_Otriple__valid(X1,X3,X4)
    | c_Hoare__Mirabelle_Otriple__valid(X2,X3,X4) ) ).

cnf(i_0_19283,axiom,
    ( X1 != X2
    | ~ c_Hoare__Mirabelle_Otriple__valid(X3,X1,X4)
    | c_Hoare__Mirabelle_Otriple__valid(X3,X2,X4) ) ).

cnf(i_0_19284,axiom,
    ( X1 != X2
    | ~ c_Hoare__Mirabelle_Otriple__valid(X3,X4,X1)
    | c_Hoare__Mirabelle_Otriple__valid(X3,X4,X2) ) ).

cnf(i_0_19285,axiom,
    ( X1 != X2
    | ~ class_Divides_Osemiring__div(X1)
    | class_Divides_Osemiring__div(X2) ) ).

cnf(i_0_19286,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | class_Rings_Olinordered__ring__strict(X2) ) ).

cnf(i_0_19287,axiom,
    ( X1 != X2
    | ~ class_Lattices_Olattice(X1)
    | class_Lattices_Olattice(X2) ) ).

cnf(i_0_19288,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__ring(X1)
    | class_Rings_Olinordered__ring(X2) ) ).

cnf(i_0_19289,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding(X1,X3,X4,X5)
    | c_Finite__Set_Ofolding(X2,X3,X4,X5) ) ).

cnf(i_0_19290,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding(X3,X1,X4,X5)
    | c_Finite__Set_Ofolding(X3,X2,X4,X5) ) ).

cnf(i_0_19291,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding(X3,X4,X1,X5)
    | c_Finite__Set_Ofolding(X3,X4,X2,X5) ) ).

cnf(i_0_19292,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding(X3,X4,X5,X1)
    | c_Finite__Set_Ofolding(X3,X4,X5,X2) ) ).

cnf(i_0_19293,axiom,
    ( X1 != X2
    | ~ c_Relation_Osym(X1,X3)
    | c_Relation_Osym(X2,X3) ) ).

cnf(i_0_19294,axiom,
    ( X1 != X2
    | ~ c_Relation_Osym(X3,X1)
    | c_Relation_Osym(X3,X2) ) ).

cnf(i_0_19295,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__semiring__1(X1)
    | class_Rings_Olinordered__semiring__1(X2) ) ).

cnf(i_0_19296,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__semiring__1__strict(X1)
    | class_Rings_Olinordered__semiring__1__strict(X2) ) ).

cnf(i_0_19297,axiom,
    ( X1 != X2
    | ~ class_Lattices_Osemilattice__inf(X1)
    | class_Lattices_Osemilattice__inf(X2) ) ).

cnf(i_0_19298,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Ocongruent(X1,X3,X4,X5)
    | c_Equiv__Relations_Ocongruent(X2,X3,X4,X5) ) ).

cnf(i_0_19299,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Ocongruent(X3,X1,X4,X5)
    | c_Equiv__Relations_Ocongruent(X3,X2,X4,X5) ) ).

cnf(i_0_19300,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Ocongruent(X3,X4,X1,X5)
    | c_Equiv__Relations_Ocongruent(X3,X4,X2,X5) ) ).

cnf(i_0_19301,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Ocongruent(X3,X4,X5,X1)
    | c_Equiv__Relations_Ocongruent(X3,X4,X5,X2) ) ).

cnf(i_0_19302,axiom,
    ( X1 != X2
    | ~ class_Fields_Olinordered__field(X1)
    | class_Fields_Olinordered__field(X2) ) ).

cnf(i_0_19303,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Oacyclic(X1,X3)
    | c_Wellfounded_Oacyclic(X2,X3) ) ).

cnf(i_0_19304,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Oacyclic(X3,X1)
    | c_Wellfounded_Oacyclic(X3,X2) ) ).

cnf(i_0_19305,axiom,
    ( X1 != X2
    | ~ c_Relation_Oantisym(X1,X3)
    | c_Relation_Oantisym(X2,X3) ) ).

cnf(i_0_19306,axiom,
    ( X1 != X2
    | ~ c_Relation_Oantisym(X3,X1)
    | c_Relation_Oantisym(X3,X2) ) ).

cnf(i_0_19307,axiom,
    ( X1 != X2
    | ~ c_Natural_Oevaln(X1,X3,X4,X5)
    | c_Natural_Oevaln(X2,X3,X4,X5) ) ).

cnf(i_0_19308,axiom,
    ( X1 != X2
    | ~ c_Natural_Oevaln(X3,X1,X4,X5)
    | c_Natural_Oevaln(X3,X2,X4,X5) ) ).

cnf(i_0_19309,axiom,
    ( X1 != X2
    | ~ c_Natural_Oevaln(X3,X4,X1,X5)
    | c_Natural_Oevaln(X3,X4,X2,X5) ) ).

cnf(i_0_19310,axiom,
    ( X1 != X2
    | ~ c_Natural_Oevaln(X3,X4,X5,X1)
    | c_Natural_Oevaln(X3,X4,X5,X2) ) ).

cnf(i_0_19311,axiom,
    ( X1 != X2
    | ~ class_Lattices_Oab__semigroup__idem__mult(X1)
    | class_Lattices_Oab__semigroup__idem__mult(X2) ) ).

cnf(i_0_19312,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Orefl_H(X1,X3)
    | c_Nitpick_Orefl_H(X2,X3) ) ).

cnf(i_0_19313,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Orefl_H(X3,X1)
    | c_Nitpick_Orefl_H(X3,X2) ) ).

cnf(i_0_19314,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__idem(X1,X3,X4,X5)
    | c_Finite__Set_Ofolding__idem(X2,X3,X4,X5) ) ).

cnf(i_0_19315,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__idem(X3,X1,X4,X5)
    | c_Finite__Set_Ofolding__idem(X3,X2,X4,X5) ) ).

cnf(i_0_19316,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__idem(X3,X4,X1,X5)
    | c_Finite__Set_Ofolding__idem(X3,X4,X2,X5) ) ).

cnf(i_0_19317,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__idem(X3,X4,X5,X1)
    | c_Finite__Set_Ofolding__idem(X3,X4,X5,X2) ) ).

cnf(i_0_19318,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_19319,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_19320,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_19321,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_19322,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_19323,axiom,
    ( X1 != X2
    | ~ c_Hoare__Mirabelle_Ohoare__valids(X1,X3,X4)
    | c_Hoare__Mirabelle_Ohoare__valids(X2,X3,X4) ) ).

cnf(i_0_19324,axiom,
    ( X1 != X2
    | ~ c_Hoare__Mirabelle_Ohoare__valids(X3,X1,X4)
    | c_Hoare__Mirabelle_Ohoare__valids(X3,X2,X4) ) ).

cnf(i_0_19325,axiom,
    ( X1 != X2
    | ~ c_Hoare__Mirabelle_Ohoare__valids(X3,X4,X1)
    | c_Hoare__Mirabelle_Ohoare__valids(X3,X4,X2) ) ).

cnf(i_0_19326,axiom,
    ( X1 != X2
    | ~ class_Rings_Ono__zero__divisors(X1)
    | class_Rings_Ono__zero__divisors(X2) ) ).

cnf(i_0_19327,axiom,
    ( X1 != X2
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X3,X4)
    | c_Hoare__Mirabelle_Ohoare__derivs(X2,X3,X4) ) ).

cnf(i_0_19328,axiom,
    ( X1 != X2
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,X1,X4)
    | c_Hoare__Mirabelle_Ohoare__derivs(X3,X2,X4) ) ).

cnf(i_0_19329,axiom,
    ( X1 != X2
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,X4,X1)
    | c_Hoare__Mirabelle_Ohoare__derivs(X3,X4,X2) ) ).

cnf(i_0_19330,axiom,
    ( X1 != X2
    | ~ c_Typedef_Otype__definition(X1,X3,X4,X5,X6)
    | c_Typedef_Otype__definition(X2,X3,X4,X5,X6) ) ).

cnf(i_0_19331,axiom,
    ( X1 != X2
    | ~ c_Typedef_Otype__definition(X3,X1,X4,X5,X6)
    | c_Typedef_Otype__definition(X3,X2,X4,X5,X6) ) ).

cnf(i_0_19332,axiom,
    ( X1 != X2
    | ~ c_Typedef_Otype__definition(X3,X4,X1,X5,X6)
    | c_Typedef_Otype__definition(X3,X4,X2,X5,X6) ) ).

cnf(i_0_19333,axiom,
    ( X1 != X2
    | ~ c_Typedef_Otype__definition(X3,X4,X5,X1,X6)
    | c_Typedef_Otype__definition(X3,X4,X5,X2,X6) ) ).

cnf(i_0_19334,axiom,
    ( X1 != X2
    | ~ c_Typedef_Otype__definition(X3,X4,X5,X6,X1)
    | c_Typedef_Otype__definition(X3,X4,X5,X6,X2) ) ).

cnf(i_0_19335,axiom,
    ( X1 != X2
    | ~ class_Rings_Oring(X1)
    | class_Rings_Oring(X2) ) ).

cnf(i_0_19336,axiom,
    ( X1 != X2
    | ~ class_Rings_Osemiring(X1)
    | class_Rings_Osemiring(X2) ) ).

cnf(i_0_19337,axiom,
    ( X1 != X2
    | ~ class_Groups_Osemigroup__add(X1)
    | class_Groups_Osemigroup__add(X2) ) ).

cnf(i_0_19338,axiom,
    ( X1 != X2
    | ~ c_List_Olist__ex(X1,X3,X4)
    | c_List_Olist__ex(X2,X3,X4) ) ).

cnf(i_0_19339,axiom,
    ( X1 != X2
    | ~ c_List_Olist__ex(X3,X1,X4)
    | c_List_Olist__ex(X3,X2,X4) ) ).

cnf(i_0_19340,axiom,
    ( X1 != X2
    | ~ c_List_Olist__ex(X3,X4,X1)
    | c_List_Olist__ex(X3,X4,X2) ) ).

cnf(i_0_19341,axiom,
    ( X1 != X2
    | ~ c_List_Oall__interval__int(X1,X3,X4)
    | c_List_Oall__interval__int(X2,X3,X4) ) ).

cnf(i_0_19342,axiom,
    ( X1 != X2
    | ~ c_List_Oall__interval__int(X3,X1,X4)
    | c_List_Oall__interval__int(X3,X2,X4) ) ).

cnf(i_0_19343,axiom,
    ( X1 != X2
    | ~ c_List_Oall__interval__int(X3,X4,X1)
    | c_List_Oall__interval__int(X3,X4,X2) ) ).

cnf(i_0_19344,axiom,
    ( X1 != X2
    | ~ c_Relation_Oirrefl(X1,X3)
    | c_Relation_Oirrefl(X2,X3) ) ).

cnf(i_0_19345,axiom,
    ( X1 != X2
    | ~ c_Relation_Oirrefl(X3,X1)
    | c_Relation_Oirrefl(X3,X2) ) ).

cnf(i_0_19346,axiom,
    ( X1 != X2
    | ~ epred2_3(X1,X3,X4)
    | epred2_3(X2,X3,X4) ) ).

cnf(i_0_19347,axiom,
    ( X1 != X2
    | ~ epred2_3(X3,X1,X4)
    | epred2_3(X3,X2,X4) ) ).

cnf(i_0_19348,axiom,
    ( X1 != X2
    | ~ epred2_3(X3,X4,X1)
    | epred2_3(X3,X4,X2) ) ).

cnf(i_0_19349,axiom,
    ( X1 != X2
    | ~ epred1_3(X1,X3,X4)
    | epred1_3(X2,X3,X4) ) ).

cnf(i_0_19350,axiom,
    ( X1 != X2
    | ~ epred1_3(X3,X1,X4)
    | epred1_3(X3,X2,X4) ) ).

cnf(i_0_19351,axiom,
    ( X1 != X2
    | ~ epred1_3(X3,X4,X1)
    | epred1_3(X3,X4,X2) ) ).

cnf(i_0_19352,axiom,
    ( X1 != X2
    | ~ class_Groups_Oab__semigroup__add(X1)
    | class_Groups_Oab__semigroup__add(X2) ) ).

cnf(i_0_18452_001,axiom,
    X1 = X1 ).

cnf(i_0_18453_002,axiom,
    ( X1 = X2
    | X2 != X1 ) ).

cnf(i_0_18454_003,axiom,
    ( X1 = X2
    | X1 != X3
    | X3 != X2 ) ).

cnf(i_0_18455_004,axiom,
    ( X1 != X2
    | hAPP(X1,X3) = hAPP(X2,X3) ) ).

cnf(i_0_18456_005,axiom,
    ( X1 != X2
    | hAPP(X3,X1) = hAPP(X3,X2) ) ).

cnf(i_0_18457_006,axiom,
    ( X1 != X2
    | c_Big__Operators_Olinorder__class_OMin(X1,X3) = c_Big__Operators_Olinorder__class_OMin(X2,X3) ) ).

cnf(i_0_18458_007,axiom,
    ( X1 != X2
    | c_Big__Operators_Olinorder__class_OMin(X3,X1) = c_Big__Operators_Olinorder__class_OMin(X3,X2) ) ).

cnf(i_0_18459_008,axiom,
    ( X1 != X2
    | c_Big__Operators_Olinorder__class_OMax(X1,X3) = c_Big__Operators_Olinorder__class_OMax(X2,X3) ) ).

cnf(i_0_18460_009,axiom,
    ( X1 != X2
    | c_Big__Operators_Olinorder__class_OMax(X3,X1) = c_Big__Operators_Olinorder__class_OMax(X3,X2) ) ).

cnf(i_0_18461_010,axiom,
    ( X1 != X2
    | c_List_Olistrel(X1,X3) = c_List_Olistrel(X2,X3) ) ).

cnf(i_0_18462_011,axiom,
    ( X1 != X2
    | c_List_Olistrel(X3,X1) = c_List_Olistrel(X3,X2) ) ).

cnf(i_0_18463_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_18464_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_18465_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_18466_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_18467_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_18468_017,axiom,
    ( X1 != X2
    | c_List_Opartition(X1,X3,X4) = c_List_Opartition(X2,X3,X4) ) ).

cnf(i_0_18469_018,axiom,
    ( X1 != X2
    | c_List_Opartition(X3,X1,X4) = c_List_Opartition(X3,X2,X4) ) ).

cnf(i_0_18470_019,axiom,
    ( X1 != X2
    | c_List_Opartition(X3,X4,X1) = c_List_Opartition(X3,X4,X2) ) ).

cnf(i_0_18471_020,axiom,
    ( X1 != X2
    | c_Com_Ocom_OAss(X1,X3) = c_Com_Ocom_OAss(X2,X3) ) ).

cnf(i_0_18472_021,axiom,
    ( X1 != X2
    | c_Com_Ocom_OAss(X3,X1) = c_Com_Ocom_OAss(X3,X2) ) ).

cnf(i_0_18473_022,axiom,
    ( X1 != X2
    | c_Wellfounded_Olex__prod(X1,X3,X4,X5) = c_Wellfounded_Olex__prod(X2,X3,X4,X5) ) ).

cnf(i_0_18474_023,axiom,
    ( X1 != X2
    | c_Wellfounded_Olex__prod(X3,X1,X4,X5) = c_Wellfounded_Olex__prod(X3,X2,X4,X5) ) ).

cnf(i_0_18475_024,axiom,
    ( X1 != X2
    | c_Wellfounded_Olex__prod(X3,X4,X1,X5) = c_Wellfounded_Olex__prod(X3,X4,X2,X5) ) ).

cnf(i_0_18476_025,axiom,
    ( X1 != X2
    | c_Wellfounded_Olex__prod(X3,X4,X5,X1) = c_Wellfounded_Olex__prod(X3,X4,X5,X2) ) ).

cnf(i_0_18477_026,axiom,
    ( X1 != X2
    | c_Power_Opower__class_Opower(X1) = c_Power_Opower__class_Opower(X2) ) ).

cnf(i_0_18478_027,axiom,
    ( X1 != X2
    | c_List_Osublist(X1,X3,X4) = c_List_Osublist(X2,X3,X4) ) ).

cnf(i_0_18479_028,axiom,
    ( X1 != X2
    | c_List_Osublist(X3,X1,X4) = c_List_Osublist(X3,X2,X4) ) ).

cnf(i_0_18480_029,axiom,
    ( X1 != X2
    | c_List_Osublist(X3,X4,X1) = c_List_Osublist(X3,X4,X2) ) ).

cnf(i_0_18481_030,axiom,
    ( X1 != X2
    | c_List_Otranspose(X1,X3) = c_List_Otranspose(X2,X3) ) ).

cnf(i_0_18482_031,axiom,
    ( X1 != X2
    | c_List_Otranspose(X3,X1) = c_List_Otranspose(X3,X2) ) ).

cnf(i_0_18483_032,axiom,
    ( X1 != X2
    | c_List_Olist_ONil(X1) = c_List_Olist_ONil(X2) ) ).

cnf(i_0_18484_033,axiom,
    ( X1 != X2
    | c_Partial__Function_Ofun__lub(X1,X3,X4,X5,X6,X7) = c_Partial__Function_Ofun__lub(X2,X3,X4,X5,X6,X7) ) ).

cnf(i_0_18485_034,axiom,
    ( X1 != X2
    | c_Partial__Function_Ofun__lub(X3,X1,X4,X5,X6,X7) = c_Partial__Function_Ofun__lub(X3,X2,X4,X5,X6,X7) ) ).

cnf(i_0_18486_035,axiom,
    ( X1 != X2
    | c_Partial__Function_Ofun__lub(X3,X4,X1,X5,X6,X7) = c_Partial__Function_Ofun__lub(X3,X4,X2,X5,X6,X7) ) ).

cnf(i_0_18487_036,axiom,
    ( X1 != X2
    | c_Partial__Function_Ofun__lub(X3,X4,X5,X1,X6,X7) = c_Partial__Function_Ofun__lub(X3,X4,X5,X2,X6,X7) ) ).

cnf(i_0_18488_037,axiom,
    ( X1 != X2
    | c_Partial__Function_Ofun__lub(X3,X4,X5,X6,X1,X7) = c_Partial__Function_Ofun__lub(X3,X4,X5,X6,X2,X7) ) ).

cnf(i_0_18489_038,axiom,
    ( X1 != X2
    | c_Partial__Function_Ofun__lub(X3,X4,X5,X6,X7,X1) = c_Partial__Function_Ofun__lub(X3,X4,X5,X6,X7,X2) ) ).

cnf(i_0_18490_039,axiom,
    ( X1 != X2
    | c_Complete__Lattice_OInf__class_OInf(X1,X3) = c_Complete__Lattice_OInf__class_OInf(X2,X3) ) ).

cnf(i_0_18491_040,axiom,
    ( X1 != X2
    | c_Complete__Lattice_OInf__class_OInf(X3,X1) = c_Complete__Lattice_OInf__class_OInf(X3,X2) ) ).

cnf(i_0_18492_041,axiom,
    ( X1 != X2
    | c_Complete__Lattice_OSup__class_OSup(X1,X3) = c_Complete__Lattice_OSup__class_OSup(X2,X3) ) ).

cnf(i_0_18493_042,axiom,
    ( X1 != X2
    | c_Complete__Lattice_OSup__class_OSup(X3,X1) = c_Complete__Lattice_OSup__class_OSup(X3,X2) ) ).

cnf(i_0_18494_043,axiom,
    ( X1 != X2
    | c_Divides_Odivmod__int__rel(X1,X3) = c_Divides_Odivmod__int__rel(X2,X3) ) ).

cnf(i_0_18495_044,axiom,
    ( X1 != X2
    | c_Divides_Odivmod__int__rel(X3,X1) = c_Divides_Odivmod__int__rel(X3,X2) ) ).

cnf(i_0_18496_045,axiom,
    ( X1 != X2
    | c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ozero__class_Ozero(X2) ) ).

cnf(i_0_18497_046,axiom,
    ( X1 != X2
    | c_Set_Othe__elem(X1,X3) = c_Set_Othe__elem(X2,X3) ) ).

cnf(i_0_18498_047,axiom,
    ( X1 != X2
    | c_Set_Othe__elem(X3,X1) = c_Set_Othe__elem(X3,X2) ) ).

cnf(i_0_18499_048,axiom,
    ( X1 != X2
    | c_Nitpick_Osetsum_H(X1,X3,X4,X5) = c_Nitpick_Osetsum_H(X2,X3,X4,X5) ) ).

cnf(i_0_18500_049,axiom,
    ( X1 != X2
    | c_Nitpick_Osetsum_H(X3,X1,X4,X5) = c_Nitpick_Osetsum_H(X3,X2,X4,X5) ) ).

cnf(i_0_18501_050,axiom,
    ( X1 != X2
    | c_Nitpick_Osetsum_H(X3,X4,X1,X5) = c_Nitpick_Osetsum_H(X3,X4,X2,X5) ) ).

cnf(i_0_18502_051,axiom,
    ( X1 != X2
    | c_Nitpick_Osetsum_H(X3,X4,X5,X1) = c_Nitpick_Osetsum_H(X3,X4,X5,X2) ) ).

cnf(i_0_18503_052,axiom,
    ( X1 != X2
    | c_List_Omonoid__add__class_Olistsum(X1) = c_List_Omonoid__add__class_Olistsum(X2) ) ).

cnf(i_0_18504_053,axiom,
    ( X1 != X2
    | c_Hilbert__Choice_OEps(X1,X3) = c_Hilbert__Choice_OEps(X2,X3) ) ).

cnf(i_0_18505_054,axiom,
    ( X1 != X2
    | c_Hilbert__Choice_OEps(X3,X1) = c_Hilbert__Choice_OEps(X3,X2) ) ).

cnf(i_0_18506_055,axiom,
    ( X1 != X2
    | esk559_6(X1,X3,X4,X5,X6,X7) = esk559_6(X2,X3,X4,X5,X6,X7) ) ).

cnf(i_0_18507_056,axiom,
    ( X1 != X2
    | esk559_6(X3,X1,X4,X5,X6,X7) = esk559_6(X3,X2,X4,X5,X6,X7) ) ).

cnf(i_0_18508_057,axiom,
    ( X1 != X2
    | esk559_6(X3,X4,X1,X5,X6,X7) = esk559_6(X3,X4,X2,X5,X6,X7) ) ).

cnf(i_0_18509_058,axiom,
    ( X1 != X2
    | esk559_6(X3,X4,X5,X1,X6,X7) = esk559_6(X3,X4,X5,X2,X6,X7) ) ).

cnf(i_0_18510_059,axiom,
    ( X1 != X2
    | esk559_6(X3,X4,X5,X6,X1,X7) = esk559_6(X3,X4,X5,X6,X2,X7) ) ).

cnf(i_0_18511_060,axiom,
    ( X1 != X2
    | esk559_6(X3,X4,X5,X6,X7,X1) = esk559_6(X3,X4,X5,X6,X7,X2) ) ).

cnf(i_0_18512_061,axiom,
    ( X1 != X2
    | esk560_6(X1,X3,X4,X5,X6,X7) = esk560_6(X2,X3,X4,X5,X6,X7) ) ).

cnf(i_0_18513_062,axiom,
    ( X1 != X2
    | esk560_6(X3,X1,X4,X5,X6,X7) = esk560_6(X3,X2,X4,X5,X6,X7) ) ).

cnf(i_0_18514_063,axiom,
    ( X1 != X2
    | esk560_6(X3,X4,X1,X5,X6,X7) = esk560_6(X3,X4,X2,X5,X6,X7) ) ).

cnf(i_0_18515_064,axiom,
    ( X1 != X2
    | esk560_6(X3,X4,X5,X1,X6,X7) = esk560_6(X3,X4,X5,X2,X6,X7) ) ).

cnf(i_0_18516_065,axiom,
    ( X1 != X2
    | esk560_6(X3,X4,X5,X6,X1,X7) = esk560_6(X3,X4,X5,X6,X2,X7) ) ).

cnf(i_0_18517_066,axiom,
    ( X1 != X2
    | esk560_6(X3,X4,X5,X6,X7,X1) = esk560_6(X3,X4,X5,X6,X7,X2) ) ).

cnf(i_0_18518_067,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_18519_068,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_18520_069,axiom,
    ( X1 != X2
    | c_Groups_Ominus__class_Ominus(X1) = c_Groups_Ominus__class_Ominus(X2) ) ).

cnf(i_0_18521_070,axiom,
    ( X1 != X2
    | c_Random__Sequence_ORandom(X1,X3,X4,X5) = c_Random__Sequence_ORandom(X2,X3,X4,X5) ) ).

cnf(i_0_18522_071,axiom,
    ( X1 != X2
    | c_Random__Sequence_ORandom(X3,X1,X4,X5) = c_Random__Sequence_ORandom(X3,X2,X4,X5) ) ).

cnf(i_0_18523_072,axiom,
    ( X1 != X2
    | c_Random__Sequence_ORandom(X3,X4,X1,X5) = c_Random__Sequence_ORandom(X3,X4,X2,X5) ) ).

cnf(i_0_18524_073,axiom,
    ( X1 != X2
    | c_Random__Sequence_ORandom(X3,X4,X5,X1) = c_Random__Sequence_ORandom(X3,X4,X5,X2) ) ).

cnf(i_0_18525_074,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohb__not__seq(X1) = c_Lazy__Sequence_Ohb__not__seq(X2) ) ).

cnf(i_0_18526_075,axiom,
    ( X1 != X2
    | c_Wellfounded_Omax__ext(X1,X3) = c_Wellfounded_Omax__ext(X2,X3) ) ).

cnf(i_0_18527_076,axiom,
    ( X1 != X2
    | c_Wellfounded_Omax__ext(X3,X1) = c_Wellfounded_Omax__ext(X3,X2) ) ).

cnf(i_0_18528_077,axiom,
    ( X1 != X2
    | c_Divides_Odiv__class_Omod(X1,X3,X4) = c_Divides_Odiv__class_Omod(X2,X3,X4) ) ).

cnf(i_0_18529_078,axiom,
    ( X1 != X2
    | c_Divides_Odiv__class_Omod(X3,X1,X4) = c_Divides_Odiv__class_Omod(X3,X2,X4) ) ).

cnf(i_0_18530_079,axiom,
    ( X1 != X2
    | c_Divides_Odiv__class_Omod(X3,X4,X1) = c_Divides_Odiv__class_Omod(X3,X4,X2) ) ).

cnf(i_0_18531_080,axiom,
    ( X1 != X2
    | c_Wellfounded_Omin__ext(X1,X3) = c_Wellfounded_Omin__ext(X2,X3) ) ).

cnf(i_0_18532_081,axiom,
    ( X1 != X2
    | c_Wellfounded_Omin__ext(X3,X1) = c_Wellfounded_Omin__ext(X3,X2) ) ).

cnf(i_0_18533_082,axiom,
    ( X1 != X2
    | c_Com_Ocom_OCond(X1,X3,X4) = c_Com_Ocom_OCond(X2,X3,X4) ) ).

cnf(i_0_18534_083,axiom,
    ( X1 != X2
    | c_Com_Ocom_OCond(X3,X1,X4) = c_Com_Ocom_OCond(X3,X2,X4) ) ).

cnf(i_0_18535_084,axiom,
    ( X1 != X2
    | c_Com_Ocom_OCond(X3,X4,X1) = c_Com_Ocom_OCond(X3,X4,X2) ) ).

cnf(i_0_18536_085,axiom,
    ( X1 != X2
    | c_Wellfounded_Ofinite__psubset(X1) = c_Wellfounded_Ofinite__psubset(X2) ) ).

cnf(i_0_18537_086,axiom,
    ( X1 != X2
    | c_Nitpick_Ocard_H(X1,X3) = c_Nitpick_Ocard_H(X2,X3) ) ).

cnf(i_0_18538_087,axiom,
    ( X1 != X2
    | c_Nitpick_Ocard_H(X3,X1) = c_Nitpick_Ocard_H(X3,X2) ) ).

cnf(i_0_18539_088,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_18540_089,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_18541_090,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_18542_091,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_18543_092,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_18544_093,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_18545_094,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_18546_095,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_18547_096,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_18548_097,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_18549_098,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_18550_099,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_18551_100,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_18552_101,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_18553_102,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_18554_103,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_18555_104,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_18556_105,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_18557_106,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_18558_107,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_18559_108,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_18560_109,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_18561_110,axiom,
    ( X1 != X2
    | c_Int_Onumber__class_Onumber__of(X1) = c_Int_Onumber__class_Onumber__of(X2) ) ).

cnf(i_0_18562_111,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(X1,X3) = c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(X2,X3) ) ).

cnf(i_0_18563_112,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(X3,X1) = c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(X3,X2) ) ).

cnf(i_0_18564_113,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oappend(X1,X3,X4) = c_Lazy__Sequence_Oappend(X2,X3,X4) ) ).

cnf(i_0_18565_114,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oappend(X3,X1,X4) = c_Lazy__Sequence_Oappend(X3,X2,X4) ) ).

cnf(i_0_18566_115,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oappend(X3,X4,X1) = c_Lazy__Sequence_Oappend(X3,X4,X2) ) ).

cnf(i_0_18567_116,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oproduct(X1,X3,X4,X5) = c_Lazy__Sequence_Oproduct(X2,X3,X4,X5) ) ).

cnf(i_0_18568_117,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oproduct(X3,X1,X4,X5) = c_Lazy__Sequence_Oproduct(X3,X2,X4,X5) ) ).

cnf(i_0_18569_118,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oproduct(X3,X4,X1,X5) = c_Lazy__Sequence_Oproduct(X3,X4,X2,X5) ) ).

cnf(i_0_18570_119,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oproduct(X3,X4,X5,X1) = c_Lazy__Sequence_Oproduct(X3,X4,X5,X2) ) ).

cnf(i_0_18571_120,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oempty(X1) = c_Lazy__Sequence_Oempty(X2) ) ).

cnf(i_0_18572_121,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Oneg__bind(X1,X3,X4,X5) = c_New__Random__Sequence_Oneg__bind(X2,X3,X4,X5) ) ).

cnf(i_0_18573_122,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Oneg__bind(X3,X1,X4,X5) = c_New__Random__Sequence_Oneg__bind(X3,X2,X4,X5) ) ).

cnf(i_0_18574_123,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Oneg__bind(X3,X4,X1,X5) = c_New__Random__Sequence_Oneg__bind(X3,X4,X2,X5) ) ).

cnf(i_0_18575_124,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Oneg__bind(X3,X4,X5,X1) = c_New__Random__Sequence_Oneg__bind(X3,X4,X5,X2) ) ).

cnf(i_0_18576_125,axiom,
    ( X1 != X2
    | c_New__DSequence_Oneg__bind(X1,X3,X4,X5) = c_New__DSequence_Oneg__bind(X2,X3,X4,X5) ) ).

cnf(i_0_18577_126,axiom,
    ( X1 != X2
    | c_New__DSequence_Oneg__bind(X3,X1,X4,X5) = c_New__DSequence_Oneg__bind(X3,X2,X4,X5) ) ).

cnf(i_0_18578_127,axiom,
    ( X1 != X2
    | c_New__DSequence_Oneg__bind(X3,X4,X1,X5) = c_New__DSequence_Oneg__bind(X3,X4,X2,X5) ) ).

cnf(i_0_18579_128,axiom,
    ( X1 != X2
    | c_New__DSequence_Oneg__bind(X3,X4,X5,X1) = c_New__DSequence_Oneg__bind(X3,X4,X5,X2) ) ).

cnf(i_0_18580_129,axiom,
    ( X1 != X2
    | c_Groups_Oone__class_Oone(X1) = c_Groups_Oone__class_Oone(X2) ) ).

cnf(i_0_18581_130,axiom,
    ( X1 != X2
    | esk450_5(X1,X3,X4,X5,X6) = esk450_5(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18582_131,axiom,
    ( X1 != X2
    | esk450_5(X3,X1,X4,X5,X6) = esk450_5(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18583_132,axiom,
    ( X1 != X2
    | esk450_5(X3,X4,X1,X5,X6) = esk450_5(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18584_133,axiom,
    ( X1 != X2
    | esk450_5(X3,X4,X5,X1,X6) = esk450_5(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18585_134,axiom,
    ( X1 != X2
    | esk450_5(X3,X4,X5,X6,X1) = esk450_5(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18586_135,axiom,
    ( X1 != X2
    | esk451_5(X1,X3,X4,X5,X6) = esk451_5(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18587_136,axiom,
    ( X1 != X2
    | esk451_5(X3,X1,X4,X5,X6) = esk451_5(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18588_137,axiom,
    ( X1 != X2
    | esk451_5(X3,X4,X1,X5,X6) = esk451_5(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18589_138,axiom,
    ( X1 != X2
    | esk451_5(X3,X4,X5,X1,X6) = esk451_5(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18590_139,axiom,
    ( X1 != X2
    | esk451_5(X3,X4,X5,X6,X1) = esk451_5(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18591_140,axiom,
    ( X1 != X2
    | esk449_5(X1,X3,X4,X5,X6) = esk449_5(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18592_141,axiom,
    ( X1 != X2
    | esk449_5(X3,X1,X4,X5,X6) = esk449_5(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18593_142,axiom,
    ( X1 != X2
    | esk449_5(X3,X4,X1,X5,X6) = esk449_5(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18594_143,axiom,
    ( X1 != X2
    | esk449_5(X3,X4,X5,X1,X6) = esk449_5(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18595_144,axiom,
    ( X1 != X2
    | esk449_5(X3,X4,X5,X6,X1) = esk449_5(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18596_145,axiom,
    ( X1 != X2
    | esk448_5(X1,X3,X4,X5,X6) = esk448_5(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18597_146,axiom,
    ( X1 != X2
    | esk448_5(X3,X1,X4,X5,X6) = esk448_5(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18598_147,axiom,
    ( X1 != X2
    | esk448_5(X3,X4,X1,X5,X6) = esk448_5(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18599_148,axiom,
    ( X1 != X2
    | esk448_5(X3,X4,X5,X1,X6) = esk448_5(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18600_149,axiom,
    ( X1 != X2
    | esk448_5(X3,X4,X5,X6,X1) = esk448_5(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18601_150,axiom,
    ( X1 != X2
    | c_HOL_OThe(X1,X3) = c_HOL_OThe(X2,X3) ) ).

cnf(i_0_18602_151,axiom,
    ( X1 != X2
    | c_HOL_OThe(X3,X1) = c_HOL_OThe(X3,X2) ) ).

cnf(i_0_18603_152,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Opos__bind(X1,X3,X4,X5) = c_New__Random__Sequence_Opos__bind(X2,X3,X4,X5) ) ).

cnf(i_0_18604_153,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Opos__bind(X3,X1,X4,X5) = c_New__Random__Sequence_Opos__bind(X3,X2,X4,X5) ) ).

cnf(i_0_18605_154,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Opos__bind(X3,X4,X1,X5) = c_New__Random__Sequence_Opos__bind(X3,X4,X2,X5) ) ).

cnf(i_0_18606_155,axiom,
    ( X1 != X2
    | c_New__Random__Sequence_Opos__bind(X3,X4,X5,X1) = c_New__Random__Sequence_Opos__bind(X3,X4,X5,X2) ) ).

cnf(i_0_18607_156,axiom,
    ( X1 != X2
    | c_New__DSequence_Opos__bind(X1,X3,X4,X5) = c_New__DSequence_Opos__bind(X2,X3,X4,X5) ) ).

cnf(i_0_18608_157,axiom,
    ( X1 != X2
    | c_New__DSequence_Opos__bind(X3,X1,X4,X5) = c_New__DSequence_Opos__bind(X3,X2,X4,X5) ) ).

cnf(i_0_18609_158,axiom,
    ( X1 != X2
    | c_New__DSequence_Opos__bind(X3,X4,X1,X5) = c_New__DSequence_Opos__bind(X3,X4,X2,X5) ) ).

cnf(i_0_18610_159,axiom,
    ( X1 != X2
    | c_New__DSequence_Opos__bind(X3,X4,X5,X1) = c_New__DSequence_Opos__bind(X3,X4,X5,X2) ) ).

cnf(i_0_18611_160,axiom,
    ( X1 != X2
    | c_Nitpick_Oprod(X1,X3,X4,X5) = c_Nitpick_Oprod(X2,X3,X4,X5) ) ).

cnf(i_0_18612_161,axiom,
    ( X1 != X2
    | c_Nitpick_Oprod(X3,X1,X4,X5) = c_Nitpick_Oprod(X3,X2,X4,X5) ) ).

cnf(i_0_18613_162,axiom,
    ( X1 != X2
    | c_Nitpick_Oprod(X3,X4,X1,X5) = c_Nitpick_Oprod(X3,X4,X2,X5) ) ).

cnf(i_0_18614_163,axiom,
    ( X1 != X2
    | c_Nitpick_Oprod(X3,X4,X5,X1) = c_Nitpick_Oprod(X3,X4,X5,X2) ) ).

cnf(i_0_18615_164,axiom,
    ( X1 != X2
    | c_List_OtakeWhile(X1,X3,X4) = c_List_OtakeWhile(X2,X3,X4) ) ).

cnf(i_0_18616_165,axiom,
    ( X1 != X2
    | c_List_OtakeWhile(X3,X1,X4) = c_List_OtakeWhile(X3,X2,X4) ) ).

cnf(i_0_18617_166,axiom,
    ( X1 != X2
    | c_List_OtakeWhile(X3,X4,X1) = c_List_OtakeWhile(X3,X4,X2) ) ).

cnf(i_0_18618_167,axiom,
    ( X1 != X2
    | c_Fun_Oid(X1) = c_Fun_Oid(X2) ) ).

cnf(i_0_18619_168,axiom,
    ( X1 != X2
    | esk239_6(X1,X3,X4,X5,X6,X7) = esk239_6(X2,X3,X4,X5,X6,X7) ) ).

cnf(i_0_18620_169,axiom,
    ( X1 != X2
    | esk239_6(X3,X1,X4,X5,X6,X7) = esk239_6(X3,X2,X4,X5,X6,X7) ) ).

cnf(i_0_18621_170,axiom,
    ( X1 != X2
    | esk239_6(X3,X4,X1,X5,X6,X7) = esk239_6(X3,X4,X2,X5,X6,X7) ) ).

cnf(i_0_18622_171,axiom,
    ( X1 != X2
    | esk239_6(X3,X4,X5,X1,X6,X7) = esk239_6(X3,X4,X5,X2,X6,X7) ) ).

cnf(i_0_18623_172,axiom,
    ( X1 != X2
    | esk239_6(X3,X4,X5,X6,X1,X7) = esk239_6(X3,X4,X5,X6,X2,X7) ) ).

cnf(i_0_18624_173,axiom,
    ( X1 != X2
    | esk239_6(X3,X4,X5,X6,X7,X1) = esk239_6(X3,X4,X5,X6,X7,X2) ) ).

cnf(i_0_18625_174,axiom,
    ( X1 != X2
    | esk238_6(X1,X3,X4,X5,X6,X7) = esk238_6(X2,X3,X4,X5,X6,X7) ) ).

cnf(i_0_18626_175,axiom,
    ( X1 != X2
    | esk238_6(X3,X1,X4,X5,X6,X7) = esk238_6(X3,X2,X4,X5,X6,X7) ) ).

cnf(i_0_18627_176,axiom,
    ( X1 != X2
    | esk238_6(X3,X4,X1,X5,X6,X7) = esk238_6(X3,X4,X2,X5,X6,X7) ) ).

cnf(i_0_18628_177,axiom,
    ( X1 != X2
    | esk238_6(X3,X4,X5,X1,X6,X7) = esk238_6(X3,X4,X5,X2,X6,X7) ) ).

cnf(i_0_18629_178,axiom,
    ( X1 != X2
    | esk238_6(X3,X4,X5,X6,X1,X7) = esk238_6(X3,X4,X5,X6,X2,X7) ) ).

cnf(i_0_18630_179,axiom,
    ( X1 != X2
    | esk238_6(X3,X4,X5,X6,X7,X1) = esk238_6(X3,X4,X5,X6,X7,X2) ) ).

cnf(i_0_18631_180,axiom,
    ( X1 != X2
    | c_Enum_On__lists(X1,X3,X4) = c_Enum_On__lists(X2,X3,X4) ) ).

cnf(i_0_18632_181,axiom,
    ( X1 != X2
    | c_Enum_On__lists(X3,X1,X4) = c_Enum_On__lists(X3,X2,X4) ) ).

cnf(i_0_18633_182,axiom,
    ( X1 != X2
    | c_Enum_On__lists(X3,X4,X1) = c_Enum_On__lists(X3,X4,X2) ) ).

cnf(i_0_18634_183,axiom,
    ( X1 != X2
    | c_Nitpick_Otimes__frac(X1,X3,X4) = c_Nitpick_Otimes__frac(X2,X3,X4) ) ).

cnf(i_0_18635_184,axiom,
    ( X1 != X2
    | c_Nitpick_Otimes__frac(X3,X1,X4) = c_Nitpick_Otimes__frac(X3,X2,X4) ) ).

cnf(i_0_18636_185,axiom,
    ( X1 != X2
    | c_Nitpick_Otimes__frac(X3,X4,X1) = c_Nitpick_Otimes__frac(X3,X4,X2) ) ).

cnf(i_0_18637_186,axiom,
    ( X1 != X2
    | c_Divides_OnegDivAlg(X1,X3) = c_Divides_OnegDivAlg(X2,X3) ) ).

cnf(i_0_18638_187,axiom,
    ( X1 != X2
    | c_Divides_OnegDivAlg(X3,X1) = c_Divides_OnegDivAlg(X3,X2) ) ).

cnf(i_0_18639_188,axiom,
    ( X1 != X2
    | c_Divides_OposDivAlg(X1,X3) = c_Divides_OposDivAlg(X2,X3) ) ).

cnf(i_0_18640_189,axiom,
    ( X1 != X2
    | c_Divides_OposDivAlg(X3,X1) = c_Divides_OposDivAlg(X3,X2) ) ).

cnf(i_0_18641_190,axiom,
    ( X1 != X2
    | c_Nat_Osemiring__1__class_Oof__nat(X1) = c_Nat_Osemiring__1__class_Oof__nat(X2) ) ).

cnf(i_0_18642_191,axiom,
    ( X1 != X2
    | c_Nat_Onat_Onat__case(X1,X3,X4,X5) = c_Nat_Onat_Onat__case(X2,X3,X4,X5) ) ).

cnf(i_0_18643_192,axiom,
    ( X1 != X2
    | c_Nat_Onat_Onat__case(X3,X1,X4,X5) = c_Nat_Onat_Onat__case(X3,X2,X4,X5) ) ).

cnf(i_0_18644_193,axiom,
    ( X1 != X2
    | c_Nat_Onat_Onat__case(X3,X4,X1,X5) = c_Nat_Onat_Onat__case(X3,X4,X2,X5) ) ).

cnf(i_0_18645_194,axiom,
    ( X1 != X2
    | c_Nat_Onat_Onat__case(X3,X4,X5,X1) = c_Nat_Onat_Onat__case(X3,X4,X5,X2) ) ).

cnf(i_0_18646_195,axiom,
    ( X1 != X2
    | c_Relation_OId__on(X1,X3) = c_Relation_OId__on(X2,X3) ) ).

cnf(i_0_18647_196,axiom,
    ( X1 != X2
    | c_Relation_OId__on(X3,X1) = c_Relation_OId__on(X3,X2) ) ).

cnf(i_0_18648_197,axiom,
    ( X1 != X2
    | c_Int_Oint__ge__less__than(X1) = c_Int_Oint__ge__less__than(X2) ) ).

cnf(i_0_18649_198,axiom,
    ( X1 != X2
    | c_List_Olistrel1(X1,X3) = c_List_Olistrel1(X2,X3) ) ).

cnf(i_0_18650_199,axiom,
    ( X1 != X2
    | c_List_Olistrel1(X3,X1) = c_List_Olistrel1(X3,X2) ) ).

cnf(i_0_18651_200,axiom,
    ( X1 != X2
    | c_Finite__Set_Ofold(X1,X3,X4) = c_Finite__Set_Ofold(X2,X3,X4) ) ).

cnf(i_0_18652_201,axiom,
    ( X1 != X2
    | c_Finite__Set_Ofold(X3,X1,X4) = c_Finite__Set_Ofold(X3,X2,X4) ) ).

cnf(i_0_18653_202,axiom,
    ( X1 != X2
    | c_Finite__Set_Ofold(X3,X4,X1) = c_Finite__Set_Ofold(X3,X4,X2) ) ).

cnf(i_0_18654_203,axiom,
    ( X1 != X2
    | c_Nitpick_Ouminus__frac(X1,X3) = c_Nitpick_Ouminus__frac(X2,X3) ) ).

cnf(i_0_18655_204,axiom,
    ( X1 != X2
    | c_Nitpick_Ouminus__frac(X3,X1) = c_Nitpick_Ouminus__frac(X3,X2) ) ).

cnf(i_0_18656_205,axiom,
    ( X1 != X2
    | c_Nitpick_OAbs__Frac(X1,X3) = c_Nitpick_OAbs__Frac(X2,X3) ) ).

cnf(i_0_18657_206,axiom,
    ( X1 != X2
    | c_Nitpick_OAbs__Frac(X3,X1) = c_Nitpick_OAbs__Frac(X3,X2) ) ).

cnf(i_0_18658_207,axiom,
    ( X1 != X2
    | esk345_4(X1,X3,X4,X5) = esk345_4(X2,X3,X4,X5) ) ).

cnf(i_0_18659_208,axiom,
    ( X1 != X2
    | esk345_4(X3,X1,X4,X5) = esk345_4(X3,X2,X4,X5) ) ).

cnf(i_0_18660_209,axiom,
    ( X1 != X2
    | esk345_4(X3,X4,X1,X5) = esk345_4(X3,X4,X2,X5) ) ).

cnf(i_0_18661_210,axiom,
    ( X1 != X2
    | esk345_4(X3,X4,X5,X1) = esk345_4(X3,X4,X5,X2) ) ).

cnf(i_0_18662_211,axiom,
    ( X1 != X2
    | esk344_4(X1,X3,X4,X5) = esk344_4(X2,X3,X4,X5) ) ).

cnf(i_0_18663_212,axiom,
    ( X1 != X2
    | esk344_4(X3,X1,X4,X5) = esk344_4(X3,X2,X4,X5) ) ).

cnf(i_0_18664_213,axiom,
    ( X1 != X2
    | esk344_4(X3,X4,X1,X5) = esk344_4(X3,X4,X2,X5) ) ).

cnf(i_0_18665_214,axiom,
    ( X1 != X2
    | esk344_4(X3,X4,X5,X1) = esk344_4(X3,X4,X5,X2) ) ).

cnf(i_0_18666_215,axiom,
    ( X1 != X2
    | c_Orderings_Obot__class_Obot(X1) = c_Orderings_Obot__class_Obot(X2) ) ).

cnf(i_0_18667_216,axiom,
    ( X1 != X2
    | c_Hilbert__Choice_Oinv__into(X1,X3,X4,X5) = c_Hilbert__Choice_Oinv__into(X2,X3,X4,X5) ) ).

cnf(i_0_18668_217,axiom,
    ( X1 != X2
    | c_Hilbert__Choice_Oinv__into(X3,X1,X4,X5) = c_Hilbert__Choice_Oinv__into(X3,X2,X4,X5) ) ).

cnf(i_0_18669_218,axiom,
    ( X1 != X2
    | c_Hilbert__Choice_Oinv__into(X3,X4,X1,X5) = c_Hilbert__Choice_Oinv__into(X3,X4,X2,X5) ) ).

cnf(i_0_18670_219,axiom,
    ( X1 != X2
    | c_Hilbert__Choice_Oinv__into(X3,X4,X5,X1) = c_Hilbert__Choice_Oinv__into(X3,X4,X5,X2) ) ).

cnf(i_0_18671_220,axiom,
    ( X1 != X2
    | c_List_Olistsp(X1,X3) = c_List_Olistsp(X2,X3) ) ).

cnf(i_0_18672_221,axiom,
    ( X1 != X2
    | c_List_Olistsp(X3,X1) = c_List_Olistsp(X3,X2) ) ).

cnf(i_0_18673_222,axiom,
    ( X1 != X2
    | c_List_Olists(X1,X3) = c_List_Olists(X2,X3) ) ).

cnf(i_0_18674_223,axiom,
    ( X1 != X2
    | c_List_Olists(X3,X1) = c_List_Olists(X3,X2) ) ).

cnf(i_0_18675_224,axiom,
    ( X1 != X2
    | c_Orderings_Oord__class_Omax(X1) = c_Orderings_Oord__class_Omax(X2) ) ).

cnf(i_0_18676_225,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice_OInf__fin(X1,X3,X4) = c_Big__Operators_Olattice_OInf__fin(X2,X3,X4) ) ).

cnf(i_0_18677_226,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice_OInf__fin(X3,X1,X4) = c_Big__Operators_Olattice_OInf__fin(X3,X2,X4) ) ).

cnf(i_0_18678_227,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice_OInf__fin(X3,X4,X1) = c_Big__Operators_Olattice_OInf__fin(X3,X4,X2) ) ).

cnf(i_0_18679_228,axiom,
    ( X1 != X2
    | c_Orderings_Oord__class_Omin(X1) = c_Orderings_Oord__class_Omin(X2) ) ).

cnf(i_0_18680_229,axiom,
    ( X1 != X2
    | c_Int_Oint__ge__less__than2(X1) = c_Int_Oint__ge__less__than2(X2) ) ).

cnf(i_0_18681_230,axiom,
    ( X1 != X2
    | c_Nitpick_Oof__frac(X1,X3,X4) = c_Nitpick_Oof__frac(X2,X3,X4) ) ).

cnf(i_0_18682_231,axiom,
    ( X1 != X2
    | c_Nitpick_Oof__frac(X3,X1,X4) = c_Nitpick_Oof__frac(X3,X2,X4) ) ).

cnf(i_0_18683_232,axiom,
    ( X1 != X2
    | c_Nitpick_Oof__frac(X3,X4,X1) = c_Nitpick_Oof__frac(X3,X4,X2) ) ).

cnf(i_0_18684_233,axiom,
    ( X1 != X2
    | c_List_Omeasures(X1,X3) = c_List_Omeasures(X2,X3) ) ).

cnf(i_0_18685_234,axiom,
    ( X1 != X2
    | c_List_Omeasures(X3,X1) = c_List_Omeasures(X3,X2) ) ).

cnf(i_0_18686_235,axiom,
    ( X1 != X2
    | c_Random__Sequence_Omap(X1,X3,X4,X5) = c_Random__Sequence_Omap(X2,X3,X4,X5) ) ).

cnf(i_0_18687_236,axiom,
    ( X1 != X2
    | c_Random__Sequence_Omap(X3,X1,X4,X5) = c_Random__Sequence_Omap(X3,X2,X4,X5) ) ).

cnf(i_0_18688_237,axiom,
    ( X1 != X2
    | c_Random__Sequence_Omap(X3,X4,X1,X5) = c_Random__Sequence_Omap(X3,X4,X2,X5) ) ).

cnf(i_0_18689_238,axiom,
    ( X1 != X2
    | c_Random__Sequence_Omap(X3,X4,X5,X1) = c_Random__Sequence_Omap(X3,X4,X5,X2) ) ).

cnf(i_0_18690_239,axiom,
    ( X1 != X2
    | c_Random__Sequence_Obind(X1,X3,X4,X5) = c_Random__Sequence_Obind(X2,X3,X4,X5) ) ).

cnf(i_0_18691_240,axiom,
    ( X1 != X2
    | c_Random__Sequence_Obind(X3,X1,X4,X5) = c_Random__Sequence_Obind(X3,X2,X4,X5) ) ).

cnf(i_0_18692_241,axiom,
    ( X1 != X2
    | c_Random__Sequence_Obind(X3,X4,X1,X5) = c_Random__Sequence_Obind(X3,X4,X2,X5) ) ).

cnf(i_0_18693_242,axiom,
    ( X1 != X2
    | c_Random__Sequence_Obind(X3,X4,X5,X1) = c_Random__Sequence_Obind(X3,X4,X5,X2) ) ).

cnf(i_0_18694_243,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X4) ) ).

cnf(i_0_18695_244,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastAtMost(X3,X1,X4) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X2,X4) ) ).

cnf(i_0_18696_245,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X2) ) ).

cnf(i_0_18697_246,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice_OSup__fin(X1,X3,X4) = c_Big__Operators_Olattice_OSup__fin(X2,X3,X4) ) ).

cnf(i_0_18698_247,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice_OSup__fin(X3,X1,X4) = c_Big__Operators_Olattice_OSup__fin(X3,X2,X4) ) ).

cnf(i_0_18699_248,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice_OSup__fin(X3,X4,X1) = c_Big__Operators_Olattice_OSup__fin(X3,X4,X2) ) ).

cnf(i_0_18700_249,axiom,
    ( X1 != X2
    | c_Lattices_Osemilattice__inf__class_Oinf(X1) = c_Lattices_Osemilattice__inf__class_Oinf(X2) ) ).

cnf(i_0_18701_250,axiom,
    ( X1 != X2
    | c_List_Olist_Olist__size(X1,X3,X4) = c_List_Olist_Olist__size(X2,X3,X4) ) ).

cnf(i_0_18702_251,axiom,
    ( X1 != X2
    | c_List_Olist_Olist__size(X3,X1,X4) = c_List_Olist_Olist__size(X3,X2,X4) ) ).

cnf(i_0_18703_252,axiom,
    ( X1 != X2
    | c_List_Olist_Olist__size(X3,X4,X1) = c_List_Olist_Olist__size(X3,X4,X2) ) ).

cnf(i_0_18704_253,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice__class_OSup__fin(X1,X3) = c_Big__Operators_Olattice__class_OSup__fin(X2,X3) ) ).

cnf(i_0_18705_254,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice__class_OSup__fin(X3,X1) = c_Big__Operators_Olattice__class_OSup__fin(X3,X2) ) ).

cnf(i_0_18706_255,axiom,
    ( X1 != X2
    | c_Lattices_Osemilattice__sup__class_Osup(X1) = c_Lattices_Osemilattice__sup__class_Osup(X2) ) ).

cnf(i_0_18707_256,axiom,
    ( X1 != X2
    | c_Enum_Osublists(X1,X3) = c_Enum_Osublists(X2,X3) ) ).

cnf(i_0_18708_257,axiom,
    ( X1 != X2
    | c_Enum_Osublists(X3,X1) = c_Enum_Osublists(X3,X2) ) ).

cnf(i_0_18709_258,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice__class_OInf__fin(X1,X3) = c_Big__Operators_Olattice__class_OInf__fin(X2,X3) ) ).

cnf(i_0_18710_259,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice__class_OInf__fin(X3,X1) = c_Big__Operators_Olattice__class_OInf__fin(X3,X2) ) ).

cnf(i_0_18711_260,axiom,
    ( X1 != X2
    | c_Random_Oselect__weight(X1,X3) = c_Random_Oselect__weight(X2,X3) ) ).

cnf(i_0_18712_261,axiom,
    ( X1 != X2
    | c_Random_Oselect__weight(X3,X1) = c_Random_Oselect__weight(X3,X2) ) ).

cnf(i_0_18713_262,axiom,
    ( X1 != X2
    | c_Random_Opick(X1,X3) = c_Random_Opick(X2,X3) ) ).

cnf(i_0_18714_263,axiom,
    ( X1 != X2
    | c_Random_Opick(X3,X1) = c_Random_Opick(X3,X2) ) ).

cnf(i_0_18715_264,axiom,
    ( X1 != X2
    | c_Fun_Ofun__upd(X1,X3,X4,X5,X6) = c_Fun_Ofun__upd(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18716_265,axiom,
    ( X1 != X2
    | c_Fun_Ofun__upd(X3,X1,X4,X5,X6) = c_Fun_Ofun__upd(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18717_266,axiom,
    ( X1 != X2
    | c_Fun_Ofun__upd(X3,X4,X1,X5,X6) = c_Fun_Ofun__upd(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18718_267,axiom,
    ( X1 != X2
    | c_Fun_Ofun__upd(X3,X4,X5,X1,X6) = c_Fun_Ofun__upd(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18719_268,axiom,
    ( X1 != X2
    | c_Fun_Ofun__upd(X3,X4,X5,X6,X1) = c_Fun_Ofun__upd(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18720_269,axiom,
    ( X1 != X2
    | c_List_Oset__Cons(X1,X3,X4) = c_List_Oset__Cons(X2,X3,X4) ) ).

cnf(i_0_18721_270,axiom,
    ( X1 != X2
    | c_List_Oset__Cons(X3,X1,X4) = c_List_Oset__Cons(X3,X2,X4) ) ).

cnf(i_0_18722_271,axiom,
    ( X1 != X2
    | c_List_Oset__Cons(X3,X4,X1) = c_List_Oset__Cons(X3,X4,X2) ) ).

cnf(i_0_18723_272,axiom,
    ( X1 != X2
    | c_Wellfounded_Omlex__prod(X1,X3,X4) = c_Wellfounded_Omlex__prod(X2,X3,X4) ) ).

cnf(i_0_18724_273,axiom,
    ( X1 != X2
    | c_Wellfounded_Omlex__prod(X3,X1,X4) = c_Wellfounded_Omlex__prod(X3,X2,X4) ) ).

cnf(i_0_18725_274,axiom,
    ( X1 != X2
    | c_Wellfounded_Omlex__prod(X3,X4,X1) = c_Wellfounded_Omlex__prod(X3,X4,X2) ) ).

cnf(i_0_18726_275,axiom,
    ( X1 != X2
    | c_Nitpick_Onorm__frac(X1,X3) = c_Nitpick_Onorm__frac(X2,X3) ) ).

cnf(i_0_18727_276,axiom,
    ( X1 != X2
    | c_Nitpick_Onorm__frac(X3,X1) = c_Nitpick_Onorm__frac(X3,X2) ) ).

cnf(i_0_18728_277,axiom,
    ( X1 != X2
    | c_List_Oremove1(X1,X3,X4) = c_List_Oremove1(X2,X3,X4) ) ).

cnf(i_0_18729_278,axiom,
    ( X1 != X2
    | c_List_Oremove1(X3,X1,X4) = c_List_Oremove1(X3,X2,X4) ) ).

cnf(i_0_18730_279,axiom,
    ( X1 != X2
    | c_List_Oremove1(X3,X4,X1) = c_List_Oremove1(X3,X4,X2) ) ).

cnf(i_0_18731_280,axiom,
    ( X1 != X2
    | esk525_4(X1,X3,X4,X5) = esk525_4(X2,X3,X4,X5) ) ).

cnf(i_0_18732_281,axiom,
    ( X1 != X2
    | esk525_4(X3,X1,X4,X5) = esk525_4(X3,X2,X4,X5) ) ).

cnf(i_0_18733_282,axiom,
    ( X1 != X2
    | esk525_4(X3,X4,X1,X5) = esk525_4(X3,X4,X2,X5) ) ).

cnf(i_0_18734_283,axiom,
    ( X1 != X2
    | esk525_4(X3,X4,X5,X1) = esk525_4(X3,X4,X5,X2) ) ).

cnf(i_0_18735_284,axiom,
    ( X1 != X2
    | esk524_4(X1,X3,X4,X5) = esk524_4(X2,X3,X4,X5) ) ).

cnf(i_0_18736_285,axiom,
    ( X1 != X2
    | esk524_4(X3,X1,X4,X5) = esk524_4(X3,X2,X4,X5) ) ).

cnf(i_0_18737_286,axiom,
    ( X1 != X2
    | esk524_4(X3,X4,X1,X5) = esk524_4(X3,X4,X2,X5) ) ).

cnf(i_0_18738_287,axiom,
    ( X1 != X2
    | esk524_4(X3,X4,X5,X1) = esk524_4(X3,X4,X5,X2) ) ).

cnf(i_0_18739_288,axiom,
    ( X1 != X2
    | c_Com_Ocom_OSemi(X1,X3) = c_Com_Ocom_OSemi(X2,X3) ) ).

cnf(i_0_18740_289,axiom,
    ( X1 != X2
    | c_Com_Ocom_OSemi(X3,X1) = c_Com_Ocom_OSemi(X3,X2) ) ).

cnf(i_0_18741_290,axiom,
    ( X1 != X2
    | esk116_3(X1,X3,X4) = esk116_3(X2,X3,X4) ) ).

cnf(i_0_18742_291,axiom,
    ( X1 != X2
    | esk116_3(X3,X1,X4) = esk116_3(X3,X2,X4) ) ).

cnf(i_0_18743_292,axiom,
    ( X1 != X2
    | esk116_3(X3,X4,X1) = esk116_3(X3,X4,X2) ) ).

cnf(i_0_18744_293,axiom,
    ( X1 != X2
    | esk115_3(X1,X3,X4) = esk115_3(X2,X3,X4) ) ).

cnf(i_0_18745_294,axiom,
    ( X1 != X2
    | esk115_3(X3,X1,X4) = esk115_3(X3,X2,X4) ) ).

cnf(i_0_18746_295,axiom,
    ( X1 != X2
    | esk115_3(X3,X4,X1) = esk115_3(X3,X4,X2) ) ).

cnf(i_0_18747_296,axiom,
    ( X1 != X2
    | c_Random_Oselect(X1,X3) = c_Random_Oselect(X2,X3) ) ).

cnf(i_0_18748_297,axiom,
    ( X1 != X2
    | c_Random_Oselect(X3,X1) = c_Random_Oselect(X3,X2) ) ).

cnf(i_0_18749_298,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_18750_299,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_18751_300,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_18752_301,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_18753_302,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_18754_303,axiom,
    ( X1 != X2
    | c_Finite__Set_Ofold1(X1,X3) = c_Finite__Set_Ofold1(X2,X3) ) ).

cnf(i_0_18755_304,axiom,
    ( X1 != X2
    | c_Finite__Set_Ofold1(X3,X1) = c_Finite__Set_Ofold1(X3,X2) ) ).

cnf(i_0_18756_305,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_18757_306,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_18758_307,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_18759_308,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_18760_309,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_18761_310,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_18762_311,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_18763_312,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_18764_313,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_18765_314,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_18766_315,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_18767_316,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_18768_317,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_18769_318,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_18770_319,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_18771_320,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_18772_321,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_18773_322,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_18774_323,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_18775_324,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Olazy__sequence_OInsert(X1,X3,X4) = c_Lazy__Sequence_Olazy__sequence_OInsert(X2,X3,X4) ) ).

cnf(i_0_18776_325,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Olazy__sequence_OInsert(X3,X1,X4) = c_Lazy__Sequence_Olazy__sequence_OInsert(X3,X2,X4) ) ).

cnf(i_0_18777_326,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Olazy__sequence_OInsert(X3,X4,X1) = c_Lazy__Sequence_Olazy__sequence_OInsert(X3,X4,X2) ) ).

cnf(i_0_18778_327,axiom,
    ( X1 != X2
    | c_Divides_Odivmod__int(X1,X3) = c_Divides_Odivmod__int(X2,X3) ) ).

cnf(i_0_18779_328,axiom,
    ( X1 != X2
    | c_Divides_Odivmod__int(X3,X1) = c_Divides_Odivmod__int(X3,X2) ) ).

cnf(i_0_18780_329,axiom,
    ( X1 != X2
    | esk249_5(X1,X3,X4,X5,X6) = esk249_5(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18781_330,axiom,
    ( X1 != X2
    | esk249_5(X3,X1,X4,X5,X6) = esk249_5(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18782_331,axiom,
    ( X1 != X2
    | esk249_5(X3,X4,X1,X5,X6) = esk249_5(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18783_332,axiom,
    ( X1 != X2
    | esk249_5(X3,X4,X5,X1,X6) = esk249_5(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18784_333,axiom,
    ( X1 != X2
    | esk249_5(X3,X4,X5,X6,X1) = esk249_5(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18785_334,axiom,
    ( X1 != X2
    | esk447_3(X1,X3,X4) = esk447_3(X2,X3,X4) ) ).

cnf(i_0_18786_335,axiom,
    ( X1 != X2
    | esk447_3(X3,X1,X4) = esk447_3(X3,X2,X4) ) ).

cnf(i_0_18787_336,axiom,
    ( X1 != X2
    | esk447_3(X3,X4,X1) = esk447_3(X3,X4,X2) ) ).

cnf(i_0_18788_337,axiom,
    ( X1 != X2
    | esk446_3(X1,X3,X4) = esk446_3(X2,X3,X4) ) ).

cnf(i_0_18789_338,axiom,
    ( X1 != X2
    | esk446_3(X3,X1,X4) = esk446_3(X3,X2,X4) ) ).

cnf(i_0_18790_339,axiom,
    ( X1 != X2
    | esk446_3(X3,X4,X1) = esk446_3(X3,X4,X2) ) ).

cnf(i_0_18791_340,axiom,
    ( X1 != X2
    | c_Groups_Osgn__class_Osgn(X1,X3) = c_Groups_Osgn__class_Osgn(X2,X3) ) ).

cnf(i_0_18792_341,axiom,
    ( X1 != X2
    | c_Groups_Osgn__class_Osgn(X3,X1) = c_Groups_Osgn__class_Osgn(X3,X2) ) ).

cnf(i_0_18793_342,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_18794_343,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_18795_344,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_18796_345,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_18797_346,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_18798_347,axiom,
    ( X1 != X2
    | esk409_2(X1,X3) = esk409_2(X2,X3) ) ).

cnf(i_0_18799_348,axiom,
    ( X1 != X2
    | esk409_2(X3,X1) = esk409_2(X3,X2) ) ).

cnf(i_0_18800_349,axiom,
    ( X1 != X2
    | esk410_2(X1,X3) = esk410_2(X2,X3) ) ).

cnf(i_0_18801_350,axiom,
    ( X1 != X2
    | esk410_2(X3,X1) = esk410_2(X3,X2) ) ).

cnf(i_0_18802_351,axiom,
    ( X1 != X2
    | c_Nitpick_Onat__gcd(X1,X3) = c_Nitpick_Onat__gcd(X2,X3) ) ).

cnf(i_0_18803_352,axiom,
    ( X1 != X2
    | c_Nitpick_Onat__gcd(X3,X1) = c_Nitpick_Onat__gcd(X3,X2) ) ).

cnf(i_0_18804_353,axiom,
    ( X1 != X2
    | c_Divides_Opdivmod(X1,X3) = c_Divides_Opdivmod(X2,X3) ) ).

cnf(i_0_18805_354,axiom,
    ( X1 != X2
    | c_Divides_Opdivmod(X3,X1) = c_Divides_Opdivmod(X3,X2) ) ).

cnf(i_0_18806_355,axiom,
    ( X1 != X2
    | c_List_Oremdups(X1,X3) = c_List_Oremdups(X2,X3) ) ).

cnf(i_0_18807_356,axiom,
    ( X1 != X2
    | c_List_Oremdups(X3,X1) = c_List_Oremdups(X3,X2) ) ).

cnf(i_0_18808_357,axiom,
    ( X1 != X2
    | c_Partial__Function_Oflat__lub(X1,X3,X4) = c_Partial__Function_Oflat__lub(X2,X3,X4) ) ).

cnf(i_0_18809_358,axiom,
    ( X1 != X2
    | c_Partial__Function_Oflat__lub(X3,X1,X4) = c_Partial__Function_Oflat__lub(X3,X2,X4) ) ).

cnf(i_0_18810_359,axiom,
    ( X1 != X2
    | c_Partial__Function_Oflat__lub(X3,X4,X1) = c_Partial__Function_Oflat__lub(X3,X4,X2) ) ).

cnf(i_0_18811_360,axiom,
    ( X1 != X2
    | c_List_Olenlex(X1,X3) = c_List_Olenlex(X2,X3) ) ).

cnf(i_0_18812_361,axiom,
    ( X1 != X2
    | c_List_Olenlex(X3,X1) = c_List_Olenlex(X3,X2) ) ).

cnf(i_0_18813_362,axiom,
    ( X1 != X2
    | c_Product__Type_Ocurry(X1,X3,X4,X5) = c_Product__Type_Ocurry(X2,X3,X4,X5) ) ).

cnf(i_0_18814_363,axiom,
    ( X1 != X2
    | c_Product__Type_Ocurry(X3,X1,X4,X5) = c_Product__Type_Ocurry(X3,X2,X4,X5) ) ).

cnf(i_0_18815_364,axiom,
    ( X1 != X2
    | c_Product__Type_Ocurry(X3,X4,X1,X5) = c_Product__Type_Ocurry(X3,X4,X2,X5) ) ).

cnf(i_0_18816_365,axiom,
    ( X1 != X2
    | c_Product__Type_Ocurry(X3,X4,X5,X1) = c_Product__Type_Ocurry(X3,X4,X5,X2) ) ).

cnf(i_0_18817_366,axiom,
    ( X1 != X2
    | c_List_Oreplicate(X1,X3,X4) = c_List_Oreplicate(X2,X3,X4) ) ).

cnf(i_0_18818_367,axiom,
    ( X1 != X2
    | c_List_Oreplicate(X3,X1,X4) = c_List_Oreplicate(X3,X2,X4) ) ).

cnf(i_0_18819_368,axiom,
    ( X1 != X2
    | c_List_Oreplicate(X3,X4,X1) = c_List_Oreplicate(X3,X4,X2) ) ).

cnf(i_0_18820_369,axiom,
    ( X1 != X2
    | c_List_Olex(X1,X3) = c_List_Olex(X2,X3) ) ).

cnf(i_0_18821_370,axiom,
    ( X1 != X2
    | c_List_Olex(X3,X1) = c_List_Olex(X3,X2) ) ).

cnf(i_0_18822_371,axiom,
    ( X1 != X2
    | esk93_3(X1,X3,X4) = esk93_3(X2,X3,X4) ) ).

cnf(i_0_18823_372,axiom,
    ( X1 != X2
    | esk93_3(X3,X1,X4) = esk93_3(X3,X2,X4) ) ).

cnf(i_0_18824_373,axiom,
    ( X1 != X2
    | esk93_3(X3,X4,X1) = esk93_3(X3,X4,X2) ) ).

cnf(i_0_18825_374,axiom,
    ( X1 != X2
    | esk556_3(X1,X3,X4) = esk556_3(X2,X3,X4) ) ).

cnf(i_0_18826_375,axiom,
    ( X1 != X2
    | esk556_3(X3,X1,X4) = esk556_3(X3,X2,X4) ) ).

cnf(i_0_18827_376,axiom,
    ( X1 != X2
    | esk556_3(X3,X4,X1) = esk556_3(X3,X4,X2) ) ).

cnf(i_0_18828_377,axiom,
    ( X1 != X2
    | esk522_4(X1,X3,X4,X5) = esk522_4(X2,X3,X4,X5) ) ).

cnf(i_0_18829_378,axiom,
    ( X1 != X2
    | esk522_4(X3,X1,X4,X5) = esk522_4(X3,X2,X4,X5) ) ).

cnf(i_0_18830_379,axiom,
    ( X1 != X2
    | esk522_4(X3,X4,X1,X5) = esk522_4(X3,X4,X2,X5) ) ).

cnf(i_0_18831_380,axiom,
    ( X1 != X2
    | esk522_4(X3,X4,X5,X1) = esk522_4(X3,X4,X5,X2) ) ).

cnf(i_0_18832_381,axiom,
    ( X1 != X2
    | esk511_4(X1,X3,X4,X5) = esk511_4(X2,X3,X4,X5) ) ).

cnf(i_0_18833_382,axiom,
    ( X1 != X2
    | esk511_4(X3,X1,X4,X5) = esk511_4(X3,X2,X4,X5) ) ).

cnf(i_0_18834_383,axiom,
    ( X1 != X2
    | esk511_4(X3,X4,X1,X5) = esk511_4(X3,X4,X2,X5) ) ).

cnf(i_0_18835_384,axiom,
    ( X1 != X2
    | esk511_4(X3,X4,X5,X1) = esk511_4(X3,X4,X5,X2) ) ).

cnf(i_0_18836_385,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X1,X3,X4,X5) = c_List_Ofoldl(X2,X3,X4,X5) ) ).

cnf(i_0_18837_386,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X3,X1,X4,X5) = c_List_Ofoldl(X3,X2,X4,X5) ) ).

cnf(i_0_18838_387,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X3,X4,X1,X5) = c_List_Ofoldl(X3,X4,X2,X5) ) ).

cnf(i_0_18839_388,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X3,X4,X5,X1) = c_List_Ofoldl(X3,X4,X5,X2) ) ).

cnf(i_0_18840_389,axiom,
    ( X1 != X2
    | esk232_4(X1,X3,X4,X5) = esk232_4(X2,X3,X4,X5) ) ).

cnf(i_0_18841_390,axiom,
    ( X1 != X2
    | esk232_4(X3,X1,X4,X5) = esk232_4(X3,X2,X4,X5) ) ).

cnf(i_0_18842_391,axiom,
    ( X1 != X2
    | esk232_4(X3,X4,X1,X5) = esk232_4(X3,X4,X2,X5) ) ).

cnf(i_0_18843_392,axiom,
    ( X1 != X2
    | esk232_4(X3,X4,X5,X1) = esk232_4(X3,X4,X5,X2) ) ).

cnf(i_0_18844_393,axiom,
    ( X1 != X2
    | esk234_4(X1,X3,X4,X5) = esk234_4(X2,X3,X4,X5) ) ).

cnf(i_0_18845_394,axiom,
    ( X1 != X2
    | esk234_4(X3,X1,X4,X5) = esk234_4(X3,X2,X4,X5) ) ).

cnf(i_0_18846_395,axiom,
    ( X1 != X2
    | esk234_4(X3,X4,X1,X5) = esk234_4(X3,X4,X2,X5) ) ).

cnf(i_0_18847_396,axiom,
    ( X1 != X2
    | esk234_4(X3,X4,X5,X1) = esk234_4(X3,X4,X5,X2) ) ).

cnf(i_0_18848_397,axiom,
    ( X1 != X2
    | c_Enum_Oproduct(X1,X3,X4,X5) = c_Enum_Oproduct(X2,X3,X4,X5) ) ).

cnf(i_0_18849_398,axiom,
    ( X1 != X2
    | c_Enum_Oproduct(X3,X1,X4,X5) = c_Enum_Oproduct(X3,X2,X4,X5) ) ).

cnf(i_0_18850_399,axiom,
    ( X1 != X2
    | c_Enum_Oproduct(X3,X4,X1,X5) = c_Enum_Oproduct(X3,X4,X2,X5) ) ).

cnf(i_0_18851_400,axiom,
    ( X1 != X2
    | c_Enum_Oproduct(X3,X4,X5,X1) = c_Enum_Oproduct(X3,X4,X5,X2) ) ).

cnf(i_0_18852_401,axiom,
    ( X1 != X2
    | esk216_4(X1,X3,X4,X5) = esk216_4(X2,X3,X4,X5) ) ).

cnf(i_0_18853_402,axiom,
    ( X1 != X2
    | esk216_4(X3,X1,X4,X5) = esk216_4(X3,X2,X4,X5) ) ).

cnf(i_0_18854_403,axiom,
    ( X1 != X2
    | esk216_4(X3,X4,X1,X5) = esk216_4(X3,X4,X2,X5) ) ).

cnf(i_0_18855_404,axiom,
    ( X1 != X2
    | esk216_4(X3,X4,X5,X1) = esk216_4(X3,X4,X5,X2) ) ).

cnf(i_0_18856_405,axiom,
    ( X1 != X2
    | esk215_4(X1,X3,X4,X5) = esk215_4(X2,X3,X4,X5) ) ).

cnf(i_0_18857_406,axiom,
    ( X1 != X2
    | esk215_4(X3,X1,X4,X5) = esk215_4(X3,X2,X4,X5) ) ).

cnf(i_0_18858_407,axiom,
    ( X1 != X2
    | esk215_4(X3,X4,X1,X5) = esk215_4(X3,X4,X2,X5) ) ).

cnf(i_0_18859_408,axiom,
    ( X1 != X2
    | esk215_4(X3,X4,X5,X1) = esk215_4(X3,X4,X5,X2) ) ).

cnf(i_0_18860_409,axiom,
    ( X1 != X2
    | c_Fun_Ocomp(X1,X3,X4,X5) = c_Fun_Ocomp(X2,X3,X4,X5) ) ).

cnf(i_0_18861_410,axiom,
    ( X1 != X2
    | c_Fun_Ocomp(X3,X1,X4,X5) = c_Fun_Ocomp(X3,X2,X4,X5) ) ).

cnf(i_0_18862_411,axiom,
    ( X1 != X2
    | c_Fun_Ocomp(X3,X4,X1,X5) = c_Fun_Ocomp(X3,X4,X2,X5) ) ).

cnf(i_0_18863_412,axiom,
    ( X1 != X2
    | c_Fun_Ocomp(X3,X4,X5,X1) = c_Fun_Ocomp(X3,X4,X5,X2) ) ).

cnf(i_0_18864_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_18865_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_18866_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_18867_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_18868_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_18869_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_18870_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_18871_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_18872_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_18873_422,axiom,
    ( X1 != X2
    | esk379_3(X1,X3,X4) = esk379_3(X2,X3,X4) ) ).

cnf(i_0_18874_423,axiom,
    ( X1 != X2
    | esk379_3(X3,X1,X4) = esk379_3(X3,X2,X4) ) ).

cnf(i_0_18875_424,axiom,
    ( X1 != X2
    | esk379_3(X3,X4,X1) = esk379_3(X3,X4,X2) ) ).

cnf(i_0_18876_425,axiom,
    ( X1 != X2
    | esk380_3(X1,X3,X4) = esk380_3(X2,X3,X4) ) ).

cnf(i_0_18877_426,axiom,
    ( X1 != X2
    | esk380_3(X3,X1,X4) = esk380_3(X3,X2,X4) ) ).

cnf(i_0_18878_427,axiom,
    ( X1 != X2
    | esk380_3(X3,X4,X1) = esk380_3(X3,X4,X2) ) ).

cnf(i_0_18879_428,axiom,
    ( X1 != X2
    | esk248_4(X1,X3,X4,X5) = esk248_4(X2,X3,X4,X5) ) ).

cnf(i_0_18880_429,axiom,
    ( X1 != X2
    | esk248_4(X3,X1,X4,X5) = esk248_4(X3,X2,X4,X5) ) ).

cnf(i_0_18881_430,axiom,
    ( X1 != X2
    | esk248_4(X3,X4,X1,X5) = esk248_4(X3,X4,X2,X5) ) ).

cnf(i_0_18882_431,axiom,
    ( X1 != X2
    | esk248_4(X3,X4,X5,X1) = esk248_4(X3,X4,X5,X2) ) ).

cnf(i_0_18883_432,axiom,
    ( X1 != X2
    | c_Nitpick_Oplus__frac(X1,X3,X4) = c_Nitpick_Oplus__frac(X2,X3,X4) ) ).

cnf(i_0_18884_433,axiom,
    ( X1 != X2
    | c_Nitpick_Oplus__frac(X3,X1,X4) = c_Nitpick_Oplus__frac(X3,X2,X4) ) ).

cnf(i_0_18885_434,axiom,
    ( X1 != X2
    | c_Nitpick_Oplus__frac(X3,X4,X1) = c_Nitpick_Oplus__frac(X3,X4,X2) ) ).

cnf(i_0_18886_435,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_18887_436,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_18888_437,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_18889_438,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_18890_439,axiom,
    ( X1 != X2
    | c_Sum__Type_OPlus(X1,X3,X4,X5) = c_Sum__Type_OPlus(X2,X3,X4,X5) ) ).

cnf(i_0_18891_440,axiom,
    ( X1 != X2
    | c_Sum__Type_OPlus(X3,X1,X4,X5) = c_Sum__Type_OPlus(X3,X2,X4,X5) ) ).

cnf(i_0_18892_441,axiom,
    ( X1 != X2
    | c_Sum__Type_OPlus(X3,X4,X1,X5) = c_Sum__Type_OPlus(X3,X4,X2,X5) ) ).

cnf(i_0_18893_442,axiom,
    ( X1 != X2
    | c_Sum__Type_OPlus(X3,X4,X5,X1) = c_Sum__Type_OPlus(X3,X4,X5,X2) ) ).

cnf(i_0_18894_443,axiom,
    ( X1 != X2
    | esk374_3(X1,X3,X4) = esk374_3(X2,X3,X4) ) ).

cnf(i_0_18895_444,axiom,
    ( X1 != X2
    | esk374_3(X3,X1,X4) = esk374_3(X3,X2,X4) ) ).

cnf(i_0_18896_445,axiom,
    ( X1 != X2
    | esk374_3(X3,X4,X1) = esk374_3(X3,X4,X2) ) ).

cnf(i_0_18897_446,axiom,
    ( X1 != X2
    | esk373_3(X1,X3,X4) = esk373_3(X2,X3,X4) ) ).

cnf(i_0_18898_447,axiom,
    ( X1 != X2
    | esk373_3(X3,X1,X4) = esk373_3(X3,X2,X4) ) ).

cnf(i_0_18899_448,axiom,
    ( X1 != X2
    | esk373_3(X3,X4,X1) = esk373_3(X3,X4,X2) ) ).

cnf(i_0_18900_449,axiom,
    ( X1 != X2
    | c_List_Oupto(X1,X3) = c_List_Oupto(X2,X3) ) ).

cnf(i_0_18901_450,axiom,
    ( X1 != X2
    | c_List_Oupto(X3,X1) = c_List_Oupto(X3,X2) ) ).

cnf(i_0_18902_451,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_18903_452,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_18904_453,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_18905_454,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_18906_455,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_18907_456,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_18908_457,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_18909_458,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_18910_459,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_18911_460,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_18912_461,axiom,
    ( X1 != X2
    | c_List_Olast(X1,X3) = c_List_Olast(X2,X3) ) ).

cnf(i_0_18913_462,axiom,
    ( X1 != X2
    | c_List_Olast(X3,X1) = c_List_Olast(X3,X2) ) ).

cnf(i_0_18914_463,axiom,
    ( X1 != X2
    | c_List_Obutlast(X1,X3) = c_List_Obutlast(X2,X3) ) ).

cnf(i_0_18915_464,axiom,
    ( X1 != X2
    | c_List_Obutlast(X3,X1) = c_List_Obutlast(X3,X2) ) ).

cnf(i_0_18916_465,axiom,
    ( X1 != X2
    | esk547_2(X1,X3) = esk547_2(X2,X3) ) ).

cnf(i_0_18917_466,axiom,
    ( X1 != X2
    | esk547_2(X3,X1) = esk547_2(X3,X2) ) ).

cnf(i_0_18918_467,axiom,
    ( X1 != X2
    | c_Nitpick_Oint__lcm(X1,X3) = c_Nitpick_Oint__lcm(X2,X3) ) ).

cnf(i_0_18919_468,axiom,
    ( X1 != X2
    | c_Nitpick_Oint__lcm(X3,X1) = c_Nitpick_Oint__lcm(X3,X2) ) ).

cnf(i_0_18920_469,axiom,
    ( X1 != X2
    | esk546_2(X1,X3) = esk546_2(X2,X3) ) ).

cnf(i_0_18921_470,axiom,
    ( X1 != X2
    | esk546_2(X3,X1) = esk546_2(X3,X2) ) ).

cnf(i_0_18922_471,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohb__bind(X1,X3,X4,X5) = c_Lazy__Sequence_Ohb__bind(X2,X3,X4,X5) ) ).

cnf(i_0_18923_472,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohb__bind(X3,X1,X4,X5) = c_Lazy__Sequence_Ohb__bind(X3,X2,X4,X5) ) ).

cnf(i_0_18924_473,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohb__bind(X3,X4,X1,X5) = c_Lazy__Sequence_Ohb__bind(X3,X4,X2,X5) ) ).

cnf(i_0_18925_474,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohb__bind(X3,X4,X5,X1) = c_Lazy__Sequence_Ohb__bind(X3,X4,X5,X2) ) ).

cnf(i_0_18926_475,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Olazy__sequence_OEmpty(X1) = c_Lazy__Sequence_Olazy__sequence_OEmpty(X2) ) ).

cnf(i_0_18927_476,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_18928_477,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_18929_478,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_18930_479,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_18931_480,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_18932_481,axiom,
    ( X1 != X2
    | esk140_3(X1,X3,X4) = esk140_3(X2,X3,X4) ) ).

cnf(i_0_18933_482,axiom,
    ( X1 != X2
    | esk140_3(X3,X1,X4) = esk140_3(X3,X2,X4) ) ).

cnf(i_0_18934_483,axiom,
    ( X1 != X2
    | esk140_3(X3,X4,X1) = esk140_3(X3,X4,X2) ) ).

cnf(i_0_18935_484,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Osmall__lazy_H(X1,X3) = c_Lazy__Sequence_Osmall__lazy_H(X2,X3) ) ).

cnf(i_0_18936_485,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Osmall__lazy_H(X3,X1) = c_Lazy__Sequence_Osmall__lazy_H(X3,X2) ) ).

cnf(i_0_18937_486,axiom,
    ( X1 != X2
    | esk527_4(X1,X3,X4,X5) = esk527_4(X2,X3,X4,X5) ) ).

cnf(i_0_18938_487,axiom,
    ( X1 != X2
    | esk527_4(X3,X1,X4,X5) = esk527_4(X3,X2,X4,X5) ) ).

cnf(i_0_18939_488,axiom,
    ( X1 != X2
    | esk527_4(X3,X4,X1,X5) = esk527_4(X3,X4,X2,X5) ) ).

cnf(i_0_18940_489,axiom,
    ( X1 != X2
    | esk527_4(X3,X4,X5,X1) = esk527_4(X3,X4,X5,X2) ) ).

cnf(i_0_18941_490,axiom,
    ( X1 != X2
    | c_FunDef_OTHE__default(X1,X3,X4) = c_FunDef_OTHE__default(X2,X3,X4) ) ).

cnf(i_0_18942_491,axiom,
    ( X1 != X2
    | c_FunDef_OTHE__default(X3,X1,X4) = c_FunDef_OTHE__default(X3,X2,X4) ) ).

cnf(i_0_18943_492,axiom,
    ( X1 != X2
    | c_FunDef_OTHE__default(X3,X4,X1) = c_FunDef_OTHE__default(X3,X4,X2) ) ).

cnf(i_0_18944_493,axiom,
    ( X1 != X2
    | c_List_Omaps(X1,X3,X4,X5) = c_List_Omaps(X2,X3,X4,X5) ) ).

cnf(i_0_18945_494,axiom,
    ( X1 != X2
    | c_List_Omaps(X3,X1,X4,X5) = c_List_Omaps(X3,X2,X4,X5) ) ).

cnf(i_0_18946_495,axiom,
    ( X1 != X2
    | c_List_Omaps(X3,X4,X1,X5) = c_List_Omaps(X3,X4,X2,X5) ) ).

cnf(i_0_18947_496,axiom,
    ( X1 != X2
    | c_List_Omaps(X3,X4,X5,X1) = c_List_Omaps(X3,X4,X5,X2) ) ).

cnf(i_0_18948_497,axiom,
    ( X1 != X2
    | esk436_2(X1,X3) = esk436_2(X2,X3) ) ).

cnf(i_0_18949_498,axiom,
    ( X1 != X2
    | esk436_2(X3,X1) = esk436_2(X3,X2) ) ).

cnf(i_0_18950_499,axiom,
    ( X1 != X2
    | esk385_2(X1,X3) = esk385_2(X2,X3) ) ).

cnf(i_0_18951_500,axiom,
    ( X1 != X2
    | esk385_2(X3,X1) = esk385_2(X3,X2) ) ).

cnf(i_0_18952_501,axiom,
    ( X1 != X2
    | esk386_2(X1,X3) = esk386_2(X2,X3) ) ).

cnf(i_0_18953_502,axiom,
    ( X1 != X2
    | esk386_2(X3,X1) = esk386_2(X3,X2) ) ).

cnf(i_0_18954_503,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_18955_504,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_18956_505,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_18957_506,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_18958_507,axiom,
    ( X1 != X2
    | c_Orderings_Otop__class_Otop(X1) = c_Orderings_Otop__class_Otop(X2) ) ).

cnf(i_0_18959_508,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X3,X4) = c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X4) ) ).

cnf(i_0_18960_509,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X1,X4) = c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X2,X4) ) ).

cnf(i_0_18961_510,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X1) = c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X2) ) ).

cnf(i_0_18962_511,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X3,X4) = c_SetInterval_Oord__class_OgreaterThanLessThan(X2,X3,X4) ) ).

cnf(i_0_18963_512,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OgreaterThanLessThan(X3,X1,X4) = c_SetInterval_Oord__class_OgreaterThanLessThan(X3,X2,X4) ) ).

cnf(i_0_18964_513,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OgreaterThanLessThan(X3,X4,X1) = c_SetInterval_Oord__class_OgreaterThanLessThan(X3,X4,X2) ) ).

cnf(i_0_18965_514,axiom,
    ( X1 != X2
    | c_Predicate_Opred__comp(X1,X3,X4,X5,X6) = c_Predicate_Opred__comp(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18966_515,axiom,
    ( X1 != X2
    | c_Predicate_Opred__comp(X3,X1,X4,X5,X6) = c_Predicate_Opred__comp(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18967_516,axiom,
    ( X1 != X2
    | c_Predicate_Opred__comp(X3,X4,X1,X5,X6) = c_Predicate_Opred__comp(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18968_517,axiom,
    ( X1 != X2
    | c_Predicate_Opred__comp(X3,X4,X5,X1,X6) = c_Predicate_Opred__comp(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18969_518,axiom,
    ( X1 != X2
    | c_Predicate_Opred__comp(X3,X4,X5,X6,X1) = c_Predicate_Opred__comp(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18970_519,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_18971_520,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_18972_521,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_18973_522,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_18974_523,axiom,
    ( X1 != X2
    | c_Power_Opower_Opower(X1,X3,X4) = c_Power_Opower_Opower(X2,X3,X4) ) ).

cnf(i_0_18975_524,axiom,
    ( X1 != X2
    | c_Power_Opower_Opower(X3,X1,X4) = c_Power_Opower_Opower(X3,X2,X4) ) ).

cnf(i_0_18976_525,axiom,
    ( X1 != X2
    | c_Power_Opower_Opower(X3,X4,X1) = c_Power_Opower_Opower(X3,X4,X2) ) ).

cnf(i_0_18977_526,axiom,
    ( X1 != X2
    | esk341_2(X1,X3) = esk341_2(X2,X3) ) ).

cnf(i_0_18978_527,axiom,
    ( X1 != X2
    | esk341_2(X3,X1) = esk341_2(X3,X2) ) ).

cnf(i_0_18979_528,axiom,
    ( X1 != X2
    | c_Transitive__Closure_Ortrancl(X1,X3) = c_Transitive__Closure_Ortrancl(X2,X3) ) ).

cnf(i_0_18980_529,axiom,
    ( X1 != X2
    | c_Transitive__Closure_Ortrancl(X3,X1) = c_Transitive__Closure_Ortrancl(X3,X2) ) ).

cnf(i_0_18981_530,axiom,
    ( X1 != X2
    | esk231_3(X1,X3,X4) = esk231_3(X2,X3,X4) ) ).

cnf(i_0_18982_531,axiom,
    ( X1 != X2
    | esk231_3(X3,X1,X4) = esk231_3(X3,X2,X4) ) ).

cnf(i_0_18983_532,axiom,
    ( X1 != X2
    | esk231_3(X3,X4,X1) = esk231_3(X3,X4,X2) ) ).

cnf(i_0_18984_533,axiom,
    ( X1 != X2
    | esk233_3(X1,X3,X4) = esk233_3(X2,X3,X4) ) ).

cnf(i_0_18985_534,axiom,
    ( X1 != X2
    | esk233_3(X3,X1,X4) = esk233_3(X3,X2,X4) ) ).

cnf(i_0_18986_535,axiom,
    ( X1 != X2
    | esk233_3(X3,X4,X1) = esk233_3(X3,X4,X2) ) ).

cnf(i_0_18987_536,axiom,
    ( X1 != X2
    | esk122_3(X1,X3,X4) = esk122_3(X2,X3,X4) ) ).

cnf(i_0_18988_537,axiom,
    ( X1 != X2
    | esk122_3(X3,X1,X4) = esk122_3(X3,X2,X4) ) ).

cnf(i_0_18989_538,axiom,
    ( X1 != X2
    | esk122_3(X3,X4,X1) = esk122_3(X3,X4,X2) ) ).

cnf(i_0_18990_539,axiom,
    ( X1 != X2
    | esk121_3(X1,X3,X4) = esk121_3(X2,X3,X4) ) ).

cnf(i_0_18991_540,axiom,
    ( X1 != X2
    | esk121_3(X3,X1,X4) = esk121_3(X3,X2,X4) ) ).

cnf(i_0_18992_541,axiom,
    ( X1 != X2
    | esk121_3(X3,X4,X1) = esk121_3(X3,X4,X2) ) ).

cnf(i_0_18993_542,axiom,
    ( X1 != X2
    | esk521_3(X1,X3,X4) = esk521_3(X2,X3,X4) ) ).

cnf(i_0_18994_543,axiom,
    ( X1 != X2
    | esk521_3(X3,X1,X4) = esk521_3(X3,X2,X4) ) ).

cnf(i_0_18995_544,axiom,
    ( X1 != X2
    | esk521_3(X3,X4,X1) = esk521_3(X3,X4,X2) ) ).

cnf(i_0_18996_545,axiom,
    ( X1 != X2
    | esk510_3(X1,X3,X4) = esk510_3(X2,X3,X4) ) ).

cnf(i_0_18997_546,axiom,
    ( X1 != X2
    | esk510_3(X3,X1,X4) = esk510_3(X3,X2,X4) ) ).

cnf(i_0_18998_547,axiom,
    ( X1 != X2
    | esk510_3(X3,X4,X1) = esk510_3(X3,X4,X2) ) ).

cnf(i_0_18999_548,axiom,
    ( X1 != X2
    | c_List_Osplice(X1,X3,X4) = c_List_Osplice(X2,X3,X4) ) ).

cnf(i_0_19000_549,axiom,
    ( X1 != X2
    | c_List_Osplice(X3,X1,X4) = c_List_Osplice(X3,X2,X4) ) ).

cnf(i_0_19001_550,axiom,
    ( X1 != X2
    | c_List_Osplice(X3,X4,X1) = c_List_Osplice(X3,X4,X2) ) ).

cnf(i_0_19002_551,axiom,
    ( X1 != X2
    | c_Hoare__Mirabelle_Otriple_Otriple__case(X1,X3,X4,X5) = c_Hoare__Mirabelle_Otriple_Otriple__case(X2,X3,X4,X5) ) ).

cnf(i_0_19003_552,axiom,
    ( X1 != X2
    | c_Hoare__Mirabelle_Otriple_Otriple__case(X3,X1,X4,X5) = c_Hoare__Mirabelle_Otriple_Otriple__case(X3,X2,X4,X5) ) ).

cnf(i_0_19004_553,axiom,
    ( X1 != X2
    | c_Hoare__Mirabelle_Otriple_Otriple__case(X3,X4,X1,X5) = c_Hoare__Mirabelle_Otriple_Otriple__case(X3,X4,X2,X5) ) ).

cnf(i_0_19005_554,axiom,
    ( X1 != X2
    | c_Hoare__Mirabelle_Otriple_Otriple__case(X3,X4,X5,X1) = c_Hoare__Mirabelle_Otriple_Otriple__case(X3,X4,X5,X2) ) ).

cnf(i_0_19006_555,axiom,
    ( X1 != X2
    | c_Hoare__Mirabelle_Otriple_Otriple__rec(X1,X3,X4,X5) = c_Hoare__Mirabelle_Otriple_Otriple__rec(X2,X3,X4,X5) ) ).

cnf(i_0_19007_556,axiom,
    ( X1 != X2
    | c_Hoare__Mirabelle_Otriple_Otriple__rec(X3,X1,X4,X5) = c_Hoare__Mirabelle_Otriple_Otriple__rec(X3,X2,X4,X5) ) ).

cnf(i_0_19008_557,axiom,
    ( X1 != X2
    | c_Hoare__Mirabelle_Otriple_Otriple__rec(X3,X4,X1,X5) = c_Hoare__Mirabelle_Otriple_Otriple__rec(X3,X4,X2,X5) ) ).

cnf(i_0_19009_558,axiom,
    ( X1 != X2
    | c_Hoare__Mirabelle_Otriple_Otriple__rec(X3,X4,X5,X1) = c_Hoare__Mirabelle_Otriple_Otriple__rec(X3,X4,X5,X2) ) ).

cnf(i_0_19010_559,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohit__bound(X1) = c_Lazy__Sequence_Ohit__bound(X2) ) ).

cnf(i_0_19011_560,axiom,
    ( X1 != X2
    | c_Nat__Transfer_Otsub(X1,X3) = c_Nat__Transfer_Otsub(X2,X3) ) ).

cnf(i_0_19012_561,axiom,
    ( X1 != X2
    | c_Nat__Transfer_Otsub(X3,X1) = c_Nat__Transfer_Otsub(X3,X2) ) ).

cnf(i_0_19013_562,axiom,
    ( X1 != X2
    | c_Random_Olog(X1,X3) = c_Random_Olog(X2,X3) ) ).

cnf(i_0_19014_563,axiom,
    ( X1 != X2
    | c_Random_Olog(X3,X1) = c_Random_Olog(X3,X2) ) ).

cnf(i_0_19015_564,axiom,
    ( X1 != X2
    | c_Com_Ocom_Ocom__size(X1) = c_Com_Ocom_Ocom__size(X2) ) ).

cnf(i_0_19016_565,axiom,
    ( X1 != X2
    | c_Random_Ominus__shift(X1,X3,X4) = c_Random_Ominus__shift(X2,X3,X4) ) ).

cnf(i_0_19017_566,axiom,
    ( X1 != X2
    | c_Random_Ominus__shift(X3,X1,X4) = c_Random_Ominus__shift(X3,X2,X4) ) ).

cnf(i_0_19018_567,axiom,
    ( X1 != X2
    | c_Random_Ominus__shift(X3,X4,X1) = c_Random_Ominus__shift(X3,X4,X2) ) ).

cnf(i_0_19019_568,axiom,
    ( X1 != X2
    | c_Random__Sequence_Oempty(X1,X3,X4) = c_Random__Sequence_Oempty(X2,X3,X4) ) ).

cnf(i_0_19020_569,axiom,
    ( X1 != X2
    | c_Random__Sequence_Oempty(X3,X1,X4) = c_Random__Sequence_Oempty(X3,X2,X4) ) ).

cnf(i_0_19021_570,axiom,
    ( X1 != X2
    | c_Random__Sequence_Oempty(X3,X4,X1) = c_Random__Sequence_Oempty(X3,X4,X2) ) ).

cnf(i_0_19022_571,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_19023_572,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_19024_573,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_19025_574,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_19026_575,axiom,
    ( X1 != X2
    | esk389_2(X1,X3) = esk389_2(X2,X3) ) ).

cnf(i_0_19027_576,axiom,
    ( X1 != X2
    | esk389_2(X3,X1) = esk389_2(X3,X2) ) ).

cnf(i_0_19028_577,axiom,
    ( X1 != X2
    | c_List_Olistset(X1,X3) = c_List_Olistset(X2,X3) ) ).

cnf(i_0_19029_578,axiom,
    ( X1 != X2
    | c_List_Olistset(X3,X1) = c_List_Olistset(X3,X2) ) ).

cnf(i_0_19030_579,axiom,
    ( X1 != X2
    | c_Code__Numeral_Odiv__mod__code__numeral(X1,X3) = c_Code__Numeral_Odiv__mod__code__numeral(X2,X3) ) ).

cnf(i_0_19031_580,axiom,
    ( X1 != X2
    | c_Code__Numeral_Odiv__mod__code__numeral(X3,X1) = c_Code__Numeral_Odiv__mod__code__numeral(X3,X2) ) ).

cnf(i_0_19032_581,axiom,
    ( X1 != X2
    | esk340_2(X1,X3) = esk340_2(X2,X3) ) ).

cnf(i_0_19033_582,axiom,
    ( X1 != X2
    | esk340_2(X3,X1) = esk340_2(X3,X2) ) ).

cnf(i_0_19034_583,axiom,
    ( X1 != X2
    | esk339_2(X1,X3) = esk339_2(X2,X3) ) ).

cnf(i_0_19035_584,axiom,
    ( X1 != X2
    | esk339_2(X3,X1) = esk339_2(X3,X2) ) ).

cnf(i_0_19036_585,axiom,
    ( X1 != X2
    | c_List_Oinsert(X1,X3,X4) = c_List_Oinsert(X2,X3,X4) ) ).

cnf(i_0_19037_586,axiom,
    ( X1 != X2
    | c_List_Oinsert(X3,X1,X4) = c_List_Oinsert(X3,X2,X4) ) ).

cnf(i_0_19038_587,axiom,
    ( X1 != X2
    | c_List_Oinsert(X3,X4,X1) = c_List_Oinsert(X3,X4,X2) ) ).

cnf(i_0_19039_588,axiom,
    ( X1 != X2
    | c_Int_Oring__1__class_Oof__int(X1) = c_Int_Oring__1__class_Oof__int(X2) ) ).

cnf(i_0_19040_589,axiom,
    ( X1 != X2
    | esk528_3(X1,X3,X4) = esk528_3(X2,X3,X4) ) ).

cnf(i_0_19041_590,axiom,
    ( X1 != X2
    | esk528_3(X3,X1,X4) = esk528_3(X3,X2,X4) ) ).

cnf(i_0_19042_591,axiom,
    ( X1 != X2
    | esk528_3(X3,X4,X1) = esk528_3(X3,X4,X2) ) ).

cnf(i_0_19043_592,axiom,
    ( X1 != X2
    | c_SMT_Oz3div(X1,X3) = c_SMT_Oz3div(X2,X3) ) ).

cnf(i_0_19044_593,axiom,
    ( X1 != X2
    | c_SMT_Oz3div(X3,X1) = c_SMT_Oz3div(X3,X2) ) ).

cnf(i_0_19045_594,axiom,
    ( X1 != X2
    | c_Hoare__Mirabelle_Otriple_Otriple__size(X1,X3,X4) = c_Hoare__Mirabelle_Otriple_Otriple__size(X2,X3,X4) ) ).

cnf(i_0_19046_595,axiom,
    ( X1 != X2
    | c_Hoare__Mirabelle_Otriple_Otriple__size(X3,X1,X4) = c_Hoare__Mirabelle_Otriple_Otriple__size(X3,X2,X4) ) ).

cnf(i_0_19047_596,axiom,
    ( X1 != X2
    | c_Hoare__Mirabelle_Otriple_Otriple__size(X3,X4,X1) = c_Hoare__Mirabelle_Otriple_Otriple__size(X3,X4,X2) ) ).

cnf(i_0_19048_597,axiom,
    ( X1 != X2
    | c_Orderings_Oord_Omax(X1,X3) = c_Orderings_Oord_Omax(X2,X3) ) ).

cnf(i_0_19049_598,axiom,
    ( X1 != X2
    | c_Orderings_Oord_Omax(X3,X1) = c_Orderings_Oord_Omax(X3,X2) ) ).

cnf(i_0_19050_599,axiom,
    ( X1 != X2
    | c_Orderings_Oord_Omin(X1,X3) = c_Orderings_Oord_Omin(X2,X3) ) ).

cnf(i_0_19051_600,axiom,
    ( X1 != X2
    | c_Orderings_Oord_Omin(X3,X1) = c_Orderings_Oord_Omin(X3,X2) ) ).

cnf(i_0_19052_601,axiom,
    ( X1 != X2
    | c_Com_Ocom_OLocal(X1,X3,X4) = c_Com_Ocom_OLocal(X2,X3,X4) ) ).

cnf(i_0_19053_602,axiom,
    ( X1 != X2
    | c_Com_Ocom_OLocal(X3,X1,X4) = c_Com_Ocom_OLocal(X3,X2,X4) ) ).

cnf(i_0_19054_603,axiom,
    ( X1 != X2
    | c_Com_Ocom_OLocal(X3,X4,X1) = c_Com_Ocom_OLocal(X3,X4,X2) ) ).

cnf(i_0_19055_604,axiom,
    ( X1 != X2
    | c_Predicate_Oconversep(X1,X3,X4) = c_Predicate_Oconversep(X2,X3,X4) ) ).

cnf(i_0_19056_605,axiom,
    ( X1 != X2
    | c_Predicate_Oconversep(X3,X1,X4) = c_Predicate_Oconversep(X3,X2,X4) ) ).

cnf(i_0_19057_606,axiom,
    ( X1 != X2
    | c_Predicate_Oconversep(X3,X4,X1) = c_Predicate_Oconversep(X3,X4,X2) ) ).

cnf(i_0_19058_607,axiom,
    ( X1 != X2
    | c_New__DSequence_Opos__single(X1,X3) = c_New__DSequence_Opos__single(X2,X3) ) ).

cnf(i_0_19059_608,axiom,
    ( X1 != X2
    | c_New__DSequence_Opos__single(X3,X1) = c_New__DSequence_Opos__single(X3,X2) ) ).

cnf(i_0_19060_609,axiom,
    ( X1 != X2
    | c_New__DSequence_Oneg__single(X1,X3) = c_New__DSequence_Oneg__single(X2,X3) ) ).

cnf(i_0_19061_610,axiom,
    ( X1 != X2
    | c_New__DSequence_Oneg__single(X3,X1) = c_New__DSequence_Oneg__single(X3,X2) ) ).

cnf(i_0_19062_611,axiom,
    ( X1 != X2
    | c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(X1) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(X2) ) ).

cnf(i_0_19063_612,axiom,
    ( X1 != X2
    | c_SMT_Oz3mod(X1,X3) = c_SMT_Oz3mod(X2,X3) ) ).

cnf(i_0_19064_613,axiom,
    ( X1 != X2
    | c_SMT_Oz3mod(X3,X1) = c_SMT_Oz3mod(X3,X2) ) ).

cnf(i_0_19065_614,axiom,
    ( X1 != X2
    | esk432_2(X1,X3) = esk432_2(X2,X3) ) ).

cnf(i_0_19066_615,axiom,
    ( X1 != X2
    | esk432_2(X3,X1) = esk432_2(X3,X2) ) ).

cnf(i_0_19067_616,axiom,
    ( X1 != X2
    | esk348_1(X1) = esk348_1(X2) ) ).

cnf(i_0_19068_617,axiom,
    ( X1 != X2
    | c_Com_Ocom_OCall(X1,X3,X4) = c_Com_Ocom_OCall(X2,X3,X4) ) ).

cnf(i_0_19069_618,axiom,
    ( X1 != X2
    | c_Com_Ocom_OCall(X3,X1,X4) = c_Com_Ocom_OCall(X3,X2,X4) ) ).

cnf(i_0_19070_619,axiom,
    ( X1 != X2
    | c_Com_Ocom_OCall(X3,X4,X1) = c_Com_Ocom_OCall(X3,X4,X2) ) ).

cnf(i_0_19071_620,axiom,
    ( X1 != X2
    | c_Quickcheck_Obeyond(X1,X3) = c_Quickcheck_Obeyond(X2,X3) ) ).

cnf(i_0_19072_621,axiom,
    ( X1 != X2
    | c_Quickcheck_Obeyond(X3,X1) = c_Quickcheck_Obeyond(X3,X2) ) ).

cnf(i_0_19073_622,axiom,
    ( X1 != X2
    | c_Nat_Onat_Onat__size(X1) = c_Nat_Onat_Onat__size(X2) ) ).

cnf(i_0_19074_623,axiom,
    ( X1 != X2
    | c_Random_Oinc__shift(X1,X3) = c_Random_Oinc__shift(X2,X3) ) ).

cnf(i_0_19075_624,axiom,
    ( X1 != X2
    | c_Random_Oinc__shift(X3,X1) = c_Random_Oinc__shift(X3,X2) ) ).

cnf(i_0_19076_625,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohb__single(X1,X3) = c_Lazy__Sequence_Ohb__single(X2,X3) ) ).

cnf(i_0_19077_626,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohb__single(X3,X1) = c_Lazy__Sequence_Ohb__single(X3,X2) ) ).

cnf(i_0_19078_627,axiom,
    ( X1 != X2
    | c_HOL_Obool_Obool__size(X1) = c_HOL_Obool_Obool__size(X2) ) ).

cnf(i_0_19079_628,axiom,
    ( X1 != X2
    | c_Divides_Oadjust(X1) = c_Divides_Oadjust(X2) ) ).

cnf(i_0_19080_629,axiom,
    ( X1 != X2
    | c_FunDef_Orp__inv__image(X1,X3) = c_FunDef_Orp__inv__image(X2,X3) ) ).

cnf(i_0_19081_630,axiom,
    ( X1 != X2
    | c_FunDef_Orp__inv__image(X3,X1) = c_FunDef_Orp__inv__image(X3,X2) ) ).

cnf(i_0_19082_631,axiom,
    ( X1 != X2
    | c_Com_Ocom_OWhile(X1,X3) = c_Com_Ocom_OWhile(X2,X3) ) ).

cnf(i_0_19083_632,axiom,
    ( X1 != X2
    | c_Com_Ocom_OWhile(X3,X1) = c_Com_Ocom_OWhile(X3,X2) ) ).

cnf(i_0_19084_633,axiom,
    ( X1 != X2
    | ~ hBOOL(X1)
    | hBOOL(X2) ) ).

cnf(i_0_19085_634,axiom,
    ( X1 != X2
    | ~ class_Groups_Ocomm__monoid__add(X1)
    | class_Groups_Ocomm__monoid__add(X2) ) ).

cnf(i_0_19086_635,axiom,
    ( X1 != X2
    | ~ class_Int_Oring__char__0(X1)
    | class_Int_Oring__char__0(X2) ) ).

cnf(i_0_19087_636,axiom,
    ( X1 != X2
    | ~ class_Rings_Oordered__semiring(X1)
    | class_Rings_Oordered__semiring(X2) ) ).

cnf(i_0_19088_637,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__semiring__strict(X1)
    | class_Rings_Olinordered__semiring__strict(X2) ) ).

cnf(i_0_19089_638,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__semiring(X1)
    | class_Rings_Olinordered__semiring(X2) ) ).

cnf(i_0_19090_639,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | class_Groups_Oordered__ab__semigroup__add__imp__le(X2) ) ).

cnf(i_0_19091_640,axiom,
    ( X1 != X2
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ) ).

cnf(i_0_19092_641,axiom,
    ( X1 != X2
    | ~ c_Predicate_Oreflp(X1,X3)
    | c_Predicate_Oreflp(X2,X3) ) ).

cnf(i_0_19093_642,axiom,
    ( X1 != X2
    | ~ c_Predicate_Oreflp(X3,X1)
    | c_Predicate_Oreflp(X3,X2) ) ).

cnf(i_0_19094_643,axiom,
    ( X1 != X2
    | ~ class_Rings_Oordered__comm__semiring(X1)
    | class_Rings_Oordered__comm__semiring(X2) ) ).

cnf(i_0_19095_644,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__comm__semiring__strict(X1)
    | class_Rings_Olinordered__comm__semiring__strict(X2) ) ).

cnf(i_0_19096_645,axiom,
    ( X1 != X2
    | ~ c_Predicate_Osymp(X1,X3)
    | c_Predicate_Osymp(X2,X3) ) ).

cnf(i_0_19097_646,axiom,
    ( X1 != X2
    | ~ c_Predicate_Osymp(X3,X1)
    | c_Predicate_Osymp(X3,X2) ) ).

cnf(i_0_19098_647,axiom,
    ( X1 != X2
    | ~ class_Rings_Oring__1(X1)
    | class_Rings_Oring__1(X2) ) ).

cnf(i_0_19099_648,axiom,
    ( X1 != X2
    | ~ c_Predicate_Otransp(X1,X3)
    | c_Predicate_Otransp(X2,X3) ) ).

cnf(i_0_19100_649,axiom,
    ( X1 != X2
    | ~ c_Predicate_Otransp(X3,X1)
    | c_Predicate_Otransp(X3,X2) ) ).

cnf(i_0_19101_650,axiom,
    ( X1 != X2
    | ~ class_Divides_Oring__div(X1)
    | class_Divides_Oring__div(X2) ) ).

cnf(i_0_19102_651,axiom,
    ( X1 != X2
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | class_Groups_Olinordered__ab__group__add(X2) ) ).

cnf(i_0_19103_652,axiom,
    ( X1 != X2
    | ~ class_Rings_Oordered__cancel__semiring(X1)
    | class_Rings_Oordered__cancel__semiring(X2) ) ).

cnf(i_0_19104_653,axiom,
    ( X1 != X2
    | ~ class_Rings_Oordered__ring__abs(X1)
    | class_Rings_Oordered__ring__abs(X2) ) ).

cnf(i_0_19105_654,axiom,
    ( X1 != X2
    | ~ class_Orderings_Owellorder(X1)
    | class_Orderings_Owellorder(X2) ) ).

cnf(i_0_19106_655,axiom,
    ( X1 != X2
    | ~ class_Lattices_Oboolean__algebra(X1)
    | class_Lattices_Oboolean__algebra(X2) ) ).

cnf(i_0_19107_656,axiom,
    ( X1 != X2
    | ~ class_Rings_Odivision__ring(X1)
    | class_Rings_Odivision__ring(X2) ) ).

cnf(i_0_19108_657,axiom,
    ( X1 != X2
    | ~ class_Rings_Ocomm__semiring(X1)
    | class_Rings_Ocomm__semiring(X2) ) ).

cnf(i_0_19109_658,axiom,
    ( X1 != X2
    | ~ class_Groups_Ominus(X1)
    | class_Groups_Ominus(X2) ) ).

cnf(i_0_19110_659,axiom,
    ( X1 != X2
    | ~ class_Groups_Ocomm__monoid__mult(X1)
    | class_Groups_Ocomm__monoid__mult(X2) ) ).

cnf(i_0_19111_660,axiom,
    ( X1 != X2
    | ~ class_Orderings_Opreorder(X1)
    | class_Orderings_Opreorder(X2) ) ).

cnf(i_0_19112_661,axiom,
    ( X1 != X2
    | ~ class_Groups_Ogroup__add(X1)
    | class_Groups_Ogroup__add(X2) ) ).

cnf(i_0_19113_662,axiom,
    ( X1 != X2
    | ~ c_Nat__Transfer_Otransfer__morphism(X1,X3,X4,X5)
    | c_Nat__Transfer_Otransfer__morphism(X2,X3,X4,X5) ) ).

cnf(i_0_19114_663,axiom,
    ( X1 != X2
    | ~ c_Nat__Transfer_Otransfer__morphism(X3,X1,X4,X5)
    | c_Nat__Transfer_Otransfer__morphism(X3,X2,X4,X5) ) ).

cnf(i_0_19115_664,axiom,
    ( X1 != X2
    | ~ c_Nat__Transfer_Otransfer__morphism(X3,X4,X1,X5)
    | c_Nat__Transfer_Otransfer__morphism(X3,X4,X2,X5) ) ).

cnf(i_0_19116_665,axiom,
    ( X1 != X2
    | ~ c_Nat__Transfer_Otransfer__morphism(X3,X4,X5,X1)
    | c_Nat__Transfer_Otransfer__morphism(X3,X4,X5,X2) ) ).

cnf(i_0_19117_666,axiom,
    ( X1 != X2
    | ~ class_Nat_Osemiring__char__0(X1)
    | class_Nat_Osemiring__char__0(X2) ) ).

cnf(i_0_19118_667,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Owf_H(X1,X3)
    | c_Nitpick_Owf_H(X2,X3) ) ).

cnf(i_0_19119_668,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Owf_H(X3,X1)
    | c_Nitpick_Owf_H(X3,X2) ) ).

cnf(i_0_19120_669,axiom,
    ( X1 != X2
    | ~ c_List_Onat__list(X1)
    | c_List_Onat__list(X2) ) ).

cnf(i_0_19121_670,axiom,
    ( X1 != X2
    | ~ class_Groups_Osgn__if(X1)
    | class_Groups_Osgn__if(X2) ) ).

cnf(i_0_19122_671,axiom,
    ( X1 != X2
    | ~ class_Power_Opower(X1)
    | class_Power_Opower(X2) ) ).

cnf(i_0_19123_672,axiom,
    ( X1 != X2
    | ~ class_Groups_Oabs__if(X1)
    | class_Groups_Oabs__if(X2) ) ).

cnf(i_0_19124_673,axiom,
    ( X1 != X2
    | ~ class_Groups_Ouminus(X1)
    | class_Groups_Ouminus(X2) ) ).

cnf(i_0_19125_674,axiom,
    ( X1 != X2
    | ~ class_Orderings_Oord(X1)
    | class_Orderings_Oord(X2) ) ).

cnf(i_0_19126_675,axiom,
    ( X1 != X2
    | ~ c_Big__Operators_Osemilattice__big(X1,X3,X4)
    | c_Big__Operators_Osemilattice__big(X2,X3,X4) ) ).

cnf(i_0_19127_676,axiom,
    ( X1 != X2
    | ~ c_Big__Operators_Osemilattice__big(X3,X1,X4)
    | c_Big__Operators_Osemilattice__big(X3,X2,X4) ) ).

cnf(i_0_19128_677,axiom,
    ( X1 != X2
    | ~ c_Big__Operators_Osemilattice__big(X3,X4,X1)
    | c_Big__Operators_Osemilattice__big(X3,X4,X2) ) ).

cnf(i_0_19129_678,axiom,
    ( X1 != X2
    | ~ class_Rings_Oidom(X1)
    | class_Rings_Oidom(X2) ) ).

cnf(i_0_19130_679,axiom,
    ( X1 != X2
    | ~ class_Rings_Ocomm__ring__1(X1)
    | class_Rings_Ocomm__ring__1(X2) ) ).

cnf(i_0_19131_680,axiom,
    ( X1 != X2
    | ~ class_Groups_Ocancel__semigroup__add(X1)
    | class_Groups_Ocancel__semigroup__add(X2) ) ).

cnf(i_0_19132_681,axiom,
    ( X1 != X2
    | ~ class_Groups_Ocancel__ab__semigroup__add(X1)
    | class_Groups_Ocancel__ab__semigroup__add(X2) ) ).

cnf(i_0_19133_682,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Ounknown(X1)
    | c_Nitpick_Ounknown(X2) ) ).

cnf(i_0_19134_683,axiom,
    ( X1 != X2
    | ~ class_Finite__Set_Ofinite(X1)
    | class_Finite__Set_Ofinite(X2) ) ).

cnf(i_0_19135_684,axiom,
    ( X1 != X2
    | ~ class_Orderings_Obot(X1)
    | class_Orderings_Obot(X2) ) ).

cnf(i_0_19136_685,axiom,
    ( X1 != X2
    | ~ class_Orderings_Otop(X1)
    | class_Orderings_Otop(X2) ) ).

cnf(i_0_19137_686,axiom,
    ( X1 != X2
    | ~ class_Rings_Omult__zero(X1)
    | class_Rings_Omult__zero(X2) ) ).

cnf(i_0_19138_687,axiom,
    ( X1 != X2
    | ~ class_Groups_Olinordered__ab__semigroup__add(X1)
    | class_Groups_Olinordered__ab__semigroup__add(X2) ) ).

cnf(i_0_19139_688,axiom,
    ( X1 != X2
    | ~ class_Rings_Ozero__neq__one(X1)
    | class_Rings_Ozero__neq__one(X2) ) ).

cnf(i_0_19140_689,axiom,
    ( X1 != X2
    | ~ class_Rings_Oring__no__zero__divisors(X1)
    | class_Rings_Oring__no__zero__divisors(X2) ) ).

cnf(i_0_19141_690,axiom,
    ( X1 != X2
    | ~ class_Lattices_Obounded__lattice__top(X1)
    | class_Lattices_Obounded__lattice__top(X2) ) ).

cnf(i_0_19142_691,axiom,
    ( X1 != X2
    | ~ class_Lattices_Obounded__lattice__bot(X1)
    | class_Lattices_Obounded__lattice__bot(X2) ) ).

cnf(i_0_19143_692,axiom,
    ( X1 != X2
    | ~ class_Rings_Odivision__ring__inverse__zero(X1)
    | class_Rings_Odivision__ring__inverse__zero(X2) ) ).

cnf(i_0_19144_693,axiom,
    ( X1 != X2
    | ~ class_Lattices_Obounded__lattice(X1)
    | class_Lattices_Obounded__lattice(X2) ) ).

cnf(i_0_19145_694,axiom,
    ( X1 != X2
    | ~ class_Nat_Osize(X1)
    | class_Nat_Osize(X2) ) ).

cnf(i_0_19146_695,axiom,
    ( X1 != X2
    | ~ class_Groups_Oone(X1)
    | class_Groups_Oone(X2) ) ).

cnf(i_0_19147_696,axiom,
    ( X1 != X2
    | ~ class_Groups_Ozero(X1)
    | class_Groups_Ozero(X2) ) ).

cnf(i_0_19148_697,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_19149_698,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_19150_699,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_19151_700,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_19152_701,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_19153_702,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_19154_703,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__idom(X1)
    | class_Rings_Olinordered__idom(X2) ) ).

cnf(i_0_19155_704,axiom,
    ( X1 != X2
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | class_Complete__Lattice_Ocomplete__lattice(X2) ) ).

cnf(i_0_19156_705,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_19157_706,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_19158_707,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_19159_708,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_19160_709,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_19161_710,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_19162_711,axiom,
    ( X1 != X2
    | ~ class_Int_Onumber__ring(X1)
    | class_Int_Onumber__ring(X2) ) ).

cnf(i_0_19163_712,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_19164_713,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_19165_714,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_19166_715,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_19167_716,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_19168_717,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_19169_718,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Opart__equivp(X1,X3)
    | c_Equiv__Relations_Opart__equivp(X2,X3) ) ).

cnf(i_0_19170_719,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Opart__equivp(X3,X1)
    | c_Equiv__Relations_Opart__equivp(X3,X2) ) ).

cnf(i_0_19171_720,axiom,
    ( X1 != X2
    | ~ c_Relation_Orefl__on(X1,X3,X4)
    | c_Relation_Orefl__on(X2,X3,X4) ) ).

cnf(i_0_19172_721,axiom,
    ( X1 != X2
    | ~ c_Relation_Orefl__on(X3,X1,X4)
    | c_Relation_Orefl__on(X3,X2,X4) ) ).

cnf(i_0_19173_722,axiom,
    ( X1 != X2
    | ~ c_Relation_Orefl__on(X3,X4,X1)
    | c_Relation_Orefl__on(X3,X4,X2) ) ).

cnf(i_0_19174_723,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Omax__extp(X1,X3,X4,X5)
    | c_Wellfounded_Omax__extp(X2,X3,X4,X5) ) ).

cnf(i_0_19175_724,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Omax__extp(X3,X1,X4,X5)
    | c_Wellfounded_Omax__extp(X3,X2,X4,X5) ) ).

cnf(i_0_19176_725,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Omax__extp(X3,X4,X1,X5)
    | c_Wellfounded_Omax__extp(X3,X4,X2,X5) ) ).

cnf(i_0_19177_726,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Omax__extp(X3,X4,X5,X1)
    | c_Wellfounded_Omax__extp(X3,X4,X5,X2) ) ).

cnf(i_0_19178_727,axiom,
    ( X1 != X2
    | ~ c_List_Olistrelp(X1,X3,X4,X5)
    | c_List_Olistrelp(X2,X3,X4,X5) ) ).

cnf(i_0_19179_728,axiom,
    ( X1 != X2
    | ~ c_List_Olistrelp(X3,X1,X4,X5)
    | c_List_Olistrelp(X3,X2,X4,X5) ) ).

cnf(i_0_19180_729,axiom,
    ( X1 != X2
    | ~ c_List_Olistrelp(X3,X4,X1,X5)
    | c_List_Olistrelp(X3,X4,X2,X5) ) ).

cnf(i_0_19181_730,axiom,
    ( X1 != X2
    | ~ c_List_Olistrelp(X3,X4,X5,X1)
    | c_List_Olistrelp(X3,X4,X5,X2) ) ).

cnf(i_0_19182_731,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Oequivp(X1,X3)
    | c_Equiv__Relations_Oequivp(X2,X3) ) ).

cnf(i_0_19183_732,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Oequivp(X3,X1)
    | c_Equiv__Relations_Oequivp(X3,X2) ) ).

cnf(i_0_19184_733,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Owf(X1,X3)
    | c_Wellfounded_Owf(X2,X3) ) ).

cnf(i_0_19185_734,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Owf(X3,X1)
    | c_Wellfounded_Owf(X3,X2) ) ).

cnf(i_0_19186_735,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_OwfP(X1,X3)
    | c_Wellfounded_OwfP(X2,X3) ) ).

cnf(i_0_19187_736,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_OwfP(X3,X1)
    | c_Wellfounded_OwfP(X3,X2) ) ).

cnf(i_0_19188_737,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofun__left__comm(X1,X3,X4)
    | c_Finite__Set_Ofun__left__comm(X2,X3,X4) ) ).

cnf(i_0_19189_738,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofun__left__comm(X3,X1,X4)
    | c_Finite__Set_Ofun__left__comm(X3,X2,X4) ) ).

cnf(i_0_19190_739,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofun__left__comm(X3,X4,X1)
    | c_Finite__Set_Ofun__left__comm(X3,X4,X2) ) ).

cnf(i_0_19191_740,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__semidom(X1)
    | class_Rings_Olinordered__semidom(X2) ) ).

cnf(i_0_19192_741,axiom,
    ( X1 != X2
    | ~ class_Lazy__Sequence_Osmall__lazy(X1)
    | class_Lazy__Sequence_Osmall__lazy(X2) ) ).

cnf(i_0_19193_742,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Oequiv(X1,X3,X4)
    | c_Equiv__Relations_Oequiv(X2,X3,X4) ) ).

cnf(i_0_19194_743,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Oequiv(X3,X1,X4)
    | c_Equiv__Relations_Oequiv(X3,X2,X4) ) ).

cnf(i_0_19195_744,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Oequiv(X3,X4,X1)
    | c_Equiv__Relations_Oequiv(X3,X4,X2) ) ).

cnf(i_0_19196_745,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__ab__group__add(X1)
    | class_Groups_Oordered__ab__group__add(X2) ) ).

cnf(i_0_19197_746,axiom,
    ( X1 != X2
    | ~ class_Groups_Omonoid__mult(X1)
    | class_Groups_Omonoid__mult(X2) ) ).

cnf(i_0_19198_747,axiom,
    ( X1 != X2
    | ~ class_Groups_Oab__semigroup__mult(X1)
    | class_Groups_Oab__semigroup__mult(X2) ) ).

cnf(i_0_19199_748,axiom,
    ( X1 != X2
    | ~ class_Groups_Omonoid__add(X1)
    | class_Groups_Omonoid__add(X2) ) ).

cnf(i_0_19200_749,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__ab__semigroup__add(X1)
    | class_Groups_Oordered__ab__semigroup__add(X2) ) ).

cnf(i_0_19201_750,axiom,
    ( X1 != X2
    | ~ c_List_Olist__all2(X1,X3,X4,X5,X6)
    | c_List_Olist__all2(X2,X3,X4,X5,X6) ) ).

cnf(i_0_19202_751,axiom,
    ( X1 != X2
    | ~ c_List_Olist__all2(X3,X1,X4,X5,X6)
    | c_List_Olist__all2(X3,X2,X4,X5,X6) ) ).

cnf(i_0_19203_752,axiom,
    ( X1 != X2
    | ~ c_List_Olist__all2(X3,X4,X1,X5,X6)
    | c_List_Olist__all2(X3,X4,X2,X5,X6) ) ).

cnf(i_0_19204_753,axiom,
    ( X1 != X2
    | ~ c_List_Olist__all2(X3,X4,X5,X1,X6)
    | c_List_Olist__all2(X3,X4,X5,X2,X6) ) ).

cnf(i_0_19205_754,axiom,
    ( X1 != X2
    | ~ c_List_Olist__all2(X3,X4,X5,X6,X1)
    | c_List_Olist__all2(X3,X4,X5,X6,X2) ) ).

cnf(i_0_19206_755,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
    | class_Groups_Oordered__cancel__ab__semigroup__add(X2) ) ).

cnf(i_0_19207_756,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__one__idem(X1,X3,X4)
    | c_Finite__Set_Ofolding__one__idem(X2,X3,X4) ) ).

cnf(i_0_19208_757,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__one__idem(X3,X1,X4)
    | c_Finite__Set_Ofolding__one__idem(X3,X2,X4) ) ).

cnf(i_0_19209_758,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__one__idem(X3,X4,X1)
    | c_Finite__Set_Ofolding__one__idem(X3,X4,X2) ) ).

cnf(i_0_19210_759,axiom,
    ( X1 != X2
    | ~ class_Rings_Ocomm__semiring__1(X1)
    | class_Rings_Ocomm__semiring__1(X2) ) ).

cnf(i_0_19211_760,axiom,
    ( X1 != X2
    | ~ class_Rings_Osemiring__1(X1)
    | class_Rings_Osemiring__1(X2) ) ).

cnf(i_0_19212_761,axiom,
    ( X1 != X2
    | ~ class_Rings_Osemiring__0(X1)
    | class_Rings_Osemiring__0(X2) ) ).

cnf(i_0_19213_762,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__one(X1,X3,X4)
    | c_Finite__Set_Ofolding__one(X2,X3,X4) ) ).

cnf(i_0_19214_763,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__one(X3,X1,X4)
    | c_Finite__Set_Ofolding__one(X3,X2,X4) ) ).

cnf(i_0_19215_764,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__one(X3,X4,X1)
    | c_Finite__Set_Ofolding__one(X3,X4,X2) ) ).

cnf(i_0_19216_765,axiom,
    ( X1 != X2
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | class_Fields_Olinordered__field__inverse__zero(X2) ) ).

cnf(i_0_19217_766,axiom,
    ( X1 != X2
    | ~ c_FunDef_Oreduction__pair(X1,X3)
    | c_FunDef_Oreduction__pair(X2,X3) ) ).

cnf(i_0_19218_767,axiom,
    ( X1 != X2
    | ~ c_FunDef_Oreduction__pair(X3,X1)
    | c_FunDef_Oreduction__pair(X3,X2) ) ).

cnf(i_0_19219_768,axiom,
    ( X1 != X2
    | ~ c_List_Olinorder__class_Osorted(X1,X3)
    | c_List_Olinorder__class_Osorted(X2,X3) ) ).

cnf(i_0_19220_769,axiom,
    ( X1 != X2
    | ~ c_List_Olinorder__class_Osorted(X3,X1)
    | c_List_Olinorder__class_Osorted(X3,X2) ) ).

cnf(i_0_19221_770,axiom,
    ( X1 != X2
    | ~ class_Orderings_Oorder(X1)
    | class_Orderings_Oorder(X2) ) ).

cnf(i_0_19222_771,axiom,
    ( X1 != X2
    | ~ class_Enum_Oenum(X1)
    | class_Enum_Oenum(X2) ) ).

cnf(i_0_19223_772,axiom,
    ( X1 != X2
    | ~ c_Nat__Transfer_Ois__nat(X1)
    | c_Nat__Transfer_Ois__nat(X2) ) ).

cnf(i_0_19224_773,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Oless__eq__frac(X1,X3,X4)
    | c_Nitpick_Oless__eq__frac(X2,X3,X4) ) ).

cnf(i_0_19225_774,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Oless__eq__frac(X3,X1,X4)
    | c_Nitpick_Oless__eq__frac(X3,X2,X4) ) ).

cnf(i_0_19226_775,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Oless__eq__frac(X3,X4,X1)
    | c_Nitpick_Oless__eq__frac(X3,X4,X2) ) ).

cnf(i_0_19227_776,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Oless__frac(X1,X3,X4)
    | c_Nitpick_Oless__frac(X2,X3,X4) ) ).

cnf(i_0_19228_777,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Oless__frac(X3,X1,X4)
    | c_Nitpick_Oless__frac(X3,X2,X4) ) ).

cnf(i_0_19229_778,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Oless__frac(X3,X4,X1)
    | c_Nitpick_Oless__frac(X3,X4,X2) ) ).

cnf(i_0_19230_779,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__comm__monoid__add(X1)
    | class_Groups_Oordered__comm__monoid__add(X2) ) ).

cnf(i_0_19231_780,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X1,X3,X4,X5)
    | c_Fun_Oinj__on(X2,X3,X4,X5) ) ).

cnf(i_0_19232_781,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X1,X4,X5)
    | c_Fun_Oinj__on(X3,X2,X4,X5) ) ).

cnf(i_0_19233_782,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X4,X1,X5)
    | c_Fun_Oinj__on(X3,X4,X2,X5) ) ).

cnf(i_0_19234_783,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X4,X5,X1)
    | c_Fun_Oinj__on(X3,X4,X5,X2) ) ).

cnf(i_0_19235_784,axiom,
    ( X1 != X2
    | ~ class_Rings_Oordered__ring(X1)
    | class_Rings_Oordered__ring(X2) ) ).

cnf(i_0_19236_785,axiom,
    ( X1 != X2
    | ~ class_Groups_Oab__group__add(X1)
    | class_Groups_Oab__group__add(X2) ) ).

cnf(i_0_19237_786,axiom,
    ( X1 != X2
    | ~ class_Rings_Oinverse(X1)
    | class_Rings_Oinverse(X2) ) ).

cnf(i_0_19238_787,axiom,
    ( X1 != X2
    | ~ class_Fields_Ofield(X1)
    | class_Fields_Ofield(X2) ) ).

cnf(i_0_19239_788,axiom,
    ( X1 != X2
    | ~ c_List_Olist__ex1(X1,X3,X4)
    | c_List_Olist__ex1(X2,X3,X4) ) ).

cnf(i_0_19240_789,axiom,
    ( X1 != X2
    | ~ c_List_Olist__ex1(X3,X1,X4)
    | c_List_Olist__ex1(X3,X2,X4) ) ).

cnf(i_0_19241_790,axiom,
    ( X1 != X2
    | ~ c_List_Olist__ex1(X3,X4,X1)
    | c_List_Olist__ex1(X3,X4,X2) ) ).

cnf(i_0_19242_791,axiom,
    ( X1 != X2
    | ~ c_List_Olist__all(X1,X3,X4)
    | c_List_Olist__all(X2,X3,X4) ) ).

cnf(i_0_19243_792,axiom,
    ( X1 != X2
    | ~ c_List_Olist__all(X3,X1,X4)
    | c_List_Olist__all(X3,X2,X4) ) ).

cnf(i_0_19244_793,axiom,
    ( X1 != X2
    | ~ c_List_Olist__all(X3,X4,X1)
    | c_List_Olist__all(X3,X4,X2) ) ).

cnf(i_0_19245_794,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_19246_795,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_19247_796,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_19248_797,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_19249_798,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_19250_799,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_19251_800,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__ab__group__add__abs(X1)
    | class_Groups_Oordered__ab__group__add__abs(X2) ) ).

cnf(i_0_19252_801,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_19253_802,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_19254_803,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_19255_804,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_19256_805,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_19257_806,axiom,
    ( X1 != X2
    | ~ class_Rings_Oring__1__no__zero__divisors(X1)
    | class_Rings_Oring__1__no__zero__divisors(X2) ) ).

cnf(i_0_19258_807,axiom,
    ( X1 != X2
    | ~ class_Orderings_Olinorder(X1)
    | class_Orderings_Olinorder(X2) ) ).

cnf(i_0_19259_808,axiom,
    ( X1 != X2
    | ~ c_Nat__Transfer_Onat__set(X1)
    | c_Nat__Transfer_Onat__set(X2) ) ).

cnf(i_0_19260_809,axiom,
    ( X1 != X2
    | ~ c_Fun_Obij__betw(X1,X3,X4,X5,X6)
    | c_Fun_Obij__betw(X2,X3,X4,X5,X6) ) ).

cnf(i_0_19261_810,axiom,
    ( X1 != X2
    | ~ c_Fun_Obij__betw(X3,X1,X4,X5,X6)
    | c_Fun_Obij__betw(X3,X2,X4,X5,X6) ) ).

cnf(i_0_19262_811,axiom,
    ( X1 != X2
    | ~ c_Fun_Obij__betw(X3,X4,X1,X5,X6)
    | c_Fun_Obij__betw(X3,X4,X2,X5,X6) ) ).

cnf(i_0_19263_812,axiom,
    ( X1 != X2
    | ~ c_Fun_Obij__betw(X3,X4,X5,X1,X6)
    | c_Fun_Obij__betw(X3,X4,X5,X2,X6) ) ).

cnf(i_0_19264_813,axiom,
    ( X1 != X2
    | ~ c_Fun_Obij__betw(X3,X4,X5,X6,X1)
    | c_Fun_Obij__betw(X3,X4,X5,X6,X2) ) ).

cnf(i_0_19265_814,axiom,
    ( X1 != X2
    | ~ class_Fields_Ofield__inverse__zero(X1)
    | class_Fields_Ofield__inverse__zero(X2) ) ).

cnf(i_0_19266_815,axiom,
    ( X1 != X2
    | ~ c_Relation_Otrans(X1,X3)
    | c_Relation_Otrans(X2,X3) ) ).

cnf(i_0_19267_816,axiom,
    ( X1 != X2
    | ~ c_Relation_Otrans(X3,X1)
    | c_Relation_Otrans(X3,X2) ) ).

cnf(i_0_19268_817,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_19269_818,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_19270_819,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_19271_820,axiom,
    ( X1 != X2
    | ~ class_Lattices_Osemilattice__sup(X1)
    | class_Lattices_Osemilattice__sup(X2) ) ).

cnf(i_0_19272_821,axiom,
    ( X1 != X2
    | ~ c_Int_Oiszero(X1,X3)
    | c_Int_Oiszero(X2,X3) ) ).

cnf(i_0_19273_822,axiom,
    ( X1 != X2
    | ~ c_Int_Oiszero(X3,X1)
    | c_Int_Oiszero(X3,X2) ) ).

cnf(i_0_19274_823,axiom,
    ( X1 != X2
    | ~ c_Relation_Ototal__on(X1,X3,X4)
    | c_Relation_Ototal__on(X2,X3,X4) ) ).

cnf(i_0_19275_824,axiom,
    ( X1 != X2
    | ~ c_Relation_Ototal__on(X3,X1,X4)
    | c_Relation_Ototal__on(X3,X2,X4) ) ).

cnf(i_0_19276_825,axiom,
    ( X1 != X2
    | ~ c_Relation_Ototal__on(X3,X4,X1)
    | c_Relation_Ototal__on(X3,X4,X2) ) ).

cnf(i_0_19277_826,axiom,
    ( X1 != X2
    | ~ c_Relation_Osingle__valued(X1,X3,X4)
    | c_Relation_Osingle__valued(X2,X3,X4) ) ).

cnf(i_0_19278_827,axiom,
    ( X1 != X2
    | ~ c_Relation_Osingle__valued(X3,X1,X4)
    | c_Relation_Osingle__valued(X3,X2,X4) ) ).

cnf(i_0_19279_828,axiom,
    ( X1 != X2
    | ~ c_Relation_Osingle__valued(X3,X4,X1)
    | c_Relation_Osingle__valued(X3,X4,X2) ) ).

cnf(i_0_19280_829,axiom,
    ( X1 != X2
    | ~ class_Int_Onumber(X1)
    | class_Int_Onumber(X2) ) ).

cnf(i_0_19281_830,axiom,
    ( X1 != X2
    | ~ class_Lattices_Odistrib__lattice(X1)
    | class_Lattices_Odistrib__lattice(X2) ) ).

cnf(i_0_19282_831,axiom,
    ( X1 != X2
    | ~ c_Hoare__Mirabelle_Otriple__valid(X1,X3,X4)
    | c_Hoare__Mirabelle_Otriple__valid(X2,X3,X4) ) ).

cnf(i_0_19283_832,axiom,
    ( X1 != X2
    | ~ c_Hoare__Mirabelle_Otriple__valid(X3,X1,X4)
    | c_Hoare__Mirabelle_Otriple__valid(X3,X2,X4) ) ).

cnf(i_0_19284_833,axiom,
    ( X1 != X2
    | ~ c_Hoare__Mirabelle_Otriple__valid(X3,X4,X1)
    | c_Hoare__Mirabelle_Otriple__valid(X3,X4,X2) ) ).

cnf(i_0_19285_834,axiom,
    ( X1 != X2
    | ~ class_Divides_Osemiring__div(X1)
    | class_Divides_Osemiring__div(X2) ) ).

cnf(i_0_19286_835,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | class_Rings_Olinordered__ring__strict(X2) ) ).

cnf(i_0_19287_836,axiom,
    ( X1 != X2
    | ~ class_Lattices_Olattice(X1)
    | class_Lattices_Olattice(X2) ) ).

cnf(i_0_19288_837,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__ring(X1)
    | class_Rings_Olinordered__ring(X2) ) ).

cnf(i_0_19289_838,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding(X1,X3,X4,X5)
    | c_Finite__Set_Ofolding(X2,X3,X4,X5) ) ).

cnf(i_0_19290_839,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding(X3,X1,X4,X5)
    | c_Finite__Set_Ofolding(X3,X2,X4,X5) ) ).

cnf(i_0_19291_840,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding(X3,X4,X1,X5)
    | c_Finite__Set_Ofolding(X3,X4,X2,X5) ) ).

cnf(i_0_19292_841,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding(X3,X4,X5,X1)
    | c_Finite__Set_Ofolding(X3,X4,X5,X2) ) ).

cnf(i_0_19293_842,axiom,
    ( X1 != X2
    | ~ c_Relation_Osym(X1,X3)
    | c_Relation_Osym(X2,X3) ) ).

cnf(i_0_19294_843,axiom,
    ( X1 != X2
    | ~ c_Relation_Osym(X3,X1)
    | c_Relation_Osym(X3,X2) ) ).

cnf(i_0_19295_844,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__semiring__1(X1)
    | class_Rings_Olinordered__semiring__1(X2) ) ).

cnf(i_0_19296_845,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__semiring__1__strict(X1)
    | class_Rings_Olinordered__semiring__1__strict(X2) ) ).

cnf(i_0_19297_846,axiom,
    ( X1 != X2
    | ~ class_Lattices_Osemilattice__inf(X1)
    | class_Lattices_Osemilattice__inf(X2) ) ).

cnf(i_0_19298_847,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Ocongruent(X1,X3,X4,X5)
    | c_Equiv__Relations_Ocongruent(X2,X3,X4,X5) ) ).

cnf(i_0_19299_848,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Ocongruent(X3,X1,X4,X5)
    | c_Equiv__Relations_Ocongruent(X3,X2,X4,X5) ) ).

cnf(i_0_19300_849,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Ocongruent(X3,X4,X1,X5)
    | c_Equiv__Relations_Ocongruent(X3,X4,X2,X5) ) ).

cnf(i_0_19301_850,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Ocongruent(X3,X4,X5,X1)
    | c_Equiv__Relations_Ocongruent(X3,X4,X5,X2) ) ).

cnf(i_0_19302_851,axiom,
    ( X1 != X2
    | ~ class_Fields_Olinordered__field(X1)
    | class_Fields_Olinordered__field(X2) ) ).

cnf(i_0_19303_852,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Oacyclic(X1,X3)
    | c_Wellfounded_Oacyclic(X2,X3) ) ).

cnf(i_0_19304_853,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Oacyclic(X3,X1)
    | c_Wellfounded_Oacyclic(X3,X2) ) ).

cnf(i_0_19305_854,axiom,
    ( X1 != X2
    | ~ c_Relation_Oantisym(X1,X3)
    | c_Relation_Oantisym(X2,X3) ) ).

cnf(i_0_19306_855,axiom,
    ( X1 != X2
    | ~ c_Relation_Oantisym(X3,X1)
    | c_Relation_Oantisym(X3,X2) ) ).

cnf(i_0_19307_856,axiom,
    ( X1 != X2
    | ~ c_Natural_Oevaln(X1,X3,X4,X5)
    | c_Natural_Oevaln(X2,X3,X4,X5) ) ).

cnf(i_0_19308_857,axiom,
    ( X1 != X2
    | ~ c_Natural_Oevaln(X3,X1,X4,X5)
    | c_Natural_Oevaln(X3,X2,X4,X5) ) ).

cnf(i_0_19309_858,axiom,
    ( X1 != X2
    | ~ c_Natural_Oevaln(X3,X4,X1,X5)
    | c_Natural_Oevaln(X3,X4,X2,X5) ) ).

cnf(i_0_19310_859,axiom,
    ( X1 != X2
    | ~ c_Natural_Oevaln(X3,X4,X5,X1)
    | c_Natural_Oevaln(X3,X4,X5,X2) ) ).

cnf(i_0_19311_860,axiom,
    ( X1 != X2
    | ~ class_Lattices_Oab__semigroup__idem__mult(X1)
    | class_Lattices_Oab__semigroup__idem__mult(X2) ) ).

cnf(i_0_19312_861,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Orefl_H(X1,X3)
    | c_Nitpick_Orefl_H(X2,X3) ) ).

cnf(i_0_19313_862,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Orefl_H(X3,X1)
    | c_Nitpick_Orefl_H(X3,X2) ) ).

cnf(i_0_19314_863,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__idem(X1,X3,X4,X5)
    | c_Finite__Set_Ofolding__idem(X2,X3,X4,X5) ) ).

cnf(i_0_19315_864,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__idem(X3,X1,X4,X5)
    | c_Finite__Set_Ofolding__idem(X3,X2,X4,X5) ) ).

cnf(i_0_19316_865,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__idem(X3,X4,X1,X5)
    | c_Finite__Set_Ofolding__idem(X3,X4,X2,X5) ) ).

cnf(i_0_19317_866,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__idem(X3,X4,X5,X1)
    | c_Finite__Set_Ofolding__idem(X3,X4,X5,X2) ) ).

cnf(i_0_19318_867,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_19319_868,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_19320_869,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_19321_870,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_19322_871,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_19323_872,axiom,
    ( X1 != X2
    | ~ c_Hoare__Mirabelle_Ohoare__valids(X1,X3,X4)
    | c_Hoare__Mirabelle_Ohoare__valids(X2,X3,X4) ) ).

cnf(i_0_19324_873,axiom,
    ( X1 != X2
    | ~ c_Hoare__Mirabelle_Ohoare__valids(X3,X1,X4)
    | c_Hoare__Mirabelle_Ohoare__valids(X3,X2,X4) ) ).

cnf(i_0_19325_874,axiom,
    ( X1 != X2
    | ~ c_Hoare__Mirabelle_Ohoare__valids(X3,X4,X1)
    | c_Hoare__Mirabelle_Ohoare__valids(X3,X4,X2) ) ).

cnf(i_0_19326_875,axiom,
    ( X1 != X2
    | ~ class_Rings_Ono__zero__divisors(X1)
    | class_Rings_Ono__zero__divisors(X2) ) ).

cnf(i_0_19327_876,axiom,
    ( X1 != X2
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X3,X4)
    | c_Hoare__Mirabelle_Ohoare__derivs(X2,X3,X4) ) ).

cnf(i_0_19328_877,axiom,
    ( X1 != X2
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,X1,X4)
    | c_Hoare__Mirabelle_Ohoare__derivs(X3,X2,X4) ) ).

cnf(i_0_19329_878,axiom,
    ( X1 != X2
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,X4,X1)
    | c_Hoare__Mirabelle_Ohoare__derivs(X3,X4,X2) ) ).

cnf(i_0_19330_879,axiom,
    ( X1 != X2
    | ~ c_Typedef_Otype__definition(X1,X3,X4,X5,X6)
    | c_Typedef_Otype__definition(X2,X3,X4,X5,X6) ) ).

cnf(i_0_19331_880,axiom,
    ( X1 != X2
    | ~ c_Typedef_Otype__definition(X3,X1,X4,X5,X6)
    | c_Typedef_Otype__definition(X3,X2,X4,X5,X6) ) ).

cnf(i_0_19332_881,axiom,
    ( X1 != X2
    | ~ c_Typedef_Otype__definition(X3,X4,X1,X5,X6)
    | c_Typedef_Otype__definition(X3,X4,X2,X5,X6) ) ).

cnf(i_0_19333_882,axiom,
    ( X1 != X2
    | ~ c_Typedef_Otype__definition(X3,X4,X5,X1,X6)
    | c_Typedef_Otype__definition(X3,X4,X5,X2,X6) ) ).

cnf(i_0_19334_883,axiom,
    ( X1 != X2
    | ~ c_Typedef_Otype__definition(X3,X4,X5,X6,X1)
    | c_Typedef_Otype__definition(X3,X4,X5,X6,X2) ) ).

cnf(i_0_19335_884,axiom,
    ( X1 != X2
    | ~ class_Rings_Oring(X1)
    | class_Rings_Oring(X2) ) ).

cnf(i_0_19336_885,axiom,
    ( X1 != X2
    | ~ class_Rings_Osemiring(X1)
    | class_Rings_Osemiring(X2) ) ).

cnf(i_0_19337_886,axiom,
    ( X1 != X2
    | ~ class_Groups_Osemigroup__add(X1)
    | class_Groups_Osemigroup__add(X2) ) ).

cnf(i_0_19338_887,axiom,
    ( X1 != X2
    | ~ c_List_Olist__ex(X1,X3,X4)
    | c_List_Olist__ex(X2,X3,X4) ) ).

cnf(i_0_19339_888,axiom,
    ( X1 != X2
    | ~ c_List_Olist__ex(X3,X1,X4)
    | c_List_Olist__ex(X3,X2,X4) ) ).

cnf(i_0_19340_889,axiom,
    ( X1 != X2
    | ~ c_List_Olist__ex(X3,X4,X1)
    | c_List_Olist__ex(X3,X4,X2) ) ).

cnf(i_0_19341_890,axiom,
    ( X1 != X2
    | ~ c_List_Oall__interval__int(X1,X3,X4)
    | c_List_Oall__interval__int(X2,X3,X4) ) ).

cnf(i_0_19342_891,axiom,
    ( X1 != X2
    | ~ c_List_Oall__interval__int(X3,X1,X4)
    | c_List_Oall__interval__int(X3,X2,X4) ) ).

cnf(i_0_19343_892,axiom,
    ( X1 != X2
    | ~ c_List_Oall__interval__int(X3,X4,X1)
    | c_List_Oall__interval__int(X3,X4,X2) ) ).

cnf(i_0_19344_893,axiom,
    ( X1 != X2
    | ~ c_Relation_Oirrefl(X1,X3)
    | c_Relation_Oirrefl(X2,X3) ) ).

cnf(i_0_19345_894,axiom,
    ( X1 != X2
    | ~ c_Relation_Oirrefl(X3,X1)
    | c_Relation_Oirrefl(X3,X2) ) ).

cnf(i_0_19346_895,axiom,
    ( X1 != X2
    | ~ epred2_3(X1,X3,X4)
    | epred2_3(X2,X3,X4) ) ).

cnf(i_0_19347_896,axiom,
    ( X1 != X2
    | ~ epred2_3(X3,X1,X4)
    | epred2_3(X3,X2,X4) ) ).

cnf(i_0_19348_897,axiom,
    ( X1 != X2
    | ~ epred2_3(X3,X4,X1)
    | epred2_3(X3,X4,X2) ) ).

cnf(i_0_19349_898,axiom,
    ( X1 != X2
    | ~ epred1_3(X1,X3,X4)
    | epred1_3(X2,X3,X4) ) ).

cnf(i_0_19350_899,axiom,
    ( X1 != X2
    | ~ epred1_3(X3,X1,X4)
    | epred1_3(X3,X2,X4) ) ).

cnf(i_0_19351_900,axiom,
    ( X1 != X2
    | ~ epred1_3(X3,X4,X1)
    | epred1_3(X3,X4,X2) ) ).

cnf(i_0_19352_901,axiom,
    ( X1 != X2
    | ~ class_Groups_Oab__semigroup__add(X1)
    | class_Groups_Oab__semigroup__add(X2) ) ).

cnf(i_0_19353,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),esk159_7(X4,X4,X6,X5,X3,X2,X1)),esk160_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,[],[11130]) ).

cnf(i_0_19354,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),esk477_8(X6,X7,hAPP(c_Set_Oimage(X1,X2,X3),X4),X4,X3,X2,X1,X5)),X4)) ),
    inference(equality_inference,[],[11146]) ).

cnf(i_0_19355,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),esk224_8(X6,X7,hAPP(c_Set_Oimage(X1,X2,X3),X4),X4,X3,X2,X1,X5)),X4)) ),
    inference(equality_inference,[],[11147]) ).

cnf(i_0_19356,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)),esk329_4(X3,X2,X2,X1))) ),
    inference(equality_inference,[],[11170]) ).

cnf(i_0_19357,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),esk160_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_19358,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),esk159_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,[],[11231]) ).

cnf(i_0_19359,plain,
    X1 = X1,
    inference(equality_inference,[],[11272]) ).

cnf(i_0_19360,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,esk159_7(X1,X1,X6,X5,X4,X3,X2)) = hAPP(X6,esk160_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,[],[11285]) ).

cnf(i_0_19361,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,esk241_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,[],[11345]) ).

cnf(i_0_19362,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),esk241_6(X5,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X4),X3),X4,X3,X2,X1)),X3)) ),
    inference(equality_inference,[],[11404]) ).

cnf(i_0_19363,plain,
    ( c_List_Olist__all2(X1,X1,X2,X3,X3)
    | ~ hBOOL(hAPP(hAPP(X2,hAPP(hAPP(c_List_Onth(X1),X3),esk427_5(X2,X3,X1,X3,X1))),hAPP(hAPP(c_List_Onth(X1),X3),esk427_5(X2,X3,X1,X3,X1)))) ),
    inference(equality_inference,[],[11406]) ).

cnf(i_0_19364,plain,
    ( c_List_Olist__all2(X1,X1,X2,X3,X3)
    | ~ hBOOL(hAPP(hAPP(X2,hAPP(hAPP(c_List_Onth(X1),X3),esk365_5(X3,X3,X2,X1,X1))),hAPP(hAPP(c_List_Onth(X1),X3),esk365_5(X3,X3,X2,X1,X1)))) ),
    inference(equality_inference,[],[11407]) ).

cnf(i_0_19365,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),esk390_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,[],[11415]) ).

cnf(i_0_19366,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),esk319_4(X3,X2,X2,X1))),hAPP(hAPP(c_List_Onth(X1),X2),esk319_4(X3,X2,X2,X1)))),X3)) ),
    inference(equality_inference,[],[11427]) ).

cnf(i_0_19367,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,[],[11470]) ).

cnf(i_0_19368,plain,
    hAPP(X1,hAPP(c_Product__Type_Osnd(X2,X3),X4)) = hAPP(X1,hAPP(c_Product__Type_Osnd(X2,X3),X4)),
    inference(equality_inference,[],[11478]) ).

cnf(i_0_19369,plain,
    hAPP(X1,hAPP(c_Product__Type_Ofst(X2,X3),X4)) = hAPP(X1,hAPP(c_Product__Type_Ofst(X2,X3),X4)),
    inference(equality_inference,[],[11479]) ).

cnf(i_0_19370,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,[],[11491]) ).

cnf(i_0_19371,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,[],[11541]) ).

cnf(i_0_19372,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,[],[11542]) ).

cnf(i_0_19373,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,[],[11562]) ).

cnf(i_0_19374,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,[],[11624]) ).

cnf(i_0_19375,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,[],[11627]) ).

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)),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,[],[11724]) ).

cnf(i_0_19377,plain,
    ( c_List_Olist__all2(X1,X1,X2,X3,X3)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk366_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,[],[11725]) ).

cnf(i_0_19378,plain,
    ( c_List_Olist__all2(X1,X1,X2,X3,X3)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk364_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,[],[11726]) ).

cnf(i_0_19379,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,[],[11742]) ).

cnf(i_0_19380,plain,
    ( c_List_Olist__all2(X1,X1,X2,X3,X3)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk427_5(X2,X3,X1,X3,X1)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))) ),
    inference(equality_inference,[],[11747]) ).

cnf(i_0_19381,plain,
    ( c_List_Olist__all2(X1,X1,X2,X3,X3)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk365_5(X3,X3,X2,X1,X1)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))) ),
    inference(equality_inference,[],[11748]) ).

cnf(i_0_19382,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,[],[11789]) ).

cnf(i_0_19383,plain,
    ( hAPP(hAPP(c_List_Oappend(X1),esk297_5(X2,X3,X2,X3,X1)),X2) = X2
    | X2 = hAPP(hAPP(c_List_Oappend(X1),esk298_5(X2,X3,X2,X3,X1)),X2) ),
    inference(equality_inference,[],[11830]) ).

cnf(i_0_19384,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),esk366_5(X2,X3,X3,X1,X1))) ),
    inference(equality_inference,[],[11836]) ).

cnf(i_0_19385,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),esk364_5(X3,X3,X2,X1,X1))) ),
    inference(equality_inference,[],[11837]) ).

cnf(i_0_19386,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,esk223_4(X4,X1,X2,hAPP(c_Set_Oimage(X1,X2,X3),X4))),hAPP(c_Set_Oimage(X1,X2,X3),X4))),X4)) ),
    inference(equality_inference,[],[11849]) ).

cnf(i_0_19387,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,[],[11877]) ).

cnf(i_0_19388,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,[],[11888]) ).

cnf(i_0_19389,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,[],[11889]) ).

cnf(i_0_19390,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,[],[11890]) ).

cnf(i_0_19391,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,[],[11891]) ).

cnf(i_0_19392,plain,
    hAPP(hAPP(c_List_Omap(X1,X2),X3),X4) = hAPP(hAPP(c_List_Omap(X1,X2),X3),X4),
    inference(equality_inference,[],[11926]) ).

cnf(i_0_19393,plain,
    ( hAPP(hAPP(c_List_Oappend(X1),X2),esk298_5(X3,X2,X3,X2,X1)) = X2
    | hAPP(hAPP(c_List_Oappend(X1),esk297_5(X3,X2,X3,X2,X1)),X3) = X3 ),
    inference(equality_inference,[],[11950]) ).

cnf(i_0_19394,plain,
    ( X1 = hAPP(hAPP(c_List_Oappend(X2),X1),esk297_5(X3,X1,X3,X1,X2))
    | X3 = hAPP(hAPP(c_List_Oappend(X2),esk298_5(X3,X1,X3,X1,X2)),X3) ),
    inference(equality_inference,[],[11951]) ).

cnf(i_0_19395,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,[],[11983]) ).

cnf(i_0_19396,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,[],[11988]) ).

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)),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,[],[11989]) ).

cnf(i_0_19398,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,[],[11990]) ).

cnf(i_0_19399,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),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,[],[11991]) ).

cnf(i_0_19400,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,[],[11992]) ).

cnf(i_0_19401,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,[],[12011]) ).

cnf(i_0_19402,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,[],[12054]) ).

cnf(i_0_19403,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,[],[12061]) ).

cnf(i_0_19404,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,[],[12115]) ).

cnf(i_0_19405,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,[],[12127]) ).

cnf(i_0_19406,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,[],[12132]) ).

cnf(i_0_19407,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,[],[12133]) ).

cnf(i_0_19408,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,[],[12134]) ).

cnf(i_0_19409,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)),esk247_5(X4,X3,X1,X1,X2))) ),
    inference(equality_inference,[],[12147]) ).

cnf(i_0_19410,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)),esk246_5(X4,X3,X1,X1,X2))) ),
    inference(equality_inference,[],[12148]) ).

cnf(i_0_19411,plain,
    ( X1 = hAPP(hAPP(c_List_Oappend(X2),X1),esk297_5(X3,X1,X3,X1,X2))
    | hAPP(hAPP(c_List_Oappend(X2),X1),esk298_5(X3,X1,X3,X1,X2)) = X1 ),
    inference(equality_inference,[],[12151]) ).

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)),X2),X2)),c_List_Olistrel(X1,X3)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk329_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,[],[12154]) ).

cnf(i_0_19413,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,[],[12241]) ).

cnf(i_0_19414,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,[],[12244]) ).

cnf(i_0_19415,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,[],[12286]) ).

cnf(i_0_19416,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),esk319_4(X3,X2,X2,X1)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))) ),
    inference(equality_inference,[],[12291]) ).

cnf(i_0_19417,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,[],[12372]) ).

cnf(i_0_19418,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,[],[12373]) ).

cnf(i_0_19419,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,[],[12387]) ).

cnf(i_0_19420,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,[],[12449]) ).

cnf(i_0_19421,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,[],[12463]) ).

cnf(i_0_19422,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,[],[12508]) ).

cnf(i_0_19423,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,[],[12509]) ).

cnf(i_0_19424,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,[],[12518]) ).

cnf(i_0_19425,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,[],[12541]) ).

cnf(i_0_19426,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),esk195_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,[],[12666]) ).

cnf(i_0_19427,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),esk187_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,[],[12667]) ).

cnf(i_0_19428,plain,
    hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),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,[],[12704]) ).

cnf(i_0_19429,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,[],[12707]) ).

cnf(i_0_19430,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,[],[12745]) ).

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(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,[],[12758]) ).

cnf(i_0_19432,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),esk232_4(c_Nat_OSuc,X2,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2)) ),
    inference(equality_inference,[],[12761]) ).

cnf(i_0_19433,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),esk196_4(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2),X2,X1)),X3)) ),
    inference(equality_inference,[],[12763]) ).

cnf(i_0_19434,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),esk188_4(X3,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2),X2,X1)),X3)) ),
    inference(equality_inference,[],[12764]) ).

cnf(i_0_19435,plain,
    hAPP(c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X4) = X5,
    inference(equality_inference,[],[12780]) ).

cnf(i_0_19436,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,[],[12812]) ).

cnf(i_0_19437,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,[],[12824]) ).

cnf(i_0_19438,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),esk407_4(hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3),X1,X3,X2)),hAPP(c_List_Oset(X1),X3))) ),
    inference(equality_inference,[],[12847]) ).

cnf(i_0_19439,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,[],[12849]) ).

cnf(i_0_19440,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,[],[12851]) ).

cnf(i_0_19441,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,[],[12886]) ).

cnf(i_0_19442,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,[],[12887]) ).

cnf(i_0_19443,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,[],[12899]) ).

cnf(i_0_19444,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,[],[12945]) ).

cnf(i_0_19445,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,[],[12946]) ).

cnf(i_0_19446,plain,
    ( X1 = esk248_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,[],[13020]) ).

cnf(i_0_19447,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,[],[13055]) ).

cnf(i_0_19448,plain,
    ( X1 = X1
    | ~ c_Typedef_Otype__definition(X2,X3,X4,X5,X6) ),
    inference(equality_inference,[],[13062]) ).

cnf(i_0_19449,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,[],[13067]) ).

cnf(i_0_19450,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),esk188_4(X3,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2),X2,X1)),esk187_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,[],[13072]) ).

cnf(i_0_19451,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),esk196_4(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2),X2,X1)),esk195_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,[],[13073]) ).

cnf(i_0_19452,plain,
    ( c_Fun_Obij__betw(X1,X1,esk565_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,[],[13087]) ).

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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X2)),X3)),X4) = X4 ),
    inference(equality_inference,[],[13095]) ).

cnf(i_0_19454,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,[],[13096]) ).

cnf(i_0_19455,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,[],[13105]) ).

cnf(i_0_19456,plain,
    ( X1 = X1
    | hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),esk332_3(X2,X1,X1)),hAPP(c_List_Oset(tc_prod(X2,X2)),hAPP(hAPP(c_List_Ozip(X2,X2),X1),X1)))) ),
    inference(equality_inference,[],[13107]) ).

cnf(i_0_19457,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),esk407_4(hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2),X1,X2,X3))) ),
    inference(equality_inference,[],[13113]) ).

cnf(i_0_19458,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,[],[13148]) ).

cnf(i_0_19459,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,[],[13149]) ).

cnf(i_0_19460,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,[],[13167]) ).

cnf(i_0_19461,plain,
    hAPP(X1,hAPP(X2,X3)) = hAPP(X1,hAPP(X2,X3)),
    inference(equality_inference,[],[13251]) ).

cnf(i_0_19462,plain,
    hAPP(c_Fun_Oid(X1),hAPP(X2,X3)) = hAPP(X2,X3),
    inference(equality_inference,[],[13255]) ).

cnf(i_0_19463,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,[],[13264]) ).

cnf(i_0_19464,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,[],[13284]) ).

cnf(i_0_19465,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,[],[13285]) ).

cnf(i_0_19466,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,[],[13286]) ).

cnf(i_0_19467,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,[],[13414]) ).

cnf(i_0_19468,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,[],[13471]) ).

cnf(i_0_19469,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,[],[13493]) ).

cnf(i_0_19470,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,[],[13514]) ).

cnf(i_0_19471,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,[],[13536]) ).

cnf(i_0_19472,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,[],[13639]) ).

cnf(i_0_19473,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,[],[13667]) ).

cnf(i_0_19474,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,[],[13717]) ).

cnf(i_0_19475,plain,
    c_Fun_Ofun__upd(X1,X2,X3,X4,hAPP(X3,X4)) = X3,
    inference(equality_inference,[],[13731]) ).

cnf(i_0_19476,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,[],[13743]) ).

cnf(i_0_19477,plain,
    c_List_Olist__all2(X1,X2,X3,c_List_Olist_ONil(X1),c_List_Olist_ONil(X2)),
    inference(equality_inference,[],[13746]) ).

cnf(i_0_19478,plain,
    c_List_Olist__all2(X1,X2,X3,c_List_Olist_ONil(X1),c_List_Olist_ONil(X2)),
    inference(equality_inference,[],[13747]) ).

cnf(i_0_19479,plain,
    c_Fun_Obij__betw(X1,X1,c_Fun_Oid(X1),X2,X2),
    inference(equality_inference,[],[13758]) ).

cnf(i_0_19480,plain,
    ( X1 = X1
    | ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X2,X2,tc_HOL_Obool),c_fequal),esk332_3(X2,X1,X1))) ),
    inference(equality_inference,[],[13762]) ).

cnf(i_0_19481,plain,
    c_List_Olist__all2(X1,X1,c_fequal,X2,X2),
    inference(equality_inference,[],[13768]) ).

cnf(i_0_19482,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,[],[13826]) ).

cnf(i_0_19483,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,[],[13829]) ).

cnf(i_0_19484,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,[],[13848]) ).

cnf(i_0_19485,plain,
    ( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | X2 = X3
    | X4 = X4 ),
    inference(equality_inference,[],[13873]) ).

cnf(i_0_19486,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,[],[13923]) ).

cnf(i_0_19487,plain,
    X1 = X1,
    inference(equality_inference,[],[13925]) ).

cnf(i_0_19488,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,[],[13949]) ).

cnf(i_0_19489,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,[],[13968]) ).

cnf(i_0_19490,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,[],[13970]) ).

cnf(i_0_19491,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,[],[13971]) ).

cnf(i_0_19492,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,[],[13996]) ).

cnf(i_0_19493,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,[],[14013]) ).

cnf(i_0_19494,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,[],[14071]) ).

cnf(i_0_19495,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,[],[14083]) ).

cnf(i_0_19496,plain,
    ( X1 = X1
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X3),X4)) ),
    inference(equality_inference,[],[14130]) ).

cnf(i_0_19497,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,[],[14174]) ).

cnf(i_0_19498,plain,
    ( c_Fun_Oinj__on(X1,X2,esk223_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,[],[14185]) ).

cnf(i_0_19499,plain,
    ( ~ epred1_3(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4),X2)
    | hBOOL(hAPP(X1,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,[],[14187]) ).

cnf(i_0_19500,plain,
    ( ~ epred2_3(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4),X2)
    | hBOOL(hAPP(X1,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,[],[14188]) ).

cnf(i_0_19501,plain,
    ( ~ epred1_3(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4),X2)
    | hBOOL(hAPP(X1,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,[],[14234]) ).

cnf(i_0_19502,plain,
    ( ~ epred2_3(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4),X2)
    | hBOOL(hAPP(X1,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,[],[14235]) ).

cnf(i_0_19503,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,[],[14297]) ).

cnf(i_0_19504,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,[],[14309]) ).

cnf(i_0_19505,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,[],[14310]) ).

cnf(i_0_19506,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,[],[14324]) ).

cnf(i_0_19507,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,[],[14351]) ).

cnf(i_0_19508,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,[],[14374]) ).

cnf(i_0_19509,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,[],[14411]) ).

cnf(i_0_19510,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,[],[14433]) ).

cnf(i_0_19511,plain,
    ( X1 = X1
    | ~ c_Fun_Oinj__on(X2,X3,X4,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ),
    inference(equality_inference,[],[14464]) ).

cnf(i_0_19512,plain,
    hAPP(X1,hAPP(X2,X3)) = hAPP(hAPP(c_Fun_Ocomp(X4,X5,X6,X1),X2),X3),
    inference(equality_inference,[],[14468]) ).

cnf(i_0_19513,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,[],[14509]) ).

cnf(i_0_19514,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,[],[14515]) ).

cnf(i_0_19515,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,[],[14531]) ).

cnf(i_0_19516,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,[],[14532]) ).

cnf(i_0_19517,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,[],[14543]) ).

cnf(i_0_19518,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,[],[14545]) ).

cnf(i_0_19519,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,[],[14546]) ).

cnf(i_0_19520,plain,
    ( X1 = X2
    | X1 = X1 ),
    inference(equality_inference,[],[14547]) ).

cnf(i_0_19521,plain,
    ( X1 = X2
    | X1 = X1 ),
    inference(equality_inference,[],[14548]) ).

cnf(i_0_19522,plain,
    ( X1 = X2
    | X2 = X2 ),
    inference(equality_inference,[],[14549]) ).

cnf(i_0_19523,plain,
    ( X1 = X2
    | X2 = X2 ),
    inference(equality_inference,[],[14550]) ).

cnf(i_0_19524,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,[],[14553]) ).

cnf(i_0_19525,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,[],[14609]) ).

cnf(i_0_19526,plain,
    X1 = X1,
    inference(equality_inference,[],[14655]) ).

cnf(i_0_19527,plain,
    X1 = X1,
    inference(equality_inference,[],[14656]) ).

cnf(i_0_19528,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),esk341_2(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_List_Oset(tc_Nat_Onat),X1))) ),
    inference(equality_inference,[],[14659]) ).

cnf(i_0_19529,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,[],[14660]) ).

cnf(i_0_19530,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,[],[14663]) ).

cnf(i_0_19531,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,[],[14675]) ).

cnf(i_0_19532,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,[],[14682]) ).

cnf(i_0_19533,plain,
    ( X1 = X1
    | ~ c_Fun_Oinj__on(X2,X3,X4,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ),
    inference(equality_inference,[],[14693]) ).

cnf(i_0_19534,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,[],[14733]) ).

cnf(i_0_19535,plain,
    ( X1 = X1
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk320_3(X2,X1,X1)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1))) ),
    inference(equality_inference,[],[14741]) ).

cnf(i_0_19536,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,[],[14815]) ).

cnf(i_0_19537,plain,
    X1 = X1,
    inference(equality_inference,[],[14866]) ).

cnf(i_0_19538,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,[],[14887]) ).

cnf(i_0_19539,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,[],[14960]) ).

cnf(i_0_19540,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),esk67_3(X1,X2,X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X1)) ),
    inference(equality_inference,[],[14987]) ).

cnf(i_0_19541,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,[],[15016]) ).

cnf(i_0_19542,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,[],[15149]) ).

cnf(i_0_19543,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,[],[15159]) ).

cnf(i_0_19544,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,[],[15170]) ).

cnf(i_0_19545,plain,
    ( hAPP(X1,X2) = hAPP(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(c_List_Oset(X3),X4))) ),
    inference(equality_inference,[],[15176]) ).

cnf(i_0_19546,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,[],[15224]) ).

cnf(i_0_19547,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,[],[15306]) ).

cnf(i_0_19548,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,[],[15312]) ).

cnf(i_0_19549,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,[],[15325]) ).

cnf(i_0_19550,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,[],[15326]) ).

cnf(i_0_19551,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,[],[15327]) ).

cnf(i_0_19552,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,[],[15332]) ).

cnf(i_0_19553,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,[],[15346]) ).

cnf(i_0_19554,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,[],[15438]) ).

cnf(i_0_19555,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,[],[15439]) ).

cnf(i_0_19556,plain,
    X1 = X1,
    inference(equality_inference,[],[15456]) ).

cnf(i_0_19557,plain,
    X1 = X1,
    inference(equality_inference,[],[15457]) ).

cnf(i_0_19558,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,[],[15473]) ).

cnf(i_0_19559,plain,
    hBOOL(hAPP(hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),X2)),
    inference(equality_inference,[],[15489]) ).

cnf(i_0_19560,plain,
    ( X1 = X1
    | ~ c_Fun_Oinj__on(X2,X3,X4,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ),
    inference(equality_inference,[],[15496]) ).

cnf(i_0_19561,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,[],[15499]) ).

cnf(i_0_19562,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,[],[15500]) ).

cnf(i_0_19563,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,[],[15601]) ).

cnf(i_0_19564,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,[],[15626]) ).

cnf(i_0_19565,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,[],[15652]) ).

cnf(i_0_19566,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,[],[15653]) ).

cnf(i_0_19567,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X2)),
    inference(equality_inference,[],[15692]) ).

cnf(i_0_19568,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,[],[15705]) ).

cnf(i_0_19569,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,[],[15745]) ).

cnf(i_0_19570,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,[],[15774]) ).

cnf(i_0_19571,plain,
    ~ c_Wellfounded_Omax__extp(X1,X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
    inference(equality_inference,[],[15789]) ).

cnf(i_0_19572,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,[],[15800]) ).

cnf(i_0_19573,plain,
    ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X3)),
    inference(equality_inference,[],[15827]) ).

cnf(i_0_19574,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,[],[15832]) ).

cnf(i_0_19575,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,[],[15840]) ).

cnf(i_0_19576,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,[],[15848]) ).

cnf(i_0_19577,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,[],[15849]) ).

cnf(i_0_19578,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,[],[15924]) ).

cnf(i_0_19579,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,[],[15952]) ).

cnf(i_0_19580,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,[],[15999]) ).

cnf(i_0_19581,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,[],[16014]) ).

cnf(i_0_19582,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,[],[16015]) ).

cnf(i_0_19583,plain,
    X1 = X1,
    inference(equality_inference,[],[16024]) ).

cnf(i_0_19584,plain,
    ( X1 = X1
    | hBOOL(hAPP(hAPP(c_member(X2),X3),X1))
    | hBOOL(hAPP(hAPP(c_member(X2),X3),X1)) ),
    inference(equality_inference,[],[16037]) ).

cnf(i_0_19585,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,[],[16038]) ).

cnf(i_0_19586,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,[],[16042]) ).

cnf(i_0_19587,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,[],[16055]) ).

cnf(i_0_19588,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,[],[16070]) ).

cnf(i_0_19589,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,[],[16072]) ).

cnf(i_0_19590,plain,
    ( ~ c_Nat__Transfer_Onat__set(X1)
    | ~ c_Nat__Transfer_Onat__set(X1)
    | X1 = X1 ),
    inference(equality_inference,[],[16084]) ).

cnf(i_0_19591,plain,
    X1 = X1,
    inference(equality_inference,[],[16085]) ).

cnf(i_0_19592,plain,
    X1 = X1,
    inference(equality_inference,[],[16086]) ).

cnf(i_0_19593,plain,
    X1 = X1,
    inference(equality_inference,[],[16087]) ).

cnf(i_0_19594,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,[],[16106]) ).

cnf(i_0_19595,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,[],[16155]) ).

cnf(i_0_19596,plain,
    X1 = hAPP(c_Product__Type_Ofst(X2,X3),hAPP(hAPP(c_Product__Type_OPair(X2,X3),X1),X4)),
    inference(equality_inference,[],[16160]) ).

cnf(i_0_19597,plain,
    X1 = hAPP(c_Product__Type_Osnd(X2,X3),hAPP(hAPP(c_Product__Type_OPair(X2,X3),X4),X1)),
    inference(equality_inference,[],[16161]) ).

cnf(i_0_19598,plain,
    ( hBOOL(hAPP(X1,X2))
    | hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X1,X3)),X2),X2)) ),
    inference(equality_inference,[],[16173]) ).

cnf(i_0_19599,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,[],[16215]) ).

cnf(i_0_19600,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,[],[16243]) ).

cnf(i_0_19601,plain,
    X1 = X1,
    inference(equality_inference,[],[16261]) ).

cnf(i_0_19602,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,[],[16274]) ).

cnf(i_0_19603,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,[],[16301]) ).

cnf(i_0_19604,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,[],[16324]) ).

cnf(i_0_19605,plain,
    hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))),
    inference(equality_inference,[],[16328]) ).

cnf(i_0_19606,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,[],[16349]) ).

cnf(i_0_19607,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,[],[16355]) ).

cnf(i_0_19608,plain,
    ( c_Natural_Oevaln(c_Com_Ocom_OWhile(X1,X2),X3,X4,X3)
    | hBOOL(hAPP(X1,X3)) ),
    inference(equality_inference,[],[16362]) ).

cnf(i_0_19609,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X2)),
    inference(equality_inference,[],[16434]) ).

cnf(i_0_19610,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X2)),
    inference(equality_inference,[],[16435]) ).

cnf(i_0_19611,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,[],[16436]) ).

cnf(i_0_19612,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,[],[16441]) ).

cnf(i_0_19613,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,[],[16443]) ).

cnf(i_0_19614,plain,
    X1 = X1,
    inference(equality_inference,[],[16444]) ).

cnf(i_0_19615,plain,
    X1 = X1,
    inference(equality_inference,[],[16446]) ).

cnf(i_0_19616,plain,
    X1 = X1,
    inference(equality_inference,[],[16448]) ).

cnf(i_0_19617,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,[],[16452]) ).

cnf(i_0_19618,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,[],[16475]) ).

cnf(i_0_19619,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,[],[16477]) ).

cnf(i_0_19620,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,[],[16478]) ).

cnf(i_0_19621,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,[],[16541]) ).

cnf(i_0_19622,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,[],[16542]) ).

cnf(i_0_19623,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,[],[16577]) ).

cnf(i_0_19624,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,[],[16600]) ).

cnf(i_0_19625,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,[],[16601]) ).

cnf(i_0_19626,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,[],[16623]) ).

cnf(i_0_19627,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,[],[16635]) ).

cnf(i_0_19628,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,[],[16636]) ).

cnf(i_0_19629,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,[],[16654]) ).

cnf(i_0_19630,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,[],[16668]) ).

cnf(i_0_19631,plain,
    X1 = X1,
    inference(equality_inference,[],[16669]) ).

cnf(i_0_19632,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,[],[16681]) ).

cnf(i_0_19633,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,[],[16720]) ).

cnf(i_0_19634,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,[],[16746]) ).

cnf(i_0_19635,plain,
    hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X2)),
    inference(equality_inference,[],[16753]) ).

cnf(i_0_19636,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,[],[16778]) ).

cnf(i_0_19637,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,[],[16779]) ).

cnf(i_0_19638,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,[],[16832]) ).

cnf(i_0_19639,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,[],[16833]) ).

cnf(i_0_19640,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,[],[16852]) ).

cnf(i_0_19641,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,[],[16891]) ).

cnf(i_0_19642,plain,
    hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),c_List_Olists(X1,X2))),
    inference(equality_inference,[],[16912]) ).

cnf(i_0_19643,plain,
    ( ~ c_List_Olinorder__class_Osorted(X1,X2)
    | ~ class_Orderings_Olinorder(X1)
    | X2 = esk432_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,[],[16930]) ).

cnf(i_0_19644,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,[],[16936]) ).

cnf(i_0_19645,plain,
    ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
    inference(equality_inference,[],[16939]) ).

cnf(i_0_19646,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,[],[16947]) ).

cnf(i_0_19647,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,[],[16948]) ).

cnf(i_0_19648,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,[],[16949]) ).

cnf(i_0_19649,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,[],[16950]) ).

cnf(i_0_19650,plain,
    X1 = X1,
    inference(equality_inference,[],[16951]) ).

cnf(i_0_19651,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,[],[16959]) ).

cnf(i_0_19652,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,[],[16960]) ).

cnf(i_0_19653,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,[],[16961]) ).

cnf(i_0_19654,plain,
    ( ~ class_Rings_Oidom(X1)
    | X2 = X2
    | X2 = hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2) ),
    inference(equality_inference,[],[17035]) ).

cnf(i_0_19655,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,[],[17039]) ).

cnf(i_0_19656,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,[],[17040]) ).

cnf(i_0_19657,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,[],[17041]) ).

cnf(i_0_19658,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,[],[17044]) ).

cnf(i_0_19659,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,[],[17045]) ).

cnf(i_0_19660,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,[],[17112]) ).

cnf(i_0_19661,plain,
    ( ~ class_Orderings_Oorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)) ),
    inference(equality_inference,[],[17116]) ).

cnf(i_0_19662,plain,
    ( ~ class_Orderings_Oorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)) ),
    inference(equality_inference,[],[17117]) ).

cnf(i_0_19663,plain,
    ( ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)) ),
    inference(equality_inference,[],[17118]) ).

cnf(i_0_19664,plain,
    ( ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)) ),
    inference(equality_inference,[],[17119]) ).

cnf(i_0_19665,plain,
    ( X1 = X1
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(equality_inference,[],[17124]) ).

cnf(i_0_19666,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,[],[17139]) ).

cnf(i_0_19667,plain,
    ( X1 = X1
    | ~ class_Groups_Ocancel__semigroup__add(X2) ),
    inference(equality_inference,[],[17141]) ).

cnf(i_0_19668,plain,
    ( X1 = X1
    | ~ class_Groups_Ocancel__ab__semigroup__add(X2) ),
    inference(equality_inference,[],[17142]) ).

cnf(i_0_19669,plain,
    ( X1 = X1
    | ~ class_Groups_Ocancel__semigroup__add(X2) ),
    inference(equality_inference,[],[17144]) ).

cnf(i_0_19670,plain,
    X1 = X1,
    inference(equality_inference,[],[17145]) ).

cnf(i_0_19671,plain,
    X1 = X1,
    inference(equality_inference,[],[17146]) ).

cnf(i_0_19672,plain,
    X1 = X1,
    inference(equality_inference,[],[17147]) ).

cnf(i_0_19673,plain,
    X1 = X1,
    inference(equality_inference,[],[17148]) ).

cnf(i_0_19674,plain,
    X1 = X1,
    inference(equality_inference,[],[17149]) ).

cnf(i_0_19675,plain,
    X1 = X1,
    inference(equality_inference,[],[17150]) ).

cnf(i_0_19676,plain,
    X1 = X1,
    inference(equality_inference,[],[17151]) ).

cnf(i_0_19677,plain,
    X1 = X1,
    inference(equality_inference,[],[17152]) ).

cnf(i_0_19678,plain,
    X1 = X1,
    inference(equality_inference,[],[17153]) ).

cnf(i_0_19679,plain,
    X1 = X1,
    inference(equality_inference,[],[17154]) ).

cnf(i_0_19680,plain,
    X1 = X1,
    inference(equality_inference,[],[17155]) ).

cnf(i_0_19681,plain,
    X1 = X1,
    inference(equality_inference,[],[17156]) ).

cnf(i_0_19682,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,[],[17162]) ).

cnf(i_0_19683,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,[],[17163]) ).

cnf(i_0_19684,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,[],[17164]) ).

cnf(i_0_19685,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,[],[17183]) ).

cnf(i_0_19686,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,[],[17184]) ).

cnf(i_0_19687,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,[],[17185]) ).

cnf(i_0_19688,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,[],[17188]) ).

cnf(i_0_19689,plain,
    X1 = X1,
    inference(equality_inference,[],[17196]) ).

cnf(i_0_19690,plain,
    X1 = X1,
    inference(equality_inference,[],[17197]) ).

cnf(i_0_19691,plain,
    X1 = X1,
    inference(equality_inference,[],[17198]) ).

cnf(i_0_19692,plain,
    X1 = X1,
    inference(equality_inference,[],[17199]) ).

cnf(i_0_19693,plain,
    c_List_Oremove1(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)) = X3,
    inference(equality_inference,[],[17223]) ).

cnf(i_0_19694,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,[],[17232]) ).

cnf(i_0_19695,plain,
    hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X2))),
    inference(equality_inference,[],[17255]) ).

cnf(i_0_19696,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(equality_inference,[],[17262]) ).

cnf(i_0_19697,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X1)),
    inference(equality_inference,[],[17270]) ).

cnf(i_0_19698,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
    inference(equality_inference,[],[17274]) ).

cnf(i_0_19699,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
    inference(equality_inference,[],[17275]) ).

cnf(i_0_19700,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,[],[17278]) ).

cnf(i_0_19701,plain,
    ( X1 = X1
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(equality_inference,[],[17281]) ).

cnf(i_0_19702,plain,
    ( X1 = X1
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(equality_inference,[],[17283]) ).

cnf(i_0_19703,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,[],[17284]) ).

cnf(i_0_19704,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,[],[17293]) ).

cnf(i_0_19705,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,[],[17294]) ).

cnf(i_0_19706,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,[],[17296]) ).

cnf(i_0_19707,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,[],[17297]) ).

cnf(i_0_19708,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,[],[17298]) ).

cnf(i_0_19709,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,[],[17299]) ).

cnf(i_0_19710,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,[],[17301]) ).

cnf(i_0_19711,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,[],[17302]) ).

cnf(i_0_19712,plain,
    ( ~ c_Equiv__Relations_Oequivp(X1,X2)
    | hBOOL(hAPP(hAPP(X2,X3),X3)) ),
    inference(equality_inference,[],[17309]) ).

cnf(i_0_19713,plain,
    X1 = X1,
    inference(equality_inference,[],[17319]) ).

cnf(i_0_19714,plain,
    X1 = X1,
    inference(equality_inference,[],[17320]) ).

cnf(i_0_19715,plain,
    X1 = X1,
    inference(equality_inference,[],[17321]) ).

cnf(i_0_19716,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,[],[17327]) ).

cnf(i_0_19717,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,[],[17335]) ).

cnf(i_0_19718,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1))),
    inference(equality_inference,[],[17344]) ).

cnf(i_0_19719,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,[],[17362]) ).

cnf(i_0_19720,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,[],[17364]) ).

cnf(i_0_19721,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,[],[17369]) ).

cnf(i_0_19722,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,[],[17377]) ).

cnf(i_0_19723,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,[],[17394]) ).

cnf(i_0_19724,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,[],[17395]) ).

cnf(i_0_19725,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,[],[17417]) ).

cnf(i_0_19726,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,[],[17418]) ).

cnf(i_0_19727,plain,
    ( ~ epred2_3(X1,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(equality_inference,[],[17420]) ).

cnf(i_0_19728,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,[],[17421]) ).

cnf(i_0_19729,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,[],[17424]) ).

cnf(i_0_19730,plain,
    X1 = X1,
    inference(equality_inference,[],[17425]) ).

cnf(i_0_19731,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,[],[17430]) ).

cnf(i_0_19732,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,[],[17431]) ).

cnf(i_0_19733,plain,
    c_List_Olast(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1))) = X2,
    inference(equality_inference,[],[17434]) ).

cnf(i_0_19734,plain,
    ( ~ epred1_3(X1,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | hBOOL(hAPP(X1,X2)) ),
    inference(equality_inference,[],[17451]) ).

cnf(i_0_19735,plain,
    ( ~ class_Orderings_Oorder(X1)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X2)) ),
    inference(equality_inference,[],[17482]) ).

cnf(i_0_19736,plain,
    ( ~ class_Orderings_Opreorder(X1)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X2)) ),
    inference(equality_inference,[],[17483]) ).

cnf(i_0_19737,plain,
    ( ~ class_Orderings_Oorder(X1)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X2)) ),
    inference(equality_inference,[],[17484]) ).

cnf(i_0_19738,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,[],[17532]) ).

cnf(i_0_19739,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,[],[17537]) ).

cnf(i_0_19740,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,[],[17559]) ).

cnf(i_0_19741,plain,
    hAPP(hAPP(c_List_Omap(X1,X2),X3),c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X2),
    inference(equality_inference,[],[17590]) ).

cnf(i_0_19742,plain,
    hAPP(hAPP(c_List_Olist__update(X1,c_List_Olist_ONil(X1)),X2),X3) = c_List_Olist_ONil(X1),
    inference(equality_inference,[],[17591]) ).

cnf(i_0_19743,plain,
    c_List_Olist_ONil(X1) = hAPP(hAPP(c_List_Omap(X2,X1),X3),c_List_Olist_ONil(X2)),
    inference(equality_inference,[],[17592]) ).

cnf(i_0_19744,plain,
    ( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X2,X1)))
    | ~ hBOOL(hAPP(X1,X3)) ),
    inference(equality_inference,[],[17597]) ).

cnf(i_0_19745,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,[],[17619]) ).

cnf(i_0_19746,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,[],[17623]) ).

cnf(i_0_19747,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,[],[17624]) ).

cnf(i_0_19748,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X1)),
    inference(equality_inference,[],[17629]) ).

cnf(i_0_19749,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,[],[17633]) ).

cnf(i_0_19750,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,[],[17639]) ).

cnf(i_0_19751,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,[],[17672]) ).

cnf(i_0_19752,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,[],[17689]) ).

cnf(i_0_19753,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,[],[17693]) ).

cnf(i_0_19754,plain,
    ( ~ class_Int_Onumber__ring(X1)
    | ~ class_Int_Oring__char__0(X1)
    | X2 = X2 ),
    inference(equality_inference,[],[17749]) ).

cnf(i_0_19755,plain,
    hBOOL(hAPP(hAPP(c_fequal,X1),X1)),
    inference(equality_inference,[],[17751]) ).

cnf(i_0_19756,plain,
    ( ~ class_Orderings_Olinorder(X1)
    | X2 = X2 ),
    inference(equality_inference,[],[17794]) ).

cnf(i_0_19757,plain,
    ( ~ class_Orderings_Olinorder(X1)
    | X2 = X2 ),
    inference(equality_inference,[],[17795]) ).

cnf(i_0_19758,plain,
    ( ~ class_Orderings_Olinorder(X1)
    | X2 = X2 ),
    inference(equality_inference,[],[17796]) ).

cnf(i_0_19759,plain,
    ( ~ class_Orderings_Olinorder(X1)
    | X2 = X2 ),
    inference(equality_inference,[],[17797]) ).

cnf(i_0_19760,plain,
    ( ~ class_Lattices_Oboolean__algebra(X1)
    | X2 = X2 ),
    inference(equality_inference,[],[17798]) ).

cnf(i_0_19761,plain,
    ( ~ class_Groups_Ogroup__add(X1)
    | X2 = X2 ),
    inference(equality_inference,[],[17799]) ).

cnf(i_0_19762,plain,
    ( ~ class_Int_Oring__char__0(X1)
    | X2 = X2 ),
    inference(equality_inference,[],[17800]) ).

cnf(i_0_19763,plain,
    ( ~ class_Nat_Osemiring__char__0(X1)
    | X2 = X2 ),
    inference(equality_inference,[],[17801]) ).

cnf(i_0_19764,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,[],[17810]) ).

cnf(i_0_19765,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,[],[17811]) ).

cnf(i_0_19766,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,[],[17812]) ).

cnf(i_0_19767,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,[],[17813]) ).

cnf(i_0_19768,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,[],[17814]) ).

cnf(i_0_19769,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,[],[17815]) ).

cnf(i_0_19770,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,[],[17816]) ).

cnf(i_0_19771,plain,
    X1 = hAPP(hAPP(c_List_Oappend(X2),c_List_Olist_ONil(X2)),X1),
    inference(equality_inference,[],[17831]) ).

cnf(i_0_19772,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,[],[17832]) ).

cnf(i_0_19773,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,[],[17844]) ).

cnf(i_0_19774,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,[],[17845]) ).

cnf(i_0_19775,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,[],[17846]) ).

cnf(i_0_19776,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,[],[17847]) ).

cnf(i_0_19777,plain,
    X1 = X1,
    inference(equality_inference,[],[17870]) ).

cnf(i_0_19778,plain,
    hAPP(hAPP(c_List_Otake(X1),X2),c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
    inference(equality_inference,[],[17877]) ).

cnf(i_0_19779,plain,
    c_List_Oreplicate(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) = c_List_Olist_ONil(X1),
    inference(equality_inference,[],[17882]) ).

cnf(i_0_19780,plain,
    c_List_Olist_ONil(X1) = c_List_Oreplicate(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2),
    inference(equality_inference,[],[17883]) ).

cnf(i_0_19781,plain,
    hAPP(hAPP(c_List_Otake(X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2) = c_List_Olist_ONil(X1),
    inference(equality_inference,[],[17895]) ).

cnf(i_0_19782,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,[],[17897]) ).

cnf(i_0_19783,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,[],[17899]) ).

cnf(i_0_19784,plain,
    hAPP(hAPP(c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2) = X2,
    inference(equality_inference,[],[17901]) ).

cnf(i_0_19785,plain,
    hAPP(hAPP(c_List_Oappend(X1),X2),c_List_Olist_ONil(X1)) = X2,
    inference(equality_inference,[],[17902]) ).

cnf(i_0_19786,plain,
    X1 = hAPP(hAPP(c_List_Oappend(X2),c_List_Olist_ONil(X2)),X1),
    inference(equality_inference,[],[17903]) ).

cnf(i_0_19787,plain,
    X1 = hAPP(hAPP(c_List_Oappend(X2),X1),c_List_Olist_ONil(X2)),
    inference(equality_inference,[],[17904]) ).

cnf(i_0_19788,plain,
    X1 = X1,
    inference(equality_inference,[],[17953]) ).

cnf(i_0_19789,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,[],[17954]) ).

cnf(i_0_19790,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,[],[17955]) ).

cnf(i_0_19791,plain,
    hAPP(c_List_Orev(X1),hAPP(c_List_Orev(X1),X2)) = X2,
    inference(equality_inference,[],[17957]) ).

cnf(i_0_19792,plain,
    X1 = hAPP(c_List_Orev(X2),hAPP(c_List_Orev(X2),X1)),
    inference(equality_inference,[],[17958]) ).

cnf(i_0_19793,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,[],[17964]) ).

cnf(i_0_19794,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,[],[17965]) ).

cnf(i_0_19795,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,[],[17967]) ).

cnf(i_0_19796,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,[],[17968]) ).

cnf(i_0_19797,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) = X1,
    inference(equality_inference,[],[17979]) ).

cnf(i_0_19798,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls) = c_Int_OPls,
    inference(equality_inference,[],[18008]) ).

cnf(i_0_19799,plain,
    c_Int_OPls = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls),
    inference(equality_inference,[],[18009]) ).

cnf(i_0_19800,plain,
    X1 = X1,
    inference(equality_inference,[],[18016]) ).

cnf(i_0_19801,plain,
    X1 = X1,
    inference(equality_inference,[],[18017]) ).

cnf(i_0_19802,plain,
    X1 = X1,
    inference(equality_inference,[],[18018]) ).

cnf(i_0_19803,plain,
    X1 = X1,
    inference(equality_inference,[],[18019]) ).

cnf(i_0_19804,plain,
    X1 = X1,
    inference(equality_inference,[],[18020]) ).

cnf(i_0_19805,plain,
    X1 = X1,
    inference(equality_inference,[],[18021]) ).

cnf(i_0_19806,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,[],[18049]) ).

cnf(i_0_19807,plain,
    X1 = hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),
    inference(equality_inference,[],[18055]) ).

cnf(i_0_19808,plain,
    X1 = X1,
    inference(equality_inference,[],[18067]) ).

cnf(i_0_19809,plain,
    X1 = X1,
    inference(equality_inference,[],[18068]) ).

cnf(i_0_19810,plain,
    X1 = X1,
    inference(equality_inference,[],[18069]) ).

cnf(i_0_19811,plain,
    X1 = X1,
    inference(equality_inference,[],[18071]) ).

cnf(i_0_19812,plain,
    X1 = X1,
    inference(equality_inference,[],[18072]) ).

cnf(i_0_19813,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,[],[18081]) ).

cnf(i_0_19814,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,[],[18082]) ).

cnf(i_0_19815,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,[],[18083]) ).

cnf(i_0_19816,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,[],[18110]) ).

cnf(i_0_19817,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,[],[18111]) ).

cnf(i_0_19818,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,[],[18112]) ).

cnf(i_0_19819,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,[],[18126]) ).

cnf(i_0_19820,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,[],[18127]) ).

cnf(i_0_19821,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,[],[18142]) ).

cnf(i_0_19822,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,[],[18143]) ).

cnf(i_0_19823,plain,
    hAPP(c_List_Orev(X1),c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
    inference(equality_inference,[],[18144]) ).

cnf(i_0_19824,plain,
    hAPP(c_List_Orotate1(X1),c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
    inference(equality_inference,[],[18145]) ).

cnf(i_0_19825,plain,
    c_List_Olist_ONil(X1) = hAPP(c_List_Orev(X1),c_List_Olist_ONil(X1)),
    inference(equality_inference,[],[18146]) ).

cnf(i_0_19826,plain,
    ( ~ class_Orderings_Olinorder(X1)
    | c_List_Olinorder__class_Osorted(X1,c_List_Olist_ONil(X1)) ),
    inference(equality_inference,[],[18163]) ).

cnf(i_0_19827,plain,
    ( ~ class_Rings_Osemiring__1(X1)
    | c_Int_Oiszero(X1,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(equality_inference,[],[18164]) ).

cnf(i_0_19828,plain,
    c_List_Oremdups(X1,c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
    inference(equality_inference,[],[18171]) ).

cnf(i_0_19829,plain,
    c_List_Olist_ONil(X1) = c_List_Oremdups(X1,c_List_Olist_ONil(X1)),
    inference(equality_inference,[],[18172]) ).

cnf(i_0_19830,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,[],[18173]) ).

cnf(i_0_19831,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,[],[18206]) ).

cnf(i_0_19832,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,[],[18207]) ).

cnf(i_0_19833,plain,
    c_Nitpick_Onat__gcd(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
    inference(equality_inference,[],[18208]) ).

cnf(i_0_19834,plain,
    c_Random_Oinc__shift(X1,X1) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral),
    inference(equality_inference,[],[18214]) ).

cnf(i_0_19835,plain,
    $false,
    inference(scs_inference,[],[i_0_12103,i_0_12877,i_0_15562,i_0_14746]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem    : SWW318+1 : TPTP v9.2.1. Released v5.2.0.
% 0.00/0.11  % Command    : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.32  % Computer : n014.cluster.edu
% 0.16/0.32  % Model    : x86_64 x86_64
% 0.16/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.32  % Memory   : 8042.1875MB
% 0.16/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.32  % CPULimit   : 300
% 0.16/0.32  % WCLimit    : 300
% 0.16/0.32  % DateTime   : Tue May  5 06:36:51 EDT 2026
% 0.16/0.32  % CPUTime    : 
% 0.16/0.33  % start to proof: theBenchmark
% 36.09/22.32  % Version  : CSE_E---1.7
% 36.09/22.32  % Problem  : theBenchmark.p
% 36.09/22.32  % SZS status Theorem for theBenchmark.p
% 36.09/22.32  % SZS output start CNFRefutation
% See solution above
% 36.88/22.77  % Total time : 21.962s
%------------------------------------------------------------------------------